Roastidio.us in webspace https://en.wikipedia.org/ https://roastidio.us/webspace/4172 Roastidio.us in webspace https://en.wikipedia.org/ The Anatomy of Revolution - Wikipedia https://en.wikipedia.org/wiki/The_Anatomy_of_Revolution 2XFO3-4Nn8OJaTrGcH4alVDGRDfwX5rJleJBJA== Wed, 13 May 2026 11:24:37 +0000 This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (March 2023) (Learn how and when to remove this message) <table><tbody><tr><td></td><td><div>This article includes a <a href="https://en.wikipedia.org/wiki/Wikipedia:Citing_sources">list of references</a>, <a href="https://en.wikipedia.org/wiki/Wikipedia:Further_reading">related reading</a>, or <a href="https://en.wikipedia.org/wiki/Wikipedia:External_links">external links</a>, <b>but its sources remain unclear because it lacks <a href="https://en.wikipedia.org/wiki/Wikipedia:Citing_sources#Inline_citations">inline citations</a></b>.<span> Please help <a href="https://en.wikipedia.org/wiki/Wikipedia:WikiProject_Fact_and_Reference_Check">improve</a> this article by <a href="https://en.wikipedia.org/wiki/Wikipedia:When_to_cite">introducing</a> more precise citations.</span> <span><i>(<span>March 2023</span>)</i></span><span><i> (<small><a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table><div>1938 book by Crane Brinton</div><p><i><b>The Anatomy of Revolution</b></i> is a 1938 book by <a href="https://en.wikipedia.org/wiki/Crane_Brinton">Crane Brinton</a> outlining the &quot;uniformities&quot; of four major political revolutions: the <a href="https://en.wikipedia.org/wiki/English_Civil_War">English Revolution</a> of the 1640s, the <a href="https://en.wikipedia.org/wiki/American_Revolution">American</a>, the <a href="https://en.wikipedia.org/wiki/French_Revolution">French</a>, and the <a href="https://en.wikipedia.org/wiki/Russian_Revolution">Russian</a> revolutions. Brinton notes how the revolutions followed a life-cycle from the Old Order to a moderate regime to a radical regime, to <a href="https://en.wikipedia.org/wiki/Thermidorian_reaction">Thermidorian reaction</a>. </p><p>The book has been called &quot;classic,<sup><span>[</span>1<span>]</span></sup> &quot;famous&quot;, and a &quot;watershed in the study of revolution&quot;<sup><span>[</span>2<span>]</span></sup> and has been influential enough to have inspired advice given to US President <a href="https://en.wikipedia.org/wiki/Jimmy_Carter">Jimmy Carter</a> by his National Security Advisor <a href="https://en.wikipedia.org/wiki/Zbigniew_Brzezinski">Zbigniew Brzezinski</a> during the <a href="https://en.wikipedia.org/wiki/Iranian_Revolution">Iranian Revolution</a>.<sup><span>[</span>notes 1<span>]</span></sup> It has been referenced in the well-known text <i>Political Science: An Introduction</i> by <a href="https://en.wikipedia.org/wiki/Michael_G._Roskin">Michael G. Roskin</a> et al. </p><p>A revised edition was published in 1952, a revised and expanded edition in 1965, and the book remains in print.<sup><span>[</span>3<span>]</span></sup> Brinton summarizes the revolutionary process as moving from &quot;financial breakdown, [to] organization of the discontented to remedy this breakdown … revolutionary demands on the part of these organized discontented, demands which if granted would mean the virtual abdication of those governing, attempted use of force by the government, its failure, and the attainment of power by the revolutionists. These revolutionists have hitherto been acting as an organized and nearly unanimous group, but with the attainment of power it is clear that they are not united. The group which dominates these first stages we call the moderates … power passes by violent … methods from <a href="https://en.wikipedia.org/wiki/Right-wing_politics">Right</a> to <a href="https://en.wikipedia.org/wiki/Left-wing_politics">Left</a>&quot; (p. 253). </p><div><h2>Themes</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>According to Brinton, while &quot;we must not expect our revolutions to be identical&quot; (p. 226), three of the four (the English, French and Russian) began &quot;in hope and moderation&quot;, reached &quot;a crisis in a <a href="https://en.wikipedia.org/wiki/Reign_of_Terror">reign of terror</a>&quot;, and ended &quot;in something like <a href="https://en.wikipedia.org/wiki/Dictatorship">dictatorship</a>—<a href="https://en.wikipedia.org/wiki/Oliver_Cromwell">Cromwell</a>, <a href="https://en.wikipedia.org/wiki/Napoleon_I_of_France">Bonaparte</a>, <a href="https://en.wikipedia.org/wiki/Joseph_Stalin">Stalin</a>&quot;. The exception is the American Revolution, which &quot;does not quite follow this pattern&quot; (p. 24). </p><div><h3>Fall of the old regime</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>The revolutions begin with problems in the pre-revolutionary regime. These include problems functioning—&quot;government deficits, more than usual complaints over taxation, conspicuous governmental favoring of one set of economic interests over another, administrative entanglements and confusions&quot;. There are also social problems, such as the feeling by some that careers are not &quot;open to talents&quot;, and economic power is separated from political power and social distinction. There is a &quot;loss of self-confidence among many members of the ruling class&quot;, the &quot;conversion of many members of that class to the belief that their privileges are unjust or harmful to society&quot; (p. 65). &quot;Intellectuals&quot; switch their allegiance away from the government (p. 251). In short, &quot;the ruling class becomes politically inept&quot; (p. 252). </p><p>Financial problems play an important role, as &quot;three of our four revolutions started among people who objected to certain taxes, who organized to protest them …. even in Russia in 1917 the financial problems were real and important&quot; (p. 78). </p><p>The revolutions&#39; enemies and supporters disagree over whether plots and manipulation by revolutionists, or the corruption and tyranny of the old regime are responsible for the old regime&#39;s fall. Brinton argues both are right, as both the right circumstances and active agitation are necessary for the revolution to succeed (p. 85–86). </p><p>At some point in the first stages of the revolutions &quot;there is a point where constituted authority is challenged by illegal acts of revolutionists&quot; and the response of security forces is strikingly unsuccessful. In France in 1789 the &quot;king didn&#39;t really try&quot; to subdue riots effectively. In England the king &quot;didn&#39;t have enough good soldiers&quot;. In Russia &quot;at the critical moment the soldiers refused to march against the people&quot; and instead joined them (p. 88). </p><div><h3>Background of the revolutionaries</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Revolutions &quot;are born of hope&quot; rather than misery (p. 250). Contrary to the belief that revolutionaries are disproportionately <a href="https://en.wikipedia.org/wiki/Poverty">poor</a> or down-and-out, &quot;revolutionists are more or less a cross section of common humanity&quot;. While revolutionaries &quot;behave in a way we should not expect such people to behave&quot;, this can be explained by the &quot;revolutionary environment&quot; rather than their background (p. 120). &quot;&#39;<a href="https://en.wikipedia.org/wiki/Dalit">Untouchables</a>&#39; very rarely revolt&quot;, and successful slave revolutions, like <a href="https://en.wikipedia.org/wiki/Haitian_Revolution">Haiti</a>&#39;s, are few in number (p. 250). Revolutionaries are &quot;not unprosperous&quot; but &quot;feel restraint, cramp, … rather than downright crushing oppression&quot; (p. 250). </p><div><h3>Revolutionary regimes</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>In each revolution a short &quot;honeymoon&quot; period follows the fall of the old regime, lasting until the &quot;contradictory elements&quot; among the victorious revolutionaries assert themselves (p. 91). Power then has a tendency &quot;to go from Right to Center to Left&quot; (p. 123). In the process, Brinton says, &#39;the revolution, like <a href="https://en.wikipedia.org/wiki/Saturn_(mythology)">Saturn</a>, devours its children&#39;, quoting <a href="https://en.wikipedia.org/wiki/Pierre_Victurnien_Vergniaud">Pierre Victurnien Vergniaud</a> (p. 121). </p><div><h4>Moderates and dual power</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>The revolutions being studied first produce a &quot;legal&quot; moderate government. It vies with a more radical &quot;illegal&quot; government in a process known as &quot;<a href="https://en.wikipedia.org/wiki/Dual_power">dual power</a>&quot;, or as Brinton prefers to call it &quot;dual sovereignty&quot;. In England the &quot;Presbyterian moderates in Parliament&quot; were rivals of &quot;the illegal government of the extremist Independents in the New Model Army&quot; (p. 135). In France, the National Assembly was controlled by the &quot;<a href="https://en.wikipedia.org/wiki/Girondist">Girondin</a> moderates&quot;, while the <a href="https://en.wikipedia.org/wiki/The_Mountain">Montagnard</a> &quot;extremists&quot; controlled &quot;the Jacobin network&quot;, &quot;the Paris commune&quot;, (p. 136) and the Societies of the Friends of the Constitution (p. 162). In Russia, the moderate provisional government of the Duma clashed with the radical Bolsheviks whose illegal government was a &quot;network of soviets&quot; (p. 136). </p><p>The <b>radicals</b> triumph because: </p><ul><li>they are &quot;better organized, better staffed, better obeyed&quot; (p. 134),</li> <li>they have &quot;relatively few responsibilities, while the legal government &quot;has to shoulder some of the unpopularity of the government of the old regime&quot; with &quot;the worn-out machinery, the institutions of the old regime&quot; (p. 134).</li> <li>the moderates are hindered by their hesitancy to change direction and fight back against the radical revolutionaries, &quot;with whom they recently stood united&quot;, in favor of conservatives, &quot;against whom they have so recently risen&quot; (p. 140). They are drawn to the slogan &#39;no enemies to the Left&#39; (p. 168).</li> <li>the moderates are attacked on one side by &quot;disgruntled but not yet silenced conservatives, and the confident, aggressive extremists&quot;, on the other. The moderate revolutionary policies can please neither side. An example is the <a href="https://en.wikipedia.org/wiki/Root_and_Branch_petition">Root and Branch</a> Bill in the English Revolution which abolished the episcopacy, angering conservatives and established institutions without earning the loyalty of radicals (pp. 141–143).</li> <li>the moderates &quot;prove poor war leaders&quot; of the wars which accompany the revolutions, unable to &quot;provide the discipline, the enthusiasm&quot;, needed (p. 144).</li></ul><div><h4>Radicals and &quot;Reigns of Terror and Virtue&quot;</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>In contrast to the moderates, the radicals are aided by a fanatical devotion to their cause, discipline and (in recent revolutions) a study of technique of revolutionary action, obedience to their leadership, ability to ignore contradictions between their rhetoric and action, and drive boldly ahead (pp. 155–160). Even their small numbers are an advantage, giving them &quot;the ability to move swiftly, to make clear and final decisions, to push through to a goal without regard for injured human dispositions&quot; (p. 154). </p><p>The radicals took power in Russia with the <a href="https://en.wikipedia.org/wiki/October_Revolution">October Revolution</a>, in France with the purge of the <a href="https://en.wikipedia.org/wiki/Girondin">Girondins</a>, in England &quot;<a href="https://en.wikipedia.org/wiki/Pride%27s_Purge">Pride&#39;s Purge</a>&quot; (p. 163). The American Revolution never had a radical dictatorship and Reign of Terror, &quot;though in the treatment of Loyalists, in the pressure to support the army, in some of the phases of social life, you can discern … many of the phenomena of the Terror as it is seen in our three other societies&quot; (p. 254). </p><p>The radical reign is one of &quot;Terror and Virtue&quot;. Terror stemming from the abundance of <a href="https://en.wikipedia.org/wiki/Summary_execution">summary executions</a>, foreign and civil war, struggle for power; virtue in the form of <a href="https://en.wikipedia.org/wiki/Puritan">puritanical</a> &quot;organized asceticism&quot; and suppression of vices such as drunkenness, gambling and prostitution (p. 180). In its ardor, revolutionary &quot;tragicomedy&quot; touches the average citizen, for whom &quot;politics becomes as real, as pressing, as unavoidable … as food and drink&quot;, their &quot;job, and the weather&quot; (p. 177). </p><p>On taking power the radicals rule through dictatorship and &quot;rough-and-ready centralization&quot;. &quot;The characteristic form of this supreme authority is that of a committee&quot; (p. 171). The <a href="https://en.wikipedia.org/wiki/English_Council_of_State">Council of State</a> in England, <a href="https://en.wikipedia.org/wiki/Committee_of_Public_Safety">Committee of Public Safety</a> in France. </p><p>At some point in these revolutions, the &quot;process of transfer of power from Right to Left ceases&quot;, and groups even more radical than those in power are suppressed (p. 167). (In France, the <a href="https://en.wikipedia.org/wiki/H%C3%A9bertists">Hébertists</a> are sent to the guillotine (p. 168), in Russia the <a href="https://en.wikipedia.org/wiki/Kronstadt_rebellion">Kronstadt rebellion</a> is crushed.) </p><p>At least in France and Russia, the accession of radicals is also accompanied by a decline in political participation measured in votes cast, as &quot;ordinary, peaceful&quot;, &quot;humdrum men and women&quot; favoring moderation find no outlet for their political beliefs (pp. 153–154). </p><p>Along with centralization, lethal force in suppression of opposition, rule by committee, radical policies include the spreading of &quot;the gospel of their revolution&quot; to other countries. This is found not only in the Russian and French revolutions, but even seventeenth century England, where <a href="https://en.wikipedia.org/wiki/Edward_Sexby">Edward Sexby</a> &quot;proposed to the French radicals&quot; in <a href="https://en.wikipedia.org/wiki/Bordeaux">Bordeaux</a> &quot;a republican constitution which was to be called &#39;L&#39;Accord du Peuple&#39;—an adaptation of the English Agreement of the People&quot; (p. 193). These attempts seldom make a significant impact as the revolutionaries &quot;are usually too poor, and too occupied at home&quot; (p. 213). </p><div><h3>&quot;Thermidor&quot;</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>The radical reign of terror, or &quot;crisis&quot; period, is fairly soon replaced by <a href="https://en.wikipedia.org/wiki/Thermidorian_Reaction">Thermidor</a> period, a period of relaxation from revolutionary policies or &quot;convalescence&quot; from the &quot;fever&quot; of radicalism. Thermidor is named for the period following the fall of <a href="https://en.wikipedia.org/wiki/Maximilien_Robespierre">Maximilien Robespierre</a> in the French Revolution, in Russia the <a href="https://en.wikipedia.org/wiki/New_Economic_Policy">New Economic Policy</a> of 1921 &quot;can be called Russia&#39;s Thermidor&quot; (p. 207), and &quot;perhaps the best date&quot; for that period in England is &quot;Cromwell&#39;s <a href="https://en.wikipedia.org/wiki/Commonwealth_of_England#The_dismissal_of_the_Rump">dissolution of the Rump</a>&quot; (p. 206). </p><p>The Thermidor is characterized by </p><ul><li>the &quot;establishment of a &#39;tyrant&#39;&quot;, i.e. &quot;an unconstitutional ruler brought to power by revolution&quot; (p. 207). The &quot;&#39;silken threads&#39; of habit, tradition, legality&quot; having been broken, &quot;men must be held together in society by the &#39;iron chains&#39; of dictatorship&quot; (p. 208).<sup><span>[</span>4<span>]</span></sup></li> <li>restoration of many pre-revolutionary ways. In Russia this meant an abandonment of the <a href="https://en.wikipedia.org/wiki/Bolshevik">Bolshevik</a>&#39;s avant-garde stance against the institution of the family—formerly disparaged as &quot;a stuffy little nest breeding selfishness, jealousy, love of property, indifference toward the great needs of society&quot; (p. 224). The Bolshevik regime restored roadblocks to divorce (p. 225), laws against homosexuality (p. 226), and moderated its anti-religious, <a href="https://en.wikipedia.org/wiki/Anti-Eastern_Orthodox">anti-Eastern Orthodox</a> Church stance.</li> <li>reaction against Puritanism of the revolution. In England, the <a href="https://en.wikipedia.org/wiki/Restoration_comedy">Restoration comedy</a> that appeared after the revolution is now &quot;a symbol of naughtiness&quot; (p. 220). In France the post-revolutionary <a href="https://en.wikipedia.org/wiki/French_Directory">Directory</a> era was known as boom time for reopened dance halls and swaggering <i>jeunesse doree</i> (p. 218). During the New Economic Policy in Soviet Russia advertising began to appear (p. 225), as did a new class of entrepreneurs known as the <a href="https://en.wikipedia.org/wiki/Nepmen">Nepmen</a> who were reputed to be &#39;exceptionally vulgar, profiteering, crude, and noisy&#39; (p. 221).</li> <li>the replacement of &quot;missionary spirit&quot; to spread revolution by an &quot;aggressive nationalism&quot; (p. 213). In England Cromwell reconquered Ireland and seized <a href="https://en.wikipedia.org/wiki/History_of_Jamaica#British_rule">Jamaica</a>. In France <a href="https://en.wikipedia.org/wiki/Napoleon">Napoleon</a> created an empire (p. 213).</li></ul><p>America did not have a proper Reign of Terror and Virtue, but &quot;the decade of the 1780s displays in incomplete forms some of the marks of Thermidor&quot;, as evidenced by the complaint of historian J.F. Jameson<sup><span>[</span>5<span>]</span></sup> that &#39;sober Americans of 1784 lamented the spirit of speculation which war and its attendant disturbances had generated, the restlessness of the young, disrespect for tradition and authority, increase of crime, the frivolity and extravagance of society&#39; (pp. 235–236). </p><div><h3>Lasting results</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>Brinton finds the lasting results of the revolutions disappointing. In France, the revolution did away with &quot;the old overlapping jurisdictions, the confusions and the compromises inherited from, the thousand-year struggle&quot; between Crown and feudal nobility. Weights and measure &quot;that varied from region to region, indeed from town to town&quot; were replaced with the metric system. Also gone was non-decimal coinage unsuited &quot;for long division&quot;(p. 239). Some antiquated practices were also eliminated in England (p. 239). In Russia, the Bolsheviks brought industrialization, and eventually the <a href="https://en.wikipedia.org/wiki/Sputnik">Sputnik</a> space satellite (p. 240). Confiscated lands stayed in the hands of the new owners for the most part, redistributing land to many &quot;small independent peasants&quot; in France (pp. 241–242), and <a href="https://en.wikipedia.org/wiki/Puritan">Puritan</a> businessmen and clergymen in England (p. 242). </p><p>Remaining essentially &quot;untouched&quot; were day-to-day social relations between husband and wife and children. Attempts at establishing new religions and personal habits come to naught. The revolutions&#39; &quot;results look rather petty as measured by the brotherhood of man and the achievement of justice on this earth. The blood of the martyrs seems hardly necessary to establish decimal coinage&quot; (p. 259). </p><div><h4>Comparisons</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>Brinton concludes that despite their ambitions, the political revolutions he studied brought much less lasting social changes than the disruptions and changes of &quot;what is loosely called the <a href="https://en.wikipedia.org/wiki/Industrial_Revolution">Industrial Revolution</a>&quot;, and the top-down reforms of Mustapha Kemal&#39;s <a href="https://en.wikipedia.org/wiki/Atat%C3%BCrk%27s_Reforms">reforms</a> in <a href="https://en.wikipedia.org/wiki/Turkey">Turkey</a>, and the <a href="https://en.wikipedia.org/wiki/Meiji_Restoration">Meiji Restoration</a> or post-<a href="https://en.wikipedia.org/wiki/World_War_II">World War II</a> <a href="https://en.wikipedia.org/wiki/Occupation_of_Japan">MacArthur era</a> in Japan (p. 246). </p><div><h2>Limitations of the theory</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><ol><li>Brinton admits that &#39;revolution is one of the looser words&#39;.<sup><span>[</span>6<span>]</span></sup> Must a revolution always be violent? can it occur by consent, as in the UK general election of 1945? He is unsure.<sup><span>[</span>7<span>]</span></sup></li> <li>He assumes that the US is &#39;a stable society in the midst of societies undergoing revolutionary change&#39;<sup><span>[</span>8<span>]</span></sup> … &#39;the US looks like a stable society in which a real revolution is highly unlikely&#39;.<sup><span>[</span>9<span>]</span></sup> <br/> This is disputed, then and later by, among others; <a href="https://en.wikipedia.org/w/index.php?title=Murray_Friedman&amp;action=edit&amp;redlink=1">Murray Friedman</a>,<sup><span>[</span>10<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Lee_Edwards">Lee Edwards</a>,<sup><span>[</span>11<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Paul_Craig_Roberts">Paul Craig Roberts</a>,<sup><span>[</span>12<span>]</span></sup> <a href="https://en.wikipedia.org/w/index.php?title=Bernard_Sternsher&amp;action=edit&amp;redlink=1">Bernard Sternsher</a>,<sup><span>[</span>13<span>]</span></sup> <a href="https://en.wikipedia.org/w/index.php?title=Mario_Enaudi&amp;action=edit&amp;redlink=1">Mario Enaudi</a>,<sup><span>[</span>14<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Carl_N._Degler">Carl N. Degler</a>, who wrote of the <a href="https://en.wikipedia.org/wiki/US_civil_war">US civil war</a> as a &#39;Second American Revolution&#39; and of the <a href="https://en.wikipedia.org/wiki/Great_Depression">Great Depression</a> as a third revolution.<sup><span>[</span>15<span>]</span></sup></li> <li>Brinton asserts that &#39;the Great Russian Revolution is quite over, finished&#39;.<sup><span>[</span>16<span>]</span></sup> Also, &#39;revolutions end in a return to an equilibrium … the stable Russian society should finally emerge … no longer in the midst of perpetual nightmare … abundance seems on its way in the 1960s&#39;.<sup><span>[</span>17<span>]</span></sup> Like most, he failed to notice the internal contradictions which caused the USSR collapse just 25 years later.<sup><span>[</span>18<span>]</span></sup></li> <li>Brinton called his book &#39;A work of systematization still in its infancy&#39;.<sup><span>[</span>19<span>]</span></sup> There was &#39;a necessity for a more rigorous treatment of the problems involved …, wider uniformities will … someday emerge from more complete studies&#39;.<sup><span>[</span>20<span>]</span></sup> <br/> He admitted to a lack of objectivity; &#39;Absolute detachment is a polar region, unfit for human life.&#39;<sup><span>[</span>21<span>]</span></sup></li> <li>with reference to points 2) and 3) above, it is widely accepted that polities cannot always be on the rise in a stable fashion. see, for example, <a href="https://en.wikipedia.org/wiki/Ibn_Khaldun">Ibn Khaldun</a><sup><span>[</span>22<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Joshua_S_Goldstein">Joshua S Goldstein</a>;<sup><span>[</span>23<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Paul_Kennedy">Paul Kennedy</a>;<sup><span>[</span>24<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/William_Shirer">William Shirer</a><sup><span>[</span>25<span>]</span></sup> and <a href="https://en.wikipedia.org/wiki/Sakwa">Sakwa</a>.<sup><span>[</span>26<span>]</span></sup></li></ol><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/State_collapse">State collapse</a></li> <li><a href="https://en.wikipedia.org/wiki/Ideology">Ideology</a></li> <li><a href="https://en.wikipedia.org/wiki/Ideocracy">Ideocracy</a></li> <li><a href="https://en.wikipedia.org/wiki/Eric_Hoffer">Eric Hoffer</a></li> <li><a href="https://en.wikipedia.org/wiki/Crane_Brinton">Crane Brinton</a></li> <li><a href="https://en.wikipedia.org/wiki/Power_politics">Power politics</a></li> <li><a href="https://en.wikipedia.org/wiki/Revolutionary_wave">Revolutionary wave</a></li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span><a href="https://www.washingtonpost.com/archive/entertainment/books/1994/03/06/research-and-the-rise-of-capitalism/52757895-372f-4969-8582-9c5fc781b539/">&quot;Research And the Rise of Capitalism; John Schwartz&quot;</a>, <i>The Washington Post</i>, March 6, 1994. p. x.07</span> </li> <li><span><b>^</b></span> <span><a href="https://journals.sagepub.com/doi/10.1177/0022343389026004009">&quot;Over the Hill? The Anatomy of Revolution at Fifty&quot;</a> <a href="https://web.archive.org/web/20221118062544/https://journals.sagepub.com/doi/10.1177/0022343389026004009">Archived</a> 2022-11-18 at the <a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a> Torbjørn L. Knutsen and Jennifer L. Bailey, <i>Journal of Peace Research</i>, Vol. 26, No. 4 (Nov., 1989), pp. 421–431</span> </li> <li><span><b>^</b></span> <span><a href="https://en.wikipedia.org/wiki/Crane_Brinton">Crane Brinton</a>, <i>The Anatomy of Revolution</i>, New York, Vintage Books. first ed., 1938; revised ed., 1952; revised and expanded ed., 1965.</span> </li> <li><span><b>^</b></span> <span>quoting Guglielmo Ferrero [Ferrero, Guglielmo, 1871–1942, <i>The Principles of Power</i>, translated by Theodore R. Jaeckel, New York, 1942]</span> </li> <li><span><b>^</b></span> <span>Jameson, J.F. <i>The American Revolution Considered as a Social Movement</i>, Princeton, 1926</span> </li> <li><span><b>^</b></span> <span><cite>Brinton, Crane (1965). <i>The Anatomy of Revolution</i>. Vintage Books. p. 3.</cite></span> </li> <li><span><b>^</b></span> <span>Brinton 1965, p. 4</span> </li> <li><span><b>^</b></span> <span>Brinton 1965, p. 5</span> </li> <li><span><b>^</b></span> <span>Brinton 1965, p. 266</span> </li> <li><span><b>^</b></span> <span><cite>Friedman, Murray (2006). <a href="https://books.google.com/books?id=DD8oNl63gBEC&amp;q=The%20Neoconservative%20revolution%2C%20Temple%20University%2C%202007&amp;pg=PP1"><i>The Neoconservative Revolution: Jewish Intellectuals and the Shaping of Public Policy</i></a>. Cambridge University Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9780521545013"><bdi>9780521545013</bdi></a>.</cite> </span> </li> <li><span><b>^</b></span> <span><cite>Edwards, Lee (17 November 2014). <a href="https://www.washingtontimes.com/news/2014/nov/17/goldwater-the-man-who-ignited-a-revolution/">&quot;Goldwater: The man who ignited a revolution&quot;</a>. <i>The Washington Times</i>. <a href="https://web.archive.org/web/20190102152540/https://www.washingtontimes.com/news/2014/nov/17/goldwater-the-man-who-ignited-a-revolution/">Archived</a> from the original on 2 January 2019<span>. Retrieved <span>2 January</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Roberts, Paul Craig (1984). <span><a href="https://archive.org/details/supplysiderevolu00robe"><i>The Supply-Side Revolution</i></a></span>. Harvard University Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9780674420427"><bdi>9780674420427</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Sternsher, Bernard (1966). &quot;The New Deal &quot;Revolution&quot;&quot;. <i>The Social Studies</i>. <b>57</b> (4): <span>157–</span>162. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1080%2F00220973.1941.11018764">10.1080/00220973.1941.11018764</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Enoudi, Mario (1959). <i>The Roosevelt Revolution</i>. Harcourt, Brace.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Degler, Carl N. (1970). <span><a href="https://archive.org/details/isbn_0060900024"><i>Out of Our Past: The Forces That Shaped Modern America</i></a></span> (Revised ed.). Harper Colophon Books. p. <a href="https://archive.org/details/isbn_0060900024/page/379">379</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9780060900021"><bdi>9780060900021</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span>The Anatomy of revolution, 1956 preface</span> </li> <li><span><b>^</b></span> <span><i>ibid</i> pp. 226–230</span> </li> <li><span><b>^</b></span> <span>The Soviet Collapse, Richard Sakwa, <a href="https://en.wikipedia.org/wiki/Journal_of_Eurasian_Studies">Journal of Eurasian Studies</a>, Jan 2013</span> </li> <li><span><b>^</b></span> <span><i>ibid</i>, p. 7</span> </li> <li><span><b>^</b></span> <span><i>ibid</i> p. 261</span> </li> <li><span><b>^</b></span> <span><i>ibid</i> p. 20</span> </li> <li><span><b>^</b></span> <span>the <a href="https://en.wikipedia.org/wiki/Muqadimmah">Muqadimmah</a> pp. 130–285</span> </li> <li><span><b>^</b></span> <span>&#39;Empires experience midlife crises&#39; in his book Long Cycles, Yale UP, 1988</span> </li> <li><span><b>^</b></span> <span><i>The rise and fall of the Great Powers</i>, Vintage, 1987</span> </li> <li><span><b>^</b></span> <span>The rise and fall of the Third Reich, Arrow, 1998</span> </li> <li><span><b>^</b></span> <span><i>The rise and fall of the Soviet Union</i>, Routledge, 1991</span> </li> </ol></div></div><div><h3>Notes</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span>Later books that used the same title in part include &quot;Cuba: Anatomy of a Revolution&quot; in 1969 by <a href="https://en.wikipedia.org/wiki/Leo_Huberman">Leo Huberman</a>; <i>Portugal, anatomy of a revolution</i>, London : Chartist Publications, [1976]; <i>Anatomy of a revolution&quot; : the JVP insurrection in Sri Lanka, 1987–1989</i>, by SinhaRaja Tammita-Delgoda; <a href="https://en.wikipedia.org/wiki/Nehru_Memorial_Museum_%26_Library">Nehru Memorial Museum and Library</a>. Centre for Contemporary Studies</span> </li> </ol></div></div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Anatomy_of_Revolution&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://archive.org/details/anatomyofrevolut0000cran/page/n5/mode/1up"><i>The Anatomy of Revolution</i> (1965 Revised and Expanded Edition)</a> on <a href="https://en.wikipedia.org/wiki/Internet_Archive">Internet Archive</a></li> <li><a href="https://americanarchive.org/catalog/cpb-aacip-512-z31ng4hw45">American Archive of Public Broadcasting</a> has archived videos of the series of the same name in which <a href="https://en.wikipedia.org/wiki/Crane_Brinton">Crane Brinton</a>, the author, delivers lectures based on the contents of this book. They were produced by <a href="https://en.wikipedia.org/wiki/WGBH_Educational_Foundation">WGBH</a> and broadcast in 1961.</li></ul> Moore Hall, County Mayo - Wikipedia https://en.wikipedia.org/wiki/Moore_Hall,_County_Mayo CktjCK0PYygGi37OjXZEZ7R0rUAs8vOp6GnwuA== Wed, 13 May 2026 11:24:37 +0000 Building in County Mayo, Ireland <p> </p><div>Building in County Mayo, Ireland</div><table><tbody><tr><th colspan="2">Moore Hall</th></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Moore_Hall,_Co._Mayo,_late_1800s_02_(cropped).jpg"></a></span><div>Moore Hall, <abbr>c.</abbr><span> 1880s</span></div></td></tr><tr><td colspan="2"><img src="https://maps.wikimedia.org/img/osm-intl,13,a,a,250x200.png?lang=en&amp;domain=en.wikipedia.org&amp;title=Moore_Hall%2C_County_Mayo&amp;revid=1331084057&amp;groups=_55b8a9f223ba4d57e1e3a62bf697e15d714cf8df&amp;parser=legacy" alt="Map" title=""/><div>Interactive map of the Moore Hall area</div></td></tr><tr><th colspan="2">General information</th></tr><tr><th>Status</th><td>Derelict</td></tr><tr><th>Architectural style</th><td><a href="https://en.wikipedia.org/wiki/Georgian_architecture">Georgian</a></td></tr><tr><th>Location</th><td><a href="https://en.wikipedia.org/wiki/County_Mayo">County Mayo</a>, Ireland</td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Geographic_coordinate_system">Coordinates</a></th><td><span><span><a href="https://geohack.toolforge.org/geohack.php?pagename=Moore_Hall,_County_Mayo&amp;params=53.7134_N_9.2264_W_type:landmark_region:IE"><span><span><span>53°42′48″N</span> <span>9°13′35″W</span></span></span><span> / </span><span><span>53.7134°N 9.2264°W</span><span> / <span>53.7134; -9.2264</span></span></span></a></span></span></td></tr><tr><th>Estimated completion</th><td>1795</td></tr><tr><th>Destroyed</th><td>1923</td></tr><tr><th colspan="2">Technical details</th></tr><tr><th>Floor count</th><td>3 over part-raised basement<sup><span>[</span>2<span>]</span></sup></td></tr><tr><th colspan="2">Design and construction</th></tr><tr><th>Architect</th><td><a href="https://en.wikipedia.org/wiki/John_Roberts_(architect)">John Roberts</a><sup><span>[</span>1<span>]</span></sup></td></tr></tbody></table><p><b>Moore Hall</b> is a ruined 18th-century manor house located near <a href="https://en.wikipedia.org/wiki/Carnacon">Carnacon</a> in <a href="https://en.wikipedia.org/wiki/County_Mayo">County Mayo</a>, <a href="https://en.wikipedia.org/wiki/Ireland">Ireland</a>. Built around 1792, it became the ancestral home of the Moore family, including the novelist <a href="https://en.wikipedia.org/wiki/George_Moore_(novelist)">George Augustus Moore</a>.<sup><span>[</span>2<span>]</span></sup> The house was burned during the <a href="https://en.wikipedia.org/wiki/Irish_Civil_War">Irish Civil War</a> in 1923 and remains a ruin.<sup><span>[</span>3<span>]</span></sup> The surrounding forested estate is now managed by <i><a href="https://en.wikipedia.org/wiki/Coillte">Coillte</a></i> as a public amenity,<sup><span>[</span>4<span>]</span></sup> while the house and parts of the former estate are owned by <a href="https://en.wikipedia.org/wiki/Mayo_County_Council">Mayo County Council</a>.<sup><span>[</span>5<span>]</span></sup> </p><div><h2>History</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Moore_Hall,_County_Mayo&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Moore_Hall_22nd_Aug_2010_003.JPG"></a><figcaption>Ruined facade of Moore Hall in 2010</figcaption></figure><p>Built for the Moore family, who had purchased land in the area in the early 1790s,<sup><span>[</span>6<span>]</span></sup> Moore Hall was completed between <abbr>c.</abbr><span> 1792</span> and 1795.<sup><span>[</span>7<span>]</span></sup> The house was commissioned by the wine merchant George Moore (1727–1799) and built to the designs of the architect <a href="https://en.wikipedia.org/wiki/John_Roberts_(architect)">John Roberts</a>.<sup><span>[</span>8<span>]</span></sup> The <a href="https://en.wikipedia.org/wiki/Georgian_architecture">Georgian</a> house had three-storeys (over a part-raised basement) and was five bays wide and three bays deep.<sup><span>[</span>2<span>]</span></sup> The front elevation&#39;s design features a full-height breakfront with a Doric portico on the groundfloor.<sup><span>[</span>2<span>]</span></sup> </p><p>Used as their primary residence until the early 20th century,<sup><span>[</span>3<span>]</span></sup><sup><span>[</span>6<span>]</span></sup> members of the Moore family associated with the estate include <a href="https://en.wikipedia.org/wiki/John_Moore_(Irish_politician)">John Moore</a> (1763–1799), the politician <a href="https://en.wikipedia.org/wiki/George_Henry_Moore_(politician)">George Henry Moore</a> (1810–1870), writer <a href="https://en.wikipedia.org/wiki/George_Moore_(novelist)">George Augustus Moore</a> (1852–1933) and soldier and senator <a href="https://en.wikipedia.org/wiki/Maurice_George_Moore">Maurice George Moore</a> (1854–1939).<sup><span>[</span>6<span>]</span></sup> </p><p>The house was vacant by 1921 and was burned down in 1923 during the Irish Civil War.<sup><span>[</span>2<span>]</span></sup> It was burned by the <a href="https://en.wikipedia.org/wiki/Anti-Treaty_Irish_Republican_Army">Anti-Treaty Irish Republican Army</a>, during a period in which <a href="https://en.wikipedia.org/wiki/Destruction_of_Irish_country_houses_(1919%E2%80%931923)">a number of other Irish country houses were destroyed</a>, as the then owner and <a href="https://en.wikipedia.org/wiki/Seanad_%C3%89ireann_(Irish_Free_State)">Irish Free State Senator</a>, Maurice George Moore, was perceived to hold a Pro-Treaty stance.<sup><span>[</span>7<span>]</span></sup><sup><span>[</span>9<span>]</span></sup> </p><p>The Moore Hall estate ultimately came into the ownership of the state, with the forested areas managed by <i><a href="https://en.wikipedia.org/wiki/Coillte">Coillte</a></i>.<sup><span>[</span>4<span>]</span></sup> In January 2018, <a href="https://en.wikipedia.org/wiki/Mayo_County_Council">Mayo County Council</a> announced, that it had acquired parts of the estate, including the ruined 18th-century house and approximately 80 acres of woodland.<sup><span>[</span>5<span>]</span></sup> As of 2023, <i>Coillte</i> reportedly retained ownership of 300 acres at Moore Hall.<sup><span>[</span>10<span>]</span></sup> In March 2023, Mayo County Council, in conjunction with <i>Coillte</i> and the <a href="https://en.wikipedia.org/wiki/National_Parks_and_Wildlife_Service_(Ireland)">National Parks and Wildlife Service</a>, published a &quot;draft masterplan&quot; for the proposed redevelopment of the house and lands.<sup><span>[</span>11<span>]</span></sup> </p><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Moore_Hall,_County_Mayo&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span><cite><a href="https://www.buildingsofireland.ie/app/uploads/2019/10/Mayo.pdf">&quot;An Introduction to the Architectural Heritage of County Mayo&quot;</a> <span>(PDF)</span>, <i>buildingsofireland.ie</i>, p. 36<span>, retrieved <span>18 October</span> 2025</span></cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup> <sup><i><b>e</b></i></sup></span> <span><cite><a href="https://www.buildingsofireland.ie/buildings-search/building/31310009/moore-hall-muckloon-or-moorehall-mayo">&quot;Moore Hall, Muckloon or Moorehall, Mayo&quot;</a>. <i>buildingsofireland.ie</i>. National Inventory of Architectural Heritage<span>. Retrieved <span>17 October</span> 2025</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://landedestates.ie/property/10">&quot;Property - Moore Hall&quot;</a>. <i>Landed Estates Database</i>. NUI Galway<span>. Retrieved <span>17 October</span> 2025</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://www.coillte.ie/site/moore-hall/">&quot;Moore Hall&quot;</a>. <i>coillte.ie</i><span>. Retrieved <span>17 October</span> 2025</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://www.mayonews.ie/news/home/1119459/moorehall-bought-by-mayo-county-council.html">&quot;Moorehall bought by Mayo County Council&quot;</a>. <i>mayonews.ie</i>. 5 January 2018<span>. Retrieved <span>18 October</span> 2025</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite><a href="https://landedestates.ie/estate/7">&quot;Estates - Moore (Moore Hall)&quot;</a>. <i>Landed Estates Database</i>. NUI Galway<span>. Retrieved <span>18 October</span> 2025</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://www.archiseek.com/1785-moore-hall-co-mayo/">&quot;1785 - Moore Hall, Co. Mayo - Architecture of Mayo, Lost Buildings of Ireland&quot;</a>. <i>archiseek.com</i>. 6 October 2012<span>. Retrieved <span>18 October</span> 2025</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.mayonews.ie/news/living/1105410/culture-moore-hall-continues-to-yield-its-secrets.html">&quot;Culture: Moore Hall continues to yield its secrets&quot;</a>. <i>mayonews.ie</i>. 18 November 2014<span>. Retrieved <span>18 October</span> 2025</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>O&#39;Sullivan, Donal (1940). <a href="https://archive.org/details/in.ernet.dli.2015.115100/page/105"><i>The Irish Free State and Its Senate</i></a>. Faber and Faber. p. 105.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.con-telegraph.ie/2023/02/06/masterplan-for-mayos-moorehall-needs-to-be-expedited/">&quot;Masterplan for Mayo&#39;s Moorehall needs to be expedited&quot;</a>. <i>Connaught Telegraph</i>. 6 February 2023<span>. Retrieved <span>18 October</span> 2025</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://consult.mayo.ie/en/system/files/materials/4027/2303%20Moorehall%20Draft%20Masterplan_Final.pdf">&quot;Draft Masterplan for Moorehall and Environs, County Mayo&quot;</a> <span>(PDF)</span>, <i>consult.mayo.ie</i>, Mayo County Council, March 2023<span>, retrieved <span>18 October</span> 2025</span></cite></span> </li> </ol></div></div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Moore_Hall,_County_Mayo&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Commons-logo.svg"></a></span></div> <div>Wikimedia Commons has media related to <span><a href="https://commons.wikimedia.org/wiki/Category:Moore_Hall">Moore Hall</a></span>.</div></div> </div><ul><li><a href="https://www.historicalballinrobe.org/places/townlands-and-surrounding-areas/moore-hall-and-the-moores-of-moorehall">Historicalballinrobe.org - Moore Hall and the Moores of Moorehall</a></li></ul> Horace Plunkett - Wikipedia https://en.wikipedia.org/wiki/Horace_Plunkett zGHqdfDA57R-_Xuoo-j-N5qxjkQBOlB0Tbsn2A== Wed, 13 May 2026 11:24:37 +0000 Irish agricultural reformer and politician (1854–1932) <div>Irish agricultural reformer and politician (1854–1932)</div><p> </p><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/The_Right_Honourable">The Right Honourable</a></div><div>Sir Horace Plunkett</div><div><span><span><a href="https://en.wikipedia.org/wiki/Knight_Commander_of_the_Royal_Victorian_Order">KCVO</a></span> <span><a href="https://en.wikipedia.org/wiki/Justice_of_the_Peace#United_Kingdom">JP</a></span> <span><a href="https://en.wikipedia.org/wiki/Deputy_Lieutenant">DL</a></span> <span><a href="https://en.wikipedia.org/wiki/Fellow_of_the_Royal_Society">FRS</a></span></span></div></th></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Sir_Horace_Plunkett,_1-15-23_LOC_npcc.07656_(cropped).jpg"></a></span></td></tr><tr><td colspan="2"></td></tr><tr><th colspan="2"><a href="https://en.wikipedia.org/wiki/Seanad_%C3%89ireann_(Irish_Free_State)">Seanad Éireann</a></th></tr><tr><td colspan="2"><span><b>In office</b></span><br/>11 December 1922 – 14 November 1923</td></tr><tr><th colspan="2"><a href="https://en.wikipedia.org/wiki/Irish_Dominion_League">Leader of the Irish Dominion League</a></th></tr><tr><td colspan="2"><span><b>In office</b></span><br/>1919–1921</td></tr><tr><th colspan="2">Chairman of the <a href="https://en.wikipedia.org/wiki/Irish_Convention">Irish Convention</a></th></tr><tr><td colspan="2"><span><b>In office</b></span><br/>1917–1918</td></tr><tr><th colspan="2">MP for <a href="https://en.wikipedia.org/wiki/South_Dublin_(UK_Parliament_constituency)">South Dublin</a></th></tr><tr><td colspan="2"><span><b>In office</b></span><br/>1892–1900</td></tr><tr><th><span>Preceded by</span></th><td><a href="https://en.wikipedia.org/wiki/Sir_Thomas_Esmonde,_11th_Baronet">Sir Thomas Esmonde</a></td></tr><tr><th><span>Succeeded by</span></th><td><a href="https://en.wikipedia.org/wiki/John_Joseph_Mooney">John Joseph Mooney</a></td></tr><tr><th colspan="2"><a href="https://en.wikipedia.org/wiki/Congested_Districts_Board_for_Ireland">Congested Districts Board for Ireland</a></th></tr><tr><td colspan="2"><span><b>In office</b></span><br/>1891–1918</td></tr><tr><td colspan="2"> </td></tr><tr><th colspan="2">Personal details</th></tr><tr><th>Born</th><td><span>(<span>1854-10-24</span>)</span>24 October 1854<br/><div><a href="https://en.wikipedia.org/wiki/Sherborne,_Gloucestershire">Sherborne, Gloucestershire</a>, England</div></td></tr><tr><th>Died</th><td>26 March 1932<span>(1932-03-26)</span> (aged 77)<br/><div><a href="https://en.wikipedia.org/wiki/Weybridge">Weybridge</a>, <a href="https://en.wikipedia.org/wiki/Surrey">Surrey</a>, England</div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Political_party">Party</a></th><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Irish_Conservative_Party">Irish Conservative Party</a></li><li><a href="https://en.wikipedia.org/wiki/Irish_Unionist_Alliance">Irish Unionist Alliance</a></li><li><a href="https://en.wikipedia.org/wiki/Irish_Dominion_League">Irish Dominion League</a></li><li><a href="https://en.wikipedia.org/wiki/Independent_politician_(Ireland)">Independent</a></li></ul></div></td></tr><tr><th>Education</th><td><a href="https://en.wikipedia.org/wiki/Eton_College">Eton College</a></td></tr><tr><th><div><a href="https://en.wikipedia.org/wiki/Alma_mater">Alma mater</a></div></th><td><a href="https://en.wikipedia.org/wiki/University_College,_Oxford">University College, Oxford</a></td></tr><tr><td colspan="2"></td></tr></tbody></table><p><b>Sir Horace Curzon Plunkett</b> <span><span><a href="https://en.wikipedia.org/wiki/Knight_Commander_of_the_Royal_Victorian_Order">KCVO</a></span> <span><a href="https://en.wikipedia.org/wiki/Privy_Council_of_Ireland">PC (Ire)</a></span> <span><a href="https://en.wikipedia.org/wiki/Justice_of_the_Peace#United_Kingdom">JP</a></span> <span><a href="https://en.wikipedia.org/wiki/Deputy_Lieutenant">DL</a></span> <span><a href="https://en.wikipedia.org/wiki/Fellow_of_the_Royal_Society">FRS</a></span></span> (24 October 1854 – 26 March 1932), was an <a href="https://en.wikipedia.org/wiki/Anglo-Irish">Anglo-Irish</a> agricultural reformer, pioneer of <a href="https://en.wikipedia.org/wiki/Agricultural_cooperative">agricultural cooperatives</a> and author. In politics, he had been elected as a <a href="https://en.wikipedia.org/wiki/Unionism_in_Ireland">Unionist</a> <a href="https://en.wikipedia.org/wiki/Member_of_Parliament_(United_Kingdom)">MP</a>, but later became a supporter of a form of <a href="https://en.wikipedia.org/wiki/Irish_Home_Rule_movement">Home Rule</a> and served for a year as a <a href="https://en.wikipedia.org/wiki/Seanad_%C3%89ireann_(Irish_Free_State)">senator</a> in the <a href="https://en.wikipedia.org/wiki/Irish_Free_State">Irish Free State</a>. </p><p>Plunkett, a younger brother of <a href="https://en.wikipedia.org/wiki/John_Plunkett,_17th_Baron_of_Dunsany">John Plunkett, 17th Baron of Dunsany</a>, was a member of the <a href="https://en.wikipedia.org/wiki/Congested_Districts_Board_for_Ireland">Congested Districts Board for Ireland</a> for over 27 years, founder of the Recess Committee and the <a href="https://en.wikipedia.org/wiki/Irish_Agricultural_Organisation_Society">Irish Agricultural Organisation Society</a> (IAOS), vice-president (operational head) of the <a href="https://en.wikipedia.org/wiki/Department_of_Agriculture_and_Technical_Instruction_for_Ireland">Department of Agriculture and Technical Instruction</a> (DATI) for Ireland (predecessor to the Department of Agriculture) from October 1899 to May 1907, <a href="https://en.wikipedia.org/wiki/Irish_Unionist">Unionist</a> MP for <a href="https://en.wikipedia.org/wiki/South_Dublin_(UK_Parliament_constituency)">South Dublin</a> in the <a href="https://en.wikipedia.org/wiki/House_of_Commons_of_the_United_Kingdom">House of Commons of the United Kingdom</a> from 1892 to 1900, and Chairman of the <a href="https://en.wikipedia.org/wiki/Irish_Convention">Irish Convention</a> of 1917–18.<sup><span>[</span>1<span>]</span></sup> In 1919 he founded the <a href="https://en.wikipedia.org/wiki/Irish_Dominion_League">Irish Dominion League</a>, aiming to keep Ireland united. In 1922 he became a member of the first formation of <a href="https://en.wikipedia.org/wiki/Seanad_%C3%89ireann_(Irish_Free_State)">Seanad Éireann</a>, the upper chamber in the Parliament of the new <a href="https://en.wikipedia.org/wiki/Irish_Free_State">Irish Free State</a>. He has been described as a <a href="https://en.wikipedia.org/wiki/Christian_socialist">Christian socialist</a>.<sup><span>[</span>2<span>]</span></sup> </p><div><h2>Family and background</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>Plunkett was born in <a href="https://en.wikipedia.org/wiki/Sherborne,_Gloucestershire">Sherborne, Gloucestershire</a>, England, the third son of <a href="https://en.wikipedia.org/wiki/Admiral_(Royal_Navy)">Admiral</a> Edward Plunkett, the 16th <a href="https://en.wikipedia.org/wiki/Baron_of_Dunsany">Baron of Dunsany</a>, of <a href="https://en.wikipedia.org/wiki/Dunsany_Castle">Dunsany Castle</a>, <a href="https://en.wikipedia.org/wiki/Category:Dunsany">Dunsany</a>, near <a href="https://en.wikipedia.org/wiki/Dunshaughlin">Dunshaughlin</a>, <a href="https://en.wikipedia.org/wiki/County_Meath">County Meath</a>, and the Honourable Anne Constance Dutton (d. 1858; daughter of <a href="https://en.wikipedia.org/wiki/John_Dutton,_2nd_Baron_Sherborne">John Dutton, 2nd Baron Sherborne</a>). Raised in County Meath, Plunkett was <a href="https://en.wikipedia.org/wiki/Anglo-Irish">Anglo-Irish</a>, being of a <a href="https://en.wikipedia.org/wiki/Church_of_Ireland">Church of Ireland</a> and <a href="https://en.wikipedia.org/wiki/Unionism_in_Ireland">unionist</a> background, educated at <a href="https://en.wikipedia.org/wiki/Eton_College">Eton College</a> and <a href="https://en.wikipedia.org/wiki/University_College,_Oxford">University College, Oxford</a>, of which he became an honorary fellow in 1909.<sup><span>[</span>3<span>]</span></sup> </p><p>His older brother was <a href="https://en.wikipedia.org/wiki/John_Plunkett,_17th_Baron_of_Dunsany">John Plunkett, 17th Baron of Dunsany</a> and a distant cousin was <a href="https://en.wikipedia.org/wiki/George_Noble_Plunkett">George Noble Plunkett</a>, a Catholic, a <a href="https://en.wikipedia.org/wiki/Papal_Count">Papal Count</a> and father of <a href="https://en.wikipedia.org/wiki/Joseph_Plunkett">Joseph Plunkett</a>, one of the signatories of the <a href="https://en.wikipedia.org/wiki/Proclamation_of_the_Irish_Republic">Proclamation of the Irish Republic</a> and a leader of the <a href="https://en.wikipedia.org/wiki/Easter_Rising">Easter Rising</a> of 1916.<sup><span>[</span>4<span>]</span></sup> </p><p>Threatened by lung trouble in 1879, Horace Plunkett sought health in ranching for ten years (1879–1889) in the <a href="https://en.wikipedia.org/wiki/Bighorn_Mountains">Bighorn Mountains</a> of <a href="https://en.wikipedia.org/wiki/Wyoming">Wyoming</a>, where he acquired, together with a substantial fortune, extensive agricultural and business experience that proved invaluable in the work of agricultural education, improvement and development.<sup><span>[</span>5<span>]</span></sup> On visits back to Ireland, and for much of the time when he returned, he devoted himself to these topics.<sup><span>[</span>4<span>]</span></sup> </p><p>He devoted his career to agricultural and rural development, as well as to politics, diplomacy, public administration, and economics. He played a central role in the development of the Irish cooperative movement, which later included large creamery and food ingredient enterprises such as Avonmore and Kerry Group. He was also the prime driver in the establishment of the first government department for agriculture in Ireland, and founded the Plunkett Foundation. His work also influenced the formation of organisations including the Irish Countrywomen&#39;s Association and the Women&#39;s Institutes in the United Kingdom.<sup><span>[</span>4<span>]</span></sup> </p><div><h2>Career</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><div><h3>Early political career</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Although a Unionist, Plunkett resolved to bring together people of all political views for the promotion of the material prosperity of the Irish people.<sup><span>[</span>5<span>]</span></sup> In 1891 he was appointed to the newly established <a href="https://en.wikipedia.org/wiki/Congested_Districts_Board_for_Ireland">Congested Districts Board</a> and learned at first-hand about the wretched conditions of the rural population, especially west of the <a href="https://en.wikipedia.org/wiki/River_Shannon">River Shannon</a>. The experience hardened his conviction that the one remedy for social and economic ills was cooperative self-help. The Congested Districts Board were a major plank of the ultimately failed <a href="https://en.wikipedia.org/wiki/Conservative_Party_(UK)">Conservative</a> policy of <a href="https://en.wikipedia.org/wiki/Constructive_Unionism">Constructive Unionism</a> or &quot;killing <a href="https://en.wikipedia.org/wiki/Irish_Home_Rule_movement">Home Rule</a> with kindness&quot;.<sup><span>[</span>6<span>]</span></sup> </p><p>Around him, he saw a troubled economy, racked with dissension, denuded by emigration, impoverished in its countryside and economically stagnant in its towns.<sup><span>[</span>7<span>]</span></sup> </p><figure><a href="https://en.wikipedia.org/wiki/File:First_Irish_Dairy_Cooperative1889,_Doneraile,_co._Cork.JPG"></a><figcaption>First Irish Dairy Cooperative, erected and established 1889, in Doneraile, County Cork.</figcaption></figure><p>Before going to America he had become an enthusiast for the <a href="https://en.wikipedia.org/wiki/Rochdale_principles">Rochdale principles</a> of Consumer cooperatives and in 1878 had set a store up on the family estate.<sup><span>[</span>3<span>]</span></sup> </p><div><h3>Agricultural reform</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Plunkett took a leading part in developing <a href="https://en.wikipedia.org/wiki/Agricultural_cooperative">agricultural co-operation</a> in Ireland, of which he had learned from isolated American farmers, taking account of Scandinavian models of cooperation and the invention of the steam-powered cream separator. Working with a few colleagues, including two members of the clergy, and advocating self-reliance, he set his ideas into practice first among dairy farmers in the south of Ireland, who established Ireland&#39;s first cooperative at <a href="https://en.wikipedia.org/wiki/Doneraile">Doneraile</a>, <a href="https://en.wikipedia.org/wiki/County_Cork">County Cork</a>. He also opened the first creamery in <a href="https://en.wikipedia.org/wiki/Dromcollogher">Dromcollogher</a>, <a href="https://en.wikipedia.org/wiki/County_Limerick">County Limerick</a>, now the site of the National Dairy Cooperative Museum.<sup><span>[</span>8<span>]</span></sup> </p><p>In the setting up of creameries, the cooperative movement experienced its greatest success. Plunkett got farmers to join to establish units to process and market their own butter, milk and cheese to standards suitable for the profitable British market, rather than producing unhygienic, poor-quality output in their homes for local traders. This enabled farmers to deal directly with companies established by themselves, which guaranteed fair prices without middlemen absorbing the profits.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><div><h3>Work with Roosevelt</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>Plunkett believed that the <a href="https://en.wikipedia.org/wiki/Industrial_Revolution">Industrial Revolution</a> needed to be redressed by an agricultural revolution through cooperation, and proclaimed his ideals under the slogan &quot;Better farming, better business, better living&quot;. (US president <a href="https://en.wikipedia.org/wiki/Theodore_Roosevelt">Theodore Roosevelt</a> adopted the slogan for his conservation and country life policy.)<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p><a href="https://en.wikipedia.org/wiki/Gifford_Pinchot">Gifford Pinchot</a>, Theodore Roosevelt&#39;s head of the <a href="https://en.wikipedia.org/wiki/Bureau_of_Forestry">Bureau of Forestry</a> introduced Plunkett to Roosevelt in 1906. Roosevelt had recently set up the <a href="https://en.wikipedia.org/wiki/National_Conservation_Commission">National Conservation Commission</a> and was also interested in Irish cooperatives. Arguing that it was not enough to conserve natural resources without tackling the problems of rural life, Plunkett and Pinchot helped draft Roosevelt&#39;s letter recommending the Commission on Country Life&#39;s report to congress. The <i><a href="https://en.wikipedia.org/wiki/Dictionary_of_Irish_Biography">Dictionary of Irish Biography</a></i> credits Plunket with persuading Roosevelt to establish the commission as a complement to the conservation work.<sup><span>[</span>3<span>]</span></sup> </p><div><h3>Success and opposition</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>Public opinion, initially lukewarm, grew hostile in some sectors as the cooperative movement developed, and shopkeepers, butter-buyers and sections of the press led a campaign of virulent opposition. Cooperatives and Plunkett were denounced for supposedly ruining the dairy industry but the movement caught hold, with the mass of farmers benefitting. Plunkett and his colleagues including the poet and painter <a href="https://en.wikipedia.org/wiki/George_William_Russell">George William Russell</a> (&quot;Æ&quot;) made a good working team, writing widely on economic and cultural development, and on the role of labour. </p><p>As early as 1894, when his campaign reached a size too big to be directed by a few individuals, Plunkett founded the <a href="https://en.wikipedia.org/wiki/Irish_Agricultural_Organisation_Society">Irish Agricultural Organisation Society</a> (IAOS), with <a href="https://en.wikipedia.org/wiki/Thomas_Spring_Rice,_2nd_Baron_Monteagle_of_Brandon">Lord Monteagle</a>, <a href="https://en.wikipedia.org/wiki/Thomas_A._Finlay">Thomas A. Finlay</a><sup><span>[</span>9<span>]</span></sup> and others. Robert A. Anderson acted as secretary,<sup><span>[</span>10<span>]</span></sup><sup><span>[</span>11<span>]</span></sup> with Æ and PJ Hannon his assistants. IAOS soon became the powerhouse of cooperation, with 33 affiliated dairy <a href="https://en.wikipedia.org/wiki/Agricultural_cooperative">cooperative</a> societies and <a href="https://en.wikipedia.org/wiki/Cooperative_banking">cooperative banks</a>, introducing cooperation among Irish farmers by proving the benefits obtainable through more economical and efficient management. The following year he and Russell began publishing its journal <i><a href="https://en.wikipedia.org/wiki/The_Irish_Homestead">The Irish Homestead</a></i> to spread information on farming. Four years later there were 243 affiliated societies. Within a decade, 800 societies were in existence, with a trade turnover of three million pounds sterling (over 300 million sterling in today&#39;s money, and the turnover of the resulting companies is in excess of a billion euro). </p><p>Plunkett&#39;s task was frustrating. He was a pioneer of the concept of systematic rural development, who, in spite of his role in Irish affairs being often overlooked, influenced many international reformers, and can be credited as one of the few who had a long-term vision for the development of rural Ireland. He was apt to remind audiences that, even if full peasant proprietorship was achieved and Home Rule was implemented, rural underdevelopment would still have to be faced. But class conflict between farmers and shopkeepers intervened to frustrate much of what he aimed to do.<sup><span>[</span>12<span>]</span></sup> </p><div><h3>MP for South Dublin</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>Before entering Parliament, Plunkett had been involved in the Unionist reaction to the <a href="https://en.wikipedia.org/wiki/Leader_of_the_Liberal_Party_(UK)">Liberal leader</a> <a href="https://en.wikipedia.org/wiki/William_Ewart_Gladstone">William Ewart Gladstone</a>&#39;s conversion to <a href="https://en.wikipedia.org/wiki/Home_Rule">Home Rule</a>, predicting in a speech to an 1886 Unionist demonstration that Home rule would lead to &quot;squalid poverty and violent social disorder, which before long is almost certain to end in civil war&quot;.<sup><span>[</span>13<span>]</span></sup> </p><p>At the <a href="https://en.wikipedia.org/wiki/1892_United_Kingdom_general_election">1892 general election</a> he was elected as the <a href="https://en.wikipedia.org/wiki/Irish_Unionist_Alliance">Irish Unionist Alliance</a> Member of Parliament (MP) for <a href="https://en.wikipedia.org/wiki/South_Dublin_(UK_Parliament_constituency)">South Dublin</a>,<sup><span>[</span>14<span>]</span></sup> gaining it from the <a href="https://en.wikipedia.org/wiki/Irish_National_Federation">Anti-Parnellite</a> incumbent <a href="https://en.wikipedia.org/wiki/Sir_Thomas_Esmonde,_11th_Baronet">Sir Thomas Esmonde</a> against a split nationalist vote. He successfully held the seat against a sole nationalist (<a href="https://en.wikipedia.org/wiki/Parnellite">Parnellite Nationalist</a>) challenger <a href="https://en.wikipedia.org/wiki/Edmund_Haviland-Burke">Edmund Haviland-Burke</a> in <a href="https://en.wikipedia.org/wiki/1895_United_Kingdom_general_election">1895</a>. </p><p>Early in his career, Plunkett opposed home rule because of the danger of partition. In 1893 he asserted that one of the leading objections to any measure of home rule was that if it were possible to enforce it on Ulster &quot;... it would intensify and perpetuate a state of things in which the Boyne seemed to be broader, deeper and stormier than the Irish Sea&quot;.<sup><span>[</span>15<span>]</span></sup> </p><p>At the <a href="https://en.wikipedia.org/wiki/1900_United_Kingdom_general_election_in_Ireland">1900</a>, <a href="https://en.wikipedia.org/wiki/F._Elrington_Ball">F. Elrington Ball</a> stood as an <a href="https://en.wikipedia.org/wiki/Independent_Unionist">independent Unionist</a> candidate against Plunkett&#39;s conciliatory approach. This split the unionist vote, and Plunkett was defeated by <a href="https://en.wikipedia.org/wiki/John_Mooney_(Irish_politician)">John Mooney</a> of the <a href="https://en.wikipedia.org/wiki/Irish_Parliamentary_Party">Irish Parliamentary Party</a>.<sup><span>[</span>16<span>]</span></sup> </p><div><h3>Expanding cooperation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Sir_Horace_Curzon_Plunkett_in_1915_(cropped).jpg"></a><figcaption>Plunkett in 1915</figcaption></figure><p>Continuing his policy of conciliation, Plunkett suggested in a letter to the Irish press in August 1895 that a few prominent persons of various political opinions, both nationalist and unionist, should meet to discuss and frame a scheme of practical legislation for pursuing national development,<sup><span>[</span>5<span>]</span></sup> and to make recommendations on the Agriculture and Industries (Ireland) Bill of 1897.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>The outcome of this proposal was the formation of the Recess Committee, with Plunkett as chairman and members of divergent views, such as the <a href="https://en.wikipedia.org/wiki/Earl_of_Mayo">Earl of Mayo</a>, <a href="https://en.wikipedia.org/wiki/John_Redmond">John Redmond</a>, <a href="https://en.wikipedia.org/wiki/Denis_O%27Conor">The O&#39;Conor Don</a>, <a href="https://en.wikipedia.org/wiki/Thomas_Sinclair_(politician,_1838%E2%80%931914)">Thomas Sinclair</a>,<sup><span>[</span>5<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Thomas_Spring_Rice,_2nd_Baron_Monteagle_of_Brandon">Thomas Spring Rice</a>, Rev Dr Kane (Grand Master of the Belfast Orangemen), Father <a href="https://en.wikipedia.org/wiki/Thomas_A._Finlay">Thomas A. Finlay</a>, Mr John Ross, MP, <a href="https://en.wikipedia.org/wiki/Timothy_Harrington">Timothy Harrington</a> MP, Sir <a href="https://en.wikipedia.org/wiki/John_Arnott">John Arnott</a>, Sir William Ewart, Sir <a href="https://en.wikipedia.org/wiki/Sir_Daniel_Dixon,_1st_Baronet">Daniel Dixon</a> (after Lord Mayor of Belfast), Sir James Musgrave (Chairman of the Belfast Harbour Board), Thomas Andrews (Chairman of the Belfast and County Down Railway). <a href="https://en.wikipedia.org/wiki/T._P._Gill">T. P. Gill</a> acted as Honorary Secretary to the committee.<sup><span>[</span>17<span>]</span></sup> </p><p>In July 1896, the Recess Committee issued a report, of which Plunkett was the author, containing accounts of the systems of state aid to agriculture and technical instruction in foreign countries. This report, and the growing influence of Plunkett, who became a member of the <a href="https://en.wikipedia.org/wiki/Irish_Privy_Council">Irish Privy Council</a> in 1897, led to the passing in 1899 of an Act establishing the <a href="https://en.wikipedia.org/wiki/Department_of_Agriculture_and_Technical_Instruction_for_Ireland">Department of Agriculture and Technical Instruction</a> (DATI) for Ireland, of which the <a href="https://en.wikipedia.org/wiki/Chief_Secretary_for_Ireland">Chief Secretary for Ireland</a> was to be President <span><i>ex officio</i></span>.<sup><span>[</span>5<span>]</span></sup> Plunkett was appointed vice-president, a position of de facto leadership.<sup><span>[</span>18<span>]</span></sup> He guided the policy and administration of the DATI in its first seven critical years.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>The DATI worked: </p><ul><li>to improve the quality of crops and livestock</li> <li>to deal with animal and plant disease</li> <li>to encourage fishing and planting of forests</li> <li>to collect statistics on many aspects of Irish life.</li></ul><p>By 1914 the DATI had 138 instructors travelling the country, informing farmers about new methods in agriculture, horticulture and poultry-keeping. The start of the 20th century saw the high water mark in Plunket&#39;s achievements. The IAOS was flourishing and vigorous. In 1903 there were 370 dairy societies, 201 cooperative banks and 146 agricultural societies under the auspices of the IAOS, and by 1914 there were over 1,000 societies and nearly 90,000 members.<sup><span>[</span>19<span>]</span></sup> However, most unionists considered Plunkett too conciliatory and their hostility cost him his seat at the <a href="https://en.wikipedia.org/wiki/1900_United_Kingdom_general_election_in_Ireland">1900 general election</a>, when they put up a candidate to split the unionist vote.<sup><span>[</span>20<span>]</span></sup> </p><p>It had been intended that the vice-president should be responsible for the DATI in the <a href="https://en.wikipedia.org/wiki/House_of_Commons_of_the_United_Kingdom">House of Commons</a>, but an extensively signed memo, supported by the Agricultural Council, prayed that Plunkett might not be removed from office, and at the government&#39;s request he continued to direct the policy of the DATI without a seat in Parliament.<sup><span>[</span>5<span>]</span></sup> He was created <a href="https://en.wikipedia.org/wiki/Royal_Victorian_Order">Knight Commander of the Royal Victorian Order</a> in 1903 at Queenstown, on the personal initiative of the King.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>On the accession of the <a href="https://en.wikipedia.org/wiki/Liberal_Party_(UK)">Liberal Party</a> to power in 1906 <a href="https://en.wikipedia.org/wiki/James_Bryce,_1st_Viscount_Bryce">James Bryce</a>, the new Chief Secretary, asked Plunkett to remain at the head of the department he had created.<sup><span>[</span>5<span>]</span></sup> </p><div><h3>Efforts obstructed</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>Having sat in the House of Commons as a Unionist, attitudes among the nationalist party were exacerbated by the opinions in his book, <i>Ireland in the New Century</i> (1904). Here he described the economic condition and needs of the country, and the nature of the agricultural improvement schemes he had promoted.<sup><span>[</span>5<span>]</span></sup> Plunkett put forth the view that economics was more important than politics for the future of Ireland, classed the huge sums invested in the building of Catholic churches as &quot;uneconomic&quot; and remarked negatively on the power of the Catholic hierarchy. </p><p><a href="https://en.wikipedia.org/wiki/John_Redmond">John Redmond</a>, leader of the <a href="https://en.wikipedia.org/wiki/Irish_Parliamentary_Party">Irish Parliamentary Party</a>, turned against Plunkett for suggesting that anything but Home Rule might be the answer to Ireland&#39;s problems,<sup><span>[</span>21<span>]</span></sup> and other mainstream nationalists, led by <a href="https://en.wikipedia.org/wiki/John_Dillon">John Dillon</a>, rejected economic development, whether through Plunkett&#39;s agricultural cooperatives, <a href="https://en.wikipedia.org/wiki/William_O%27Brien">William O&#39;Brien</a>&#39;s tenant land purchase or <a href="https://en.wikipedia.org/wiki/D._D._Sheehan">D. D. Sheehan</a>&#39;s housing of rural labourers, in advance of &quot;national development&quot;. </p><p>Ultimately the DATI ceased to work harmoniously with the IAOS, wrecking Plunkett&#39;s hopes, and the Irish Parliamentary Party made a determined effort to drive him from office, moving a resolution to that effect in the House of Commons in 1907. The government gave way, and although Plunkett was re-elected president of the IAOS in the summer of 1907, he retired from office in the DATI. From the year 1900 the DATI had made an annual grant of about £4,000 to the IAOS, but in 1907 the new vice-president of the DATI, <a href="https://en.wikipedia.org/wiki/Sir_Thomas_Russell,_1st_Baronet">T.W. Russell</a>, who had previously been a member of the Unionist administration, withdrew it.<sup><span>[</span>5<span>]</span></sup> Nonetheless, many continued to be inspired by Plunkett&#39;s vision and to establish creamery cooperatives around the country. </p><figure><a href="https://en.wikipedia.org/wiki/File:Plunkett_House_nameplate,_Dublin,_Ireland.jpg"></a><figcaption>The Plunkett House nameplate</figcaption></figure><p>In 1908 public appreciation of Plunkett&#39;s service was marked by the purchase and gift to him of 84 Merrion Square, Dublin, which became the headquarters of the IAOS under the name The Plunkett House.<sup><span>[</span>22<span>]</span></sup><sup><span>[</span>23<span>]</span></sup> </p><p><i>The Irish Homestead</i> had frequently drawn attention to the status of women in rural Ireland (its assistant editor was <a href="https://en.wikipedia.org/wiki/Susan_L._Mitchell">Susan L. Mitchell</a>), and in 1910 Plunkett helped to found the United Irishwomen to improve their domestic economy, welfare and education, with <a href="https://en.wikipedia.org/wiki/Ellice_Pilkington">Ellice Pilkington</a> and <a href="https://en.wikipedia.org/wiki/Anita_Lett">Anita Lett</a>. This would develop in the 1930s into the powerful <a href="https://en.wikipedia.org/wiki/Irish_Countrywomen%27s_Association">Irish Countrywomen&#39;s Association</a>. It also inspired the foundation of the Women&#39;s Institutes in the UK. </p><div><h3>Political reorientation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><p>Having previously focused his attention pragmatically on economic factors, Plunkett now began to reorient to political and social issues. The failure of the <a href="https://en.wikipedia.org/wiki/Irish_Council_Bill">Irish Council Bill</a> in 1907 made him realise the critical importance of self-government and by 1912 he was a convinced Home Ruler. He spent the first half of 1914 in negotiations intended to prevent partition and the exclusion of <a href="https://en.wikipedia.org/wiki/Ulster">Ulster</a>, to no avail. </p><p>Hitherto he had been regarded as a moderate Unionist, but this suggestion rendered him suspect in Ulster eyes, and the suspicion was confirmed when he published in the third week of July a pamphlet entitled The Better Way: an Appeal to Ulster not to Desert Ireland, in which he announced his conversion to Home Rule and appealed to Ulster to give Home Rule a chance, re-stating the arguments of his previous letter, and suggesting a conference of Irishmen on the bill. This was his attempt to avert civil war; but the situation was revolutionized by the outbreak of the <a href="https://en.wikipedia.org/wiki/World_War_I">First World War</a>.<sup><span>[</span>24<span>]</span></sup> </p><p>During the war the cooperatives were severely hit as farmers avoided their high standards, supplying inferior produce directly to Britain, where food shortages led to a boom period for Irish agriculture. </p><p>Much of Plunkett&#39;s time was spent as an unofficial envoy between Britain and the United States. After the <a href="https://en.wikipedia.org/wiki/Easter_Rising">Easter Rising of 1916</a>, when he heard of executions, he sought clemency for its remaining leaders, including <a href="https://en.wikipedia.org/wiki/Constance_Markievicz">Constance Markievicz</a>, except for anyone involved in regular crime. </p><p>Once again, in 1917, he took the lead in an attempt to solve the <a href="https://en.wikipedia.org/wiki/Irish_question">Irish question</a>. When <a href="https://en.wikipedia.org/wiki/David_Lloyd_George">Lloyd George</a> set up a convention of Irishmen to consider the suspended <a href="https://en.wikipedia.org/wiki/Government_of_Ireland_Act_1914">Third Home Rule Act 1914</a>, and report their conclusions, there was great difficulty in finding a suitable chairman; but the first meeting unanimously chose Sir Horace for the post. He was himself sanguine, and worked at his task with singular devotion until May 1918; but the absence of <a href="https://en.wikipedia.org/wiki/Sinn_F%C3%A9in">Sinn Féin</a> from the gathering, and the impossibility of reconciling the views of the Ulstermen and the southern Unionists, prevented the adoption of any report with unanimity.<sup><span>[</span>24<span>]</span></sup> He may have lost what would have been a historic deal in January 1918 by diverting the debate to the issue of land purchase.<sup><span>[</span>25<span>]</span></sup> </p><p>Until 1922 Plunkett worked to keep Ireland united within the <a href="https://en.wikipedia.org/wiki/British_Commonwealth">British Commonwealth</a>, founding the <a href="https://en.wikipedia.org/wiki/Irish_Dominion_League">Irish Dominion League</a> and a weekly journal, the <i>Irish Statesman</i>, to advance that aim, for which he was rejected by those working for an Irish Republic. He met <a href="https://en.wikipedia.org/wiki/Michael_Collins_(Irish_leader)">Michael Collins</a>, whom he described as &quot;simple yet cunning&quot;.<sup><span>[</span>26<span>]</span></sup> </p><div><h3>Marginalisation and departure from Ireland</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><p>In 1922, after the <a href="https://en.wikipedia.org/wiki/Anglo-Irish_Treaty">Anglo-Irish Treaty</a> was implemented, Plunkett was nominated to the first <a href="https://en.wikipedia.org/wiki/Seanad_%C3%89ireann_(Irish_Free_State)">Seanad Éireann</a>, the upper chamber of the parliament of the new Irish state.<sup><span>[</span>27<span>]</span></sup> He took his seat on 18 December 1922.<sup><span>[</span>28<span>]</span></sup> In recognition of his contributions and ideas, he was one of those appointed for a term of 12 years. </p><p>His work on cooperation took him abroad frequently, and when he was in the United States during the <a href="https://en.wikipedia.org/wiki/Irish_Civil_War">Irish Civil War</a> in 1923, his home, Kilteragh, in <a href="https://en.wikipedia.org/wiki/Foxrock">Foxrock</a>, County Dublin, was one of some 300 country houses <a href="https://en.wikipedia.org/wiki/Destruction_of_country_houses_in_the_Irish_revolutionary_period">targeted by the IRA</a> and burned down,<sup><span>[</span>29<span>]</span></sup> the fire taking with it many of the records of the Plunkett family, which he had gathered to prepare a work on the subject. Plunkett wrote of his sorrow that &quot;the healthiest house in the world, and the meeting place of a splendid body of Irishmen and friends of Ireland&quot; had been destroyed. He resigned from the Seanad in November 1923.<sup><span>[</span>30<span>]</span></sup> </p><div><h3>Later years and the Plunkett Foundation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><p>Plunkett moved to <a href="https://en.wikipedia.org/wiki/Weybridge">Weybridge</a>, England. On 21 December 1918 he set up the Sir Horace Plunkett Foundation, which moved fully to England in 1924, and is now the charitable <a href="https://en.wikipedia.org/wiki/Plunkett_Foundation">Plunkett Foundation</a>.<sup><span>[</span>3<span>]</span></sup> The foundation launched in 1919 with £5,000 to support its work, including education, with the co-operative movement and other community organisations. As of 2022, the foundation continues its work.<sup><span>[</span>31<span>]</span></sup> </p><p>Plunkett continued to promote and spread his ideas for agricultural cooperatives. In 1924 he presided over a conference on agricultural cooperation in the British Commonwealth in London, and in 1925 he visited South Africa to help the movement there. As late in 1930, he was consulting with the Prime Minister of Great Britain on agricultural policy.<sup><span>[</span>32<span>]</span></sup> </p><div><h2>Personal life</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><p>Plunkett was close to his nephews, <a href="https://en.wikipedia.org/wiki/Lord_Dunsany">Edward</a> and Reginald Dunsany, helping manage their, and their father&#39;s, affairs. He also worked to reconcile the 17th Lord Dunsany and his wife over several years.<sup><span>[</span>33<span>]</span></sup> He was very involved in the affairs of the 18th Lord Dunsany (Edward) until some failures of investments in the 1920s, after which their contact was more occasional but continued to near the end.<sup><span>[</span>34<span>]</span></sup> His dealings with Reginald were more limited in earlier years but he continued to visit him at Charborough and elsewhere, right up to the month of his death.<sup><span>[</span>35<span>]</span></sup><sup><span>[</span>36<span>]</span></sup> </p><p>He was also close friends with Elizabeth &quot;Daisy&quot; Burke Plunkett, Lady Fingall, the wife of his remote cousin. He became interested in aviation late in life and was still flying – presumably from <a href="https://en.wikipedia.org/wiki/Brooklands">Brooklands</a> – at least as late as 1930. </p><div><h3>Last years</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><p>During Plunkett&#39;s last years, <a href="https://en.wikipedia.org/wiki/Gerald_Heard">Gerald Heard</a> was his personal secretary. <a href="https://en.wikipedia.org/wiki/Naomi_Mitchison">Naomi Mitchison</a>, who admired Plunkett and was a friend of Heard, wrote: &quot;H.P., as we all called him, was getting past his prime and often ill but struggling to go on with the work to which he was devoted. Gerald [Heard] who was shepherding him about fairly continually, apologized once for leaving a dinner party abruptly when H.P. was suddenly overwhelmed by exhaustion&quot;.<sup><span>[</span>37<span>]</span></sup> </p><p>Plunkett died at Weybridge on 26 March 1932 and was buried in St Mary&#39;s Churchyard in nearby <a href="https://en.wikipedia.org/wiki/Byfleet">Byfleet</a>, where his gravestone survives.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><div><h2>Writings</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div><ul><li><a href="http://www.gutenberg.org/ebooks/14342"><i>Ireland in the New Century</i></a> (1904), Sir Horace Plunkett, new edition with additional material, 1905</li> <li><i>Noblesse Oblige: An Irish Rendering</i> (1908), Sir Horace Plunkett</li> <li><a href="http://www.gutenberg.org/ebooks/27305"><i>The Rural Life Problem of the United States</i></a>, (1910), Sir Horace Plunkett</li></ul><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div><ul><li><cite><a href="https://en.wikipedia.org/wiki/Edward_MacLysaght">MacLysaght, Edward</a> (1916). <i>Sir Horace Plunkett and his place in the Irish nation</i>. Dublin: Maunsel &amp; Co.</cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/Margaret_Digby">Digby, Margaret</a> (1949). <i>Horace Plunkett: an Anglo-American Irishman</i>. Oxford: Blackwell.</cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/Trevor_West">West, Trevor</a> (1986). <i>Horace Plunkett: co-operation and politics, an Irish biography</i>. Washington DC: <a href="https://en.wikipedia.org/wiki/Catholic_University_of_America">Catholic University of America</a>.</cite></li> <li><cite>Woods, Lawrence M. (2010). <i>Horace Plunkett in America: An Irish Aristocrat on the Wyoming Range</i>. The Arthur H. Clark Company. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9780870623943"><bdi>9780870623943</bdi></a>.</cite>)</li> <li><cite>Rempe, Paul Leonhard (1979). <i>Sir Horace Plunkett and the politics of Irish agriculture, 1890–1914</i> (PhD thesis). State University of New York at Stony Brook.</cite></li> <li><cite>Savage, William W. (1966). <i>Cattle king: Sir Horace Plunkett in Wyoming, 1879–1889</i> (MA thesis). University of South California.</cite></li> <li><cite>Anderson, Robert A. (1983) [1935)]. <i>With Plunkett in Ireland: the co-op organiser&#39;s story (London: Macmillan)</i>. Blackrock (Co. Dublin): <a href="https://en.wikipedia.org/wiki/Irish_Academic_Press">Irish Academic Press</a>.</cite></li> <li><cite>Crick, Bernard R., ed. (1969). <i>The American letters of Sir Horace Plunkett, 1883–1932</i>. Microfilm: East Ardsley, Wakefield, Yorkshire: Micro Methods Ltd.</cite></li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=17"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span>Thom&#39;s Directory 1928.</span> </li> <li><span><b>^</b></span> <span><cite>Gillespie, Michael (14 February 2017). <a href="https://books.google.com/books?id=pKUuDgAAQBAJ&amp;q=horace+plunkett+christian+socialist&amp;pg=PT50"><i>Christian Socialism</i></a>. AuthorHouse. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-5246-7705-3"><bdi>978-1-5246-7705-3</bdi></a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup></span> <span><cite>West, Trevor. <a href="https://www.dib.ie/biography/plunkett-sir-horace-curzon-a7385">&quot;Plunkett, Sir Horace Curzon&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Dictionary_of_Irish_Biography">Dictionary of Irish Biography</a></i><span>. Retrieved <span>22 October</span> 2022</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>West, Trevor (1986). <i>Horace Plunkett: co-operation and politics, an Irish biography</i>. Washington, DC: C. Smythe.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup> <sup><i><b>e</b></i></sup> <sup><i><b>f</b></i></sup> <sup><i><b>g</b></i></sup> <sup><i><b>h</b></i></sup> <sup><i><b>i</b></i></sup></span> <span><span><span><a href="https://en.wikipedia.org/wiki/File:Wikisource-logo.svg"></a></span> </span>One or more of the preceding sentences incorporates text from a publication now in the <a href="https://en.wikipedia.org/wiki/Public_domain">public domain</a>: <cite><a href="https://en.wikipedia.org/wiki/Hugh_Chisholm">Chisholm, Hugh</a>, ed. (1911). &quot;<a href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Plunkett,_Sir_Horace_Curzon">Plunkett, Sir Horace Curzon</a>&quot;. <i><a href="https://en.wikipedia.org/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition">Encyclopædia Britannica</a></i>. Vol. 21 (11th ed.). Cambridge University Press. p. 857.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Hickey, D.J.; Doherty, J.E., eds. (1980). <i>A Dictionary of Irish History</i>. Dublin: <a href="https://en.wikipedia.org/wiki/Gill_and_Macmillan">Gill and Macmillan</a>. p. 87. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-7171-1567-4"><bdi>0-7171-1567-4</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span>Byrne, J.J.: <i>AE and Sir Horace Plunkett</i>, pp. 152–54: (<i>The Shaping of Modern Ireland</i> Conor-Cruise O&#39;Brien, 1960).</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.buildingsofireland.ie/buildings-search/building/21835009/national-dairy-co-op-museum-carroward-east-dromcolliher-co-limerick">&quot;National Dairy Co-Op Museum, Dromcolliher, Limerick&quot;</a>. <i>Buildings of Ireland</i>. National Inventory of Architectural Heritage<span>. Retrieved <span>4 April</span> 2021</span>.</cite></span> </li> <li><span><b>^</b></span> <span><a href="http://www.gutenberg.org/ebooks/14342"><i>Ireland in the New Century</i></a>, Chapt.7</span> </li> <li><span><b>^</b></span> <span><cite>Kennelly, James (2011). &quot;Normal Courage: Robert A. Anderson and the Irish Co-operative Movement&quot;. <i>Studies: An Irish Quarterly Review</i>. <b>100</b> (399): <span>319–</span>330. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/23059676">23059676</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>McGrath, Mike (9 July 2009). <a href="https://www.independent.ie/regionals/corkman/news/tribute-to-pioneer-of-the-coop-movement-27071156.html">&quot;Tribute to pioneer of the Co-Op movement&quot;</a>. <i>The Corkman</i><span>. Retrieved <span>23 August</span> 2018</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Diarmaid_Ferriter">Ferriter, Diarmaid</a> (2004). <i>The Transformation of Ireland, 1900–2000</i>. Profile Books. p. 68. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9781861974433"><bdi>9781861974433</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span>The Times, 15 October 1886, quoted in footnote 18, page 6, <i>The Conservatives and the Redefinition of Unionism, 1912-21</i>, Stephen Evans, Twentieth Century British History, Vol. 9, No 1, 1998, Oxford University Press</span> </li> <li><span><b>^</b></span> <span><cite>Walker, Brian M., ed. (1978). <i>Parliamentary election results in Ireland 1801–1922</i>. Dublin: Royal Irish Academy. p. 146. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-901714-12-1"><bdi>978-0-901714-12-1</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>King, Carla (2000). &quot;Chapter 7: Sir Horace Plunkett&quot;. In Boyce, D. George; O&#39;Day, Alan (eds.). <i>Defenders of the Union: A Survey of British and Irish Unionism Since 1801</i>. Routledge. pp. <span>138–</span>54. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-415-17421-X"><bdi>0-415-17421-X</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Brian M. Walker, ed. (1978). <i>Parliamentary election results in Ireland 1801–1922</i>. Dublin: Royal Irish Academy. p. 349. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-901714-12-7"><bdi>0-901714-12-7</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><a href="http://www.gutenberg.org/ebooks/14342"><i>Ireland in the New Century</i></a>, Chapt.8</span> </li> <li><span><b>^</b></span> <span>Maume, Patrick: <i>The Long Gestation, Irish Nationalist Life 1891–1918</i> p.18, Gill &amp; Macmillan (1999) <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-7171-2744-3"><bdi>0-7171-2744-3</bdi></a></span> </li> <li><span><b>^</b></span> <span>Ferriter 2004, p. 68.</span> </li> <li><span><b>^</b></span> <span>Maume, Partick: p. 241</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Robert_Kee">Kee, Robert</a> (2000) [1972]. <i>The Green Flag</i>. pp. <span>435–</span>437.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://icos.ie/contact-us/">&quot;Contact us&quot;</a>. <i>Irish Co-operative Organization Society (ICOS)</i>.</cite></span> </li> <li><span><b>^</b></span> <span><i>Directory of Irish Biographies</i> p. 367</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span> One or more of the preceding sentences incorporates text from a publication now in the <a href="https://en.wikipedia.org/wiki/Public_domain">public domain</a>: <cite>Chisholm, Hugh, ed. (1922). <a href="https://archive.org/details/encyclopdiabri32newyrich/page/109/mode/1up?view=theater">&quot;Plunkett, Sir Horace Curzon&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Encyclop%C3%A6dia_Britannica">Encyclopædia Britannica</a></i>. Vol. 32 (12th ed.). London &amp; New York: The Encyclopædia Britannica Company. p. 109.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Jackson, Alvin (2003). <i>Home Rule: An Irish History, 1800–2000</i>. Phoenix Press. pp. <span>206–</span>215. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-7538-1767-5"><bdi>0-7538-1767-5</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span>James Mackay, <i>Michael Collins: A Life</i> (Edinburgh 1996), p. 256, cited in Townshend, &quot;The Republic&quot;, p. 424.</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.oireachtas.ie/en/members/member/Horace-Plunkett.S.1922-06-12/">&quot;Horace Plunkett&quot;</a>. <i>Oireachtas Members Database</i><span>. Retrieved <span>16 January</span> 2016</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.oireachtas.ie/en/debates/debate/seanad/1922-12-18/2/">&quot;Senators Sworn In&quot;</a>. <i>Seanad Debates</i>. <b>1</b> (4). 18 December 1922.</cite></span> </li> <li><span><b>^</b></span> <span>Ferriter 2004, p. 210.</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.oireachtas.ie/en/debates/debate/seanad/1923-11-28/3/">&quot;Resignation of Senator&quot;</a>. <i>Seanad Debates</i>. <b>2</b> (6). 28 November 1923.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://plunkett.co.uk/our-story/">&quot;Plunkett Foundation - About Us - History&quot;</a>. <i>Plunkett Foundation</i><span>. Retrieved <span>14 November</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span>Weybridge, London: Diaries of Sir Horace Curzon Plunkett, 18 September 1930: Came to town to see the Foundation ... At Mount St. found a cordial invitation from the Prime Minister to meet him at lunch at the Athenaeum or anywhere else to discuss the agricultural policy of the Government!</span> </li> <li><span><b>^</b></span> <span>Dublin, London, etc.: Diaries of Horace Curzon Plunkett, 1880–1932</span> </li> <li><span><b>^</b></span> <span>Weybridge, London: Diaries of Sir Horace Curzon Plunkett, 10 May 1931: Eddie &amp; Beatrice came to tea. He was more gracious than usual. They are very happy about <a href="https://en.wikipedia.org/wiki/Randal_Plunkett,_19th_Baron_of_Dunsany">Randal</a>, as I am.</span> </li> <li><span><b>^</b></span> <span>Weybridge, London: Diaries of Sir Horace Curzon Plunkett, 6-7 Jun. 1930: Motored with E.V.L. to Charborough where we were most hospitably welcomed by Reggie &amp; Kathleen... In the morning motored to Poole Harbour where the 5 children are having a glorious time of it in a bungalow among the sand dunes along the shore. Son &amp; heir (Henry Walter Plunkett Ernle Erle Drax) aet 2¼ a fine little fellow.</span> </li> <li><span><b>^</b></span> <span>Weybridge, London: Diaries of Sir Horace Curzon Plunkett, 24 Dec. 1931: Reggie &amp; wife were most kind &amp; considerate. They had their own 5 children, her mother &amp; a godson to look after. But they had every consideration for my weak state &amp; were keen most careful to see that I was warm in their rather cold house</span> </li> <li><span><b>^</b></span> <span><a href="https://en.wikipedia.org/wiki/Naomi_Mitchison">Naomi Mitchison</a>, <i>You may well ask</i>, London, 1979, Part II, Chap. 12.</span> </li> </ol></div></div><div><h2>Related bibliography</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=18"><span>edit</span></a><span>]</span></span></div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Horace_Plunkett&amp;action=edit&amp;section=19"><span>edit</span></a><span>]</span></span></div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Commons-logo.svg"></a></span></div> <div>Wikimedia Commons has media related to <span><a href="https://commons.wikimedia.org/wiki/Category:Horace_Plunkett">Horace Plunkett</a></span>.</div></div> </div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Wikisource-logo.svg"></a></span></div> <div>English <a href="https://en.wikipedia.org/wiki/Wikisource">Wikisource</a> has original works by or about: <div><b><a href="https://en.wikisource.org/wiki/en:Author:Horace_Curzon_Plunkett">Horace Curzon Plunkett</a></b></div></div></div> </div><ul><li><a href="https://web.archive.org/web/20090328025614/http://www.plunkett.co.uk/aboutus/history.cfm">The Plunkett Foundation</a></li> <li><a href="http://catalogue.nli.ie/Collection/vtls000583319?recordID=vtls000628593">Diaries of Sir Horace Plunkett, 1881–1932</a> at the <a href="https://en.wikipedia.org/wiki/National_Library_of_Ireland">National Library of Ireland</a>; includes digitized manuscripts, annotated transcriptions, and index</li> <li><a href="https://www.gutenberg.org/ebooks/author/5482">Works by Horace Plunkett</a> at <a href="https://en.wikipedia.org/wiki/Project_Gutenberg">Project Gutenberg</a></li> <li><a href="https://archive.org/search.php?query=%28%28subject%3A%22Plunkett%2C%20Horace%20Curzon%22%20OR%20subject%3A%22Plunkett%2C%20Horace%20C%2E%22%20OR%20subject%3A%22Plunkett%2C%20H%2E%20C%2E%22%20OR%20subject%3A%22Horace%20Curzon%20Plunkett%22%20OR%20subject%3A%22Horace%20C%2E%20Plunkett%22%20OR%20subject%3A%22H%2E%20C%2E%20Plunkett%22%20OR%20subject%3A%22Plunkett%2C%20Horace%22%20OR%20subject%3A%22Horace%20Plunkett%22%20OR%20creator%3A%22Horace%20Curzon%20Plunkett%22%20OR%20creator%3A%22Horace%20C%2E%20Plunkett%22%20OR%20creator%3A%22H%2E%20C%2E%20Plunkett%22%20OR%20creator%3A%22H%2E%20Curzon%20Plunkett%22%20OR%20creator%3A%22Plunkett%2C%20Horace%20Curzon%22%20OR%20creator%3A%22Plunkett%2C%20Horace%20C%2E%22%20OR%20creator%3A%22Plunkett%2C%20H%2E%20C%2E%22%20OR%20creator%3A%22Plunkett%2C%20H%2E%20Curzon%22%20OR%20creator%3A%22Horace%20Plunkett%22%20OR%20creator%3A%22Plunkett%2C%20Horace%22%20OR%20title%3A%22Horace%20Curzon%20Plunkett%22%20OR%20title%3A%22Horace%20C%2E%20Plunkett%22%20OR%20title%3A%22H%2E%20C%2E%20Plunkett%22%20OR%20title%3A%22Horace%20Plunkett%22%20OR%20description%3A%22Horace%20Curzon%20Plunkett%22%20OR%20description%3A%22Horace%20C%2E%20Plunkett%22%20OR%20description%3A%22H%2E%20C%2E%20Plunkett%22%20OR%20description%3A%22Plunkett%2C%20Horace%20Curzon%22%20OR%20description%3A%22Plunkett%2C%20Horace%20C%2E%22%20OR%20description%3A%22Horace%20Plunkett%22%20OR%20description%3A%22Plunkett%2C%20Horace%22%29%20OR%20%28%221854-1932%22%20AND%20Plunkett%29%29%20AND%20%28-mediatype:software%29">Works by or about Horace Plunkett</a> at the <a href="https://en.wikipedia.org/wiki/Internet_Archive">Internet Archive</a></li> <li>Irish Co-operative Organisation Society <a href="https://web.archive.org/web/20071009231732/http://www.icos.ie/content/content.asp?section_id=307&amp;action=details&amp;term_id=585">[1]</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Hansard">Hansard</a></i> 1803–2005: <a href="https://api.parliament.uk/historic-hansard/people/hon-horace-plunkett">contributions in Parliament by Horace Plunkett</a></li> <li><cite><span><a href="https://en.wikisource.org/wiki/Thom%27s_Irish_Who%27s_Who/Plunkett,_Rt._Hon._Sir_Horace_Curzon">&quot;Plunkett, Rt. Hon. Sir Horace Curzon&quot; </a></span>. <span><a href="https://en.wikisource.org/wiki/Thom%27s_Irish_Who%27s_Who"><i>Thom&#39;s Irish Who&#39;s Who</i> </a></span>. Dublin: <a href="https://en.wikipedia.org/wiki/Alexander_Thom_(almanac_editor)">Alexander Thom and Son Ltd.</a> 1923. p. <span><a href="https://en.wikisource.org/wiki/Thom%27s_Irish_Who%27s_Who/Plunkett,_Rt._Hon._Sir_Horace_Curzon#207">207 </a></span> – via <a href="https://en.wikipedia.org/wiki/Wikisource">Wikisource</a>.</cite></li></ul><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Members_of_the_1922_Seanad"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Members_of_the_1922_Seanad"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Members_of_the_1922_Seanad"><abbr>e</abbr></a></li></ul></div><div><span><small>« <i><a href="https://en.wikipedia.org/wiki/Template:Members_of_the_1922_Seanad">1922 Seanad</a></i> «</small>  </span><span><a href="https://en.wikipedia.org/wiki/1922_Seanad">Members of the 1922 Seanad</a> (1922–1925)</span> <small>» <i><a href="https://en.wikipedia.org/wiki/Template:Members_of_the_1925_Seanad">1925 Seanad</a></i> »</small></div></th></tr><tr><td colspan="2"><div> <ul><li><b><a href="https://en.wikipedia.org/wiki/Cathaoirleach">Cathaoirleach</a></b> <a href="https://en.wikipedia.org/wiki/James_Campbell,_1st_Baron_Glenavy">Lord Glenavy</a> (Ind)</li></ul> </div></td></tr><tr><th>Elected in 1922</th><td><table><tbody><tr><th>3 years</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Henry_Barniville">Henry Barniville</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/Thomas_Westropp_Bennett">Thomas Westropp Bennett</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/Richard_A._Butler_(Irish_politician)">Richard A. Butler</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/John_Counihan">John Counihan</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Peter_de_Loughry">Peter de Loughry</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/Cornelius_Irwin">Cornelius Irwin</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/Thomas_Linehan">Thomas Linehan</a> (FP)</li> <li><a href="https://en.wikipedia.org/wiki/Joseph_Clayton_Love">Joseph Clayton Love</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/Edward_MacEvoy">Edward MacEvoy</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/Edward_MacLysaght">Edward MacLysaght</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Eamonn_Mansfield">Eamonn Mansfield</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/George_Nesbitt_(Irish_politician)">George Nesbitt</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Michael_O%27Dea_(Irish_politician)">Michael O&#39;Dea</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/J._T._O%27Farrell">J. T. O&#39;Farrell</a> (Lab)</li> <li><a href="https://en.wikipedia.org/wiki/James_Parkinson_(Irish_politician)">James Parkinson</a> (CnaG)</li></ul> </div></td></tr><tr><th>9 years</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/William_Barrington_(Irish_politician)">William Barrington</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Eileen_Costello">Eileen Costello</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/James_G._Douglas">James G. Douglas</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Michael_Duffy_(Irish_politician)">Michael Duffy</a> (Lab)</li> <li><a href="https://en.wikipedia.org/wiki/Thomas_Farren">Thomas Farren</a> (Lab)</li> <li><a href="https://en.wikipedia.org/wiki/Alice_Stopford_Green">Alice Stopford Green</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/John_Griffith_(engineer)">Sir John Griffith</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Patrick_W._Kenny">Patrick W. Kenny</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/James_J._MacKean">James J. MacKean</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/John_MacLoughlin">John MacLoughlin</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Thomas_MacPartlin">Thomas MacPartlin</a> (Lab)</li> <li><a href="https://en.wikipedia.org/wiki/William_Molloy_(Irish_politician)">William Molloy</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Maurice_George_Moore">Maurice George Moore</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Brian_O%27Rourke_(politician)">Brian O&#39;Rourke</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/William_O%27Sullivan_(politician)">William O&#39;Sullivan</a> (CnaG)</li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Nominated by the <a href="https://en.wikipedia.org/wiki/President_of_the_Executive_Council_of_the_Irish_Free_State">President</a></th><td><table><tbody><tr><th>6 years</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/John_Philip_Bagwell">John Philip Bagwell</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Henry_Givens_Burgess">Henry Givens Burgess</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/James_Campbell,_1st_Baron_Glenavy">Lord Glenavy</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Nugent_Everard">Sir Nugent Everard</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Edmund_W._Eyre">Edmund W. Eyre</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Oliver_St._John_Gogarty">Oliver St. John Gogarty</a> (CnaG)</li> <li><a href="https://en.wikipedia.org/wiki/James_Perry_Goodbody">James Perry Goodbody</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Henry_Greer_(politician)">Henry Greer</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Benjamin_Haughton">Benjamin Haughton</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Ralph_Howard,_7th_Earl_of_Wicklow">Earl of Wicklow</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Arthur_Jackson_(Irish_politician)">Arthur Jackson</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Andrew_Jameson_(politician)">Andrew Jameson</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Bryan_Mahon">Sir Bryan Mahon</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Geoffrey_Taylour,_4th_Marquess_of_Headfort">Marquess of Headfort</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/W._B._Yeats">W. B. Yeats</a> (Ind)</li></ul> </div></td></tr><tr><th>12 years</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Dermot_Bourke,_7th_Earl_of_Mayo">Earl of Mayo</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Ellen_Cuffe,_Countess_of_Desart">Countess of Desart</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/James_Charles_Dowdall">James Charles Dowdall</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Sir_Thomas_Esmonde,_11th_Baronet">Sir Thomas Esmonde</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Martin_Fitzgerald_(politician)">Martin Fitzgerald</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Bernard_Forbes,_8th_Earl_of_Granard">Earl of Granard</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Henry_Guinness">Henry Guinness</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Sir_John_Keane,_5th_Baronet">Sir John Keane</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/James_Moran_(Irish_politician)">James Moran</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Henry_Petty-Fitzmaurice,_6th_Marquess_of_Lansdowne">Earl of Kerry</a> (Ind)</li> <li>Sir Horace Plunkett (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Hutcheson_Po%C3%AB">Sir Hutcheson Poë</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/George_Sigerson">George Sigerson</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Windham_Wyndham-Quin,_4th_Earl_of_Dunraven_and_Mount-Earl">Earl of Dunraven and Mount-Earl</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/Jennie_Wyse_Power">Jennie Wyse Power</a> (Ind)</li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Elected or appointed later</th><td><div> <ul><li><b>Feb. 1923</b> <a href="https://en.wikipedia.org/wiki/William_Cummins_(Irish_politician)">William Cummins</a> (Lab)</li> <li><b>Nov. 1923</b> <a href="https://en.wikipedia.org/wiki/Thomas_Foran">Thomas Foran</a> (Lab)</li> <li><b>Dec. 1923</b> <a href="https://en.wikipedia.org/wiki/Samuel_Lombard_Brown">Samuel Lombard Brown</a> (Ind)</li> <li><b>1925</b> <a href="https://en.wikipedia.org/wiki/Douglas_Hyde">Douglas Hyde</a> (Ind)</li> <li><a href="https://en.wikipedia.org/wiki/John_O%27Neill_(Irish_senator)">John O&#39;Neill</a> (CnaG)</li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li>CnaG: <a href="https://en.wikipedia.org/wiki/Cumann_na_nGaedheal">Cumann na nGaedheal</a></li> <li>FP: <a href="https://en.wikipedia.org/wiki/Farmers%27_Party_(Ireland)">Farmers&#39; Party</a></li> <li>Lab: <a href="https://en.wikipedia.org/wiki/Labour_Party_(Ireland)">Labour Party</a></li> <li>Ind: <a href="https://en.wikipedia.org/wiki/Independent_politician_(Ireland)">Independent</a></li></ul> </div></td></tr></tbody></table></div> Promotion (marketing) - Wikipedia https://en.wikipedia.org/wiki/Promotion_(marketing) HjJ0K5JZ_84EdD4wyBOWiYvhoDSlcfCPuyJSpg== Wed, 13 May 2026 11:22:17 +0000 Promotion of a product or service <div>Promotion of a product or service</div><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Marketing">Marketing</a></th></tr><tr><th> Key concepts</th></tr><tr><td> <ul><li><a href="https://en.wikipedia.org/wiki/Account-based_marketing">Account-based marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_activation">Activation</a></li> <li><a href="https://en.wikipedia.org/wiki/Annoyance_factor">Annoyance factor</a></li> <li><a href="https://en.wikipedia.org/wiki/Attribution_(marketing)">Attribution</a></li> <li><a href="https://en.wikipedia.org/wiki/Distribution_(marketing)">Distribution</a></li> <li><a href="https://en.wikipedia.org/wiki/Brand_licensing">Brand licensing</a></li> <li><a href="https://en.wikipedia.org/wiki/Brand_management">Brand management</a></li> <li><a href="https://en.wikipedia.org/wiki/Cannibalization_(marketing)">Cannibalization</a></li> <li><a href="https://en.wikipedia.org/wiki/Co-creation">Co-creation</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_communications">Communications</a></li> <li><a href="https://en.wikipedia.org/wiki/Consumer_behaviour">Consumer behaviour</a></li> <li><a href="https://en.wikipedia.org/wiki/Consumer_culture">Consumer culture</a></li> <li><a href="https://en.wikipedia.org/wiki/Digital_marketing">Digital marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Dominance_(economics)">Dominance</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_effectiveness">Effectiveness</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_ethics">Ethics</a></li> <li><a href="https://en.wikipedia.org/wiki/Horizontal_integration">Horizontal integration</a></li> <li><a href="https://en.wikipedia.org/wiki/Influencer_marketing">Influencer marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_management">Management</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_mix">Mix</a></li> <li><a href="https://en.wikipedia.org/wiki/Pricing">Pricing</a></li> <li><a href="https://en.wikipedia.org/wiki/Product_marketing">Product marketing</a></li> <li>Promotion</li> <li><a href="https://en.wikipedia.org/wiki/Retail">Retail</a></li> <li><a href="https://en.wikipedia.org/wiki/Segmenting-targeting-positioning">S-T-P</a> <ul><li><a href="https://en.wikipedia.org/wiki/Market_segmentation">Segmentation</a></li> <li><a href="https://en.wikipedia.org/wiki/Targeting_(advertising)">Targeting</a></li> <li><a href="https://en.wikipedia.org/wiki/Positioning_(marketing)">Positioning</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Service_(economics)">Service</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_marketing">Social marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_strategy">Strategy</a></li> <li><a href="https://en.wikipedia.org/wiki/Vertical_integration">Vertical integration</a></li></ul></td> </tr><tr><th> Promotional content</th></tr><tr><td> <ul><li><a href="https://en.wikipedia.org/wiki/Advertising">Advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Ambush_marketing">Ambush marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Brand">Branding</a></li> <li><a href="https://en.wikipedia.org/wiki/Corporate_anniversary">Corporate anniversary</a></li> <li><a href="https://en.wikipedia.org/wiki/Direct_marketing">Direct marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Franchising">Franchising</a></li> <li><a href="https://en.wikipedia.org/wiki/Gender_in_advertising">Gender in advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Label">Label</a></li> <li><a href="https://en.wikipedia.org/wiki/Loyalty_marketing">Loyalty marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Mobile_marketing">Mobile marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Music_on_hold">On-hold messaging</a></li> <li><a href="https://en.wikipedia.org/wiki/Personal_selling">Personal selling</a></li> <li><a href="https://en.wikipedia.org/wiki/Premium_(marketing)">Premiums</a></li> <li><a href="https://en.wikipedia.org/wiki/Prize_(marketing)">Prizes</a></li> <li><a href="https://en.wikipedia.org/wiki/Product_placement">Product placement</a></li> <li><a href="https://en.wikipedia.org/wiki/Corporate_propaganda">Propaganda</a></li> <li><a href="https://en.wikipedia.org/wiki/Publicity">Publicity</a></li> <li><a href="https://en.wikipedia.org/wiki/Sales_promotion">Sales promotion</a></li> <li><a href="https://en.wikipedia.org/wiki/Sex_in_advertising">Sex in advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Underwriting_spot">Underwriting spot</a></li></ul></td> </tr><tr><th> Promotional media</th></tr><tr><td> <ul><li><a href="https://en.wikipedia.org/wiki/Behavioral_targeting">Behavioral targeting</a></li> <li><a href="https://en.wikipedia.org/wiki/Brand_ambassador">Brand ambassador</a></li> <li><a href="https://en.wikipedia.org/wiki/Counter_display_unit">Counter display unit</a></li> <li><a href="https://en.wikipedia.org/wiki/Display_advertising">Display advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Display_stand">Display stand</a></li> <li><a href="https://en.wikipedia.org/wiki/Drip_marketing">Drip marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Endcap">Endcap</a></li> <li><a href="https://en.wikipedia.org/wiki/Gondola_(retail)">Gondola</a></li> <li><a href="https://en.wikipedia.org/wiki/In-game_advertising">In-game advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Mobile_advertising">Mobile advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Native_advertising">Native advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/New_media">New media</a></li> <li><a href="https://en.wikipedia.org/wiki/Online_advertising">Online advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Out-of-home_advertising">Out-of-home advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Point_of_sale">Point of sale</a></li> <li><a href="https://en.wikipedia.org/wiki/Product_demonstration">Product demonstration</a></li> <li><a href="https://en.wikipedia.org/wiki/Promotional_merchandise">Promotional merchandise</a> <ul><li><a href="https://en.wikipedia.org/wiki/Merchandising#Promotional_merchandising">Merchandising</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Promotional_representative">Promotional representative</a></li> <li><a href="https://en.wikipedia.org/wiki/Visual_merchandising">Visual merchandising</a></li> <li><a href="https://en.wikipedia.org/wiki/Web_banner">Web banner</a></li> <li><a href="https://en.wikipedia.org/wiki/Word-of-mouth_marketing">Word-of-mouth</a></li></ul></td> </tr><tr><th> Research</th></tr><tr><td> <ul><li><a href="https://en.wikipedia.org/wiki/Market_research">Market research</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_research">Marketing research</a></li> <li><a href="https://en.wikipedia.org/wiki/Mystery_shopping">Mystery shopping</a></li> <li><a href="https://en.wikipedia.org/wiki/Consumer_research">Consumer research</a></li></ul></td> </tr><tr><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Marketing"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Marketing"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Marketing"><abbr>e</abbr></a></li></ul></div></td></tr></tbody></table><p>In marketing, <b>promotion</b> refers to any type of <a href="https://en.wikipedia.org/wiki/Marketing_communications">marketing communication</a> used to inform <a href="https://en.wikipedia.org/wiki/Target_audience">target audiences</a> of the relative merits of a product, service, brand or issue, persuasively. It helps marketers to create a distinctive place in customers&#39; mind, it can be either a <a href="https://en.wikipedia.org/wiki/Cognition">cognitive</a> or <a href="https://en.wikipedia.org/wiki/Emotion">emotional</a> route. The aim of promotion is to increase <a href="https://en.wikipedia.org/wiki/Brand_awareness">brand awareness</a>, create interest, generate sales or create <a href="https://en.wikipedia.org/wiki/Brand_loyalty">brand loyalty</a>. It is one of the basic elements of the <a href="https://en.wikipedia.org/wiki/Market_mix">market mix</a>, which includes the four Ps, i.e., product, price, place, and promotion.<sup><span>[</span>1<span>]</span></sup> </p><p>Promotion is also one of the elements in the <a href="https://en.wikipedia.org/wiki/Promotional_mix">promotional mix</a> or promotional plan. These are <a href="https://en.wikipedia.org/wiki/Personal_selling">personal selling</a>, <a href="https://en.wikipedia.org/wiki/Advertising">advertising</a>, <a href="https://en.wikipedia.org/wiki/Sales_promotion">sales promotion</a>, <a href="https://en.wikipedia.org/wiki/Direct_marketing">direct marketing</a>, <a href="https://en.wikipedia.org/wiki/Publicity">publicity</a>, <a href="https://en.wikipedia.org/wiki/Word_of_mouth">word of mouth</a> and may also include <a href="https://en.wikipedia.org/wiki/Event-driven_marketing">event marketing</a>, <a href="https://en.wikipedia.org/wiki/Exhibition">exhibitions</a> and trade shows.<sup><span>[</span>2<span>]</span></sup> A promotional plan specifies how much attention to pay to each of the elements in the promotional mix, and what proportion of the budget should be allocated to each element. </p><p>Promotion covers the methods of communication that a marketer uses to provide <a href="https://en.wikipedia.org/wiki/Product_information">information about its product</a>. Information can be both <a href="https://en.wikipedia.org/wiki/Speech">verbal</a> and <a href="https://en.wikipedia.org/wiki/Visual">visual</a>. </p><div><h2>Etymology and usage</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Promotion_(marketing)&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>The term <i>promotion</i> derives from the Old French, <i>promocion</i> meaning to &quot;move forward&quot;, &quot;push onward&quot; or to &quot;advance in rank or position&quot; which in turn, comes from the Latin, <i>promotionem</i> meaning &quot;a moving forward&quot;. The word entered the English language in the 14th century.<sup><span>[</span>3<span>]</span></sup> </p><p>The use of the term <i>promotion</i> to refer to &quot;advertising or publicity&quot; is very modern and was first recorded in 1925.<sup><span>[</span>4<span>]</span></sup> It may be a contraction of a related term, <i>sales promotion,</i> which is one element in the larger set of tools used in marketing communications. In turn, it is often further abbreviated to &#39;promo&#39; as a verb or a noun, as in &quot;<a href="https://en.wikipedia.org/wiki/Barbara_Stanwyck">Barbara Stanwyck</a> cancelled out her Chicago movie promo date here, announced for mid-month&quot;<sup><span>[</span>5<span>]</span></sup> </p><p>The terms, <i>promotion</i> and <i>marketing communications</i> can be used synonymously, but in practice, the latter is more widely used.<sup><span>[</span>6<span>]</span></sup> </p><div><h2>Purpose</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Promotion_(marketing)&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>There are three objectives of promotion. These are:<sup><span>[</span>7<span>]</span></sup> </p><ol><li>To present information to consumers and others.</li> <li>To increase <a href="https://en.wikipedia.org/wiki/Demand">demand</a>.<sup><span>[</span>8<span>]</span></sup></li> <li>To <a href="https://en.wikipedia.org/wiki/Product_differentiation">differentiate a product</a>.</li></ol><p>The purpose of a promotion and thus its promotional plan can have a wide range, including: sales increases, new product acceptance, creation of <a href="https://en.wikipedia.org/wiki/Brand_equity">brand equity</a>, <a href="https://en.wikipedia.org/wiki/Positioning_(marketing)">positioning</a>, competitive retaliations or creation of a <a href="https://en.wikipedia.org/wiki/Corporate_identity">corporate image</a>.<sup><span>[</span>2<span>]</span></sup> </p><p>The term &#39;promotion&#39; tends to be used internally by the marketing function. To the public or the market, phrases like &quot;<a href="https://en.wikipedia.org/wiki/Special_offer">special offer</a>&quot; are more common. Examples of fully integrated, long-term, and large-scale promotions are <a href="https://en.wikipedia.org/wiki/My_Coke_Rewards">My Coke Rewards</a> in the USA or Coke Zone in the UK and <a href="https://en.wikipedia.org/wiki/Pepsi_Stuff">Pepsi Stuff</a>. </p><div><h2>Types</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Promotion_(marketing)&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>There have been different ways to promote a product in person or with different media. Both person and media can be either physically real or virtual/electronic. </p><div><h3>In a physical environment</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Promotion_(marketing)&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Promotions can be held in physical environments at special events such as <a href="https://en.wikipedia.org/wiki/Concert">concerts</a>, festivals, <a href="https://en.wikipedia.org/wiki/Trade_show">trade shows</a>, and in the field, such as in grocery or department stores. Interactions in the field allow immediate purchases. The purchase of a product can be <a href="https://en.wikipedia.org/wiki/Incentive">incentive</a> with <a href="https://en.wikipedia.org/wiki/Discounts_and_allowances">discounts</a> (i.e., coupons), free items, or a <a href="https://en.wikipedia.org/wiki/Sweepstake">sweepstakes prize draw</a>. This method is used to increase the sales of a given product. </p><p>Interactions between the brand and the customer are performed by a <a href="https://en.wikipedia.org/wiki/Brand_ambassador">brand ambassador</a> or <a href="https://en.wikipedia.org/wiki/Promotional_model">promotional model</a> who represents the product in physical environments. Brand ambassadors or promotional models are hired by a <a href="https://en.wikipedia.org/wiki/Marketing_company">marketing company</a>, which in turn is booked by the brand to represent the product or service. Person-to-person interaction, as opposed to media-to-person involvement, establishes connections that add another dimension to promotion. <a href="https://en.wikipedia.org/wiki/Community_building">Building a community</a> through promoting goods and services can lead to <a href="https://en.wikipedia.org/wiki/Brand_loyalty">brand loyalty</a>. </p><div><h3>Traditional media</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Promotion_(marketing)&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>Examples of traditional media include print media such as <a href="https://en.wikipedia.org/wiki/Newspaper">newspapers</a> and magazines, electronic media such as radio and <a href="https://en.wikipedia.org/wiki/Television">television</a>, and outdoor media such as banner or <a href="https://en.wikipedia.org/wiki/Billboard">billboard</a> advertisements. Each of these platforms provides ways for brands to reach consumers with advertisements. </p><p>Printed collateral such as brochures, business cards, presentation folders, and catalogs are commonly used as sales aids and for local awareness within print advertising and direct marketing, and as support materials in personal selling<sup><span>[</span>9<span>]</span></sup> and at trade shows. Campaigns may also use <a href="https://en.wikipedia.org/wiki/Promotional_merchandise">promotional merchandise</a> as complementary giveaways to support awareness and recall. </p><div><h3>Digital media</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Promotion_(marketing)&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>Digital media, which includes Internet, <a href="https://en.wikipedia.org/wiki/Social_networking">social networking</a> and <a href="https://en.wikipedia.org/wiki/Social_media">social media</a> sites, is a modern way for brands to interact with consumers as it releases news, information and advertising from the technological limits of print and broadcast infrastructures.<sup><span>[</span>10<span>]</span></sup> Digital media is currently the most effective way for brands to reach their consumers on a daily basis. Over 2.7 billion people are online globally, which is about 40% of the world&#39;s population.<sup><span>[</span>11<span>]</span></sup> 67% of all Internet users globally use social media.<sup><span>[</span>12<span>]</span></sup> </p><p><a href="https://en.wikipedia.org/wiki/Mass_communication">Mass communication</a> has led to modern marketing strategies to continue focusing on brand awareness, large distributions and heavy promotions.<sup><span>[</span>10<span>]</span></sup> The fast-paced environment of digital media presents new methods for promotion to utilize new tools now available through technology. With the rise of technological advances, promotions can be done outside of local contexts and across geographic borders to reach a greater number of potential consumers. The goal of a promotion is then to reach the most people possible in a time efficient and a cost efficient manner. </p><p>Social media, as a modern marketing tool, offers opportunities to reach larger audiences in an interactive way. These interactions allow for conversation rather than simply educating the customer. <a href="https://en.wikipedia.org/wiki/Facebook">Facebook</a>, <a href="https://en.wikipedia.org/wiki/Snapchat">Snapchat</a>, <a href="https://en.wikipedia.org/wiki/Instagram">Instagram</a>, <a href="https://en.wikipedia.org/wiki/Twitter">Twitter</a>, <a href="https://en.wikipedia.org/wiki/Pinterest">Pinterest</a>, <a href="https://en.wikipedia.org/wiki/Tumblr">Tumblr</a>, as well as alternate audio and media sites like <a href="https://en.wikipedia.org/wiki/SoundCloud">SoundCloud</a> and <a href="https://en.wikipedia.org/wiki/Mixcloud">Mixcloud</a> allow users to interact and promote music online with little to no cost. You can purchase and buy ad space on social media platforms. Additionally, you can buy artificial <a href="https://en.wikipedia.org/wiki/Like_button">Likes</a>, Followers, and Clicks on your pages and posts with the use of third parties. As a participatory media culture, social media platforms or social networking sites are forms of mass communication that, through media technologies, allow large amounts of product and distribution of content to reach the largest audience possible.<sup>[2]</sup> However, there are downsides to virtual promotions as servers, systems, and websites may crash, fail, or become overloaded with information. You also can stand risk of losing uploaded information and storage and at a use can also be effected by a number of outside variables. </p><p>Brands can explore different strategies to keep consumers engaged. One popular tool is branded entertainment, or creating some sort of social game for the user. The benefits of such a platform include submersing the user in the brand&#39;s content. Users will be more likely to absorb and not grow tired of advertisements if they are, for example, embedded in the game as opposed to a bothersome pop-up ad.<sup><span>[</span>13<span>]</span></sup> </p><p><a href="https://en.wikipedia.org/wiki/Personalizing_advertisements">Personalizing advertisements</a> is another strategy that can work well for brands, as it can increase the likelihood that the brand will be personified by the consumer. Personalization increases click-through intentions when data has been collected about the consumer.<sup><span>[</span>14<span>]</span></sup> </p><p>Brands must navigate the line between effectively promoting their content to consumers on social media and becoming too invasive in consumers&#39; lives. Vivid Internet ads that include devices such as <a href="https://en.wikipedia.org/wiki/Animation">animation</a> might increase a user&#39;s initial attention to the ad. However, this may be seen as a distraction to the user if they are trying to absorb a different part of the site such as reading text.<sup><span>[</span>15<span>]</span></sup> Additionally, when brands make the effort of overtly collecting data about their consumers and then personalizing their ads to them, the consumer&#39;s relationship with the advertisements, following this data collection, is frequently positive. However, when data is covertly collected, consumers can quickly feel like the company betrayed their trust.<sup><span>[</span>14<span>]</span></sup> It is important for brands to utilize personalization in their ads, without making the consumer feel vulnerable or that their <a href="https://en.wikipedia.org/wiki/Internet_privacy">privacy</a> has been betrayed. </p><div><h3>Sponsorship</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Promotion_(marketing)&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>Sponsorship generally involves supplying resources (such as money) to a group or an event in exchange for advertising or publicity. Company will often help fund athletes, teams, or events in exchange for having their logo prominently visible. This is done through the use of <a href="https://en.wikipedia.org/wiki/Product_placement">product placement</a> or by placing logos on team uniforms/equipment.<sup><span>[</span>16<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Promotion_(marketing)&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Advertising">Advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Advertising_campaign">Advertising campaign</a></li> <li><a href="https://en.wikipedia.org/wiki/Advertising_management">Advertising management</a></li> <li><a href="https://en.wikipedia.org/wiki/Advertising_media_selection">Advertising media selection</a></li> <li><a href="https://en.wikipedia.org/wiki/Advertising_research">Advertising research</a></li> <li><a href="https://en.wikipedia.org/wiki/AIDA_(marketing)">AIDA</a></li> <li><a href="https://en.wikipedia.org/wiki/Ad_tracking">Ad tracking</a></li> <li><a href="https://en.wikipedia.org/wiki/Brand_awareness">Brand awareness</a></li> <li><a href="https://en.wikipedia.org/wiki/DAGMAR_marketing">DAGMAR</a></li> <li><a href="https://en.wikipedia.org/wiki/Digital_marketing">Digital marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Digital_promotion">Digital promotion</a></li> <li><a href="https://en.wikipedia.org/wiki/Integrated_marketing_communications">Integrated marketing communications</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_marketing_topics">List of marketing topics</a></li> <li><a href="https://en.wikipedia.org/wiki/Promotional_merchandise">Promotional merchandise</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_communications">Marketing communications</a></li> <li><a href="https://en.wikipedia.org/wiki/Marketing_management">Marketing management</a></li> <li><a href="https://en.wikipedia.org/wiki/Market_mix_modeling">Market mix modeling</a></li> <li><a href="https://en.wikipedia.org/wiki/Media_planning">Media planning</a></li> <li><a href="https://en.wikipedia.org/wiki/Native_advertising">Native advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Online_advertising">Online advertising</a></li> <li><a href="https://en.wikipedia.org/wiki/Promotional_mix">Promotional mix</a></li> <li><a href="https://en.wikipedia.org/wiki/Product_placement">Product placement</a></li> <li><a href="https://en.wikipedia.org/wiki/Public_relations">Public relations</a></li> <li><a href="https://en.wikipedia.org/wiki/Sales_promotion">Sales promotion</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_media_marketing">Social media marketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Spin_(public_relations)">Spin (public relations)</a></li></ul></div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Promotion_(marketing)&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><div><ol> <li><span><b>^</b></span> <span><cite>McCarthy, Jerome E. (1964). <span><a href="https://archive.org/details/basicmarketingma00mcca_1/page/769"><i>Basic Marketing. A Managerial Approach</i></a></span>. Homewood, Illinois: Irwin. pp. <a href="https://archive.org/details/basicmarketingma00mcca_1/page/769">769</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0256025339"><bdi>0256025339</bdi></a>.</cite> <span><code class="cs1-code">{{cite book}}</code>: </span><span>ISBN / Date incompatibility (<a href="https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_isbn_date">help</a>)</span></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Rajagopal (2007). <i>Marketing dynamics theory and practice</i>. New Delhi: New Age International. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-81-224-2712-7"><bdi>978-81-224-2712-7</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><i>Online Etymology Encyclopedia,</i> &lt;Online: <cite><a href="https://www.etymonline.com/word/promotion">&quot;Promotion | Etymology, origin and meaning of promotion by etymonline&quot;</a>. <a href="https://web.archive.org/web/20180108174811/https://www.etymonline.com/word/promotion">Archived</a> from the original on 2018-01-08<span>. Retrieved <span>2018-01-07</span></span>.</cite>&gt;</span> </li> <li><span><b>^</b></span> <span>Online Etymology Encyclopedia, &lt;Online: <cite><a href="https://www.etymonline.com/word/promotion">&quot;Promotion | Etymology, origin and meaning of promotion by etymonline&quot;</a>. <a href="https://web.archive.org/web/20180108174811/https://www.etymonline.com/word/promotion">Archived</a> from the original on 2018-01-08<span>. Retrieved <span>2018-01-07</span></span>.</cite>&gt;</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://newspapers.com/article/chicago-tribune-tower-ticker/187406009">&quot;Tower Ticker&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Chicago_Tribune">Chicago Tribune</a></i> – via <a href="https://en.wikipedia.org/wiki/Newspapers.com">Newspapers.com</a>.</cite></span> </li> <li><span><b>^</b></span> <span>Pickton, D. and Broderick, A. <i>Integrated Marketing Communications,</i> Harlow, Essex, Pearson, 2005, pp 4–5</span> </li> <li><span><b>^</b></span> <span><cite>Boone, Louis; Kurtz, David (1974). <i>Contemporary marketing</i>. Hinsdale, Illinois: Dryden Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-03-088518-1"><bdi>978-0-03-088518-1</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span>instead of spending on free samples, giving a larger amount to a paying customer to whom an expiration date matching that of the small size promotes self-medicating <cite>Christina Thompson (December 13, 2015). <a href="https://philadelphia.cbslocal.com/2015/12/13/philadelphia-lawyer-finds-his-true-passion-in-technology">&quot;Philadelphia Lawyer Finds His True Passion In Technology&quot;</a>. <a href="https://en.wikipedia.org/wiki/CBS">CBS</a>. <q>Why is the 100-count Advil only 25% more than the 50-count?</q></cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://resources.saylor.org/wwwresources/archived/site/textbooks/The%20Power%20of%20Selling.pdf">&quot;The Power of Selling&quot;</a> <span>(PDF)</span>. The Saylor Foundation. p. 464<span>. Retrieved <span>22 December</span> 2025</span>. <q>Almost all salespeople bring some sort of brochure or premium leave-behind on their sales calls.</q></cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>Mulhern, Frank (2009). &quot;Integrated marketing communications: From media channels to digital connectivity&quot;. <i>Journal of Marketing Communications</i> <b>15</b> (2–3): 87.</span> </li> <li><span><b>^</b></span> <span>Hudson, Simon; Huang, Li; Roth, Martin S.; Madden, Thomas J. &quot;The influence of social media interactions on consumer–brand relationships: A three-country study of brand perceptions and marketing</span> </li> <li><span><b>^</b></span> <span>Hudson, Simon; Roth, Martin S.; Madden, Thomas J.; Hudson, Rupert (2015-04-01). &quot;The effects of social media on emotions, brand relationship quality, and word of mouth: An empirical study of music festival attendees&quot;. <i>Tourism Management</i> <b>47</b>: 68–76. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1016%2Fj.tourman.2014.09.001">10.1016/j.tourman.2014.09.001</a>.</span> </li> <li><span><b>^</b></span> <span>Ashley, C., &amp; Tuten, T. (2015). Creative Strategies in Social Media Marketing: An Exploratory Study of Branded Social Content and Consumer Engagement. <i>Psychology &amp; Marketing</i>, 32(1), 15–27.</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>Aguirre, Elizabeth; Mahr, Dominik; Grewal, Dhruv; de Ruyter, Ko; Wetzels, Martin (2015-03-01). &quot;Unraveling the Personalization Paradox: The Effect of Information Collection and Trust-Building Strategies on Online Advertisement Effectiveness&quot;. <i>Journal of Retailing</i> <b>91</b> (1): 34–49. doi:10.1016/j.jretai.2014.09.005.</span> </li> <li><span><b>^</b></span> <span>Celebi, Serra Inci. &quot;How do motives affect attitudes and behaviors toward internet advertising and Facebook advertising?&quot;. <i><a href="https://en.wikipedia.org/wiki/Computers_in_Human_Behavior">Computers in Human Behavior</a></i> <b>51</b>: 312–324. doi:10.1016/j.chb.2015.05.011.</span> </li> <li><span><b>^</b></span> <span><cite>Mariela, Steeve; Portesi, Mariela; Portesi, Mariela (July 2008). &quot;Some entropic extensions of the uncertainty principle&quot;. <i>2008 IEEE International Symposium on Information Theory</i>. IEEE. pp. <span>1676–</span>1680. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1109%2Fisit.2008.4595273">10.1109/isit.2008.4595273</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-4244-2256-2"><bdi>978-1-4244-2256-2</bdi></a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:14967814">14967814</a>.</cite></span> </li> </ol></div><div><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a>: National <span><a href="https://www.wikidata.org/wiki/Q353163#identifiers"></a></span></th><td><div><ul><li><span><a href="https://id.ndl.go.jp/auth/ndlna/00570651">Japan</a></span></li></ul></div></td></tr></tbody></table></div> Parable of the broken window - Wikipedia https://en.wikipedia.org/wiki/Parable_of_the_broken_window Qgb8tXSoJSDuauG0R2PadVO87iG6TO83wN3Lvg== Wed, 13 May 2026 11:22:17 +0000 Parable by French economist Frédéric Bastiat <div>Parable by French economist Frédéric Bastiat</div><div>This article is about the economic parable. For the criminological theory, see <a href="https://en.wikipedia.org/wiki/Broken_windows_theory">Broken windows theory</a>.</div><figure><a href="https://en.wikipedia.org/wiki/File:Broken_window_large.jpg"></a><figcaption>When a child accidentally smashes a window, and then it has to be replaced, does this accident constitute a benefit to society, due to the economic activity of repairing and replacing the window?</figcaption></figure><p>The <b>parable of the broken window</b> was introduced by French economist <a href="https://en.wikipedia.org/wiki/Fr%C3%A9d%C3%A9ric_Bastiat">Frédéric Bastiat</a> in his 1850 essay &quot;That Which Is Seen, and That Which Is Not Seen&quot; (&quot;<span><i>Ce qu&#39;on voit et ce qu&#39;on ne voit pas</i></span>&quot;) to illustrate why destruction, and the money spent to recover from destruction, is not actually a net benefit to society. </p><p>The <a href="https://en.wikipedia.org/wiki/Parable">parable</a> seeks to show how <a href="https://en.wikipedia.org/wiki/Opportunity_cost">opportunity costs</a>, as well as the law of <a href="https://en.wikipedia.org/wiki/Unintended_consequences">unintended consequences</a>, affect economic activity in ways that are unseen or ignored. The belief that destruction is good for the economy is consequently known as the <b>broken window fallacy</b> or <b>glazier&#39;s fallacy</b>. </p><div><h2>Parable</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>Bastiat&#39;s original parable of the broken window from &quot;Ce qu&#39;on voit et ce qu&#39;on ne voit pas&quot; (1850): </p><blockquote> <p>Have you ever witnessed the anger of the good shopkeeper, James Goodfellow, when his careless son has happened to break a pane of glass? If you have been present at such a scene, you will most assuredly bear witness to the fact that every one of the spectators, were there even thirty of them, by common consent apparently, offered the unfortunate owner this invariable consolation – &quot;It is an ill wind that blows nobody good. Everybody must live, and what would become of the glaziers if panes of glass were never broken?&quot; </p><p>Now, this form of condolence contains an entire theory, which it will be well to show up in this simple case, seeing that it is precisely the same as that which, unhappily, regulates the greater part of our economical institutions. </p><p>Suppose it cost six francs to repair the damage, and you say that the accident brings six francs to the glazier&#39;s trade – that it encourages that trade to the amount of six francs – I grant it; I have not a word to say against it; you reason justly. The glazier comes, performs his task, receives his six francs, rubs his hands, and, in his heart, blesses the careless child. All this is that which is seen. </p><p>But if, on the other hand, you come to the conclusion, as is too often the case, that it is a good thing to break windows, that it causes money to circulate, and that the encouragement of industry in general will be the result of it, you will oblige me to call out, &quot;Stop there! Your theory is confined to that which is seen; it takes no account of that which is not seen.&quot; </p><p> It is not seen that as our shopkeeper has spent six francs upon one thing, he cannot spend them upon another. It is not seen that if he had not had a window to replace, he would, perhaps, have replaced his old shoes, or added another book to his library. In short, he would have employed his six francs in some way, which this accident has prevented.<sup><span>[</span>1<span>]</span></sup></p></blockquote><div><h2>Interpretations and evidence</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><div><h3>Bastiat&#39;s argument</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Suppose it were discovered that the little boy was actually hired by the glazier and was paid a franc for every window he broke. Suddenly the same act would be regarded as theft: the glazier was breaking windows to force people to hire his services. Yet the facts observed by the onlookers remain true: the glazier benefits from the business at the expense of the baker, the tailor, and so on. </p><p>Bastiat argues that society endorses activities that are morally equivalent to the glazier hiring a boy to break windows for him: </p><blockquote><p>Whence we arrive at this unexpected conclusion: &quot;Society loses the value of things which are uselessly destroyed;&quot; and we must assent to a maxim which will make the hair of protectionists stand on end – To break, to spoil, to waste, is not to encourage national labour; or, more briefly, &quot;destruction is not profit.&quot; </p><p>What will you say, <i>Moniteur Industriel</i><sup><span>[</span>2<span>]</span></sup> – what will you say, disciples of good M. F. Chamans, who has calculated with so much precision how much trade would gain by the burning of Paris, from the number of houses it would be necessary to rebuild?<sup><span>[</span>1<span>]</span></sup> </p> </blockquote><p>Bastiat is not addressing <a href="https://en.wikipedia.org/wiki/Production_(economics)">production</a> – he is addressing the stock of <a href="https://en.wikipedia.org/wiki/Wealth">wealth</a>. In other words, Bastiat does not merely look at the immediate but at the longer effects of breaking the window. Bastiat takes into account the consequences of breaking the window for society as a whole, rather than for just one group.<sup><span>[</span>3<span>]</span></sup><sup><span>[</span>4<span>]</span></sup> </p><p><a href="https://en.wikipedia.org/wiki/Austrian_school_of_economics">Austrian theorists</a> have cited this as a fallacy, saying it is a common element of popular thinking. The 20th century American economist <a href="https://en.wikipedia.org/wiki/Henry_Hazlitt">Henry Hazlitt</a> († 1993) devoted a chapter to the fallacy in his book <i><a href="https://en.wikipedia.org/wiki/Economics_in_One_Lesson">Economics in One Lesson</a></i>.<sup><span>[</span>5<span>]</span></sup> </p><p>On 6 May 2025, the <a href="https://en.wikipedia.org/wiki/Independent_Institute">Independent Institute</a> started a series on &quot;teaching economics through today&#39;s ongoing trade war&quot;. They quote Bastiat&#39;s parable and summarize: &quot;The moral of the story is simple: destruction doesn&#39;t create wealth. Destruction only destroys wealth.&quot;<sup><span>[</span>6<span>]</span></sup> </p><div><h3>Cost of disasters</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>The broken-window scenario is used as an analogy for destruction by <a href="https://en.wikipedia.org/wiki/Natural_disaster">natural disasters</a>.<sup><span>[</span>7<span>]</span></sup> Disasters disrupt economic activity.<sup><span>[</span>8<span>]</span></sup> The economic effects of natural disasters are varied.<sup><span>[</span>9<span>]</span></sup> </p><figure><a href="https://en.wikipedia.org/wiki/File:Taisho-suji_market_f164.jpg"></a><figcaption>Firefighters at work in the Taisho-suji Market in <a href="https://en.wikipedia.org/wiki/Kobe">Kobe</a>, Japan after a <a href="https://en.wikipedia.org/wiki/Great_Hanshin_earthquake">1995 earthquake</a>.</figcaption></figure><p>Countries are more likely to have GDP fall after a disaster if they have more unemployment, more poverty, less effective local and national governments and institutions, and weaker economic and diplomatic connections. Countries are more likely to have a GDP boost and recover quickly from a disaster if they retain a skilled workforce and the ability to mobilize resources for reconstruction, including resources from outside the disaster area.<sup><span>[</span>10<span>]</span></sup><sup><span>[</span>11<span>]</span></sup> On the one hand, prompt recovery has been attributed to prompt insurance and aid payments, with the contrast between <a href="https://en.wikipedia.org/wiki/Hurricane_Andrew">Hurricane Andrew</a> and <a href="https://en.wikipedia.org/wiki/Hurricane_Katrina">Hurricane Katrina</a> as an anecdotal example. On the other hand, slow recovery has been blamed on predatory behaviour, with those unharmed or less-harmed by the disaster taking advantage of those more harmed.<sup><span>[</span>9<span>]</span></sup> </p><p>Areas that have had repeated disasters tend to invest more in skills and education (possibly because this is preferred to riskier investment in infrastructure, which might be destroyed again), and they tend to have a higher <a href="https://en.wikipedia.org/wiki/Total_factor_productivity">total factor productivity</a> (possibly also because infrastructure destroyed in disasters is replaced with better infrastructure, as, for instance, in the <a href="https://en.wikipedia.org/wiki/Great_Fire_of_London">Great Fire of London</a>). These tendencies could in theory lead to longer-term economic benefits (which may cause GDP growth).<sup><span>[</span>9<span>]</span></sup><sup><span>[</span>12<span>]</span></sup> </p><p>There is some evidence that geological disasters do more economic harm than climate-related disasters, in the long term. Geological disasters, such as <a href="https://en.wikipedia.org/wiki/Landslides">landslides</a> and earthquakes, happen with little immediate warning and kill many people. Climate-related disasters, such as hurricanes, are more predictable on a scale of days to hours, and kill fewer people.<sup><span>[</span>9<span>]</span></sup><sup><span>[</span>12<span>]</span></sup> Such <a href="https://en.wikipedia.org/wiki/Warning_system">warning</a> saves people, but not immovable property.<sup><span>[</span>13<span>]</span></sup> This suggests that killing people does long-lasting economic harm, while destroying capital is not as harmful to GDP growth. </p><blockquote> <p>&quot;Destroy any amount of physical capital, but leave behind a critical number of knowledgeable human beings whose brains still house the culture and technology of a dynamic economy, and the physical capital will tend to reemerge almost spontaneously&quot; — George Horwich, Purdue University<sup><span>[</span>10<span>]</span></sup><sup><span>[</span>14<span>]</span></sup> </p> </blockquote><p>Even in disasters with few physical injuries, a large portion of the economic cost may be public health effects (approximately a tenth, in the case of the <a href="https://en.wikipedia.org/wiki/2007_United_Kingdom_floods">summer 2007 floods in the UK</a>). The economic costs of disruption to children&#39;s education are significant.<sup><span>[</span>15<span>]</span></sup> Mental health issues may be triggered or exacerbated by the distress suffered during the disaster.<sup><span>[</span>16<span>]</span></sup> Health advice on minimizing <a href="https://en.wikipedia.org/wiki/Psychosocial_distress">psychosocial distress</a> has been given for disasters. While public health costs may contribute to economic activity and GDP growth, growth in demand for medical or educational assistance is unlikely to be seen as beneficial. </p><div><h3>Opportunity cost of war</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><div>See also: <a href="https://en.wikipedia.org/wiki/Military_Keynesianism">Military Keynesianism</a>, <a href="https://en.wikipedia.org/wiki/Post%E2%80%93World_War_II_economic_expansion">Post–World War II economic expansion</a>, and <a href="https://en.wikipedia.org/wiki/Creative_destruction">Creative destruction</a></div><figure><a href="https://en.wikipedia.org/wiki/File:Bomb_damage_on_James_Street,_Aston_Newtown,_Birmingham,_1940._D4127.jpg"></a><figcaption>Partly-cleared bomb damage in an industrial area. The roofless buildings are houses. The corrugated metal in front of the pile of bricks and framing timber are the remains of several <a href="https://en.wikipedia.org/wiki/Anderson_shelter">air-raid shelters</a>.</figcaption></figure><p> Occasionally the argument has been made that war is a benefactor to society and that &quot;war is good for the economy.&quot; A variant of this argument suggests that, while war cannot be fairly called a benefactor, it can and sometimes does confer some economic benefits.<sup><span>[</span>17<span>]</span></sup> However, this belief is often given as an example of the broken window fallacy. The money spent on the war effort (or peacetime <a href="https://en.wikipedia.org/wiki/Military_budget">defense spending</a>), for example, is money that cannot be spent on food, clothing, health care, or other sectors of the economy. The stimulus felt in one sector of the economy comes at a direct – but hidden – cost (via <a href="https://en.wikipedia.org/wiki/Production%E2%80%93possibility_frontier">foreclosed production possibilities</a>) to other sectors. </p><p>Bastiat himself argued against the claim that hiring men to be soldiers was inherently beneficial to the economy in the second chapter of <i>That Which is Seen, and That Which is Not Seen</i>, &quot;The Disbanding of Troops&quot;. </p><p> According to <a href="https://en.wikipedia.org/wiki/Henry_Hazlitt">Hazlitt</a>: </p><blockquote><p>It is never an advantage to have one&#39;s plants destroyed by shells or bombs unless those plants have already become valueless or acquired a negative value by depreciation and obsolescence. ... Plants and equipment cannot be replaced by an individual (or a socialist government) unless he or it has acquired or can acquire the savings, the capital accumulation, to make the replacement. But war destroys accumulated capital. ... Complications should not divert us from recognizing the basic truth that the wanton destruction of anything of real value is always a net loss, a misfortune, or a disaster, and whatever the offsetting considerations in a particular instance, can never be, on net balance, a boon or a blessing.<sup><span>[</span>18<span>]</span></sup> </p></blockquote><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Cobra_effect">Cobra effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Creative_destruction">Creative destruction</a></li> <li><a href="https://en.wikipedia.org/wiki/Disaster_capitalism">Disaster capitalism</a></li> <li><a href="https://en.wikipedia.org/wiki/Dutch_disease">Dutch disease</a> (economics)</li> <li><a href="https://en.wikipedia.org/wiki/Jevons_paradox">Jevons paradox</a></li> <li><a href="https://en.wikipedia.org/wiki/Luddite_fallacy">Luddite fallacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Lump_of_labor_fallacy">Lump of labor fallacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Opportunity_cost">Opportunity cost</a></li> <li><a href="https://en.wikipedia.org/wiki/Rent-seeking">Rent-seeking</a></li> <li><a href="https://en.wikipedia.org/wiki/Robot_tax">Robot tax</a></li> <li><a href="https://en.wikipedia.org/wiki/Spending_multiplier">Spending multiplier</a></li> <li><a href="https://en.wikipedia.org/wiki/Tax_choice">Tax choice</a></li> <li><a href="https://en.wikipedia.org/wiki/Technological_unemployment">Technological unemployment</a></li> <li><a href="https://en.wikipedia.org/wiki/Uneconomic_growth">Uneconomic growth</a></li> <li><a href="https://en.wikipedia.org/wiki/Zero-sum_game">Zero-sum game</a></li> <li><a href="https://en.wikipedia.org/wiki/Zero-sum_thinking">Zero-sum thinking</a></li></ul> </div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>Bastiat 1850.</span> </li> <li><span><b>^</b></span> <span><i>Le Moniteur Industriel</i> was a famous protectionist journal.</span> </li> <li><span><b>^</b></span> <span>Fetter 1915, chapter 37: &quot;Waste and Luxury&quot;.</span> </li> <li><span><b>^</b></span> <span>Hazlitt 1946, chapter 2: &quot;The Broken Window&quot;.</span> </li> <li><span><b>^</b></span> <span>Hazlitt 1946, &quot;Preface&quot;.</span> </li> <li><span><b>^</b></span> <span><a href="https://www.independent.org/article/2025/05/06/broken-window-fallacy-trade-war-bastiat-mercantilists-mythbusting/"><i>Broken Windows and the Broken Logic of Trade Wars. Mythbusters: Debunking the New Mercantilists, Part 1.</i></a></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.economist.com/democracy-in-america/2011/03/16/japan-and-the-economics-of-natural-disaster">&quot;Japan and the economics of natural disaster&quot;</a>. <i>The Economist</i>. 16 March 2011.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Burn-Callander, Rebecca (28 December 2015). <a href="https://www.telegraph.co.uk/finance/economics/12071604/UK-flooding-cost-of-damage-to-top-5bn-but-many-homes-and-businesses-underinsured.html">&quot;UK flooding: cost of damage to top £5bn but many homes and businesses underinsured&quot;</a> – via www.telegraph.co.uk.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup></span> <span><cite>Bennett, Drake (6 July 2008). <a href="http://archive.boston.com/bostonglobe/ideas/articles/2008/07/06/how_disasters_help/?page=full">&quot;How disasters help&quot;</a>. <i>The Boston Globe</i>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://www.reuters.com/article/us-japan-quake-recovery-idUSTRE72C19320110313">&quot;Special Report: Advanced economies cope better with disasters&quot;</a>. <i>Reuters</i>. 13 March 2011 – via www.reuters.com.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.acs-aec.org/index.php?q=disaster-risk-reduction/the-broken-window-fallacy-economics-investment-and-disaster-risk-reduction">&quot;The Broken Window Fallacy: Economics, Investment and Disaster Risk Reduction&quot;</a>. <i>ACS-AEC – www.acs-aec.org</i>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Skidmore, Mark; Toya, Hideki (October 2002). &quot;Do natural disasters promote long-term growth?&quot;. <i>Economic Inquiry</i>. <b>40</b> (4): <span>664–</span>687. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1093%2Fei%2F40.4.664">10.1093/ei/40.4.664</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1465-7295">1465-7295</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>SciDev.Net. <a href="http://www.scidev.net/index.cfm?originalUrl=/global/earth-science/feature/early-warning-of-disasters-facts-and-figures-1.html&amp;">&quot;Early warning of disasters: Facts and figures&quot;</a>. <i>SciDev.Net</i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Horwich, George (April 2000). <span><a href="https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1128&amp;context=ciberwp">&quot;Economic Lessons of the Kobe Earthquake&quot;</a></span>. <i>Economic Development and Cultural Change</i>. <b>48</b> (3): <span>521–</span>542. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1086%2F452609">10.1086/452609</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/10.1086/452609">10.1086/452609</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:154588521">154588521</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.gov.uk/flood-and-coastal-erosion-risk-management-research-reports/the-costs-of-the-summer-2007-floods-in-england">&quot;The costs of the summer 2007 floods in England&quot;</a>. <i>GOV.UK</i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Stanke, Carla; Murray, Virginia; Amlôt, Richard; Nurse, Jo; Williams, Richard (30 May 2012). <a href="http://currents.plos.org/disasters/article/the-effects-of-flooding-on-mental-health-outcomes-and-recommendations-from-a-review-of-the-literature/">&quot;The Effects of Flooding on Mental Health: Outcomes and Recommendations from a Review of the Literature&quot;</a>. <i>PLOS Currents Disasters</i>. <b>4</b>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1371%2F4f9f1fa9c3cae">10.1371/4f9f1fa9c3cae</a></span> (inactive 12 July 2025). <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/2157-3999">2157-3999</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a> <span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3461973">3461973</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/23066515">23066515</a><span>. Retrieved <span>7 March</span> 2026</span>.</cite><span><code class="cs1-code">{{cite journal}}</code>: CS1 maint: DOI inactive as of July 2025 (<a href="https://en.wikipedia.org/wiki/Category:CS1_maint:_DOI_inactive_as_of_July_2025">link</a>)</span></span> </li> <li><span><b>^</b></span> <span>See for example economist <a href="https://en.wikipedia.org/wiki/Paul_Krugman">Paul Krugman</a>&#39;s article in which he refers to the Fukushima disaster in Japan: <cite><a href="https://krugman.blogs.nytimes.com/2011/03/15/meltdown-macroeconomics/">&quot;Meltdown Macroeconomics&quot;</a>. 15 March 2011.</cite> And another in which he refers to the 9-11 attacks: <cite>Krugman, Paul (14 September 2001). <a href="https://www.nytimes.com/2001/09/14/opinion/reckonings-after-the-horror.html">&quot;Reckonings: After The Horror&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/The_New_York_Times">The New York Times</a></i>.</cite></span> </li> <li><span><b>^</b></span> <span>Hazlitt 1946, chapter 3: &quot;The Blessings of Destruction&quot;.</span> </li> </ol></div></div><div><h3>Bibliography</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><ul><li><cite><a href="https://en.wikipedia.org/wiki/Fr%C3%A9d%C3%A9ric_Bastiat">Bastiat, Frédéric</a> (1850). <span><a href="https://en.wikisource.org/wiki/That_Which_Is_Seen,_and_That_Which_Is_Not_Seen"><i>That Which Is Seen, and That Which Is Not Seen</i> </a></span> [<i>original French: <a href="https://en.wikisource.org/wiki/fr:Ce_qu%27on_voit_et_ce_qu%27on_ne_voit_pas">Ce qu&#39;on voit et ce qu&#39;on ne voit pas</a></i>]. Translated by Patrick James Stirling – via <a href="https://en.wikipedia.org/wiki/Wikisource">Wikisource</a>.</cite></li> <li><cite>Hazlitt, Henry (1946). <a href="https://en.wikipedia.org/wiki/Economics_in_One_Lesson"><i>Economics in One Lesson</i></a>. Harper &amp; Brothers. <a href="https://en.wikipedia.org/wiki/LCCN_(identifier)">LCCN</a> <a href="https://lccn.loc.gov/46005937">46005937</a>.</cite> (<a href="https://mises.org/books/economics_in_one_lesson_hazlitt.pdf">PDF</a>)</li> <li><cite>Fetter, Frank A. (1915). <a href="http://oll.libertyfund.org/titles/fetter-economics-vol-1-economic-principles"><i>Economic Principles</i></a>. New York: The Century Co.</cite></li></ul><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><ul><li><cite>Abrams, Burton A; Parsons, George R (2009). &quot;Is CARS a Clunker?&quot;. <i>The Economists&#39; Voice</i>. <b>6</b> (8). <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2202%2F1553-3832.1638">10.2202/1553-3832.1638</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:153780636">153780636</a>.</cite></li> <li><cite>McGee, Robert W. (2010). <a href="http://dialnet.unirioja.es/servlet/articulo?codigo=3807818">&quot;Financial Bailouts and the philosophy of Frédéric Bastiat&quot;</a>. <i>Aestimatio</i> (1): <span>88–</span>97. <a href="https://en.wikipedia.org/wiki/SSRN_(identifier)">SSRN</a> <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2435748">2435748</a>.</cite></li> <li><cite>Stringham, Edward P.; Snow, Nicholas A. (2008). &quot;The broken trailer fallacy: Seeing the unseen effects of government policies in post-Katrina New Orleans&quot;. <i>International Journal of Social Economics</i>. <b>35</b> (7): <span>480–</span>89. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1108%2F03068290810886885">10.1108/03068290810886885</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:112186379">112186379</a>.</cite></li> <li><cite>Carabini, Louis (2007). <a href="http://mises.org/journals/jls/21_4/21_4_11.pdf">&quot;Bastiat&#39;s &#39;The Broken Window&#39;: A Critique&quot;</a> <span>(PDF)</span>. <i>Journal of Libertarian Studies</i>. <b>21</b> (4): <span>151–</span>55.</cite></li> <li><cite>Mian, Atif R.; Sufi, Amir (2010). &quot;The Effects of Fiscal Stimulus: Evidence from the 2009 &#39;Cash for Clunkers&#39; Program&quot;. <i>SSRN</i>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2139%2Fssrn.1670759">10.2139/ssrn.1670759</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:219352572">219352572</a>.</cite></li> <li><cite>Caplan, Bryan; Stringham, Edward (2005). <a href="https://mpra.ub.uni-muenchen.de/26084/1/MPRA_paper_26084.pdf">&quot;Mises, bastiat, public opinion, and public choice&quot;</a> <span>(PDF)</span>. <i>Review of Political Economy</i>. <b>17</b>: <span>79–</span>105. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1080%2F0953825042000313825">10.1080/0953825042000313825</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:17228008">17228008</a>.</cite></li> <li><cite>Stanfield, James (2010). &quot;The Broken University: What is Seen and What is Not Seen in the Uk Higher Education Sector&quot;. <i>Economic Affairs</i>. <b>30</b> (3): <span>53–</span>58. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1111%2Fj.1468-0270.2010.02022.x">10.1111/j.1468-0270.2010.02022.x</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:153198128">153198128</a>.</cite></li></ul><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Parable_of_the_broken_window&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Wikisource-logo.svg"></a></span></div> <div>English <a href="https://en.wikipedia.org/wiki/Wikisource">Wikisource</a> has original text related to this article: <div><b><a href="https://en.wikisource.org/wiki/en:That_Which_Is_Seen,_and_That_Which_Is_Not_Seen">That Which Is Seen, and That Which Is Not Seen</a></b></div></div></div> </div><ul><li><a href="http://bastiat.org/fr/cqovecqonvp.html">&quot;Ce qu&#39;on voit et ce qu&#39;on ne voit pas&quot;</a> (original essay)</li> <li><a href="http://bastiat.org/en/twisatwins.html">&quot;That Which is Seen and That Which is Not Seen&quot;</a> (English translation)</li></ul><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Misinformation"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Misinformation"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Misinformation"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Disinformation">Disinformation</a> and <a href="https://en.wikipedia.org/wiki/Misinformation">misinformation</a></div></th></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disinformation">Disinformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Misinformation">Misinformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Propaganda">Propaganda</a></li> <li><a href="https://en.wikipedia.org/wiki/Disinformation_attack">Disinformation attack</a></li> <li><a href="https://en.wikipedia.org/wiki/Disinformation_research">Disinformation research</a></li> <li><a href="https://en.wikipedia.org/wiki/Publications_about_disinformation">Publications about disinformation</a></li></ul> </div></td></tr><tr><td colspan="2"><table><tbody><tr><th colspan="2"><div>Mechanisms</div></th></tr><tr><td colspan="2"><table><tbody><tr><th>Psychological</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Cognitive_bias">Cognitive bias</a> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_cognitive_biases">List</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Denialism">Denialism</a></li> <li><a href="https://en.wikipedia.org/wiki/Manipulation_(psychology)">Manipulation</a></li> <li><a href="https://en.wikipedia.org/wiki/Misinformation_effect">Misinformation effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Political_polarization">Political polarization</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychology_of_climate_change_denial">Psychology of climate change denial</a></li></ul> </div></td></tr><tr><th>Computational</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Algorithmic_radicalization">Algorithmic radicalization</a></li> <li><a href="https://en.wikipedia.org/wiki/Content_moderation">Content moderation</a></li> <li><a href="https://en.wikipedia.org/wiki/Community_notes">Community notes</a></li> <li><a href="https://en.wikipedia.org/wiki/Internet_manipulation">Internet manipulation</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_bot">Social bot</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_networking_service">Social networking service</a> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_social_networking_services">List</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/User-generated_content">User-generated content</a></li></ul> </div></td></tr><tr><th>Economic</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Fake_news_websites">Fake news websites</a></li> <li><a href="https://en.wikipedia.org/wiki/Surveillance_capitalism">Surveillance capitalism</a></li> <li><a href="https://en.wikipedia.org/wiki/Programmatic_advertising">Programmatic advertising</a></li></ul> </div></td></tr><tr><th>Media and Politics</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Audience_fragmentation">Audience fragmentation</a></li> <li><a href="https://en.wikipedia.org/wiki/Echo_chamber_(media)">Echo chamber</a></li> <li><a href="https://en.wikipedia.org/wiki/Fake_news">Fake news</a></li> <li><a href="https://en.wikipedia.org/wiki/Media_bias">Media bias</a></li> <li><a href="https://en.wikipedia.org/wiki/Media_culture">Media culture</a></li> <li><a href="https://en.wikipedia.org/wiki/Media_manipulation">Media manipulation</a></li></ul> </div></td></tr></tbody></table></td></tr></tbody></table></td></tr><tr><td colspan="2"><table><tbody><tr><th colspan="2"><div>Tactics</div></th></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Astroturfing">Astroturfing</a></li> <li><a href="https://en.wikipedia.org/wiki/Big_Lie">Big Lie</a></li> <li><a href="https://en.wikipedia.org/wiki/Circular_reporting">Circular reporting</a></li> <li><a href="https://en.wikipedia.org/wiki/Clickbait">Clickbait</a></li> <li><a href="https://en.wikipedia.org/wiki/Conspiracy_theory">Conspiracy theory</a> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_conspiracy_theories">List</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Culture_war">Culture war</a></li> <li><a href="https://en.wikipedia.org/wiki/Deception">Deception</a></li> <li><a href="https://en.wikipedia.org/wiki/Deepfake">Deepfake</a></li> <li><a href="https://en.wikipedia.org/wiki/Disinformation_playbook">Disinformation playbook</a></li> <li><a href="https://en.wikipedia.org/wiki/Dog_whistle_(politics)">Dog whistle</a></li> <li><a href="https://en.wikipedia.org/wiki/Doublespeak">Doublespeak</a></li> <li><a href="https://en.wikipedia.org/wiki/Doxxing">Doxxing</a></li> <li><a href="https://en.wikipedia.org/wiki/Factoid">Factoid</a></li> <li><a href="https://en.wikipedia.org/wiki/Fake_news">Fake news</a> <ul><li><a href="https://en.wikipedia.org/wiki/Fake_news_website">Fake news website</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_fake_news_websites">List of fake news websites</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_satirical_fake_news_websites">List of satirical fake news websites</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Fallacy">Fallacy</a> <ul><li><a href="https://en.wikipedia.org/wiki/Cherry_picking">Cherry picking</a></li> <li><a href="https://en.wikipedia.org/wiki/False_dilemma">False dilemma</a></li> <li><a href="https://en.wikipedia.org/wiki/Gish_gallop">Gish gallop</a></li> <li><a href="https://en.wikipedia.org/wiki/Half-truth">Half-truth</a></li> <li><a href="https://en.wikipedia.org/wiki/Formal_fallacy">Formal fallacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Informal_fallacy">Informal fallacy</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_fallacies">List of fallacies</a></li> <li><a href="https://en.wikipedia.org/wiki/Quote_mining">Quote mining</a></li> <li><a href="https://en.wikipedia.org/wiki/Red_herring">Red herring</a></li> <li><a href="https://en.wikipedia.org/wiki/Whataboutism">Whataboutism</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/False_accusation">False accusation</a></li> <li><a href="https://en.wikipedia.org/wiki/False_attribution">False attribution</a></li> <li><a href="https://en.wikipedia.org/wiki/False_balance">False balance</a></li> <li><a href="https://en.wikipedia.org/wiki/Fear,_uncertainty,_and_doubt">Fear, uncertainty, and doubt</a></li> <li><a href="https://en.wikipedia.org/wiki/Firehose_of_falsehood">Firehose of falsehood</a></li> <li><a href="https://en.wikipedia.org/wiki/Forgery_as_covert_operation">Forgery as covert operation</a></li> <li><a href="https://en.wikipedia.org/wiki/Gaslighting">Gaslighting</a></li> <li><a href="https://en.wikipedia.org/wiki/Greenwashing">Greenwashing</a></li> <li><a href="https://en.wikipedia.org/wiki/Historical_negationism">Historical negationism</a></li> <li><a href="https://en.wikipedia.org/wiki/Hoax">Hoax</a></li> <li><a href="https://en.wikipedia.org/wiki/Information_warfare">Information warfare</a></li> <li><a href="https://en.wikipedia.org/wiki/Infodemic">Infodemic</a></li> <li><a href="https://en.wikipedia.org/wiki/Malinformation">Malinformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Memetic_warfare">Memetic warfare</a></li> <li><a href="https://en.wikipedia.org/wiki/Pink-slime_journalism">Pink-slime journalism</a></li> <li><a href="https://en.wikipedia.org/wiki/Post-truth_politics">Post-truth politics</a> <ul><li><a href="https://en.wikipedia.org/wiki/Alternative_facts">Alternative facts</a></li> <li><a href="https://en.wikipedia.org/wiki/Truthiness">Truthiness</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Potemkin_village">Potemkin village</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychological_warfare">Psychological warfare</a></li> <li><a href="https://en.wikipedia.org/wiki/Propaganda">Propaganda</a> <ul><li><a href="https://en.wikipedia.org/wiki/Black_propaganda">Black propaganda</a></li> <li><a href="https://en.wikipedia.org/wiki/Counterpropaganda">Counterpropaganda</a></li> <li><a href="https://en.wikipedia.org/wiki/State-sponsored_Internet_propaganda">State-sponsored Internet propaganda</a></li> <li><a href="https://en.wikipedia.org/wiki/Perception_management">Perception management</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Pseudoscience">Pseudoscience</a></li> <li><a href="https://en.wikipedia.org/wiki/Rumors">Rumors</a></li> <li><a href="https://en.wikipedia.org/wiki/Spin_(propaganda)">Spin</a></li> <li><a href="https://en.wikipedia.org/wiki/Smear_campaign">Smear campaign</a></li> <li><a href="https://en.wikipedia.org/wiki/Scientific_fabrication">Scientific fabrication</a></li> <li><a href="https://en.wikipedia.org/wiki/Strategy_of_tension">Strategy of tension</a></li> <li><a href="https://en.wikipedia.org/wiki/Tabloid_journalism">Tabloid journalism</a></li> <li><a href="https://en.wikipedia.org/wiki/Yellow_journalism">Yellow journalism</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><td colspan="2"><table><tbody><tr><th colspan="2"><div>Targets and campaigns</div></th></tr><tr><td colspan="2"><table><tbody><tr><th>International Politics</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disinformation_in_the_Russian_invasion_of_Ukraine">Disinformation in the Russian invasion of Ukraine</a></li> <li><a href="https://en.wikipedia.org/wiki/Misinformation_in_the_Gaza_war">Misinformation in the Gaza war</a></li> <li><a href="https://en.wikipedia.org/wiki/New_World_Order_conspiracy_theory">New World Order conspiracy theory</a></li> <li><a href="https://en.wikipedia.org/wiki/Russian_disinformation">Russian disinformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Genocide_denial">Genocide denial</a></li></ul> </div></td></tr><tr><th>Politics by country</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_disinformation_attacks_by_country">List of disinformation attacks by country</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_political_disinformation_website_campaigns">List of political disinformation website campaigns</a></li></ul> </div></td></tr><tr><th>Antisemitism</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Holocaust_denial">Holocaust denial</a></li> <li><a href="https://en.wikipedia.org/wiki/International_Jewish_conspiracy">International Jewish conspiracy</a></li></ul> </div></td></tr><tr><th>Environmental science</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Climate_change_denial">Climate change denial</a></li> <li>Fossil fuel industry <ul><li><a href="https://en.wikipedia.org/wiki/ExxonMobil_climate_change_denial">ExxonMobil climate change denial</a></li> <li><a href="https://en.wikipedia.org/wiki/Fossil_fuels_lobby">Fossil fuels lobby</a></li></ul></li> <li>Leaded gasoline <ul><li><a href="https://en.wikipedia.org/wiki/Ethyl_Corporation">Ethyl Corporation</a></li> <li><a href="https://en.wikipedia.org/wiki/Robert_A._Kehoe">Robert A. Kehoe</a></li> <li><a href="https://en.wikipedia.org/wiki/Clair_Cameron_Patterson">Clair Cameron Patterson</a></li></ul></li> <li>Pesticide industry <ul><li><a href="https://en.wikipedia.org/wiki/Rachel_Carson">Rachel Carson</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Silent_Spring">Silent Spring</a></i></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Red_mercury">Red mercury</a></li></ul> </div></td></tr><tr><th>Medicine and Public health</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/5G_misinformation">5G misinformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Anti-vaccine_activism">Anti-vaccine activism</a> <ul><li><a href="https://en.wikipedia.org/wiki/Lancet_MMR_autism_fraud">Lancet MMR autism fraud</a></li> <li><a href="https://en.wikipedia.org/wiki/Vaccines_and_autism">Vaccines and autism</a></li> <li><a href="https://en.wikipedia.org/wiki/Vaccine_misinformation">Vaccine misinformation</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/COVID-19_misinformation">COVID-19 misinformation</a> <ul><li><a href="https://en.wikipedia.org/wiki/COVID-19_misinformation_by_governments">COVID-19 misinformation by governments</a></li> <li><a href="https://en.wikipedia.org/wiki/COVID-19_vaccine_misinformation_and_hesitancy">COVID-19 vaccine misinformation and hesitancy</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Misinformation_related_to_birth_control">Birth control misinformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Ebola_misinformation">Ebola misinformation</a></li> <li><a href="https://en.wikipedia.org/wiki/GMO_conspiracy_theories">GMO conspiracy theories</a></li> <li><a href="https://en.wikipedia.org/wiki/HIV/AIDS_denialism">HIV/AIDS denialism</a></li> <li><a href="https://en.wikipedia.org/wiki/Mental_illness_denial">Mental illness denial</a></li> <li><a href="https://en.wikipedia.org/wiki/Misinformation_related_to_abortion">Misinformation related to abortion</a></li> <li><a href="https://en.wikipedia.org/wiki/Tobacco_industry_playbook">Tobacco industry playbook</a></li> <li><a href="https://en.wikipedia.org/wiki/Transgender_health_care_misinformation">Transgender health care misinformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Opposition_to_water_fluoridation">Opposition to water fluoridation</a></li></ul> </div></td></tr><tr><th>Journalism and journalists</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Safety_of_journalists">Safety of journalists</a></li> <li><a href="https://en.wikipedia.org/wiki/Maria_Ressa">Maria Ressa</a></li> <li><a href="https://en.wikipedia.org/wiki/Daily_Maverick">Daily Maverick</a></li> <li><a href="https://en.wikipedia.org/wiki/Rappler">Rappler</a></li> <li><a href="https://en.wikipedia.org/wiki/The_Quint">The Quint</a></li></ul> </div></td></tr></tbody></table></td></tr></tbody></table></td></tr><tr><td colspan="2"><table><tbody><tr><th colspan="2"><div>Countering disinformation</div></th></tr><tr><td colspan="2"><table><tbody><tr><th>Methods</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Academic_research">Academic research</a></li> <li><a href="https://en.wikipedia.org/wiki/Critical_thinking">Critical thinking</a></li> <li><a href="https://en.wikipedia.org/wiki/Digital_literacy">Digital literacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Health_literacy">Health literacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Information_literacy">Information literacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Media_literacy">Media literacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Science_communication">Science communication</a></li> <li><a href="https://en.wikipedia.org/wiki/Scientific_consensus">Scientific consensus</a></li> <li><a href="https://en.wikipedia.org/wiki/Scientific_literacy">Scientific literacy</a> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_climate_change_video_games">List of climate change video games</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Scientific_skepticism">Scientific skepticism</a></li> <li><a href="https://en.wikipedia.org/wiki/Skepticism">Skepticism</a></li> <li><a href="https://en.wikipedia.org/wiki/Truth_sandwich">Truth sandwich</a></li> <li><a href="https://en.wikipedia.org/wiki/Verificado_2018">Verificado 2018</a></li> <li><a href="https://en.wikipedia.org/wiki/Watchdog_journalism">Watchdog journalism</a></li></ul> </div></td></tr><tr><th>Fact-checking</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_fact-checking_websites">Websites</a></li></ul> <ul><li>Non-profits and charities <ul><li><a href="https://en.wikipedia.org/wiki/Africa_Check">Africa Check</a></li> <li><a href="https://en.wikipedia.org/wiki/FactCheck.org">FactCheck.org</a></li> <li><a href="https://en.wikipedia.org/wiki/FakeReporter">FakeReporter</a></li> <li><a href="https://en.wikipedia.org/wiki/Full_Fact">Full Fact</a></li> <li><a href="https://en.wikipedia.org/wiki/Misbar">Misbar</a></li> <li><a href="https://en.wikipedia.org/wiki/PolitiFact">PolitiFact</a></li> <li><a href="https://en.wikipedia.org/wiki/USAFacts">USAFacts</a></li></ul></li></ul> <ul><li>Private companies <ul><li><a href="https://en.wikipedia.org/wiki/Logically_(company)">Logically (company)</a></li> <li><a href="https://en.wikipedia.org/wiki/NewsGuard">NewsGuard</a></li> <li><a href="https://en.wikipedia.org/wiki/StopFake">StopFake</a></li> <li><a href="https://en.wikipedia.org/wiki/Lead_Stories">Lead Stories</a></li></ul></li></ul> <ul><li>Other <ul><li><a href="https://en.wikipedia.org/wiki/Bellingcat">Bellingcat</a></li> <li><a href="https://en.wikipedia.org/wiki/International_Fact-Checking_Network">International Fact-Checking Network</a></li> <li><a href="https://en.wikipedia.org/wiki/Media_Bias/Fact_Check">Media Bias/Fact Check</a></li> <li><a href="https://en.wikipedia.org/wiki/Snopes">Snopes</a></li> <li><a href="https://en.wikipedia.org/wiki/Quackwatch">Quackwatch</a></li> <li><a href="https://en.wikipedia.org/wiki/Projeto_Comprova">Projeto Comprova</a></li> <li><a href="https://en.wikipedia.org/wiki/Tahaqaq">Tahaqaq</a></li></ul></li></ul> </div></td></tr><tr><th>Research</th><td><div> <ul><li>Canada <ul><li><a href="https://en.wikipedia.org/wiki/Citizen_Lab">Citizen Lab</a></li></ul></li></ul> <ul><li>EU <ul><li><a href="https://en.wikipedia.org/wiki/East_StratCom_Task_Force">East StratCom Task Force</a></li></ul></li></ul> <ul><li>Finland <ul><li><a href="https://en.wikipedia.org/wiki/Faktabaari">Faktabaari</a></li></ul></li></ul> <ul><li>New Zealand <ul><li><a href="https://en.wikipedia.org/wiki/The_Disinformation_Project">The Disinformation Project</a></li></ul></li></ul> <ul><li>UK <ul><li><a href="https://en.wikipedia.org/wiki/Counter_disinformation_unit">Counter disinformation unit</a></li></ul></li></ul> <ul><li>Ukraine <ul><li><a href="https://en.wikipedia.org/wiki/Center_for_Countering_Disinformation">Center for Countering Disinformation</a></li></ul></li></ul> <ul><li>US <ul><li><a href="https://en.wikipedia.org/wiki/Active_Measures_Working_Group">Active Measures Working Group</a></li> <li><a href="https://en.wikipedia.org/wiki/Counter_Misinformation_Team">Counter Misinformation Team</a></li> <li><a href="https://en.wikipedia.org/wiki/Disinformation_Governance_Board">Disinformation Governance Board</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Countering_Foreign_Propaganda_and_Disinformation_Act">Countering Foreign Propaganda and Disinformation Act</a></i></li> <li><a href="https://en.wikipedia.org/wiki/United_States_Information_Agency">United States Information Agency</a></li></ul></li></ul> </div></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Fallacies"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Fallacies"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Fallacies"><abbr>e</abbr></a></li></ul></div><div>Common <a href="https://en.wikipedia.org/wiki/Fallacy">fallacies</a> (<a href="https://en.wikipedia.org/wiki/List_of_fallacies">list</a>)</div></th></tr><tr><th><a href="https://en.wikipedia.org/wiki/Formal_fallacy">Formal</a></th><td><table><tbody><tr><th>In <a href="https://en.wikipedia.org/wiki/Propositional_calculus">propositional logic</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Affirming_a_disjunct">Affirming a disjunct</a></li> <li><a href="https://en.wikipedia.org/wiki/Affirming_the_consequent">Affirming the consequent</a></li> <li><a href="https://en.wikipedia.org/wiki/Conflation">Conflation</a></li> <li><a href="https://en.wikipedia.org/wiki/Denying_the_antecedent">Denying the antecedent</a></li> <li><a href="https://en.wikipedia.org/wiki/Argument_from_fallacy">Argument from fallacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Masked-man_fallacy">Masked man</a></li> <li><a href="https://en.wikipedia.org/wiki/Mathematical_fallacy">Mathematical fallacy</a></li></ul> </div></td></tr><tr><th>In <a href="https://en.wikipedia.org/wiki/Quantifier_(logic)">quantificational logic</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Existential_fallacy">Existential</a></li> <li><a href="https://en.wikipedia.org/wiki/Affirming_the_consequent">Illicit conversion</a></li> <li><a href="https://en.wikipedia.org/wiki/Proof_by_example">Proof by example</a></li> <li><a href="https://en.wikipedia.org/wiki/Quantifier_shift">Quantifier shift</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Syllogistic_fallacy">Syllogistic fallacy</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Affirmative_conclusion_from_a_negative_premise">Affirmative conclusion from a negative premise</a></li> <li><a href="https://en.wikipedia.org/wiki/Negative_conclusion_from_affirmative_premises">Negative conclusion from affirmative premises</a></li> <li><a href="https://en.wikipedia.org/wiki/Fallacy_of_exclusive_premises">Exclusive premises</a></li> <li><a href="https://en.wikipedia.org/wiki/Existential_fallacy">Existential</a></li> <li><a href="https://en.wikipedia.org/wiki/Modal_scope_fallacy">Necessity</a></li> <li><a href="https://en.wikipedia.org/wiki/Fallacy_of_four_terms">Four terms</a></li> <li><a href="https://en.wikipedia.org/wiki/Illicit_major">Illicit major</a></li> <li><a href="https://en.wikipedia.org/wiki/Illicit_minor">Illicit minor</a></li> <li><a href="https://en.wikipedia.org/wiki/Fallacy_of_the_undistributed_middle">Undistributed middle</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Informal_fallacy">Informal</a></th><td><table><tbody><tr><th>Equivocation</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Equivocation">Equivocation</a></li> <li><a href="https://en.wikipedia.org/wiki/False_equivalence">False equivalence</a></li> <li><a href="https://en.wikipedia.org/wiki/False_attribution">False attribution</a></li> <li><a href="https://en.wikipedia.org/wiki/Moral_equivalence">Moral equivalence</a></li> <li><a href="https://en.wikipedia.org/wiki/Conflation">Conflation</a></li> <li><a href="https://en.wikipedia.org/wiki/Quoting_out_of_context">Quoting out of context</a></li> <li><a href="https://en.wikipedia.org/wiki/Loki%27s_Wager">Loki&#39;s Wager</a></li> <li><a href="https://en.wikipedia.org/wiki/No_true_Scotsman">No true Scotsman</a></li> <li><a href="https://en.wikipedia.org/wiki/Semantic_argument">Semantic argument</a></li> <li><a href="https://en.wikipedia.org/wiki/Reification_(fallacy)">Reification</a> <ul><li><a href="https://en.wikipedia.org/wiki/Map%E2%80%93territory_relation">Map–territory relation</a></li></ul></li></ul> </div></td></tr><tr><th>Question-begging</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Circular_reasoning">Circular reasoning</a> / <a href="https://en.wikipedia.org/wiki/Begging_the_question">Begging the question</a></li> <li><a href="https://en.wikipedia.org/wiki/Loaded_language">Loaded language</a> <ul><li><a href="https://en.wikipedia.org/wiki/Leading_question">Leading question</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Double-barreled_question">Compound question</a> / <a href="https://en.wikipedia.org/wiki/Loaded_question">Loaded question</a> / <a href="https://en.wikipedia.org/wiki/Complex_question">Complex question</a></li> <li><a href="https://en.wikipedia.org/wiki/No_true_Scotsman">No true Scotsman</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Correlative-based_fallacies">Correlative-based</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/False_dilemma">False dilemma</a> <ul><li><a href="https://en.wikipedia.org/wiki/Nirvana_fallacy">Perfect solution</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Denying_the_correlative">Denying the correlative</a></li> <li><a href="https://en.wikipedia.org/wiki/Suppressed_correlative">Suppressed correlative</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Fallacies_of_illicit_transference">Illicit transference</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Fallacy_of_composition">Composition</a></li> <li><a href="https://en.wikipedia.org/wiki/Fallacy_of_division">Division</a></li> <li><a href="https://en.wikipedia.org/wiki/Ecological_fallacy">Ecological</a></li></ul> </div></td></tr><tr><th><i><a href="https://en.wikipedia.org/wiki/Secundum_quid">Secundum quid</a></i></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Accident_(fallacy)">Accident</a></li> <li><a href="https://en.wikipedia.org/wiki/Converse_accident">Converse accident</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Faulty_generalization">Faulty generalization</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Anecdotal_evidence">Anecdotal evidence</a></li> <li><a href="https://en.wikipedia.org/wiki/Sampling_bias">Sampling bias</a> <ul><li><a href="https://en.wikipedia.org/wiki/Cherry_picking">Cherry picking</a></li> <li><a href="https://en.wikipedia.org/wiki/McNamara_fallacy">McNamara</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Base_rate_fallacy">Base rate</a> / <a href="https://en.wikipedia.org/wiki/Conjunction_fallacy">Conjunction</a></li> <li><a href="https://en.wikipedia.org/wiki/Double_counting_(fallacy)">Double counting</a></li> <li><a href="https://en.wikipedia.org/wiki/Argument_from_analogy">False analogy</a></li> <li><a href="https://en.wikipedia.org/wiki/Slothful_induction">Slothful induction</a></li> <li><a href="https://en.wikipedia.org/wiki/Overwhelming_exception">Overwhelming exception</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Ambiguity">Ambiguity</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Fallacy_of_accent">Accent</a></li> <li><a href="https://en.wikipedia.org/wiki/False_precision">False precision</a></li> <li><a href="https://en.wikipedia.org/wiki/Moving_the_goalposts">Moving the goalposts</a></li> <li><a href="https://en.wikipedia.org/wiki/Quoting_out_of_context">Quoting out of context</a></li> <li><a href="https://en.wikipedia.org/wiki/Slippery_slope">Slippery slope</a></li> <li><a href="https://en.wikipedia.org/wiki/Sorites_paradox">Sorites paradox</a></li> <li><a href="https://en.wikipedia.org/wiki/Syntactic_ambiguity">Syntactic ambiguity</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Questionable_cause">Questionable cause</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Animistic_fallacy">Animistic</a> <ul><li><a href="https://en.wikipedia.org/wiki/Furtive_fallacy">Furtive</a></li></ul></li> <li>Correlation implies causation <ul><li><i><a href="https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation">Cum hoc</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Post_hoc_ergo_propter_hoc">Post hoc</a></i></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Gambler%27s_fallacy">Gambler&#39;s</a> <ul><li><a href="https://en.wikipedia.org/wiki/Inverse_gambler%27s_fallacy">Inverse</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Regression_fallacy">Regression</a></li> <li><a href="https://en.wikipedia.org/wiki/Fallacy_of_the_single_cause">Single cause</a></li> <li><a href="https://en.wikipedia.org/wiki/Slippery_slope">Slippery slope</a></li> <li><a href="https://en.wikipedia.org/wiki/Texas_sharpshooter_fallacy">Texas sharpshooter</a></li></ul> </div></td></tr><tr><th>Appeals</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Appeal_to_the_law">Law/Legality</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_the_stone">Stone</a> / <a href="https://en.wikipedia.org/wiki/Proof_by_assertion">Proof by assertion</a></li></ul> </div><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Appeal_to_consequences">Consequences</a></th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Argumentum_ad_baculum">Argumentum ad baculum</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Wishful_thinking">Wishful thinking</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Appeal_to_emotion">Emotion</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Think_of_the_children">Children</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_fear">Fear</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_flattery">Flattery</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_novelty">Novelty</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_pity">Pity</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_ridicule">Ridicule</a></li> <li><a href="https://en.wikipedia.org/wiki/In-group_favoritism">In-group favoritism</a></li> <li><a href="https://en.wikipedia.org/wiki/Invented_here">Invented here</a> / <a href="https://en.wikipedia.org/wiki/Not_invented_here">Not invented here</a></li> <li><a href="https://en.wikipedia.org/wiki/Island_mentality">Island mentality</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_loyalty">Loyalty</a></li> <li><a href="https://en.wikipedia.org/wiki/Parade_of_horribles">Parade of horribles</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_spite">Spite</a></li> <li><a href="https://en.wikipedia.org/wiki/Flag-waving">Stirring symbols</a></li> <li><a href="https://en.wikipedia.org/wiki/Wisdom_of_repugnance">Wisdom of repugnance</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Genetic_fallacy">Genetic fallacy</a></th><td><table><tbody><tr><th><i><a href="https://en.wikipedia.org/wiki/Ad_hominem">Ad hominem</a></i></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Appeal_to_motive">Appeal to motive</a></li> <li><a href="https://en.wikipedia.org/wiki/Association_fallacy">Association</a> <ul><li><i><a href="https://en.wikipedia.org/wiki/Reductio_ad_Hitlerum">Reductio ad Hitlerum</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Red-baiting">Reductio ad Stalinum</a></i></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Bulverism">Bulverism</a></li> <li><a href="https://en.wikipedia.org/wiki/Poisoning_the_well">Poisoning the well</a></li> <li><a href="https://en.wikipedia.org/wiki/Tone_policing">Tone</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Tu_quoque">Tu quoque</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Whataboutism">Whataboutism</a></li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Argument_from_authority">Authority</a> <ul><li><a href="https://en.wikipedia.org/wiki/Appeal_to_accomplishment">Accomplishment</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Ipse_dixit">Ipse dixit</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Argumentum_ad_lazarum">Poverty</a> / <a href="https://en.wikipedia.org/wiki/Argumentum_ad_crumenam">Wealth</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Etymological_fallacy">Etymology</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_nature">Nature</a></li> <li><a href="https://en.wikipedia.org/wiki/Appeal_to_tradition">Tradition</a> / <a href="https://en.wikipedia.org/wiki/Appeal_to_novelty">Novelty</a> <ul><li><a href="https://en.wikipedia.org/wiki/Chronological_snobbery">Chronological snobbery</a></li></ul></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Other <a href="https://en.wikipedia.org/wiki/Fallacy_of_relevance">fallacies<br/> of relevance</a></th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Argument">Arguments</a></th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Ad_nauseam">Ad nauseam</a></i> <ul><li><a href="https://en.wikipedia.org/wiki/Sealioning">Sealioning</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Argument_from_anecdote">Argument from anecdote</a></li> <li><a href="https://en.wikipedia.org/wiki/Argument_from_incredulity">Argument from incredulity</a></li> <li><a href="https://en.wikipedia.org/wiki/Argument_from_silence">Argument from silence</a></li> <li><a href="https://en.wikipedia.org/wiki/Argument_to_moderation">Argument to moderation</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Argumentum_ad_populum">Argumentum ad populum</a></i></li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Clich%C3%A9">Cliché</a></li> <li><i><a href="https://en.wikipedia.org/wiki/The_Four_Great_Errors">The Four Great Errors</a></i></li> <li><a href="https://en.wikipedia.org/wiki/I%27m_entitled_to_my_opinion">I&#39;m entitled to my opinion</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Irrelevant_conclusion">Ignoratio elenchi</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Invincible_ignorance_fallacy">Invincible ignorance</a></li> <li><a href="https://en.wikipedia.org/wiki/Moralistic_fallacy">Moralistic</a> / <a href="https://en.wikipedia.org/wiki/Naturalistic_fallacy">Naturalistic</a></li> <li><a href="https://en.wikipedia.org/wiki/Motte-and-bailey_fallacy">Motte-and-bailey fallacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychologist%27s_fallacy">Psychologist&#39;s fallacy</a></li> <li><a href="https://en.wikipedia.org/wiki/Rationalization_(psychology)">Rationalization</a></li> <li><a href="https://en.wikipedia.org/wiki/Red_herring">Red herring</a> <ul><li><a href="https://en.wikipedia.org/wiki/Two_wrongs_make_a_right">Two wrongs make a right</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Special_pleading">Special pleading</a></li> <li><a href="https://en.wikipedia.org/wiki/Straw_man">Straw man</a></li></ul> </div></td></tr></tbody></table></td></tr></tbody></table></td></tr><tr><td colspan="2"><div> <ul><li> <a href="https://en.wikipedia.org/wiki/Category:Fallacies">Category</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Unintended_consequences"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Unintended_consequences"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Unintended_consequences"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Unintended_consequences">Unintended consequences</a></div></th></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Abilene_paradox">Abilene paradox</a></li> <li><a href="https://en.wikipedia.org/wiki/Adverse_effect">Adverse effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Blowback_(intelligence)">Blowback (intelligence)</a></li> <li><a href="https://en.wikipedia.org/wiki/Braess%27s_paradox">Braess&#39;s paradox</a></li> <li><a href="https://en.wikipedia.org/wiki/Butterfly_effect">Butterfly effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Campbell%27s_law">Campbell&#39;s law</a></li> <li><a href="https://en.wikipedia.org/wiki/Cobra_effect">Cobra effect</a></li> <li><a href="https://en.wikipedia.org/wiki/CSI_effect">CSI effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Externality">Externality</a></li> <li><a href="https://en.wikipedia.org/wiki/Excess_burden_of_taxation">Excess burden of taxation</a></li> <li><a href="https://en.wikipedia.org/wiki/Four_Pests_campaign">Four Pests campaign</a></li> <li><a href="https://en.wikipedia.org/wiki/Goodhart%27s_law">Goodhart&#39;s law</a></li> <li><a href="https://en.wikipedia.org/wiki/Hawthorne_effect">Hawthorne effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Hutber%27s_law">Hutber&#39;s law</a></li> <li><a href="https://en.wikipedia.org/wiki/Hydra_effect">Hydra effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Inverse_consequences">Inverse consequences</a></li> <li><a href="https://en.wikipedia.org/wiki/Jevons_paradox">Jevons paradox</a></li> <li><a href="https://en.wikipedia.org/wiki/Murphy%27s_law">Murphy&#39;s law</a></li> <li><a href="https://en.wikipedia.org/wiki/Nocebo">Nocebo</a></li> <li><a href="https://en.wikipedia.org/wiki/Osborne_effect">Osborne effect</a></li> <li>Parable of the broken window</li> <li><a href="https://en.wikipedia.org/wiki/Paradox_of_enrichment">Paradox of enrichment</a></li> <li><a href="https://en.wikipedia.org/wiki/Parkinson%27s_law">Parkinson&#39;s law</a></li> <li><a href="https://en.wikipedia.org/wiki/Perverse_incentive">Perverse incentive</a></li> <li><a href="https://en.wikipedia.org/wiki/Rebound_effect_(conservation)">Rebound effect (conservation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Risk_compensation">Risk compensation</a></li> <li><a href="https://en.wikipedia.org/wiki/Self-defeating_prophecy">Self-defeating prophecy</a></li> <li><a href="https://en.wikipedia.org/wiki/Self-refuting_idea">Self-refuting idea</a></li> <li><a href="https://en.wikipedia.org/wiki/Serendipity">Serendipity</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_trap">Social trap</a></li> <li><a href="https://en.wikipedia.org/wiki/Streisand_effect">Streisand effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Tragedy_of_the_commons">Tragedy of the commons</a></li> <li><a href="https://en.wikipedia.org/wiki/Tyranny_of_small_decisions">Tyranny of small decisions</a></li></ul> </div></td></tr></tbody></table></div><p> </p> Anatidae - Wikipedia https://en.wikipedia.org/wiki/Anatidae 1FbsGiyPOxX-j8aB85T6W45DFOjjuV8JB166kw== Wed, 13 May 2026 11:17:00 +0000 Biological family of water birds <div>Biological family of water birds</div><p> </p><table> <tbody><tr> <th colspan="2">Anatidae<br/><div>Temporal range: <a href="https://en.wikipedia.org/wiki/Early_Oligocene">Early Oligocene</a> – recent<sup><span>[</span>1<span>]</span></sup></div> </th></tr> <tr> <td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:%D7%91%D7%A8%D7%95%D7%95%D7%96%D7%99%D7%99%D7%9D-01.jpg"></a></span> </td></tr> <tr> <td colspan="2">Clockwise from top left: <a href="https://en.wikipedia.org/wiki/Mallard">mallard</a>, <a href="https://en.wikipedia.org/wiki/Mute_swan">mute swan</a>, <a href="https://en.wikipedia.org/wiki/Brazilian_teal">Brazilian teal</a>, <a href="https://en.wikipedia.org/wiki/Paradise_shelduck">paradise shelduck</a>, <a href="https://en.wikipedia.org/wiki/Bufflehead">bufflehead</a>, and <a href="https://en.wikipedia.org/wiki/Domestic_goose">domestic goose</a> </td></tr> <tr> <th colspan="2"><a href="https://en.wikipedia.org/wiki/Taxonomy_(biology)">Scientific classification</a> <span><span><a href="https://en.wikipedia.org/wiki/Template:Taxonomy/Anatidae"></a></span></span> </th></tr> <tr> <td>Kingdom: </td> <td><a href="https://en.wikipedia.org/wiki/Animal">Animalia</a> </td></tr> <tr> <td>Phylum: </td> <td><a href="https://en.wikipedia.org/wiki/Chordate">Chordata</a> </td></tr> <tr> <td>Class: </td> <td><a href="https://en.wikipedia.org/wiki/Bird">Aves</a> </td></tr> <tr> <td>Order: </td> <td><a href="https://en.wikipedia.org/wiki/Anseriformes">Anseriformes</a> </td></tr> <tr> <td>Suborder: </td> <td><a href="https://en.wikipedia.org/wiki/Anseres">Anseres</a> </td></tr> <tr> <td>Superfamily: </td> <td><a href="https://en.wikipedia.org/wiki/Anatoidea">Anatoidea</a> </td></tr> <tr> <td>Family: </td> <td>Anatidae<br/><small><a href="https://en.wikipedia.org/wiki/William_Elford_Leach">Leach</a>, 1819</small> </td></tr> <tr> <th colspan="2"><a href="https://en.wikipedia.org/wiki/Type_genus">Type genus</a> </th></tr> <tr> <td colspan="2"><i><a href="https://en.wikipedia.org/wiki/Anas">Anas</a></i><br/><div><a href="https://en.wikipedia.org/wiki/Carl_Linnaeus">Linnaeus</a>, 1758</div> </td></tr> <tr> <th colspan="2"><a href="https://en.wikipedia.org/wiki/Genera">Genera</a> </th></tr> <tr> <td colspan="2"> <ul><li><b><a href="https://en.wikipedia.org/wiki/Dendrocygninae">Dendrocygninae</a></b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Dendrocygna">Dendrocygna</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Thalassornis">Thalassornis</a></i></li></ul></li> <li><b><a href="https://en.wikipedia.org/wiki/Stictonettinae">Stictonettinae</a></b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Stictonetta">Stictonetta</a></i></li></ul></li> <li><b><a href="https://en.wikipedia.org/wiki/Anatinae">Anatinae</a></b> <ul><li><b><a href="https://en.wikipedia.org/wiki/Oxyurini">Oxyurini</a></b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Heteronetta">Heteronetta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Nomonyx">Nomonyx</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Oxyura">Oxyura</a></i></li></ul></li> <li><b><a href="https://en.wikipedia.org/wiki/Mergini">Mergini</a></b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Goldeneye_(duck)">Bucephala</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Clangula">Clangula</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Histrionicus">Histrionicus</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Lophodytes">Lophodytes</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Melanitta">Melanitta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Mergellus">Mergellus</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Mergus">Mergus</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Polysticta">Polysticta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Somateria">Somateria</a></i></li></ul></li> <li><b><a href="https://en.wikipedia.org/wiki/Anatini">Anatini</a></b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Amazonetta">Amazonetta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Anas">Anas</a></i></li> <li><abbr>†</abbr><i><a href="https://en.wikipedia.org/wiki/Chelychelynechen">Chelychelynechen</a></i></li> <li><abbr>†</abbr><i><a href="https://en.wikipedia.org/wiki/Chendytes">Chendytes</a></i> (stem group)</li> <li><i><a href="https://en.wikipedia.org/wiki/Lophonetta">Lophonetta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Mareca">Mareca</a></i></li> <li><abbr>†</abbr><i><a href="https://en.wikipedia.org/wiki/Ptaiochen">Ptaiochen</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Sibirionetta">Sibirionetta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Spatula_(bird)">Spatula</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Speculanas">Speculanas</a></i></li> <li><abbr>†</abbr><i><a href="https://en.wikipedia.org/wiki/Thambetochen">Thambetochen</a></i></li></ul></li> <li><b>Possible members of Anatini</b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Aix_(bird)">Aix</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Asarcornis">Asarcornis</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Cairina">Cairina</a></i> (perhaps Tadorninae)</li> <li><i><a href="https://en.wikipedia.org/wiki/Callonetta">Callonetta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Chenonetta">Chenonetta</a></i> (perhaps Tadorninae)</li> <li><i><a href="https://en.wikipedia.org/wiki/Nettapus">Nettapus</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Pteronetta">Pteronetta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Rhodonessa">Rhodonessa</a></i></li></ul></li></ul></li> <li><b><a href="https://en.wikipedia.org/wiki/Tadorninae">Tadorninae</a></b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Alopochen">Alopochen</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Chloephaga">Chloephaga</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Hymenolaimus">Hymenolaimus</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Merganetta">Merganetta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Neochen">Neochen</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Radjah">Radjah</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Salvadorina">Salvadorina</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Tadorna">Tadorna</a></i></li></ul></li> <li><b>Possible members of Tadorninae</b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Biziura">Biziura</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Cyanochen">Cyanochen</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Malacorhynchus">Malacorhynchus</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Sarkidiornis">Sarkidiornis</a></i> (perhaps Anatinae)</li> <li><i><a href="https://en.wikipedia.org/wiki/Tachyeres">Tachyeres</a></i></li></ul></li> <li><b><a href="https://en.wikipedia.org/wiki/Plectropterinae">Plectropterinae</a></b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Plectropterus">Plectropterus</a></i></li></ul></li> <li><b><a href="https://en.wikipedia.org/wiki/Aythyinae">Aythyinae</a></b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Aythya">Aythya</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Marmaronetta">Marmaronetta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Netta">Netta</a></i></li></ul></li> <li><b><a href="https://en.wikipedia.org/wiki/Anserinae">Anserinae</a></b> <ul><li><i><a href="https://en.wikipedia.org/wiki/Anser_(bird)">Anser</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Branta">Branta</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Cereopsis">Cereopsis</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Coscoroba">Coscoroba</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Swan">Cygnus</a></i></li></ul></li></ul> </td></tr> </tbody></table><p>The <b>Anatidae</b> are the biological <a href="https://en.wikipedia.org/wiki/Family_(biology)">family</a> of <a href="https://en.wikipedia.org/wiki/Water_bird">water birds</a> that includes <a href="https://en.wikipedia.org/wiki/Duck">ducks</a>, <a href="https://en.wikipedia.org/wiki/Goose">geese</a>, and <a href="https://en.wikipedia.org/wiki/Swan">swans</a>. The family has a <a href="https://en.wikipedia.org/wiki/Cosmopolitan_distribution">cosmopolitan distribution</a>, occurring on all the world&#39;s continents except Antarctica. These <a href="https://en.wikipedia.org/wiki/Bird">birds</a> are adapted for <a href="https://en.wikipedia.org/wiki/Aquatic_locomotion">swimming</a>, floating on the water surface, and, in some cases, diving in at least shallow water. The family contains around 174 species in 43 <a href="https://en.wikipedia.org/wiki/Genus">genera</a> (the <a href="https://en.wikipedia.org/wiki/Magpie_goose">magpie goose</a> is no longer considered to be part of the Anatidae and is now placed in its own family, <a href="https://en.wikipedia.org/wiki/Anseranatidae">Anseranatidae</a>). </p><p>They are generally herbivorous and are <a href="https://en.wikipedia.org/wiki/Monogamy_in_animals">monogamous</a> breeders. A number of species undertake <a href="https://en.wikipedia.org/wiki/Bird_migration">annual migrations</a>. A few species have been domesticated for agriculture, and many others are hunted for food and recreation. Five species have become extinct since 1600, and many more are <a href="https://en.wikipedia.org/wiki/Threatened">threatened</a> with <a href="https://en.wikipedia.org/wiki/Extinction">extinction</a>. </p><figure><a href="https://en.wikipedia.org/wiki/File:Mallard_drake_in_flight.1.jpg"></a><figcaption>Landing mallard drake</figcaption></figure><div><h2>Description and ecology</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>The ducks, geese, and swans are small- to large-sized birds with a broad and elongated general body plan.<sup><span>[</span>2<span>]</span></sup> Diving species vary from this in being rounder. Extant species range in size from the <a href="https://en.wikipedia.org/wiki/Cotton_pygmy_goose">cotton pygmy goose</a>, at as little as 26.5 cm (10.5 in) and 164 g (5.8 oz), to the <a href="https://en.wikipedia.org/wiki/Trumpeter_swan">trumpeter swan</a>, at as much as 183 cm (6 ft) and 17.2 kg (38 lb). The largest anatid ever known is the extinct flightless <i><a href="https://en.wikipedia.org/wiki/Garganornis">Garganornis ballmanni</a></i> at 22 kg (49 lb). The wings are short and pointed, and supported by strong wing muscles that generate rapid beats in <a href="https://en.wikipedia.org/wiki/Bird_flight">flight</a>. They typically have long necks, although this varies in degree between species. The legs are short, strong, and set far to the back of the body (more so in the more aquatic species), and have a leathery feel with a scaly texture. Combined with their body shape, this can make some species awkward on land, but they are stronger walkers than other marine and water birds such as <a href="https://en.wikipedia.org/wiki/Grebe">grebes</a> or <a href="https://en.wikipedia.org/wiki/Petrel">petrels</a>. They typically have <a href="https://en.wikipedia.org/wiki/Webbed_feet">webbed feet</a>, though a few species such as the <a href="https://en.wikipedia.org/wiki/Nene_(bird)">Nene</a> have secondarily lost their webbing. The bills are made of soft keratin with a thin and sensitive layer of skin on top (which has a leathery feel when touched). For most species, the shape of the bill tends to be more flattened to a greater or lesser extent. These contain serrated <a href="https://en.wikipedia.org/wiki/Lamella_(zoology)">lamellae</a> which are particularly well defined in the filter-feeding species.<sup><span>[</span>2<span>]</span></sup> </p><p>Their feathers are excellent at shedding water due to special oils. Many of the ducks display <a href="https://en.wikipedia.org/wiki/Sexual_dimorphism">sexual dimorphism</a>, with the males being more brightly coloured than the females (although the situation is reversed in species such as the <a href="https://en.wikipedia.org/wiki/Paradise_shelduck">paradise shelduck</a>). The swans, geese, and whistling-ducks lack sexually dimorphic plumage. Anatids are vocal birds, producing a range of quacks, honks, squeaks, and trumpeting sounds, depending on species; the female often has a deeper voice than the male.<sup><span>[</span>3<span>]</span></sup> </p><p>Anatids are generally <a href="https://en.wikipedia.org/wiki/Herbivore">herbivorous</a> as adults, feeding on various water-plants, although some species also eat fish, molluscs, or aquatic arthropods. One group, the <a href="https://en.wikipedia.org/wiki/Merganser">mergansers</a>, are primarily <a href="https://en.wikipedia.org/wiki/Piscivore">piscivorous</a>, and have serrated bills to help them catch fish. In a number of species, the young include a high proportion of invertebrates in their diets, but become purely herbivorous as adults.<sup><span>[</span>3<span>]</span></sup> </p><div><h2>Breeding</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>The anatids are generally seasonal and <a href="https://en.wikipedia.org/wiki/Monogamy_in_animals">monogamous</a> breeders. The level of monogamy varies within the family; many of the smaller ducks only maintain the bond for a single season and find a new partner the following year, whereas the larger swans, geese and some of the more territorial ducks maintain pair bonds over a number of years, and even for life in some species. However, forced <a href="https://en.wikipedia.org/wiki/Extrapair_copulation">extrapair copulation</a> among anatids is common, occurring in 55 species in 17 genera.<sup><span>[</span>4<span>]</span></sup> </p><p>Anatidae is a large proportion of the 3% of bird species to possess a <a href="https://en.wikipedia.org/wiki/Penis#Birds">penis</a>,<sup><span>[</span>5<span>]</span></sup><sup><span>[</span>6<span>]</span></sup> though they vary significantly in size, shape, and surface elaboration.<sup><span>[</span>7<span>]</span></sup> Most species are adapted for <a href="https://en.wikipedia.org/wiki/Copulation_(zoology)">copulation</a> on the water only. They construct simple nests from whatever material is close at hand, often lining them with a layer of down plucked from the mother&#39;s breast. In most species, only the female <a href="https://en.wikipedia.org/wiki/Avian_incubation">incubates</a> the eggs. The young are <a href="https://en.wikipedia.org/wiki/Precocial">precocial</a>, and are able to feed themselves from birth.<sup><span>[</span>3<span>]</span></sup> One aberrant species, the <a href="https://en.wikipedia.org/wiki/Black-headed_duck">black-headed duck</a>, is an obligate <a href="https://en.wikipedia.org/wiki/Brood_parasite">brood parasite</a>, laying its eggs in the nests of <a href="https://en.wikipedia.org/wiki/Gull">gulls</a> and <a href="https://en.wikipedia.org/wiki/Coot">coots</a>. While this species never raises its own young, a number of other ducks occasionally lay eggs in the nests of conspecifics (members of the same species) in addition to raising their own broods. </p><div><h2>Relationship with humans</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Duck, eider, and goose feathers and down have long been popular for bedspreads, pillows, sleeping bags, and coats. The members of this family also have long been used for food. </p><p>Humans have had a long relationship with ducks, geese, and swans; they are important economically and culturally to humans, and several duck species have benefited from an association with people. However, some anatids are <a href="https://en.wikipedia.org/wiki/Agriculture">agricultural</a> <a href="https://en.wikipedia.org/wiki/Pest_(organism)">pests</a>, and have acted as vectors for <a href="https://en.wikipedia.org/wiki/Zoonosis">zoonoses</a> such as <a href="https://en.wikipedia.org/wiki/Avian_influenza">avian influenza</a>. </p><p>Since 1600, five species of ducks have become <a href="https://en.wikipedia.org/wiki/Extinct">extinct</a> due to the activities of humans,<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> and subfossil remains have shown that humans caused numerous extinctions in prehistory. Today, many more are considered <a href="https://en.wikipedia.org/wiki/Threatened">threatened</a>. Most of the historic and prehistoric extinctions were insular species, vulnerable due to small populations (often <a href="https://en.wikipedia.org/wiki/Endemism">endemic</a> to a single island), and <a href="https://en.wikipedia.org/wiki/Island_tameness">island tameness</a>. Evolving on islands that lacked predators, these species lost antipredator behaviours, as well as the ability to fly, and were vulnerable to human hunting pressure and <a href="https://en.wikipedia.org/wiki/Introduced_species">introduced species</a>. Other extinctions and declines are attributable to overhunting, <a href="https://en.wikipedia.org/wiki/Habitat_loss">habitat loss</a> and modification, and hybridisation with introduced ducks (for example the introduced <a href="https://en.wikipedia.org/wiki/Ruddy_duck">ruddy duck</a> swamping the <a href="https://en.wikipedia.org/wiki/White-headed_duck">white-headed duck</a> in Europe). Numerous governments and conservation and hunting organisations have made considerable progress in protecting ducks and duck populations through habitat protection and creation, laws and protection, and captive-breeding programmes. </p><div><h2>Systematics</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:1996._Stamp_of_Belarus_0169-0184.jpg"></a><figcaption>Anatidae: <a href="https://en.wikipedia.org/wiki/Eurasian_teal">Eurasian teal</a> (<i>Anas crecca</i>), <a href="https://en.wikipedia.org/wiki/Gadwall">gadwall</a> (<i>Anas strepera</i>), <a href="https://en.wikipedia.org/wiki/Northern_pintail">northern pintail</a> (<i>Anas acuta</i>), <a href="https://en.wikipedia.org/wiki/Mallard">mallard</a> (<i>Anas platyrhynchos</i>), <a href="https://en.wikipedia.org/wiki/Greater_scaup">greater scaup</a> (<i>Aythya marila</i>), <a href="https://en.wikipedia.org/wiki/Long-tailed_duck">long-tailed duck</a> (<i>Clangula hyemalis</i>), <a href="https://en.wikipedia.org/wiki/Northern_shoveler">northern shoveler</a> (<i>Anas clypeata</i>), <a href="https://en.wikipedia.org/wiki/Garganey">garganey</a> (<i>Anas querquedula</i>), <a href="https://en.wikipedia.org/wiki/Eurasian_wigeon">Eurasian wigeon</a> (<i>Anas penelope</i>), <a href="https://en.wikipedia.org/wiki/Ferruginous_duck">ferruginous duck</a> (<i>Aythya nyroca</i>), <a href="https://en.wikipedia.org/wiki/Common_goldeneye">common goldeneye</a> (<i>Bucephala clangula</i>), <a href="https://en.wikipedia.org/wiki/Common_merganser">common merganser</a> (<i>Mergus merganser</i>), <a href="https://en.wikipedia.org/wiki/Smew">smew</a> (<i>Mergellus albellus</i>), <a href="https://en.wikipedia.org/wiki/Tufted_duck">tufted duck</a> (<i>Aythya fuligula</i>), <a href="https://en.wikipedia.org/wiki/Red-breasted_merganser">red-breasted merganser</a> (<i>Mergus serrator</i>), <a href="https://en.wikipedia.org/wiki/Common_pochard">common pochard</a> (<i>Aythya ferina</i>). Post of Belarus, 1996.</figcaption></figure><div><h3>History of classification</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>The name Anatidae for the <a href="https://en.wikipedia.org/wiki/Family_(biology)">family</a> was introduced by the English zoologist <a href="https://en.wikipedia.org/wiki/William_Elford_Leach">William Elford Leach</a> in a guide to the contents of the <a href="https://en.wikipedia.org/wiki/British_Museum">British Museum</a> published in 1819.<sup><span>[</span>8<span>]</span></sup><sup><span>[</span>9<span>]</span></sup> While the status of the Anatidae as a family is straightforward, and which species properly belong to it is little debated, the relationships of the different tribes and subfamilies within it are poorly understood. The listing in the box at right should be regarded as simply one of several possible ways of organising the many species within the Anatidae; see discussion in the next section. </p><p>The systematics of the Anatidae are in a state of flux. Previously divided into six subfamilies,<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> a study of anatomical characters by Livezey<sup><span>[</span>10<span>]</span></sup> suggests the Anatidae are better treated in nine subfamilies.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Please_clarify"><span>clarification needed</span></a></i>]</sup> This classification was popular in the late 1980s to 1990s.<sup><span>[</span>11<span>]</span></sup> But <a href="https://en.wikipedia.org/wiki/MtDNA">mtDNA</a> <a href="https://en.wikipedia.org/wiki/DNA_sequence">sequence</a> analyses<sup><span>[</span>12<span>]</span></sup><sup><span>[</span>13<span>]</span></sup> indicate, for example, the dabbling and diving ducks do not belong in the same subfamily. </p><p>While shortcomings certainly occur in Livezey&#39;s analysis,<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> mtDNA is an unreliable source for phylogenetic information in many waterfowl (especially dabbling ducks) due to their ability to produce fertile <a href="https://en.wikipedia.org/wiki/Hybrid_(biology)">hybrids</a>,<sup><span>[</span>2<span>]</span></sup> in rare cases possibly even beyond the level of genus (see for example the &quot;<a href="https://en.wikipedia.org/wiki/Domestic_Muscovy_duck">Barbary duck</a>&quot;). Because the <a href="https://en.wikipedia.org/wiki/Sample_size">sample size</a> of many molecular studies available to date is small, mtDNA results must be considered with caution. </p><p>While a comprehensive review of the Anatidae which unites all evidence into a robust <a href="https://en.wikipedia.org/wiki/Phylogeny">phylogeny</a> is still lacking, the reasons for the confusing data are at least clear: As demonstrated by the <a href="https://en.wikipedia.org/wiki/Late_Cretaceous">Late Cretaceous</a> <a href="https://en.wikipedia.org/wiki/Fossil">fossil</a> <i><a href="https://en.wikipedia.org/wiki/Vegavis_iaai">Vegavis iaai</a></i>—an early modern waterbird which belonged to an extinct lineage—the Anatidae are an ancient group among the modern birds. Their earliest direct ancestors, though not documented by fossils yet, likewise can be assumed<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> to have been contemporaries with the non-avian <a href="https://en.wikipedia.org/wiki/Dinosaur">dinosaurs</a>. The long period of <a href="https://en.wikipedia.org/wiki/Evolution">evolution</a> and shifts from one kind of waterbird lifestyle to another have obscured many <a href="https://en.wikipedia.org/wiki/Plesiomorph">plesiomorphies</a>, while apparent <a href="https://en.wikipedia.org/wiki/Apomorph">apomorphies</a> are quite often the result of <a href="https://en.wikipedia.org/wiki/Parallel_evolution">parallel evolution</a>, for example the &quot;non-diving duck&quot; type displayed by such unrelated genera as <i><a href="https://en.wikipedia.org/wiki/Dendrocygna">Dendrocygna</a></i>, <i><a href="https://en.wikipedia.org/wiki/Amazonetta">Amazonetta</a></i>, and <i><a href="https://en.wikipedia.org/wiki/Cairina">Cairina</a></i>. For the fossil record, see below. </p><p>Alternatively,<sup><span>[</span>14<span>]</span></sup> the Anatidae may be considered to consist of three subfamilies (ducks, geese, and swans, essentially) which contain the groups as presented here as <a href="https://en.wikipedia.org/wiki/Tribe_(biology)">tribes</a>, with the swans separated as subfamily <a href="https://en.wikipedia.org/wiki/Cygninae">Cygninae</a>, the goose subfamily Anserinae also containing the whistling ducks, and the Anatinae containing all other <a href="https://en.wikipedia.org/wiki/Clades">clades</a>. </p><div><h2>Genera</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>For the living and recently extinct members of each genus, see the article <a href="https://en.wikipedia.org/wiki/List_of_Anatidae_species">List of Anatidae species</a>. </p><ul><li><b>Subfamily: Dendrocygninae</b> (one pantropical genus, of distinctive long-legged goose-like birds) <ul><li><i><a href="https://en.wikipedia.org/wiki/Dendrocygna">Dendrocygna</a></i>, whistling ducks (8 living species)</li> <li><i><a href="https://en.wikipedia.org/wiki/Thalassornis">Thalassornis</a></i>, <a href="https://en.wikipedia.org/wiki/White-backed_duck">white-backed duck</a> <figure><a href="https://en.wikipedia.org/wiki/File:Mute_swan_flies_arp.jpg"></a><figcaption><a href="https://en.wikipedia.org/wiki/Mute_swan">Mute swan</a></figcaption></figure></li></ul></li> <li><b>Subfamily: <a href="https://en.wikipedia.org/wiki/Anserinae">Anserinae</a></b>, swans and geese (3–7 extant genera with 25–30 living species, mainly cool temperate Northern Hemisphere, but also some Southern Hemisphere species, with the <a href="https://en.wikipedia.org/wiki/Swan">swans</a> in one genus [two genera in some treatments], and the <a href="https://en.wikipedia.org/wiki/Goose">geese</a> in three genera [two genera in some treatments]. Some other species are sometimes placed herein, but seem somewhat more distinct [see below]) <ul><li><i><a href="https://en.wikipedia.org/wiki/Swan">Cygnus</a></i>, true swans (6 species, 4 sometimes separated in <i>Olor</i>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Anser_(bird)">Anser</a></i>, grey geese and white geese (11 species)</li> <li><i><a href="https://en.wikipedia.org/wiki/Branta">Branta</a></i>, black geese (6 living species)</li></ul></li> <li><b>Subfamily: Stictonettinae</b> (one genus in Australia, formerly included in the Oxyurinae, but with anatomy suggesting a distinct ancient lineage perhaps closest to the Anserinae, especially the <a href="https://en.wikipedia.org/wiki/Cape_Barren_goose">Cape Barren goose</a>) <ul><li><i><a href="https://en.wikipedia.org/wiki/Stictonetta">Stictonetta</a></i>, <a href="https://en.wikipedia.org/wiki/Freckled_duck">freckled duck</a></li></ul></li> <li><b>Subfamily: Plectropterinae</b> (one genus in Africa, formerly included in the &quot;perching ducks&quot;, but closer to the Tadorninae) <ul><li><i><a href="https://en.wikipedia.org/wiki/Plectropterus">Plectropterus</a></i>, <a href="https://en.wikipedia.org/wiki/Spur-winged_goose">spur-winged goose</a></li></ul></li> <li><b>Subfamily: <a href="https://en.wikipedia.org/wiki/Tadorninae">Tadorninae</a></b> – shelducks and sheldgeese<figure><a href="https://en.wikipedia.org/wiki/File:Common.shelduck.2.arp.750pix.jpg"></a><figcaption>Male <a href="https://en.wikipedia.org/wiki/Common_shelduck">common shelduck</a></figcaption></figure> (This group of larger, often semiterrestrial waterfowl can be seen as intermediate between Anserinae and Anatinae. The 1986 revision<sup><span>[</span>10<span>]</span></sup> has resulted in the inclusion of 10 extant genera with about two-dozen living species [one probably extinct] in this subfamily, mostly from the Southern Hemisphere but a few in the Northern Hemisphere; the affiliations of several presumed tadornine genera has later been questioned<sup><span>[</span>13<span>]</span></sup> and the group in the traditional lineup is likely to be <a href="https://en.wikipedia.org/wiki/Paraphyletic">paraphyletic</a>.) <ul><li><i><a href="https://en.wikipedia.org/wiki/Tadorna">Tadorna</a></i>, shelducks (6 species, 1 probably <a href="https://en.wikipedia.org/wiki/Extinct">extinct</a>) – possibly paraphyletic</li> <li><i><a href="https://en.wikipedia.org/wiki/Radjah">Radjah</a></i>, Radjah shelduck</li> <li><i><a href="https://en.wikipedia.org/wiki/Salvadorina">Salvadorina</a></i>, Salvadori&#39;s teal</li> <li><i><a href="https://en.wikipedia.org/wiki/Centrornis">Centrornis</a></i>, Madagascar sheldgoose (<a href="https://en.wikipedia.org/wiki/Late_Quaternary_prehistoric_birds">prehistoric</a>, tentatively placed here)</li> <li><i><a href="https://en.wikipedia.org/wiki/Alopochen">Alopochen</a></i>, Egyptian goose and Mascarene shelducks (1 living species, 2 <a href="https://en.wikipedia.org/wiki/Extinct">extinct</a>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Neochen">Neochen</a></i>, (2 species)</li> <li><i><a href="https://en.wikipedia.org/wiki/Chloephaga">Chloephaga</a></i>, sheldgeese (4 species)</li> <li><i><a href="https://en.wikipedia.org/wiki/Hymenolaimus">Hymenolaimus</a></i>, blue duck</li> <li><i><a href="https://en.wikipedia.org/wiki/Merganetta">Merganetta</a></i>, torrent duck</li></ul></li></ul><figure><a href="https://en.wikipedia.org/wiki/File:Male_mallard_duck_2.jpg"></a><figcaption>A male <a href="https://en.wikipedia.org/wiki/Mallard">mallard</a> duck</figcaption></figure><ul><li><b>Subfamily: <a href="https://en.wikipedia.org/wiki/Aythyinae">Aythyinae</a></b>, diving ducks (Some 15 species of <a href="https://en.wikipedia.org/wiki/Diving_duck">diving ducks</a>, of worldwide distribution, in two to four genera; The 1986 morphological analysis<sup><span>[</span>10<span>]</span></sup> suggested the probably extinct <a href="https://en.wikipedia.org/wiki/Pink-headed_duck">pink-headed duck</a> of India, previously treated separately in <i>Rhodonessa</i>, should be placed in <i>Netta</i>, but this has been questioned.<sup><span>[</span>15<span>]</span></sup> Furthermore, while morphologically close to dabbling ducks, the mtDNA data indicate a treatment as distinct subfamily is indeed correct, with the Tadorninae being actually closer to dabbling ducks than the diving ducks<sup><span>[</span>13<span>]</span></sup>) <ul><li><i><a href="https://en.wikipedia.org/wiki/Netta">Netta</a></i>, red-crested pochard and allies (4 species, 1 probably <a href="https://en.wikipedia.org/wiki/Extinct">extinct</a>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Aythya">Aythya</a></i>, pochards, scaups, etc. (12 species)</li></ul></li> <li><b>Subfamily: <a href="https://en.wikipedia.org/wiki/Anatinae">Anatinae</a></b>, dabbling ducks and moa-nalos (The <a href="https://en.wikipedia.org/wiki/Dabbling_duck">dabbling duck</a> group, of worldwide distribution, were previously restricted to just one or two genera, but had been extended<sup><span>[</span>10<span>]</span></sup> to include eight extant genera and about 55 living species, including several genera formerly known as the &quot;perching ducks&quot;; mtDNA on the other hand confirms that the genus <i>Anas</i> is over-lumped and casts doubt on the diving duck affiliations of several genera [see below]. The <a href="https://en.wikipedia.org/wiki/Moa-nalo">moa-nalos</a>, of which four species in three genera are known to date, are a peculiar group of flightless, extinct anatids from the <a href="https://en.wikipedia.org/wiki/Hawaiian_Islands">Hawaiian Islands</a>. Gigantic in size and with massive bills, they were believed to be geese, but have been shown to be actually very closely related to <a href="https://en.wikipedia.org/wiki/Mallard">mallards</a>. They evolved filling the <a href="https://en.wikipedia.org/wiki/Ecological_niche">ecological niche</a> of <a href="https://en.wikipedia.org/wiki/Turtles">turtles</a>, <a href="https://en.wikipedia.org/wiki/Ungulates">ungulates</a>, and other <a href="https://en.wikipedia.org/wiki/Megaherbivore">megaherbivores</a>. <figure><a href="https://en.wikipedia.org/wiki/File:Kanadagans_(Branta_canadensis)-20190424-RM-155436.jpg"></a><figcaption>A <a href="https://en.wikipedia.org/wiki/Canada_goose">Canada goose</a> tucking its bill under its wing</figcaption></figure> <ul><li><i><a href="https://en.wikipedia.org/wiki/Anas">Anas</a></i>: pintails, mallards, etc. (40–50 living species, 3 <a href="https://en.wikipedia.org/wiki/Extinct">extinct</a>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Chendytes">Chendytes</a></i>, diving-geese (extinct c. 450–250 BCE, A basal member of the dabbling duck clade<sup><span>[</span>16<span>]</span></sup>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Spatula_(bird)">Spatula</a></i>, shovelers</li> <li><i><a href="https://en.wikipedia.org/wiki/Mareca">Mareca</a></i>, wigeons and gadwalls</li> <li><i><a href="https://en.wikipedia.org/wiki/Lophonetta">Lophonetta</a></i>, crested duck</li> <li><i><a href="https://en.wikipedia.org/wiki/Speculanas">Speculanas</a></i>, bronze-winged duck</li> <li><i><a href="https://en.wikipedia.org/wiki/Amazonetta">Amazonetta</a></i>, Brazilian teal</li> <li><i><a href="https://en.wikipedia.org/wiki/Sibirionetta">Sibirionetta</a></i>, Baikal teal</li> <li><i><a href="https://en.wikipedia.org/wiki/Chelychelynechen">Chelychelynechen</a></i>, turtle-jawed moa-nalo (<a href="https://en.wikipedia.org/wiki/Late_Quaternary_prehistoric_birds">prehistoric</a>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Thambetochen">Thambetochen</a></i>, large-billed moa-nalos (2 species, <a href="https://en.wikipedia.org/wiki/Late_Quaternary_prehistoric_birds">prehistoric</a>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Ptaiochen">Ptaiochen</a></i>, small-billed moa-nalo (<a href="https://en.wikipedia.org/wiki/Late_Quaternary_prehistoric_birds">prehistoric</a>)</li></ul></li> <li><b>Tribe: <a href="https://en.wikipedia.org/wiki/Mergini">Mergini</a></b>, eiders, scoters, sawbills and other sea-ducks <figure><a href="https://en.wikipedia.org/wiki/File:Bucephala_clangula_ja_01.jpg"></a><figcaption><a href="https://en.wikipedia.org/wiki/Common_goldeneye">Common goldeneye</a> couple, male on the right</figcaption></figure> (There are 9 extant genera and some 20 living species; most of this group occur in the Northern Hemisphere, but a few [mostly extinct] mergansers in the Southern Hemisphere) <ul><li><i><a href="https://en.wikipedia.org/wiki/Shiriyanetta">Shiriyanetta</a></i> (<a href="https://en.wikipedia.org/wiki/Late_Quaternary_prehistoric_birds">prehistoric</a>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Polysticta">Polysticta</a></i>, Steller&#39;s eider</li> <li><i><a href="https://en.wikipedia.org/wiki/Somateria">Somateria</a></i>, eiders (3 species)</li> <li><i><a href="https://en.wikipedia.org/wiki/Histrionicus">Histrionicus</a></i>, harlequin duck (includes <i>Ocyplonessa</i>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Camptorhynchus">Camptorhynchus</a></i>, Labrador duck (<a href="https://en.wikipedia.org/wiki/Extinct">extinct</a>)</li> <li><i><a href="https://en.wikipedia.org/wiki/Melanitta">Melanitta</a></i>, scoters (6 species)</li> <li><i><a href="https://en.wikipedia.org/wiki/Clangula">Clangula</a></i>, long-tailed duck (1 species)</li> <li><i><a href="https://en.wikipedia.org/wiki/Goldeneye_(duck)">Bucephala</a></i>, goldeneyes (3 species)</li> <li><i><a href="https://en.wikipedia.org/wiki/Mergellus">Mergellus</a></i>, smew</li> <li><i><a href="https://en.wikipedia.org/wiki/Lophodytes">Lophodytes</a></i>, hooded merganser</li> <li><i><a href="https://en.wikipedia.org/wiki/Mergus">Mergus</a></i>, mergansers (4 living species, 1 <a href="https://en.wikipedia.org/wiki/Extinct">extinct</a>).</li></ul></li> <li><b>Tribe: <a href="https://en.wikipedia.org/wiki/Oxyurini">Oxyurini</a></b>, stiff-tail ducks (a small group of 3–4 genera, 2–3 of them monotypic, with 7–8 living species) <ul><li><i><a href="https://en.wikipedia.org/wiki/Oxyura">Oxyura</a></i>, stiff-tailed ducks (5 living species)</li> <li><i><a href="https://en.wikipedia.org/wiki/Nomonyx">Nomonyx</a></i>, masked duck</li> <li><i><a href="https://en.wikipedia.org/wiki/Heteronetta">Heteronetta</a></i>, black-headed duck</li></ul></li> <li><b>Unresolved</b>: The largest degree of uncertainty concerns whether a number of genera are closer to the shelducks or to the dabbling ducks.<figure><a href="https://en.wikipedia.org/wiki/File:White-winged.wood.duck.arp.jpg"></a><figcaption>The rare <a href="https://en.wikipedia.org/wiki/White-winged_duck">white-winged duck</a>, a species of unclear affiliation</figcaption></figure> <figure><a href="https://en.wikipedia.org/wiki/File:Wood.duck.arp.jpg"></a><figcaption><a href="https://en.wikipedia.org/wiki/Wood_duck">Wood duck</a> <i>Aix sponsa</i></figcaption></figure> See also the <a href="https://en.wikipedia.org/wiki/Monotypic">monotypic</a> subfamilies above, and the &quot;<a href="https://en.wikipedia.org/wiki/Perching_duck">perching ducks</a>&quot; <ul><li><i><a href="https://en.wikipedia.org/wiki/Coscoroba">Coscoroba</a></i>, coscoroba swan – Anserinae or same subfamily as <i>Cereopsis</i>?</li> <li><i><a href="https://en.wikipedia.org/wiki/Cereopsis">Cereopsis</a></i>, Cape Barren goose – Anserinae, Tadorninae, or own subfamily?</li> <li><i><a href="https://en.wikipedia.org/wiki/Biziura">Biziura</a></i>, musk ducks (1 living species) - Oxyurini?</li> <li><i><a href="https://en.wikipedia.org/wiki/Cnemiornis">Cnemiornis</a></i>, New Zealand geese (<a href="https://en.wikipedia.org/wiki/Late_Quaternary_prehistoric_birds">prehistoric</a>) – as <i>Cereopsis</i></li> <li><i><a href="https://en.wikipedia.org/wiki/Malacorhynchus">Malacorhynchus</a></i>, pink-eared ducks (1 living species) – Tadorninae, Oxyurinae or Dendrocheninae?</li> <li><i><a href="https://en.wikipedia.org/wiki/Sarkidiornis">Sarkidiornis</a></i>, comb duck – Tadorninae or closer to dabbling ducks?</li> <li><i><a href="https://en.wikipedia.org/wiki/Tachyeres">Tachyeres</a></i>, steamer ducks (4 species) – Tadorninae or closer to dabbling ducks?</li> <li><i><a href="https://en.wikipedia.org/wiki/Cyanochen">Cyanochen</a></i>, blue-winged goose – Tadorninae or more distant clade?</li> <li><i><a href="https://en.wikipedia.org/wiki/Nettapus">Nettapus</a></i>, pygmy geese (3 species) – Anatinae or part of Southern Hemisphere radiation?</li> <li><i><a href="https://en.wikipedia.org/wiki/Pteronetta">Pteronetta</a></i>, Hartlaub&#39;s duck – traditionally dabbling ducks, but may be closer to <i>Cyanochen</i></li> <li><i><a href="https://en.wikipedia.org/wiki/Cairina">Cairina</a></i> and <i><a href="https://en.wikipedia.org/wiki/Asarcornis">Asarcornis</a></i>, Muscovy duck and white-winged duck, respectively (2 species) – traditionally dabbling ducks, but may be paraphyletic, with one species in Tadorninae and the other closer to diving ducks</li> <li><i><a href="https://en.wikipedia.org/wiki/Aix_(bird)">Aix</a></i>, Mandarin duck and wood duck (2 species) – dabbling ducks or Tadorninae?</li> <li><i><a href="https://en.wikipedia.org/wiki/Callonetta">Callonetta</a></i>, ringed teal – dabbling ducks or Tadorninae?</li> <li><i><a href="https://en.wikipedia.org/wiki/Chenonetta">Chenonetta</a></i>, maned duck (1 living species) – dabbling ducks or Tadorninae? Includes <i>Euryanas</i>.</li> <li><i><a href="https://en.wikipedia.org/wiki/Marmaronetta">Marmaronetta</a></i>, marbled duck – formerly dabbling ducks; actually a diving duck or a distinct subfamily</li></ul></li></ul><div><h3>Prehistoric species</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Chenonetta_jubata_female_2.jpg"></a><figcaption><a href="https://en.wikipedia.org/wiki/Maned_duck">Maned duck</a> is the only living member of the genus <i>Chenonetta.</i></figcaption></figure><p>From <a href="https://en.wikipedia.org/wiki/Subfossil">subfossil</a> bones found on <a href="https://en.wikipedia.org/wiki/Kauai">Kauaʻi</a> (<a href="https://en.wikipedia.org/wiki/Hawaiian_Islands">Hawaiian Islands</a>), two enigmatic waterfowl are known.<sup><span>[</span>17<span>]</span></sup> The living and assignable prehistoric avifauna of the <a href="https://en.wikipedia.org/wiki/Archipelago">archipelago</a> contains as Anseriformes <i>Branta</i> geese and their descendants, and the <a href="https://en.wikipedia.org/wiki/Moa-nalo">moa-nalos</a> as mentioned above. The following taxa, although certainly new species, cannot be assigned even to subfamily; that Kauaʻi is the oldest of the large Hawaiian Islands, meaning the species may have been evolving in isolation for nearly 10 <a href="https://en.wikipedia.org/wiki/Mya_(unit)">mya</a> (since the Late <a href="https://en.wikipedia.org/wiki/Miocene">Miocene</a>), does not help in determining their affinities: </p><ul><li>Long-legged &quot;shelduck&quot;, Anatidae sp. et gen. indet.</li> <li><a href="https://en.wikipedia.org/wiki/Kaua%27i_mole_duck">Kaua&#39;i mole duck</a>, <i>Talpanas lippa</i></li></ul><p>Similarly, <i><a href="https://en.wikipedia.org/wiki/Branta_rhuax">Branta rhuax</a></i> from the Big Island of <a href="https://en.wikipedia.org/wiki/Hawaii_(island)">Hawaiʻi</a>, and a gigantic goose-like anatid from <a href="https://en.wikipedia.org/wiki/Oahu">Oʻahu</a> are known only from very incomplete, and in the former case much damaged, bone fragments. The former has been alleged to be a shelduck,<sup><span>[</span>18<span>]</span></sup> but this was generally dismissed because of the damage to the material and <a href="https://en.wikipedia.org/wiki/Biogeography">biogeographic</a> considerations. The long-legged Kauaʻi bird, however, hints at the possibility of a former tadornine presence on the archipelago. </p><div><h3>Fossil Anatidae</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>The fossil record of anatids is extensive, but many prehistoric genera cannot be unequivocally assigned to present-day subfamilies for the reasons given above. For prehistoric species of extant genera, see the respective genus accounts. </p><p>Dendrocheninae – a more advanced relative of the whistling-ducks or an ancestral relative of stifftail ducks paralleling whistling-ducks; if not extinct possibly belong in Oxyurinae (including <i><a href="https://en.wikipedia.org/wiki/Malacorhynchus">Malacorhynchus</a></i>) </p><ul><li><i><a href="https://en.wikipedia.org/wiki/Mionetta">Mionetta</a></i> (Late Oligocene – Middle Miocene of Central Europe and Kazakhstan) – includes <i>&quot;Anas&quot; blanchardi</i>, <i>&quot;A.&quot; consobrina</i>, <i>&quot;A.&quot; natator</i>, <i>&quot;Aythya&quot; arvernensis</i></li> <li><i><a href="https://en.wikipedia.org/wiki/Manuherikia_(bird)">Manuherikia</a></i> (Bathans Early/Middle Miocene of Otago, New Zealand)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Dendrochen&amp;action=edit&amp;redlink=1">Dendrochen</a></i> (Early – Late? Miocene) – includes <i>&quot;Anas&quot; integra</i>, <i>&quot;A.&quot; oligocaena</i></li> <li>Dendrocheninae gen. et sp. indet. (Late Miocene of Argentina)</li></ul><figure><a href="https://en.wikipedia.org/wiki/File:Black_Swan_skeleton.jpg"></a><figcaption>Black swan (<a href="https://en.wikipedia.org/wiki/Black_swan"><i>Cygnus atratus</i></a>) skeleton on display at the <a href="https://en.wikipedia.org/wiki/Museum_of_Osteology">Museum of Osteology</a></figcaption></figure><p><a href="https://en.wikipedia.org/wiki/Anserinae">Anserinae</a> </p><ul><li><i><a href="https://en.wikipedia.org/w/index.php?title=Cygnavus&amp;action=edit&amp;redlink=1">Cygnavus</a></i> (Early Miocene of Germany)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Cygnopterus&amp;action=edit&amp;redlink=1">Cygnopterus</a></i> (Middle Oligocene of Belgium – Early Miocene of France) – sometimes included in <i>Cygnavus</i></li> <li><i><a href="https://en.wikipedia.org/wiki/Megalodytes">Megalodytes</a></i> (Middle Miocene of California, US)</li> <li>&quot;cf. <i>Megalodytes&quot;</i> (Haraichi Middle Miocene of <a href="https://en.wikipedia.org/wiki/Annaka">Annaka</a>, Japan)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Anserobranta&amp;action=edit&amp;redlink=1">Anserobranta</a></i> (Late Miocene of C Europe) – includes <i>&quot;Anas&quot; robusta</i>, validity doubtful</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Presbychen&amp;action=edit&amp;redlink=1">Presbychen</a></i> (Temblor Late Miocene of Sharktooth Hill, US)</li> <li><i><a href="https://en.wikipedia.org/wiki/Afrocygnus">Afrocygnus</a></i> (Late Miocene – Early Pliocene of EC Africa)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Paracygnus&amp;action=edit&amp;redlink=1">Paracygnus</a></i> (Kimball Late Pliocene of Nebraska, US)</li> <li><i><a href="https://en.wikipedia.org/wiki/Eremochen">Eremochen</a></i> (Pliocene)</li></ul><p><a href="https://en.wikipedia.org/wiki/Tadorninae">Tadorninae</a> </p><ul><li><i><a href="https://en.wikipedia.org/wiki/Australotadorna">Australotadorna</a></i> (Late Oligocene – Early Miocene of Australia)</li> <li><i><a href="https://en.wikipedia.org/wiki/Miotadorna">Miotadorna</a></i> (Bathans Early/Middle Miocene of Otago, New Zealand)</li> <li>Tadorninae gen. et sp. indet. (Calvert Middle Miocene of Maryland, US)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Balcanas&amp;action=edit&amp;redlink=1">Balcanas</a></i> (Early Pliocene of Dorkovo, Bulgaria) – may be synonym of <i>Tadorna</i> or even <a href="https://en.wikipedia.org/wiki/Common_shelduck">common shelduck</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Anabernicula">Anabernicula</a></i> (Late Pliocene ? – Late Pleistocene of SW and W North America)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Brantadorna&amp;action=edit&amp;redlink=1">Brantadorna</a></i> (Middle Pleistocene of Vallecito Creek, US)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Nannonetta&amp;action=edit&amp;redlink=1">Nannonetta</a></i> (Late Pleistocene of Peru)</li> <li><i><a href="https://en.wikipedia.org/wiki/Zqueheanas">Zqueheanas</a></i> (Miocene of Argentina)</li></ul><p><a href="https://en.wikipedia.org/wiki/Anatinae">Anatinae</a> </p><ul><li><i><a href="https://en.wikipedia.org/wiki/Sinanas">Sinanas</a></i> (Middle Miocene of Shandong Province, China)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Wasonaka&amp;action=edit&amp;redlink=1">Wasonaka</a></i> (Middle Pliocene of Mexico)</li></ul><p><a href="https://en.wikipedia.org/wiki/Oxyurini">Oxyurinae</a> </p><ul><li><i><a href="https://en.wikipedia.org/wiki/Dunstanetta">Dunstanetta</a></i> (Bathans Early/Middle Miocene of Otago, New Zealand) – tentatively placed here</li> <li><i><a href="https://en.wikipedia.org/wiki/Lavadytis">Lavadytis</a></i> (Miocene of Nevada, USA)</li> <li><i><a href="https://en.wikipedia.org/wiki/Pinpanetta">Pinpanetta</a></i> (Late Oligocene – Early Miocene of Australia)</li> <li><i><a href="https://en.wikipedia.org/wiki/Tirarinetta">Tirarinetta</a></i> (Pliocene of Australia)</li></ul><p><i><a href="https://en.wikipedia.org/wiki/Incertae_sedis">Incertae sedis</a></i> </p><ul><li><i><a href="https://en.wikipedia.org/w/index.php?title=Aldabranas&amp;action=edit&amp;redlink=1">Aldabranas</a></i> (Late Pleistocene of Aldabra, Indian Ocean) – anatine or tadornine* <i>&quot;Anas&quot; albae</i> (Late Miocene of Polgárdi, Hungary) – mergine? Formerly in <i>Mergus</i></li> <li><i><a href="https://en.wikipedia.org/wiki/Allgoviachen">Allgoviachen</a></i> (Late Miocene of Bavaria, Germany)</li> <li><i>&quot;Anas&quot; eppelsheimensis</i> (Early Pliocene of Eppelsheim, Germany) – anatine?</li> <li><i>&quot;Anas&quot; isarensis</i> (Late Miocene of Aumeister, Germany) – anatine?</li> <li><i>&quot;Anas&quot; luederitzensis</i> (Kalahari Early Miocene of Lüderitzbucht, Namibia) – anatine?</li> <li><i>&quot;Anas&quot; meyerii</i> (Middle Miocene of Öhningen, Germany) Described from a single badly crushed tarsometatarsus and phalanges. This species was named in 1867 by <a href="https://en.wikipedia.org/wiki/Alphonse_Milne-Edwards">Milne-Edwards</a> and then recombined in 1964 by Brodkorb to the genus <i><a href="https://en.wikipedia.org/wiki/Aythya">Aythya</a></i>. This species is currently regarded as Aves <i><a href="https://en.wikipedia.org/wiki/Incertae_sedis">incertae sedis</a></i>.<sup><span>[</span>19<span>]</span></sup></li> <li><i><a href="https://en.wikipedia.org/wiki/Ankonetta">Ankonetta larriestrai</a></i> (Miocene of Argentina)</li> <li><i>&quot;Anser&quot; scaldii</i> (Late Miocene of Antwerp, Belgium) – anserine or tadornine* Anatidae gen. et sp. indet. (Waite Late Miocene of Alcoota, Australia) – anatine, oxyurine?</li> <li><i>&quot;Anas&quot; velox</i> (Middle–Late? Miocene of C Europe) – anatine? May include <i>&quot;A.&quot; meyerii</i></li> <li>Anatidae gen. et sp. indet. (Waite Late Miocene of Alcoota, Australia) – tadornine?</li> <li>Anatidae gen. et sp. indet. MNZ S42797 (Bathans Early/Middle Miocene of Otago, New Zealand)</li> <li>Anatidae gen. et sp. indet. (Middle Miocene of Nördlinger Ries, Germany) – tadornine?</li> <li>Anatidae gen. et sp. indet. (Sajóvölgyi Middle Miocene of Mátraszõlõs, Hungary)<sup><span>[</span>20<span>]</span></sup></li> <li><i>&quot;Aythya&quot; chauvirae</i> (Middle Miocene of Sansan, France and Credinţa, Romania) – 2 species</li> <li><i><a href="https://en.wikipedia.org/wiki/Caerulonettion">Caerulonettion</a></i> (Early Miocene of France and the Czech Republic, Middle Miocene of Germany)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Cayaoa&amp;action=edit&amp;redlink=1">Cayaoa</a></i> (Early Miocene of Argentina)</li> <li><i>&quot;Chenopis&quot; nanus</i> (Pleistocene of Australia) – at least 2 taxa, may be living species</li> <li><i><a href="https://en.wikipedia.org/wiki/Garganornis">Garganornis</a></i> (Late Miocene of Gargano, Italy)</li> <li><i><a href="https://en.wikipedia.org/wiki/Gracanicanetta">Gracanicanetta</a></i> (Middle Miocene of Bosnia and Herzegovina)</li> <li><i><a href="https://en.wikipedia.org/wiki/Lavanttalornis">Lavanttalornis</a></i> (Middle Miocene of Austria)</li> <li><i><a href="https://en.wikipedia.org/wiki/Matanas">Matanas</a></i> (Bathans Early/Middle Miocene of Otago, New Zealand)</li> <li><i><a href="https://en.wikipedia.org/wiki/Mioquerquedula">Mioquerquedula</a></i> (Middle Miocene of Mongolia)</li> <li><i>&quot;Oxyura&quot; doksana</i> (Early Miocene of Dolnice, Czech Republic)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Protomelanitta&amp;action=edit&amp;redlink=1">Protomelanitta</a></i> (Middle Miocene of Mongolia and Nevada, USA)</li> <li><i><a href="https://en.wikipedia.org/wiki/Uyrekura">Uyrekura</a></i> (Early Oligocene of Kazakhstan)</li></ul><p>Putative or disputed prehistoric anatids are: </p><ul><li><i><a href="https://en.wikipedia.org/w/index.php?title=Romainvillia&amp;action=edit&amp;redlink=1">Romainvillia</a></i> (Late Eocene/Early Oligocene) – anseranatid or anatid (own subfamily)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Loxornis&amp;action=edit&amp;redlink=1">Loxornis</a></i> (Deseado Early Oligocene of Argentina)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Paracygnopterus&amp;action=edit&amp;redlink=1">Paracygnopterus</a></i> (Early Oligocene of Belgium and England)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Teleornis&amp;action=edit&amp;redlink=1">Teleornis</a></i> (Deseado Early Oligocene of Argentina)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Guguschia&amp;action=edit&amp;redlink=1">Guguschia</a></i> (Late Oligocene of Pirəkəşkül, Azerbaijan) – anserine or <a href="https://en.wikipedia.org/wiki/Pelagornithidae">Pelagornithidae</a> (same as <i><a href="https://en.wikipedia.org/wiki/Caspiodontornis">Caspiodontornis</a></i>?)</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Chenornis&amp;action=edit&amp;redlink=1">Chenornis</a></i> (Early Miocene) – anserine or <a href="https://en.wikipedia.org/wiki/Phalacrocoracidae">Phalacrocoracidae</a></li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Paranyroca&amp;action=edit&amp;redlink=1">Paranyroca</a></i> (Rosebud Early Miocene of Bennett County, US) – anatid (own subfamily) or distinct family?</li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Eoneornis&amp;action=edit&amp;redlink=1">Eoneornis</a></i> (Miocene of Argentina) – anatine? A <i><a href="https://en.wikipedia.org/wiki/Nomen_dubium">nomen dubium</a></i></li> <li><i><a href="https://en.wikipedia.org/w/index.php?title=Eutelornis&amp;action=edit&amp;redlink=1">Eutelornis</a></i> (Miocene of Argentina) – anatine?</li></ul><p>The Middle Oligocene <i><a href="https://en.wikipedia.org/w/index.php?title=Limicorallus&amp;action=edit&amp;redlink=1">Limicorallus</a></i> (from Chelkar-Teniz (<a href="https://en.wikipedia.org/wiki/Kazakhstan">Kazakhstan</a>) was sometimes considered an anserine. It is now recognized as a primitive <a href="https://en.wikipedia.org/wiki/Cormorant">cormorant</a>.<sup><span>[</span>21<span>]</span></sup> The middle Eocene <i><a href="https://en.wikipedia.org/wiki/Eonessa">Eonessa</a></i> was formerly thought to belong to Anatidae, however reexamination of the holotype in 1978 resulted in the genus being placed as Aves <a href="https://en.wikipedia.org/wiki/Incertae_sedis">incertae sedis</a>.<sup><span>[</span>1<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/List_of_Anseriformes_by_population">List of Anseriformes by population</a></li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Olson, Storrs L.; Feduccia, A. (1980). <a href="https://web.archive.org/web/20120227003518/http://si-pddr.si.edu/dspace/bitstream/10088/4566/1/Presbyornis.pdf">&quot;<i>Presbyornis</i> and the Origin of the Anseriformes (Aves: Charadriomorphae)&quot;</a> <span>(PDF)</span>. <i>Smithsonian Contributions to Zoology</i>. <b>323</b> (323). Smithsonian Institution: <span>1–</span>24. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.5479%2Fsi.00810282.323">10.5479/si.00810282.323</a>. Archived from <a href="http://si-pddr.si.edu/dspace/bitstream/10088/4566/1/Presbyornis.pdf">the original</a> <span>(PDF)</span> on 2012-02-27<span>. Retrieved <span>2010-01-25</span></span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span>Carboneras, Carles (1992): Family Anatidae (Ducks, Geese and Swans). <i>In:</i> del Hoyo, Josep; Elliott, Andrew &amp; Sargatal, Jordi (eds.): <i><a href="https://en.wikipedia.org/wiki/Handbook_of_Birds_of_the_World">Handbook of Birds of the World</a></i> (Volume 1: Ostrich to Ducks): 536–629. Lynx Edicions, Barcelona. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/84-87334-10-5"><bdi>84-87334-10-5</bdi></a></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>Todd, Frank S. (1991). Forshaw, Joseph (ed.). <i>Encyclopaedia of Animals: Birds</i>. London: Merehurst Press. pp. <span>81–</span>87. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/1-85391-186-0"><bdi>1-85391-186-0</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>McKinney, Frank; Evarts, Susan (1998). &quot;Sexual coercion in waterfowl and other birds&quot;. <i>Ornithological Monographs</i>. <b>49</b> (49): <span>165–</span>193. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F40166723">10.2307/40166723</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/40166723">40166723</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>McCracken, Kevin G. (2000). <a href="https://web.archive.org/web/20080705053719/http://mercury.bio.uaf.edu/~kevin_mccracken/reprints/auk-117-820.pdf">&quot;The 20-cm Spiny Penis of the Argentine Lake Duck (<i>Oxyura vittata</i>)&quot;</a> <span>(PDF)</span>. <i><a href="https://en.wikipedia.org/wiki/The_Auk">The Auk</a></i>. <b>117</b> (3): <span>820–</span>825. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F4089612">10.2307/4089612</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/4089612">4089612</a>. Archived from <a href="http://mercury.bio.uaf.edu/~kevin_mccracken/reprints/auk-117-820.pdf">the original</a> <span>(PDF)</span> on 2008-07-05.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Brennan, Patricia; Birkhead, Tim; Zyskowski, Kristof; Van Der Waag, Jessica; Prum, Richard (2008). <a href="http://prumlab.yale.edu/sites/default/files/brennan_etal_2008_independent.pdf">&quot;Independent evolutionary reductions of the phallus in basal birds&quot;</a> <span>(PDF)</span>. <i>Journal of Avian Biology</i>. <b>39</b> (5): <span>487–</span>492. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1111%2Fj.0908-8857.2008.04610.x">10.1111/j.0908-8857.2008.04610.x</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Briskie, James; Montgomerie, Robert (1997). &quot;Sexual selection and the intromittent organ of birds&quot;. <i>Journal of Avian Biology</i>. <b>28</b> (1): <span>73–</span>86. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F3677097">10.2307/3677097</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/3677097">3677097</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/William_Elford_Leach">Leach, William Elford</a> (1819). <a href="https://books.google.com/books?id=YSlhAAAAcAAJ&amp;pg=PA67">&quot;Eleventh Room&quot;</a>. <i>Synopsis of the Contents of the British Museum</i> (15th ed.). London: British Museum. pp. 63–68 [67].</cite> The name of the author is not specified in the document, Leach was the Keeper of Zoology at the time.</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Walter_Joseph_Bock">Bock, Walter J.</a> (1994). <a href="http://digitallibrary.amnh.org/handle/2246/830"><i>History and Nomenclature of Avian Family-Group Names</i></a>. Bulletin of the American Museum of Natural History. Vol. 222. New York: American Museum of Natural History. pp. 133, 245. <a href="https://en.wikipedia.org/wiki/Hdl_(identifier)">hdl</a>:<a href="https://hdl.handle.net/2246%2F830">2246/830</a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup></span> <span><cite>Livezey, Bradley C. (1986). <a href="http://sora.unm.edu/sites/default/files/journals/auk/v103n04/p0737-p0754.pdf">&quot;A phylogenetic analysis of recent anseriform genera using morphological characters&quot;</a> <span>(PDF)</span>. <i><a href="https://en.wikipedia.org/wiki/Auk_(journal)">Auk</a></i>. <b>103</b> (4): <span>737–</span>754. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1093%2Fauk%2F103.4.737">10.1093/auk/103.4.737</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/4087184">4087184</a>.</cite></span> </li> <li><span><b>^</b></span> <span>Madge, Steve &amp; Burn, Hilary (1987): <i><a href="https://archive.org/details/waterfowl00stev/page/13/mode/2up">Wildfowl : an identification guide to the ducks, geese and swans of the world</a></i>. <a href="https://en.wikipedia.org/wiki/Helm_Identification_Guides">Christopher Helm</a>, London. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-7470-2201-1"><bdi>0-7470-2201-1</bdi></a></span> </li> <li><span><b>^</b></span> <span><cite>Sraml, M.; Christidis, L.; Easteal, S.; Horn, P.; Collet, C. (1996). &quot;Molecular Relationships Within Australasian Waterfowl (Anseriformes)&quot;. <i>Australian Journal of Zoology</i>. <b>44</b> (1): <span>47–</span>58. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1071%2FZO9960047">10.1071/ZO9960047</a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>Johnson, Kevin P.; Sorenson, Michael D. (1999). <a href="http://sora.unm.edu/sites/default/files/journals/auk/v116n03/p0792-p0805.pdf">&quot;Phylogeny and biogeography of dabbling ducks (genus Anas): a comparison of molecular and morphological evidence&quot;</a> <span>(PDF)</span>. <i><a href="https://en.wikipedia.org/wiki/Auk_(journal)">Auk</a></i>. <b>116</b> (3): <span>792–</span>805. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F4089339">10.2307/4089339</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/4089339">4089339</a>.</cite></span> </li> <li><span><b>^</b></span> <span>Terres, John K. &amp; <a href="https://en.wikipedia.org/wiki/National_Audubon_Society">National Audubon Society</a> (NAS) (1991): <i>The Audubon Society Encyclopedia of North American Birds</i>. Wings Books, New York. Reprint of 1980 edition. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0517032880"><bdi>0517032880</bdi></a></span> </li> <li><span><b>^</b></span> <span>Collar, N. J.; Andreev, A. V.; Chan, S.; Crosby, M. J.; Subramanya, S. &amp; Tobias, J. A. (eds.) (2001): <a href="http://www.rdb.or.id/view_html.php?id=73&amp;op=rhodcary">Pink-headed Duck</a> <a href="https://web.archive.org/web/20070311095312/http://www.rdb.or.id/view_html.php?id=73&amp;op=rhodcary">Archived</a> 2007-03-11 at the <a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a>. <i>In</i>:<i>Threatened Birds of Asia: The BirdLife International Red Data Book</i>: 489–501. BirdLife International. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-946888-44-2"><bdi>0-946888-44-2</bdi></a></span> </li> <li><span><b>^</b></span> <span><cite>Buckner, Janet C; Ellingson, Ryan; Gold, David A; Jones, Terry L; Jacobs, David K (2018). <a href="https://authors.library.caltech.edu/83878/1/1-s2.0-S1055790317304621-main.pdf">&quot;Mitogenomics supports an unexpected taxonomic relationship for the extinct diving duck <i>Chendytes lawi</i> and definitively places the extinct Labrador Duck&quot;</a> <span>(PDF)</span>. <i>Molecular Phylogenetics and Evolution</i>. <b>122</b>: <span>102–</span>109. <a href="https://en.wikipedia.org/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2018MolPE.122..102B">2018MolPE.122..102B</a>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1016%2Fj.ympev.2017.12.008">10.1016/j.ympev.2017.12.008</a>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/29247849">29247849</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Burney, David A.; James, Helen F.; Burney, Lida Pigott; Olson, Storrs L.; Kikuchi, William; Wagner, Warren L.; Burney, Mara; McCloskey, Deirdre; Kikuchi, Delores; Grady, Frederick V.; Gage, Reginald II; Nishek, Robert (2001). <a href="http://si-pddr.si.edu/jspui/bitstream/10088/6452/1/Kauai_paleoecology.pdf">&quot;Fossil Evidence for a Diverse Biota from Kauaʻi and Its Transformation since Human Arrival&quot;</a> <span>(PDF)</span>. <i>Ecological Monographs</i>. <b>71</b> (4): <span>615–</span>641. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F3100038">10.2307/3100038</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/3100038">3100038</a>.</cite><sup><span>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Link_rot"><span>permanent dead link</span></a></i>]</span></sup></span> </li> <li><span><b>^</b></span> <span><cite>Short, Lester L. (1970). <a href="http://sora.unm.edu/sites/default/files/journals/auk/v087n03/p0537-p0543.pdf">&quot;A new anseriform genus and species from the Nebraska Pliocene&quot;</a> <span>(PDF)</span>. <i><a href="https://en.wikipedia.org/wiki/Auk_(journal)">Auk</a></i>. <b>87</b> (3): <span>537–</span>543. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F4083796">10.2307/4083796</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/4083796">4083796</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Mlíkovský, J. (1992). <a href="https://web.archive.org/web/20120219173421/http://www.nm.cz/download/pm/zoo/mlikovsky_lit/073-1992-TertiarybirdsofCentralEurope.pdf">&quot;The present state of knowledge of Tertiary birds of Central europe&quot;</a> <span>(PDF)</span>. Science Series. Los Angeles County, CA: Natural History Museum. Archived from <a href="http://www.nm.cz/download/pm/zoo/mlikovsky_lit/073-1992-TertiarybirdsofCentralEurope.pdf">the original</a> <span>(PDF)</span> on 2012-02-19<span>. Retrieved <span>2013-03-11</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span>Gál, Erika; Hír, János; Kessler, Eugén &amp; Kókay, József (1998–99): <a href="http://www.matramuzeum.hu/Personal/folia/23/03MATSZOLOS.PDF">Középsõ-miocén õsmaradványok, a Mátraszõlõs, Rákóczi-kápolna alatti útbevágásból. I. A Mátraszõlõs 1. lelõhely</a> <a href="https://web.archive.org/web/20110721111701/http://www.matramuzeum.hu/Personal/folia/23/03MATSZOLOS.PDF">Archived</a> 2011-07-21 at the <a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a> [Middle Miocene fossils from the sections at the Rákóczi chapel at Mátraszőlős. Locality Mátraszõlõs I.]. <i>Folia Historico Naturalia Musei Matraensis</i> <b>23</b>: 33–78. [Hungarian with English abstract]</span> </li> <li><span><b>^</b></span> <span><cite>Mlíkovský, J.; Švec, P. (1986). &quot;Review of the Tertiary waterfowl (Aves: Anseridae) of Asia&quot;. <i>Věstnik Čestoslovenske Spolecnosti Zoologicke</i>. <b>50</b>: <span>259–</span>272.</cite></span> </li> </ol></div></div><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><ul><li><cite>Gonzalez, J.; Düttmann, H.; Wink, M. (2009). &quot;Phylogenetic relationships based on two mitochondrial genes and hybridization patterns in Anatidae&quot;. <i>Journal of Zoology</i>. <b>279</b> (3): <span>310–</span>318. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1111%2Fj.1469-7998.2009.00622.x">10.1111/j.1469-7998.2009.00622.x</a>.</cite></li> <li><a href="https://en.wikipedia.org/wiki/Paul_Johnsgard">Johnsgard, Paul A.</a> (2010): <a href="http://digitalcommons.unl.edu/biosciducksgeeseswans/"><i>Ducks, Geese, and Swans of the World, Revised edition</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Paul_Johnsgard">Johnsgard, Paul A.</a> (2010): <a href="http://digitalcommons.unl.edu/biosciwaterfowlna/"><i>Waterfowl of North America, Revised edition</i></a></li> <li><cite>Steadman, David William (1999). <a href="https://web.archive.org/web/20040705042210/http://www.uog.edu/up/micronesica/abstracts_31/pdfs_31_2/STEADMAN.PDF">&quot;The Prehistory of Vertebrates, Especially Birds, on Tinian, Aguiguan, and Rota, Northern Mariana Islands&quot;</a> <span>(PDF)</span>. <i>Micronesica</i>. <b>31</b> (2): <span>319–</span>345. Archived from <a href="http://www.uog.edu/up/micronesica/abstracts_31/pdfs_31_2/STEADMAN.PDF">the original</a> <span>(PDF)</span> on 2004-07-05.</cite></li></ul><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Anatidae&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Commons-logo.svg"></a></span></div> <div>Wikimedia Commons has media related to <span><a href="https://commons.wikimedia.org/wiki/Category:Anatidae">Anatidae</a></span>.</div></div> </div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Wiktionary-logo-en-v2.svg"></a></span></div> <div>Look up <i><b><a href="https://en.wiktionary.org/wiki/waterbird">waterbird</a></b></i> or <i><b><a href="https://en.wiktionary.org/wiki/anatidae">anatidae</a></b></i> in Wiktionary, the free dictionary.</div></div> </div><ul><li><a href="http://ibc.lynxeds.com/family/ducks-geese-swans-anatidae">Anatidae videos</a> on the Internet Bird Collection</li> <li><a href="https://web.archive.org/web/20130513022903/http://www.stampsbook.org/subject/Duck.html">Anatidae stamps</a> – Stamps on ducks, swans and geese</li></ul><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Birds"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Birds"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Birds"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Bird">Birds</a> (<a href="https://en.wikipedia.org/wiki/Class_(biology)">class</a>: Aves)</div></th></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Outline_of_birds">Outline</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Bird_anatomy">Anatomy</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Beak">Beak</a></li> <li><a href="https://en.wikipedia.org/wiki/Avian_brain">Brain</a></li> <li><a href="https://en.wikipedia.org/wiki/Crop_(anatomy)#Birds">Crop</a> <ul><li><a href="https://en.wikipedia.org/wiki/Crop_milk">milk</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Dactyly#bird_digits">Dactyly</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_egg">Eggs</a></li> <li><a href="https://en.wikipedia.org/wiki/Feather">Feathers</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_flight">Flight</a></li> <li><a href="https://en.wikipedia.org/wiki/Uropygial_gland">Preen gland</a></li> <li><a href="https://en.wikipedia.org/wiki/Plumage">Plumage</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_vision">Vision</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Bird_behaviour">Behaviour</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Bird_vocalization">Singing</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_intelligence">Intelligence</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_migration">Migration</a></li> <li><a href="https://en.wikipedia.org/wiki/Avian_foraging">Foraging</a></li> <li><a href="https://en.wikipedia.org/wiki/Sexual_selection_in_birds">Sexual selection</a></li> <li><a href="https://en.wikipedia.org/wiki/Lek_mating">Lek mating</a></li> <li><a href="https://en.wikipedia.org/wiki/Seabird_breeding_behavior">Seabird breeding</a></li> <li><a href="https://en.wikipedia.org/wiki/Egg_incubation#Avian_incubation">Incubation</a></li> <li><a href="https://en.wikipedia.org/wiki/Brood_parasite">Brood parasites</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_nest">Nesting</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_hybrid">Hybrids</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_colony">Colony</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Evolution">Evolution</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Origin_of_birds">Origin of birds</a> <ul><li><a href="https://en.wikipedia.org/wiki/Theropoda">Theropoda</a></li> <li><a href="https://en.wikipedia.org/wiki/Dinosaur">dinosaurs</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Origin_of_avian_flight">Origin of flight</a></li> <li><a href="https://en.wikipedia.org/wiki/Evolution_of_birds">Evolution of birds</a></li> <li><a href="https://en.wikipedia.org/wiki/Feathered_dinosaur">Feathered dinosaurs</a></li> <li><a href="https://en.wikipedia.org/wiki/Darwin%27s_finches">Darwin&#39;s finches</a></li> <li><a href="https://en.wikipedia.org/wiki/Seabird">Seabirds</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/List_of_fossil_bird_genera">Fossil birds</a></th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Archaeopteryx">Archaeopteryx</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Omnivoropterygidae">Omnivoropterygiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Jeholornithidae">Jeholornithidae</a></li> <li><a href="https://en.wikipedia.org/wiki/Confuciusornithiformes">Confuciusornithiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Enantiornithes">Enantiornithes</a></li> <li><a href="https://en.wikipedia.org/wiki/Chaoyangiformes">Chaoyangiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Patagopterygiformes">Patagopterygiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Ambiortiformes">Ambiortiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Songlingornithiformes">Songlingornithiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Hongshanornithidae">Hongshanornithidae</a></li> <li><a href="https://en.wikipedia.org/wiki/Gansus">Gansuiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Ichthyornithes">Ichthyornithiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Hesperornithes">Hesperornithes</a></li> <li><a href="https://en.wikipedia.org/wiki/Lithornithidae">Lithornithiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Moa">Dinornithiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Elephant_bird">Aepyornithiformes</a></li> <li><a href="https://en.wikipedia.org/wiki/Gastornithiformes">Gastornithiformes</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Human_uses_of_birds">Human <br/>interaction</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Bird_ringing">Ringing</a></li> <li><a href="https://en.wikipedia.org/wiki/Ornithology">Ornithology</a></li> <li><a href="https://en.wikipedia.org/wiki/Ornithomancy">Ornithomancy</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_collections">Bird collections</a></li> <li><a href="https://en.wikipedia.org/wiki/Birdwatching">Birdwatching</a> <ul><li><a href="https://en.wikipedia.org/wiki/Big_year">big year</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Bird_feeding">Bird feeding</a></li> <li><a href="https://en.wikipedia.org/wiki/Bird_conservation">Conservation</a></li> <li><a href="https://en.wikipedia.org/wiki/Aviculture">Aviculture</a></li> <li><a href="https://en.wikipedia.org/wiki/Waterfowl_hunting">Waterfowl hunting</a></li> <li><a href="https://en.wikipedia.org/wiki/Cockfight">Cockfighting</a></li> <li><a href="https://en.wikipedia.org/wiki/Pigeon_racing">Pigeon racing</a></li> <li><a href="https://en.wikipedia.org/wiki/Falconry">Falconry</a></li> <li><a href="https://en.wikipedia.org/wiki/Pheasantry">Pheasantry</a></li> <li><a href="https://en.wikipedia.org/wiki/Imping">Imping</a></li> <li><a href="https://en.wikipedia.org/wiki/Oology">Egg collecting</a></li></ul> </div></td></tr><tr><th>Lists</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_birds">Families and orders</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_bird_genera">Genera</a></li> <li><a href="https://en.wikipedia.org/wiki/Glossary_of_bird_terms">Glossary of bird terms</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_birds_by_population">List by population</a></li> <li><a href="https://en.wikipedia.org/wiki/Lists_of_birds_by_region">Lists by region</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_extinct_bird_species_since_1500">Extinct species since 1500</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_Late_Quaternary_prehistoric_bird_species">Late Quaternary prehistoric birds</a></li> <li>Notable birds <ul><li><a href="https://en.wikipedia.org/wiki/List_of_individual_birds">individuals</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_fictional_birds">fictional</a></li></ul></li></ul> </div></td></tr><tr><td colspan="2"><table><tbody><tr><td colspan="2"><table><tbody><tr><th colspan="2"><div>Neornithes</div></th></tr><tr><td colspan="2"><table><tbody><tr><td colspan="2"><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Palaeognathae">Palaeognathae</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Struthionidae">Struthioniformes <span>(ostriches)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Rheidae">Rheiformes <span>(rheas)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Tinamou">Tinamiformes <span>(tinamous)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Kiwi_(bird)">Apterygiformes <span>(kiwis)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Casuariiformes">Casuariiformes <span>(emus and cassowaries)</span></a></li></ul> </div></td></tr></tbody></table></td></tr><tr><td colspan="2"><table><tbody><tr><th><span><a href="https://en.wikipedia.org/wiki/Neognathae">Neognathae</a></span></th><td><table><tbody><tr><td colspan="2"><table><tbody><tr><th><span><a href="https://en.wikipedia.org/wiki/Galloanserae">Galloanserae</a></span><span><span>(<a href="https://en.wikipedia.org/wiki/Fowl">fowls</a>)</span></span></th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Anseriformes">Anseriformes</a> <br/> <span>(waterfowls)</span></th><td><table><tbody><tr><th>Anatidae <br/> <span>(<a href="https://en.wikipedia.org/wiki/Duck">ducks</a>)</span></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Anatinae">Anatinae</a> <ul><li><a href="https://en.wikipedia.org/wiki/Diving_duck">Aythyini</a></li> <li><a href="https://en.wikipedia.org/wiki/Mergini">Mergini</a></li> <li><a href="https://en.wikipedia.org/wiki/Oxyurini">Oxyurini</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Anserinae">Anserinae</a> <ul><li><a href="https://en.wikipedia.org/wiki/Swan"><span>swans</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Goose"><span>true geese</span></a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Whistling_duck">Dendrocygninae</a></li> <li><a href="https://en.wikipedia.org/wiki/Freckled_duck">Stictonettinae</a></li> <li><a href="https://en.wikipedia.org/wiki/Tadorninae">Tadorninae</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Anhimidae">Anhimidae</a></th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Horned_screamer">Anhima</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Chauna">Chauna</a></i></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Anseranatidae">Anseranatidae</a></th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Magpie_goose">Anseranas</a></i></li></ul> </div></td></tr></tbody></table></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Galliformes">Galliformes</a> <br/> <span>(<a href="https://en.wikipedia.org/wiki/Landfowl">landfowls</a>-</span> <br/> <span><a href="https://en.wikipedia.org/wiki/Gamebirds">gamebirds</a>)</span></th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Cracidae">Cracidae</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Cracinae">Cracinae</a></li> <li><a href="https://en.wikipedia.org/wiki/Oreophasinae">Oreophasinae</a></li> <li><a href="https://en.wikipedia.org/wiki/Penelopinae">Penelopinae</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Megapodidae">Megapodidae</a></th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Aepypodius">Aepypodius</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Alectura">Alectura</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Eulipoa">Eulipoa</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Leipoa">Leipoa</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Macrocephalon">Macrocephalon</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Megapodius">Megapodius</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Talegalla">Talegalla</a></i></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Numididae">Numididae</a></th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Vulturine_guineafowl">Acryllium</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Agelastes">Agelastes</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Guttera">Guttera</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Numida">Numida</a></i></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Odontophoridae">Odontophoridae</a></th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Callipepla">Callipepla</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Colinus">Colinus</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Cyrtonyx">Cyrtonyx</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Dactylortyx">Dactylortyx</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Dendrortyx">Dendrortyx</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Odontophorus">Odontophorus</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Oreortyx">Oreortyx</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Philortyx">Philortyx</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Rhynchortyx">Rhynchortyx</a></i></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Phasianidae">Phasianidae</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Meleagridinae">Meleagridinae <span>(turkeys)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Perdicinae">Perdicinae</a></li> <li><a href="https://en.wikipedia.org/wiki/Phasianinae">Phasianinae <span>(pheasants and relatives)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Grouse">Tetraoninae</a></li></ul> </div></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table></td></tr><tr><td colspan="2"><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Neoaves">Neoaves</a></th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Columbea">Columbea</a></th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Columbimorphae">Columbimorphae</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Columbidae">Columbiformes <span>(doves and pigeons)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Mesite">Mesitornithiformes <span>(mesites)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Sandgrouse">Pterocliformes <span>(sandgrouse)</span></a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Mirandornithes">Mirandornithes</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Flamingo">Phoenicopteriformes <span>(flamingos)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Grebe">Podicipediformes <span>(grebes)</span></a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Passerea">Passerea</a></th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Otidimorphae">Otidimorphae</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Cuckoo">Cuculiformes <span>(cuckoos)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Turaco">Musophagiformes <span>(turacos)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Bustard">Otidiformes <span>(bustards)</span></a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Strisores">Strisores</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Caprimulgiformes">Caprimulgiformes <span>(nightjars and relatives)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Steatornithiformes">Steatornithiformes <span>(oilbirds)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Nyctibiiformes">Nyctibiiformes <span>(potoos)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Podargiformes">Podargiformes <span>(frogmouths)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Aegotheliformes">Aegotheliformes <span>(owlet-nightjars)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Apodiformes">Apodiformes <span>(swifts and hummingbirds)</span></a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Opisthocomiformes">Opisthocomiformes</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Opisthocomidae">Opisthocomiformes <span>(hoatzins)</span></a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Cursorimorphae">Cursorimorphae</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Charadriiformes">Charadriiformes <span>(gulls and relatives)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Gruiformes">Gruiformes <span>(cranes and relatives)</span></a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Phaethontimorphae">Phaethontimorphae</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Tropicbird">Phaethontiformes <span>(tropicbirds)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Eurypygiformes">Eurypygiformes <span>(kagus and sunbitterns)</span></a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Aequornithes">Aequornithes</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Loon">Gaviiformes <span>(loons or divers)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Penguin">Sphenisciformes <span>(penguins)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Procellariiformes">Procellariiformes <span>(albatrosses and petrels)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Stork">Ciconiiformes <span>(storks)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Suliformes">Suliformes <span>(cormorants and relatives)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Pelecaniformes">Pelecaniformes <span>(pelicans and relatives)</span></a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Australaves">Australaves</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Cariamiformes">Cariamiformes <span>(seriemas and relatives)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Falconiformes">Falconiformes <span>(falcons and relatives)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Parrot">Psittaciformes <span>(parrots)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Passerine">Passeriformes <span>(perching birds)</span></a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Afroaves">Afroaves</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Accipitriformes">Accipitriformes <span>(raptors)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Owl">Strigiformes <span>(owls)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Mousebird">Coliiformes <span>(mousebirds)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Trogon">Trogoniformes <span>(trogons and quetzals)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Cuckoo-roller">Leptosomiformes <span>(cuckoo-rollers)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Bucerotiformes">Bucerotiformes <span>(hornbills and hoopoes)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Coraciiformes">Coraciiformes <span>(kingfishers and rollers)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Piciformes">Piciformes <span>(woodpeckers and relatives)</span></a></li></ul> </div></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table></td></tr><tr><td colspan="2"><div> <ul><li><b><a href="https://en.wikipedia.org/wiki/Category:Birds">Category</a></b></li> <li><span><a href="https://en.wikipedia.org/wiki/File:Commons-logo.svg"></a></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Birds">Commons</a></b></li> <li><span><a href="https://en.wikipedia.org/wiki/File:Symbol_portal_class.svg"></a></span> <b><a href="https://en.wikipedia.org/wiki/Portal:Birds">Portal</a></b></li> <li> <b><a href="https://en.wikipedia.org/wiki/Wikipedia:WikiProject_Birds">WikiProject</a></b></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Help:Taxon_identifiers">Taxon identifiers</a></div></th></tr><tr><th><i>Anatidae</i></th><td><div> <ul><li><span><a href="https://en.wikipedia.org/wiki/Wikidata">Wikidata</a>: <span><span><a href="https://www.wikidata.org/wiki/Q7556">Q7556</a></span></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Wikispecies">Wikispecies</a>: <span><span><a href="https://species.wikimedia.org/wiki/Anatidae">Anatidae</a></span></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Animal_Diversity_Web">ADW</a>: <span><a href="https://animaldiversity.org/accounts/Anatidae/">Anatidae</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Australian_Faunal_Directory">AFD</a>: <span><a href="https://biodiversity.org.au/afd/taxa/Anatidae">Anatidae</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Barcode_of_Life_Data_System">BOLD</a>: <span><a href="https://bench.boldsystems.org/index.php/TaxBrowser_TaxonPage?taxid=1436">1436</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Catalogue_of_Life">CoL</a>: <span><a href="https://www.catalogueoflife.org/data/taxon/9H6K5">9H6K5</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Encyclopedia_of_Life">EoL</a>: <span><a href="https://eol.org/pages/8027">8027</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/EPPO_Code">EPPO</a>: <span><a href="https://gd.eppo.int/taxon/1ANAXF">1ANAXF</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Fauna_Europaea">Fauna Europaea</a>: <span><a href="http://www.eu-nomen.eu/portal/taxon.php?GUID=urn:lsid:faunaeur.org:taxname:10712">10712</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Fauna_Europaea">Fauna Europaea (new)</a>: <span><a href="https://fauna-eu.org/cdm_dataportal/taxon/a729eb7e-2338-4b68-a7ef-099e6cb9cb13">a729eb7e-2338-4b68-a7ef-099e6cb9cb13</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Global_Biodiversity_Information_Facility">GBIF</a>: <span><a href="https://www.gbif.org/species/2986">2986</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/INaturalist">iNaturalist</a>: <span><a href="https://inaturalist.org/taxa/6912">6912</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Interim_Register_of_Marine_and_Nonmarine_Genera">IRMNG</a>: <span><a href="https://www.irmng.org/aphia.php?p=taxdetails&amp;id=104622">104622</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Integrated_Taxonomic_Information_System">ITIS</a>: <span><a href="https://www.itis.gov/servlet/SingleRpt/SingleRpt?search_topic=TSN&amp;search_value=174983">174983</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/National_Biodiversity_Network">NBN</a>: <span><a href="https://species.nbnatlas.org/species/NBNSYS0000159361">NBNSYS0000159361</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/National_Center_for_Biotechnology_Information">NCBI</a>: <span><a href="https://www.ncbi.nlm.nih.gov/Taxonomy/Browser/wwwtax.cgi?mode=Info&amp;id=8830">8830</a></span></span></li> <li><span>NZOR: <span><a href="https://www.nzor.org.nz/names/4adf5172-e238-4a40-a819-bce80997df2b">4adf5172-e238-4a40-a819-bce80997df2b</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Open_Tree_of_Life">Open Tree of Life</a>: <span><a href="https://tree.opentreeoflife.org/taxonomy/browse?id=765193">765193</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Paleobiology_Database">Paleobiology Database</a>: <span><a href="https://paleobiodb.org/classic/basicTaxonInfo?taxon_no=39624">39624</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/World_Register_of_Marine_Species">WoRMS</a>: <span><a href="https://www.marinespecies.org/aphia.php?p=taxdetails&amp;id=136973">136973</a></span></span></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q7556#identifiers"></a></span></div></th></tr><tr><th>International</th><td><div><ul><li><span><a href="https://d-nb.info/gnd/4152334-9">GND</a></span></li></ul></div></td></tr><tr><th>National</th><td><div><ul><li><span><a href="https://id.loc.gov/authorities/sh85004827">United States</a></span></li><li><span><a href="https://catalogue.bnf.fr/ark:/12148/cb120768058">France</a></span></li><li><span><a href="https://data.bnf.fr/ark:/12148/cb120768058">BnF data</a></span></li><li><span><a href="https://id.ndl.go.jp/auth/ndlna/00562236">Japan</a></span></li><li><span><span><a href="https://aleph.nkp.cz/F/?func=find-c&amp;local_base=aut&amp;ccl_term=ica=ph269135&amp;CON_LNG=ENG">Czech Republic</a></span></span></li><li><span><a href="https://datos.bne.es/resource/XX536191">Spain</a></span></li><li><span><a href="https://kopkatalogs.lv/F?func=direct&amp;local_base=lnc10&amp;doc_number=000117058&amp;P_CON_LNG=ENG">Latvia</a></span></li><li><span><a href="https://www.nli.org.il/en/authorities/987007294861605171">Israel</a></span></li></ul></div></td></tr><tr><th>Other</th><td><div><ul><li><span><a href="https://lux.collections.yale.edu/view/concept/2c40628d-d4ce-4534-b938-d25ad705f5c4">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div> 1890 United States census - Wikipedia https://en.wikipedia.org/wiki/1890_United_States_census wlnk3Tj27pgzXlciGd8G7lqX2oah6dEX-hy94w== Wed, 13 May 2026 10:11:49 +0000 11th US national census <div>11th US national census</div><p> </p><table><tbody><tr><th colspan="2">1890 United States census</th></tr><tr><td colspan="2"><hr/> <div> <div>← <a href="https://en.wikipedia.org/wiki/1880_United_States_census">1880</a></div> <div><b>June 2, 1890<span> (<span>1890-06-02</span>)</span></b></div> <div><a href="https://en.wikipedia.org/wiki/1900_United_States_census">1900</a> →</div> </div> <hr/></td></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:DeptInterior1882seal.png"></a></span><div>Seal of the Department of the Interior</div></td></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:1890_U.S._Census_form.jpg"></a></span><div>1890 census form</div></td></tr><tr><th colspan="2">General information</th></tr><tr><th>Country</th><td>United States</td></tr><tr><th>Authority</th><td><a href="https://en.wikipedia.org/wiki/United_States_Census_Bureau">Census Office</a></td></tr><tr><th colspan="2">Results</th></tr><tr><th>Total population</th><td>62,979,766 ( 25.5%)</td></tr><tr><th>Most<span> </span>populous<span> </span>state</th><td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a><br/>6,003,174</td></tr><tr><th>Least<span> </span>populous<span> </span>state</th><td><a href="https://en.wikipedia.org/wiki/Nevada">Nevada</a><br/>47,335</td></tr></tbody></table><p>The <b>1890 United States census</b> was taken beginning June 2, 1890. The census determined the resident population of the United States to be 62,979,766, an increase of 25.5 percent over the 50,189,209 persons enumerated during the <a href="https://en.wikipedia.org/wiki/1880_United_States_census">1880 census</a>. The data reported that the distribution of the population had resulted in the disappearance of the <a href="https://en.wikipedia.org/wiki/American_frontier">American frontier</a>. </p><p>This was the first <a href="https://en.wikipedia.org/wiki/Census">census</a> in which a majority of states recorded populations of over one million and the first in which three cities, <a href="https://en.wikipedia.org/wiki/New_York_City">New York City</a>, <a href="https://en.wikipedia.org/wiki/Chicago">Chicago</a>, and <a href="https://en.wikipedia.org/wiki/Philadelphia">Philadelphia</a>, recorded populations of over one million. The census also saw Chicago rise in rank to the nation&#39;s second-most populous city, a position it would hold until <a href="https://en.wikipedia.org/wiki/Los_Angeles">Los Angeles</a>, the 57th-most populous city as of 1890, supplanted it in 1990. This was the first U.S. census to use machines to tabulate the collected data. </p><p>Most of the 1890 census materials were destroyed on January 10, 1921, when the Commerce Department building caught fire, and in the subsequent disposal of the remaining damaged records. </p><div><h2>Census questions</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=1890_United_States_census&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>The 1890 census collected the following information:<sup><span>[</span>1<span>]</span></sup> </p><div> <ul><li>address</li> <li>number of families in house</li> <li>number of persons in house</li> <li>names</li> <li>whether a soldier, sailor or Marine (<a href="https://en.wikipedia.org/wiki/Union_(American_Civil_War)">Union</a> or <a href="https://en.wikipedia.org/wiki/Confederate_States_of_America">Confederate</a>) during the <a href="https://en.wikipedia.org/wiki/American_Civil_War">American Civil War</a>, or a widow of such person</li> <li>relationship to head of family</li> <li>race, described as <a href="https://en.wikipedia.org/wiki/White_American">white</a>, <a href="https://en.wikipedia.org/wiki/African_American">black</a>, <a href="https://en.wikipedia.org/wiki/Mulatto">mulatto</a>, <a href="https://en.wikipedia.org/wiki/Quadroon">quadroon</a>, <a href="https://en.wikipedia.org/wiki/Octoroon">octoroon</a>, <a href="https://en.wikipedia.org/wiki/Chinese_American">Chinese</a>, <a href="https://en.wikipedia.org/wiki/Japanese_American">Japanese</a>, or <a href="https://en.wikipedia.org/wiki/Indigenous_peoples_of_the_Americas">Indian</a></li> <li>sex</li> <li>age</li> <li>marital status</li> <li>married within the year</li> <li>mother of how many children, and number now living</li> <li>place of birth of person, and their father and mother</li> <li>if foreign-born, number of years in U.S.</li> <li>whether naturalized</li> <li>whether naturalization papers have been taken out</li> <li>profession, trade or occupation</li> <li>months unemployed during census year</li> <li>ability to read and write</li> <li>ability to speak English, and, if unable, language or dialect spoken</li> <li>whether suffering from acute or chronic disease, with name of disease and length of time afflicted</li> <li>whether defective in mind, sight, hearing or speech, or whether crippled, maimed or deformed, with name of defect</li> <li>whether a prisoner, convict, homeless child, or pauper</li> <li>home rented, or owned by head or member of family, and, if owned, whether free from mortgage</li> <li>if farmer, whether farm is rented, or owned by head or member of family; if owned, whether free from mortgage; if rented, post office box of owner</li></ul></div><div><h2>Methodology</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=1890_United_States_census&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:1890_Census_Hollerith_Electrical_Counting_Machines_Sci_Amer.jpg"></a><figcaption>A Hollerith <a href="https://en.wikipedia.org/wiki/Tabulating_machine">tabulator</a> that has been modified for the first 1890 census tabulation; the punched-card reader was removed, replaced by a simple keyboard.<sup><span>[</span>2<span>]</span></sup><sup><span>: 61 </span></sup></figcaption></figure><p>The 1890 census was the first to be compiled using methods invented by <a href="https://en.wikipedia.org/wiki/Herman_Hollerith">Herman Hollerith</a> and was overseen by Superintendents <a href="https://en.wikipedia.org/wiki/Robert_Percival_Porter">Robert P. Porter</a> (1889–1893) and Carroll D. Wright (1893–1897). Data was entered on a machine readable medium (<a href="https://en.wikipedia.org/wiki/Punched_cards">punched cards</a>) and <a href="https://en.wikipedia.org/wiki/Tabulating_machine">tabulated by machine</a>.<sup><span>[</span>2<span>]</span></sup> Changes from the 1880 census included the larger population, the number of data items to be collected from individuals, the <a href="https://en.wikipedia.org/wiki/United_States_Census_Bureau">Census Bureau</a> headcount, the volume of scheduled publications, and the use of Hollerith&#39;s electromechanical tabulators. The net effect of these changes was to reduce the time required to process the census from eight years for the <a href="https://en.wikipedia.org/wiki/U.S._Census,_1880">1880 census</a> to six years for the 1890 census.<sup><span>[</span>3<span>]</span></sup> The total population of 62,947,714, the family, or <i>rough</i>, count, was announced after only six weeks of processing (punched cards were not used for this tabulation).<sup><span>[</span>4<span>]</span></sup><sup><span>[</span>2<span>]</span></sup><sup><span>: 61 </span></sup> The public reaction to this tabulation was disbelief, as it was widely believed that the &quot;right answer&quot; was at least 75,000,000.<sup><span>[</span>5<span>]</span></sup> </p><div><h2>Significant findings</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=1890_United_States_census&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>The United States census of 1890 showed a total of 248,253 <a href="https://en.wikipedia.org/wiki/Native_Americans_in_the_United_States">Native Americans living in the United States</a>, down from 400,764 Native Americans identified in the <a href="https://en.wikipedia.org/wiki/1850_United_States_census">census of 1850</a>.<sup><span>[</span>6<span>]</span></sup> </p><p>The 1890 census announced that the <a href="https://en.wikipedia.org/wiki/American_frontier">frontier</a> region of the <a href="https://en.wikipedia.org/wiki/United_States">United States</a> no longer existed,<sup><span>[</span>7<span>]</span></sup> and that the Census Bureau would no longer track the westward migration of the U.S. population. In practice, however, said migration can still be tracked by plotting each succeeding census&#39; <a href="https://en.wikipedia.org/wiki/Mean_center_of_United_States_population">mean center of United States population</a>. </p><p>By 1890, settlement in the American West had reached sufficient population density that the frontier line had disappeared. For the 1890 census, the Census Bureau released a bulletin declaring the closing of the frontier, stating: &quot;Up to and including 1880 the country had a frontier of settlement, but at present the unsettled area has been so broken into by isolated bodies of settlement that there can hardly be said to be a frontier line. In the discussion of its extent, its westward movement, etc., it can not, therefore, any longer have a place in the census reports.&quot;<sup><span>[</span>8<span>]</span></sup> </p><p>Statisticians at the time argued that the results of the 1890 census was most likely an undercount of the total population in the United States from anywhere between one million to several millions, and that African Americans, working-class people, and young children were most likely to be undercounted.<sup><span>[</span>9<span>]</span></sup> </p><div><h2>Data availability</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=1890_United_States_census&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Photograph_of_Commerce_Department_Building_(64-NAD-264)_(cropped).jpg"></a><figcaption>Aftermath of the 1921 fire which destroyed almost the entirety of the 1890 census records</figcaption></figure><p>The original data for the 1890 census is mostly unavailable. The population schedules were damaged in a fire in the basement of the <a href="https://en.wikipedia.org/wiki/United_States_Department_of_Commerce">U.S. Department of Commerce</a> building in <a href="https://en.wikipedia.org/wiki/Washington,_D.C.">Washington, D.C.</a> in 1921. Some 25% of the materials were presumed destroyed and another 50% damaged by smoke and water, although the actual damage may have been closer to 15–25%. The damage to the records led to an outcry for a permanent <a href="https://en.wikipedia.org/wiki/National_Archives_and_Records_Administration">National Archives</a>.<sup><span>[</span>10<span>]</span></sup><sup><span>[</span>11<span>]</span></sup> In December 1932, following standard federal record-keeping procedures, the Chief Clerk of the Bureau of the Census sent the <a href="https://en.wikipedia.org/wiki/Librarian_of_Congress">Librarian of Congress</a> a list of papers to be destroyed, including the original 1890 census schedules. The Librarian was asked by the Bureau to identify any records which should be retained for historical purposes, but the Librarian did not accept the census records. Congress authorized destruction of that list of records on February 21, 1933, and the surviving original 1890 census records were destroyed by government order by 1934 or 1935. Few sets of <a href="https://en.wikipedia.org/wiki/Microdata_(statistics)">microdata</a> from the 1890 census survive.<sup><span>[</span>12<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Aggregate_data">Aggregate data</a> for small areas, together with compatible cartographic boundary files, can be downloaded from the <a href="https://en.wikipedia.org/wiki/National_Historical_Geographic_Information_System">National Historical Geographic Information System</a>. </p><div><h2>State rankings</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=1890_United_States_census&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><table> <tbody><tr> <th>Rank</th> <th>State</th> <th>Population </th></tr> <tr> <td>01</td> <td><span><span> </span><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></span></td> <td>6,003,174 </td></tr> <tr> <td>02</td> <td> <a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>5,258,113 </td></tr> <tr> <td>03</td> <td> <a href="https://en.wikipedia.org/wiki/Illinois">Illinois</a></td> <td>3,826,352 </td></tr> <tr> <td>04</td> <td> <a href="https://en.wikipedia.org/wiki/Ohio">Ohio</a></td> <td>3,672,329 </td></tr> <tr> <td>05</td> <td> <a href="https://en.wikipedia.org/wiki/Missouri">Missouri</a></td> <td>2,679,185 </td></tr> <tr> <td>06</td> <td> <a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>2,238,947 </td></tr> <tr> <td>07</td> <td> <a href="https://en.wikipedia.org/wiki/Texas">Texas</a></td> <td>2,235,527 </td></tr> <tr> <td>08</td> <td> <a href="https://en.wikipedia.org/wiki/Indiana">Indiana</a></td> <td>2,192,404 </td></tr> <tr> <td>09</td> <td> <a href="https://en.wikipedia.org/wiki/Michigan">Michigan</a></td> <td>2,093,890 </td></tr> <tr> <td>10</td> <td> <a href="https://en.wikipedia.org/wiki/Iowa">Iowa</a></td> <td>1,912,297 </td></tr> <tr> <td>11</td> <td> <a href="https://en.wikipedia.org/wiki/Kentucky">Kentucky</a></td> <td>1,858,635 </td></tr> <tr> <td>12</td> <td> <a href="https://en.wikipedia.org/wiki/Georgia_(U.S._state)">Georgia</a></td> <td>1,837,353 </td></tr> <tr> <td>13</td> <td> <a href="https://en.wikipedia.org/wiki/Tennessee">Tennessee</a></td> <td>1,767,518 </td></tr> <tr> <td>14</td> <td> <a href="https://en.wikipedia.org/wiki/Wisconsin">Wisconsin</a></td> <td>1,693,330 </td></tr> <tr> <td>15</td> <td> <a href="https://en.wikipedia.org/wiki/Virginia">Virginia</a></td> <td>1,655,980 </td></tr> <tr> <td>16</td> <td> <a href="https://en.wikipedia.org/wiki/North_Carolina">North Carolina</a></td> <td>1,617,949 </td></tr> <tr> <td>17</td> <td> <a href="https://en.wikipedia.org/wiki/Alabama">Alabama</a></td> <td>1,513,401 </td></tr> <tr> <td>18</td> <td> <a href="https://en.wikipedia.org/wiki/New_Jersey">New Jersey</a></td> <td>1,444,933 </td></tr> <tr> <td>19</td> <td> <a href="https://en.wikipedia.org/wiki/Kansas">Kansas</a></td> <td>1,428,108 </td></tr> <tr> <td>20</td> <td> <a href="https://en.wikipedia.org/wiki/Minnesota">Minnesota</a></td> <td>1,310,283 </td></tr> <tr> <td>21</td> <td> <a href="https://en.wikipedia.org/wiki/Mississippi">Mississippi</a></td> <td>1,289,600 </td></tr> <tr> <td>22</td> <td> <a href="https://en.wikipedia.org/wiki/California">California</a></td> <td>1,213,398 </td></tr> <tr> <td>23</td> <td> <a href="https://en.wikipedia.org/wiki/South_Carolina">South Carolina</a></td> <td>1,151,149 </td></tr> <tr> <td>24</td> <td> <a href="https://en.wikipedia.org/wiki/Arkansas">Arkansas</a></td> <td>1,128,211 </td></tr> <tr> <td>25</td> <td> <a href="https://en.wikipedia.org/wiki/Louisiana">Louisiana</a></td> <td>1,118,588 </td></tr> <tr> <td>26</td> <td> <a href="https://en.wikipedia.org/wiki/Nebraska">Nebraska</a></td> <td>1,062,656 </td></tr> <tr> <td>27</td> <td> <a href="https://en.wikipedia.org/wiki/Maryland">Maryland</a></td> <td>1,042,390 </td></tr> <tr> <td>28</td> <td> <a href="https://en.wikipedia.org/wiki/West_Virginia">West Virginia</a></td> <td>762,794 </td></tr> <tr> <td>29</td> <td> <a href="https://en.wikipedia.org/wiki/Connecticut">Connecticut</a></td> <td>746,258 </td></tr> <tr> <td>30</td> <td> <a href="https://en.wikipedia.org/wiki/Maine">Maine</a></td> <td>661,086 </td></tr> <tr> <td>31</td> <td> <a href="https://en.wikipedia.org/wiki/Colorado">Colorado</a></td> <td>413,249 </td></tr> <tr> <td>32</td> <td> <a href="https://en.wikipedia.org/wiki/Florida">Florida</a></td> <td>391,422 </td></tr> <tr> <td>33</td> <td> <a href="https://en.wikipedia.org/wiki/New_Hampshire">New Hampshire</a></td> <td>376,530 </td></tr> <tr> <td>34</td> <td><span><span> </span><a href="https://en.wikipedia.org/wiki/Washington_(state)">Washington</a></span></td> <td>357,232 </td></tr> <tr> <td>35</td> <td> <a href="https://en.wikipedia.org/wiki/South_Dakota">South Dakota</a></td> <td>348,600 </td></tr> <tr> <td>36</td> <td> <a href="https://en.wikipedia.org/wiki/Rhode_Island">Rhode Island</a></td> <td>345,506 </td></tr> <tr> <td>37</td> <td> <a href="https://en.wikipedia.org/wiki/Vermont">Vermont</a></td> <td>332,422 </td></tr> <tr> <td>38</td> <td> <a href="https://en.wikipedia.org/wiki/Oregon">Oregon</a></td> <td>317,704 </td></tr> <tr> <td>X</td> <td> <a href="https://en.wikipedia.org/wiki/Oklahoma">Oklahoma</a><sup><span>[</span>13<span>]</span></sup></td> <td>258,657 </td></tr> <tr> <td>X</td> <td> <a href="https://en.wikipedia.org/wiki/Washington,_D.C.">District of Columbia</a><sup><span>[</span>14<span>]</span></sup></td> <td>230,392 </td></tr> <tr> <td>X</td> <td> <a href="https://en.wikipedia.org/wiki/Utah_Territory">Utah</a></td> <td>210,779 </td></tr> <tr> <td>39</td> <td> <a href="https://en.wikipedia.org/wiki/North_Dakota">North Dakota</a></td> <td>190,983 </td></tr> <tr> <td>40</td> <td> <a href="https://en.wikipedia.org/wiki/Delaware">Delaware</a></td> <td>168,493 </td></tr> <tr> <td>X</td> <td> <a href="https://en.wikipedia.org/wiki/New_Mexico_Territory">New Mexico</a></td> <td>160,282 </td></tr> <tr> <td>41</td> <td> <a href="https://en.wikipedia.org/wiki/Montana">Montana</a></td> <td>142,924 </td></tr> <tr> <td>42</td> <td> <a href="https://en.wikipedia.org/wiki/Idaho">Idaho</a></td> <td>88,548 </td></tr> <tr> <td>X</td> <td> <a href="https://en.wikipedia.org/wiki/Arizona_Territory">Arizona</a></td> <td>88,243 </td></tr> <tr> <td>43</td> <td> <a href="https://en.wikipedia.org/wiki/Wyoming">Wyoming</a></td> <td>62,555 </td></tr> <tr> <td>44</td> <td> <a href="https://en.wikipedia.org/wiki/Nevada">Nevada</a></td> <td>47,355 </td></tr> <tr> <td>X</td> <td> <a href="https://en.wikipedia.org/wiki/Alaska_Territory">Alaska</a></td> <td>32,052 </td></tr></tbody></table><div><h2>City rankings</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=1890_United_States_census&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><table> <tbody><tr> <th>Rank</th> <th>City</th> <th>State</th> <th>Population<sup><span>[</span>15<span>]</span></sup></th> <th><a href="https://en.wikipedia.org/wiki/List_of_regions_of_the_United_States#Census_Bureau-designated_regions_and_divisions">Region (2016)</a><sup><span>[</span>16<span>]</span></sup> </th></tr> <tr> <td>01</td> <td><a href="https://en.wikipedia.org/wiki/New_York_City">New York</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>1,515,301</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>02</td> <td><a href="https://en.wikipedia.org/wiki/Chicago">Chicago</a></td> <td><a href="https://en.wikipedia.org/wiki/Illinois">Illinois</a></td> <td>1,099,850</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>03</td> <td><a href="https://en.wikipedia.org/wiki/Philadelphia">Philadelphia</a></td> <td><a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>1,046,964</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>04</td> <td><a href="https://en.wikipedia.org/wiki/Brooklyn">Brooklyn</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>806,343</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>05</td> <td><a href="https://en.wikipedia.org/wiki/St._Louis">St. Louis</a></td> <td><a href="https://en.wikipedia.org/wiki/Missouri">Missouri</a></td> <td>451,770</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>06</td> <td><a href="https://en.wikipedia.org/wiki/Boston">Boston</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>448,477</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>07</td> <td><a href="https://en.wikipedia.org/wiki/Baltimore">Baltimore</a></td> <td><a href="https://en.wikipedia.org/wiki/Maryland">Maryland</a></td> <td>434,439</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>08</td> <td><a href="https://en.wikipedia.org/wiki/San_Francisco">San Francisco</a></td> <td><a href="https://en.wikipedia.org/wiki/California">California</a></td> <td>298,997</td> <td><a href="https://en.wikipedia.org/wiki/Western_United_States">West</a> </td></tr> <tr> <td>09</td> <td><a href="https://en.wikipedia.org/wiki/Cincinnati">Cincinnati</a></td> <td><a href="https://en.wikipedia.org/wiki/Ohio">Ohio</a></td> <td>296,908</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>10</td> <td><a href="https://en.wikipedia.org/wiki/Cleveland">Cleveland</a></td> <td><a href="https://en.wikipedia.org/wiki/Ohio">Ohio</a></td> <td>261,353</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>11</td> <td><a href="https://en.wikipedia.org/wiki/Buffalo,_New_York">Buffalo</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>255,664</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>12</td> <td><a href="https://en.wikipedia.org/wiki/New_Orleans">New Orleans</a></td> <td><a href="https://en.wikipedia.org/wiki/Louisiana">Louisiana</a></td> <td>242,039</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>13</td> <td><a href="https://en.wikipedia.org/wiki/Pittsburgh">Pittsburgh</a></td> <td><a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>238,617</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>14</td> <td><a href="https://en.wikipedia.org/wiki/Washington,_D.C.">Washington</a></td> <td><a href="https://en.wikipedia.org/wiki/District_of_Columbia">District of Columbia</a></td> <td>230,392</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>15</td> <td><a href="https://en.wikipedia.org/wiki/Detroit">Detroit</a></td> <td><a href="https://en.wikipedia.org/wiki/Michigan">Michigan</a></td> <td>205,876</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>16</td> <td><a href="https://en.wikipedia.org/wiki/Milwaukee">Milwaukee</a></td> <td><a href="https://en.wikipedia.org/wiki/Wisconsin">Wisconsin</a></td> <td>204,468</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>17</td> <td><a href="https://en.wikipedia.org/wiki/Newark,_New_Jersey">Newark</a></td> <td><a href="https://en.wikipedia.org/wiki/New_Jersey">New Jersey</a></td> <td>181,830</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>18</td> <td><a href="https://en.wikipedia.org/wiki/Minneapolis">Minneapolis</a></td> <td><a href="https://en.wikipedia.org/wiki/Minnesota">Minnesota</a></td> <td>164,738</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>19</td> <td><a href="https://en.wikipedia.org/wiki/Jersey_City">Jersey City</a></td> <td><a href="https://en.wikipedia.org/wiki/New_Jersey">New Jersey</a></td> <td>163,003</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>20</td> <td><a href="https://en.wikipedia.org/wiki/Louisville,_Kentucky">Louisville</a></td> <td><a href="https://en.wikipedia.org/wiki/Kentucky">Kentucky</a></td> <td>161,129</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>21</td> <td><a href="https://en.wikipedia.org/wiki/Omaha">Omaha</a></td> <td><a href="https://en.wikipedia.org/wiki/Nebraska">Nebraska</a></td> <td>140,452</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>22</td> <td><a href="https://en.wikipedia.org/wiki/Rochester,_New_York">Rochester</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>133,896</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>23</td> <td><a href="https://en.wikipedia.org/wiki/Saint_Paul,_Minnesota">Saint Paul</a></td> <td><a href="https://en.wikipedia.org/wiki/Minnesota">Minnesota</a></td> <td>133,156</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>24</td> <td><a href="https://en.wikipedia.org/wiki/Kansas_City,_Missouri">Kansas City</a></td> <td><a href="https://en.wikipedia.org/wiki/Missouri">Missouri</a></td> <td>132,716</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>25</td> <td><a href="https://en.wikipedia.org/wiki/Providence,_Rhode_Island">Providence</a></td> <td><a href="https://en.wikipedia.org/wiki/Rhode_Island">Rhode Island</a></td> <td>132,146</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>26</td> <td><a href="https://en.wikipedia.org/wiki/Denver">Denver</a></td> <td><a href="https://en.wikipedia.org/wiki/Colorado">Colorado</a></td> <td>106,713</td> <td><a href="https://en.wikipedia.org/wiki/Western_United_States">West</a> </td></tr> <tr> <td>27</td> <td><a href="https://en.wikipedia.org/wiki/Indianapolis">Indianapolis</a></td> <td><a href="https://en.wikipedia.org/wiki/Indiana">Indiana</a></td> <td>105,436</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>28</td> <td><a href="https://en.wikipedia.org/wiki/Allegheny,_Pennsylvania">Allegheny</a></td> <td><a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>105,287</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>29</td> <td><a href="https://en.wikipedia.org/wiki/Albany,_New_York">Albany</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>94,923</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>30</td> <td><a href="https://en.wikipedia.org/wiki/Columbus,_Ohio">Columbus</a></td> <td><a href="https://en.wikipedia.org/wiki/Ohio">Ohio</a></td> <td>88,150</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>31</td> <td><a href="https://en.wikipedia.org/wiki/Syracuse,_New_York">Syracuse</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>88,143</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>32</td> <td><a href="https://en.wikipedia.org/wiki/New_Haven,_CT">New Haven</a></td> <td><a href="https://en.wikipedia.org/wiki/Connecticut">Connecticut</a></td> <td>86,045</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>33</td> <td><a href="https://en.wikipedia.org/wiki/Worcester,_Massachusetts">Worcester</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>84,655</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>34</td> <td><a href="https://en.wikipedia.org/wiki/Toledo,_Ohio">Toledo</a></td> <td><a href="https://en.wikipedia.org/wiki/Ohio">Ohio</a></td> <td>81,434</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>35</td> <td><a href="https://en.wikipedia.org/wiki/Richmond,_Virginia">Richmond</a></td> <td><a href="https://en.wikipedia.org/wiki/Virginia">Virginia</a></td> <td>81,388</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>36</td> <td><a href="https://en.wikipedia.org/wiki/Paterson,_New_Jersey">Paterson</a></td> <td><a href="https://en.wikipedia.org/wiki/New_Jersey">New Jersey</a></td> <td>78,347</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>37</td> <td><a href="https://en.wikipedia.org/wiki/Lowell,_Massachusetts">Lowell</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>77,696</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>38</td> <td><a href="https://en.wikipedia.org/wiki/Nashville,_TN">Nashville</a></td> <td><a href="https://en.wikipedia.org/wiki/Tennessee">Tennessee</a></td> <td>76,168</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>39</td> <td><a href="https://en.wikipedia.org/wiki/Scranton,_Pennsylvania">Scranton</a></td> <td><a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>75,215</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>40</td> <td><a href="https://en.wikipedia.org/wiki/Fall_River,_Massachusetts">Fall River</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>74,398</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>41</td> <td><a href="https://en.wikipedia.org/wiki/Cambridge,_Massachusetts">Cambridge</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>70,028</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>42</td> <td><a href="https://en.wikipedia.org/wiki/Atlanta">Atlanta</a></td> <td><a href="https://en.wikipedia.org/wiki/Georgia_(U.S._state)">Georgia</a></td> <td>65,533</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>43</td> <td><a href="https://en.wikipedia.org/wiki/Memphis,_Tennessee">Memphis</a></td> <td><a href="https://en.wikipedia.org/wiki/Tennessee">Tennessee</a></td> <td>64,495</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>44</td> <td><a href="https://en.wikipedia.org/wiki/Wilmington,_Delaware">Wilmington</a></td> <td><a href="https://en.wikipedia.org/wiki/Delaware">Delaware</a></td> <td>61,431</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>45</td> <td><a href="https://en.wikipedia.org/wiki/Dayton">Dayton</a></td> <td><a href="https://en.wikipedia.org/wiki/Ohio">Ohio</a></td> <td>61,220</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>46</td> <td><a href="https://en.wikipedia.org/wiki/Troy,_New_York">Troy</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>60,956</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>47</td> <td><a href="https://en.wikipedia.org/wiki/Grand_Rapids">Grand Rapids</a></td> <td><a href="https://en.wikipedia.org/wiki/Michigan">Michigan</a></td> <td>60,278</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>48</td> <td><a href="https://en.wikipedia.org/wiki/Reading,_Pennsylvania">Reading</a></td> <td><a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>58,661</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>49</td> <td><a href="https://en.wikipedia.org/wiki/Camden,_New_Jersey">Camden</a></td> <td><a href="https://en.wikipedia.org/wiki/New_Jersey">New Jersey</a></td> <td>58,313</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>50</td> <td><a href="https://en.wikipedia.org/wiki/Trenton,_New_Jersey">Trenton</a></td> <td><a href="https://en.wikipedia.org/wiki/New_Jersey">New Jersey</a></td> <td>57,458</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>51</td> <td><a href="https://en.wikipedia.org/wiki/Lynn,_Massachusetts">Lynn</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>55,727</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>52</td> <td><a href="https://en.wikipedia.org/wiki/Lincoln,_Nebraska">Lincoln</a></td> <td><a href="https://en.wikipedia.org/wiki/Nebraska">Nebraska</a></td> <td>55,154</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>53</td> <td><a href="https://en.wikipedia.org/wiki/Charleston,_South_Carolina">Charleston</a></td> <td><a href="https://en.wikipedia.org/wiki/South_Carolina">South Carolina</a></td> <td>54,955</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>54</td> <td><a href="https://en.wikipedia.org/wiki/Hartford">Hartford</a></td> <td><a href="https://en.wikipedia.org/wiki/Connecticut">Connecticut</a></td> <td>53,230</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>55</td> <td><a href="https://en.wikipedia.org/wiki/St._Joseph,_Missouri">St. Joseph</a></td> <td><a href="https://en.wikipedia.org/wiki/Missouri">Missouri</a></td> <td>52,324</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>56</td> <td><a href="https://en.wikipedia.org/wiki/Evansville">Evansville</a></td> <td><a href="https://en.wikipedia.org/wiki/Indiana">Indiana</a></td> <td>50,756</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>57</td> <td><a href="https://en.wikipedia.org/wiki/Los_Angeles">Los Angeles</a></td> <td><a href="https://en.wikipedia.org/wiki/California">California</a></td> <td>50,395</td> <td><a href="https://en.wikipedia.org/wiki/Western_United_States">West</a> </td></tr> <tr> <td>58</td> <td><a href="https://en.wikipedia.org/wiki/Des_Moines">Des Moines</a></td> <td><a href="https://en.wikipedia.org/wiki/Iowa">Iowa</a></td> <td>50,093</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>59</td> <td><a href="https://en.wikipedia.org/wiki/Bridgeport,_Connecticut">Bridgeport</a></td> <td><a href="https://en.wikipedia.org/wiki/Connecticut">Connecticut</a></td> <td>48,866</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>60</td> <td><a href="https://en.wikipedia.org/wiki/Oakland">Oakland</a></td> <td><a href="https://en.wikipedia.org/wiki/California">California</a></td> <td>48,682</td> <td><a href="https://en.wikipedia.org/wiki/Western_United_States">West</a> </td></tr> <tr> <td>61</td> <td><a href="https://en.wikipedia.org/wiki/Portland,_Oregon">Portland</a></td> <td><a href="https://en.wikipedia.org/wiki/Oregon">Oregon</a></td> <td>46,385</td> <td><a href="https://en.wikipedia.org/wiki/Western_United_States">West</a> </td></tr> <tr> <td>62</td> <td><a href="https://en.wikipedia.org/wiki/Saginaw">Saginaw</a></td> <td><a href="https://en.wikipedia.org/wiki/Michigan">Michigan</a></td> <td>46,322</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>63</td> <td><a href="https://en.wikipedia.org/wiki/Salt_Lake_City">Salt Lake City</a></td> <td><a href="https://en.wikipedia.org/wiki/Utah">Utah</a></td> <td>44,843</td> <td><a href="https://en.wikipedia.org/wiki/Western_United_States">West</a> </td></tr> <tr> <td>64</td> <td><a href="https://en.wikipedia.org/wiki/Lawrence,_Massachusetts">Lawrence</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>44,654</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>65</td> <td><a href="https://en.wikipedia.org/wiki/Springfield,_Massachusetts">Springfield</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>44,179</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>66</td> <td><a href="https://en.wikipedia.org/wiki/Manchester,_New_Hampshire">Manchester</a></td> <td><a href="https://en.wikipedia.org/wiki/New_Hampshire">New Hampshire</a></td> <td>44,126</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>67</td> <td><a href="https://en.wikipedia.org/wiki/Utica,_New_York">Utica</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>44,007</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>68</td> <td><a href="https://en.wikipedia.org/wiki/Hoboken,_New_Jersey">Hoboken</a></td> <td><a href="https://en.wikipedia.org/wiki/New_Jersey">New Jersey</a></td> <td>43,648</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>69</td> <td><a href="https://en.wikipedia.org/wiki/Savannah,_Georgia">Savannah</a></td> <td><a href="https://en.wikipedia.org/wiki/Georgia_(U.S._state)">Georgia</a></td> <td>43,189</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>70</td> <td><a href="https://en.wikipedia.org/wiki/Seattle">Seattle</a></td> <td><a href="https://en.wikipedia.org/wiki/Washington_(state)">Washington</a></td> <td>42,837</td> <td><a href="https://en.wikipedia.org/wiki/Western_United_States">West</a> </td></tr> <tr> <td>71</td> <td><a href="https://en.wikipedia.org/wiki/Peoria,_Illinois">Peoria</a></td> <td><a href="https://en.wikipedia.org/wiki/Illinois">Illinois</a></td> <td>41,024</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>72</td> <td><a href="https://en.wikipedia.org/wiki/New_Bedford">New Bedford</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>40,733</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>73</td> <td><a href="https://en.wikipedia.org/wiki/Erie,_Pennsylvania">Erie</a></td> <td><a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>40,634</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>74</td> <td><a href="https://en.wikipedia.org/wiki/Somerville,_Massachusetts">Somerville</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>40,152</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>75</td> <td><a href="https://en.wikipedia.org/wiki/Harrisburg">Harrisburg</a></td> <td><a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>39,385</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>76</td> <td><a href="https://en.wikipedia.org/wiki/Kansas_City,_Kansas">Kansas City</a></td> <td><a href="https://en.wikipedia.org/wiki/Kansas">Kansas</a></td> <td>38,316</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>77</td> <td><a href="https://en.wikipedia.org/wiki/Dallas">Dallas</a></td> <td><a href="https://en.wikipedia.org/wiki/Texas">Texas</a></td> <td>38,067</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>78</td> <td><a href="https://en.wikipedia.org/wiki/Sioux_City">Sioux City</a></td> <td><a href="https://en.wikipedia.org/wiki/Iowa">Iowa</a></td> <td>37,806</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>79</td> <td><a href="https://en.wikipedia.org/wiki/Elizabeth,_New_Jersey">Elizabeth</a></td> <td><a href="https://en.wikipedia.org/wiki/New_Jersey">New Jersey</a></td> <td>37,764</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>80</td> <td><a href="https://en.wikipedia.org/wiki/Wilkes-Barre">Wilkes-Barre</a></td> <td><a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>37,718</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>81</td> <td><a href="https://en.wikipedia.org/wiki/San_Antonio">San Antonio</a></td> <td><a href="https://en.wikipedia.org/wiki/Texas">Texas</a></td> <td>37,673</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>82</td> <td><a href="https://en.wikipedia.org/wiki/Covington,_Kentucky">Covington</a></td> <td><a href="https://en.wikipedia.org/wiki/Kentucky">Kentucky</a></td> <td>37,371</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>83</td> <td><a href="https://en.wikipedia.org/wiki/Portland,_Maine">Portland</a></td> <td><a href="https://en.wikipedia.org/wiki/Maine">Maine</a></td> <td>36,425</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>84</td> <td><a href="https://en.wikipedia.org/wiki/Tacoma,_Washington">Tacoma</a></td> <td><a href="https://en.wikipedia.org/wiki/Washington_(state)">Washington</a></td> <td>36,006</td> <td><a href="https://en.wikipedia.org/wiki/Western_United_States">West</a> </td></tr> <tr> <td>85</td> <td><a href="https://en.wikipedia.org/wiki/Holyoke,_Massachusetts">Holyoke</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>35,637</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>86</td> <td><a href="https://en.wikipedia.org/wiki/Fort_Wayne">Fort Wayne</a></td> <td><a href="https://en.wikipedia.org/wiki/Indiana">Indiana</a></td> <td>35,393</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>87</td> <td><a href="https://en.wikipedia.org/wiki/Binghamton">Binghamton</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>35,005</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>88</td> <td><a href="https://en.wikipedia.org/wiki/Norfolk,_Virginia">Norfolk</a></td> <td><a href="https://en.wikipedia.org/wiki/Virginia">Virginia</a></td> <td>34,871</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>89</td> <td><a href="https://en.wikipedia.org/wiki/Wheeling,_West_Virginia">Wheeling</a></td> <td><a href="https://en.wikipedia.org/wiki/West_Virginia">West Virginia</a></td> <td>34,522</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>90</td> <td><a href="https://en.wikipedia.org/wiki/Augusta,_Georgia">Augusta</a></td> <td><a href="https://en.wikipedia.org/wiki/Georgia_(U.S._state)">Georgia</a></td> <td>33,300</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>91</td> <td><a href="https://en.wikipedia.org/wiki/Youngstown">Youngstown</a></td> <td><a href="https://en.wikipedia.org/wiki/Ohio">Ohio</a></td> <td>33,220</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>92</td> <td><a href="https://en.wikipedia.org/wiki/Duluth">Duluth</a></td> <td><a href="https://en.wikipedia.org/wiki/Minnesota">Minnesota</a></td> <td>33,115</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>93</td> <td><a href="https://en.wikipedia.org/wiki/Yonkers">Yonkers</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>32,033</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>94</td> <td><a href="https://en.wikipedia.org/wiki/Lancaster,_Pennsylvania">Lancaster</a></td> <td><a href="https://en.wikipedia.org/wiki/Pennsylvania">Pennsylvania</a></td> <td>32,011</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>95</td> <td><a href="https://en.wikipedia.org/wiki/Springfield,_Ohio">Springfield</a></td> <td><a href="https://en.wikipedia.org/wiki/Ohio">Ohio</a></td> <td>31,895</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>96</td> <td><a href="https://en.wikipedia.org/wiki/Quincy,_Illinois">Quincy</a></td> <td><a href="https://en.wikipedia.org/wiki/Illinois">Illinois</a></td> <td>31,494</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>97</td> <td><a href="https://en.wikipedia.org/wiki/Mobile,_Alabama">Mobile</a></td> <td><a href="https://en.wikipedia.org/wiki/Alabama">Alabama</a></td> <td>31,076</td> <td><a href="https://en.wikipedia.org/wiki/Southern_United_States">South</a> </td></tr> <tr> <td>98</td> <td><a href="https://en.wikipedia.org/wiki/Topeka">Topeka</a></td> <td><a href="https://en.wikipedia.org/wiki/Kansas">Kansas</a></td> <td>31,007</td> <td><a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwest</a> </td></tr> <tr> <td>99</td> <td><a href="https://en.wikipedia.org/wiki/Elmira,_New_York">Elmira</a></td> <td><a href="https://en.wikipedia.org/wiki/New_York_(state)">New York</a></td> <td>30,893</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr> <tr> <td>100</td> <td><a href="https://en.wikipedia.org/wiki/Salem,_Massachusetts">Salem</a></td> <td><a href="https://en.wikipedia.org/wiki/Massachusetts">Massachusetts</a></td> <td>30,801</td> <td><a href="https://en.wikipedia.org/wiki/Northeastern_United_States_(U.S._Census_Bureau)">Northeast</a> </td></tr></tbody></table><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=1890_United_States_census&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span><cite><a href="http://purl.org/net/nysl/nysdocs/9643270">&quot;Library Bibliography Bulletin 88, New York State Census Records, 1790–1925&quot;</a>. <a href="https://en.wikipedia.org/wiki/New_York_State_Library">New York State Library</a>. October 1981. p. 44 (p. 50 of PDF). <a href="https://web.archive.org/web/20090130004637/http://purl.org/net/nysl/nysdocs/9643270">Archived</a> from the original on January 30, 2009<span>. Retrieved <span>December 15,</span> 2008</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite><a href="https://en.wikipedia.org/wiki/Leon_E._Truesdell">Truesdell, Leon E.</a> (1965). <i>The Development of Punch Card Tabulation in the Bureau of the Census: 1890–1940</i>. US GPO.</cite></span> </li> <li><span><b>^</b></span> <span><cite><i>Report of the Commissioner of Labor In Charge of The Eleventh Census to the Secretary of the Interior for the Fiscal Year Ending June 30, 1895</i>. Washington, DC: <a href="https://en.wikipedia.org/wiki/United_States_Government_Publishing_Office">United States Government Publishing Office</a>. July 29, 1895. <a href="https://en.wikipedia.org/wiki/Hdl_(identifier)">hdl</a>:<a href="https://hdl.handle.net/2027%2Fosu.32435067619882">2027/osu.32435067619882</a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a> <a href="https://search.worldcat.org/oclc/867910652">867910652</a>.</cite> p. 9: &quot;You may confidently look for the rapid reduction of the force of this office after the 1st of October, and the entire cessation of clerical work during the present calendar year. ... The condition of the work of the Census Division and the condition of the final reports show clearly that the work of the Eleventh Census will be completed at least two years earlier than was the work of the Tenth Census.&quot; — Carroll D. Wright, Commissioner of Labor in Charge</span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www2.census.gov/prod2/statcomp/documents/1991-02.pdf">&quot;Population and Area (Historical Censuses)&quot;</a> <span>(PDF)</span>. United States Census Bureau. <a href="https://web.archive.org/web/20080624185938/http://www2.census.gov/prod2/statcomp/documents/1991-02.pdf">Archived</a> <span>(PDF)</span> from the original on June 24, 2008<span>. Retrieved <span>June 20,</span> 2008</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Austrian, Geoffrey D. (1982). <i>Herman Hollerith: Forgotten Giant of Information Processing</i>. New York: Columbia University Press. pp. <span>85–</span>86. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-231-05146-8"><bdi>0-231-05146-8</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Dippie, Brian W. (1982). <span><a href="https://archive.org/details/vanishingamerica00bria"><i>The Vanishing American: White Attitudes and U.S. Indian Policy</i></a></span>. Middleton, CT: Wesleyan University Press. p. ??. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-8195-5056-6"><bdi>0-8195-5056-6</bdi></a>.</cite> The data yielded by this census provided strong evidence that the United States&#39; policies towards <a href="https://en.wikipedia.org/wiki/Indigenous_peoples_of_the_Americas">Native Americans</a> had had a significant impact on the enumeration of the census in the second half of the 19th century. US domestic policy combined with wars, genocide, famine, disease, a declining birthrate, and <a href="https://en.wikipedia.org/wiki/Exogamy">exogamy</a> (with the children of biracial families declaring themselves to be white rather than Indian) accounted for the decrease in the enumeration of the census. <cite>Chalk, Frank; Jonassohn, Kurt (1990). <span><a href="https://archive.org/details/historysociology00chal"><i>The History and Sociology of Genocide: Analyses and Case Studies</i></a></span>. New Haven: Yale University Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-300-04446-1"><bdi>0-300-04446-1</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Porter, Robert; Gannett, Henry; Hunt, William (1895). <i>&quot;Progress of the Nation&quot;, in &quot;Report on Population of the United States at the Eleventh Census: 1890, Part 1&quot;</i>. Bureau of the Census. pp. <span>xviii–</span>xxxiv.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Turner, Frederick Jackson (1920). <a href="https://www.gutenberg.org/files/22994/22994-h/22994-h.htm#Page_1">&quot;The Significance of the Frontier in American History&quot;</a>. <i>The Frontier in American History</i>. p. 1.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Gannett, Henry (1894). <span><a href="https://www.jstor.org/stable/2276233">&quot;Was the Count of Population in 1890 Reasonably Correct?&quot;</a></span>. <i>Publications of the American Statistical Association</i>. <b>4</b> (28/29): <span>99–</span>102. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F2276233">10.2307/2276233</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1522-5437">1522-5437</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/2276233">2276233</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Blake, Kellee (Spring 1996). <a href="https://www.archives.gov/publications/prologue/1996/spring/1890-census-1.html">&quot;First in the Path of the Firemen: The Fate of the 1890 Population Census, Part 1&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Prologue_(magazine)">Prologue Magazine</a></i>. <b>28</b> (1). Washington, DC: <a href="https://en.wikipedia.org/wiki/National_Archives_and_Records_Administration">National Archives and Records Administration</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0033-1031">0033-1031</a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a> <a href="https://search.worldcat.org/oclc/321015582">321015582</a><span>. Retrieved <span>April 13,</span> 2013</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Blake, Kellee (Spring 1996). <a href="https://www.archives.gov/publications/prologue/1996/spring/1890-census-3.html">&quot;First in the Path of the Firemen: The Fate of the 1890 Population Census, Part 3&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Prologue_(magazine)">Prologue Magazine</a></i>. <b>28</b> (1). Washington, DC: <a href="https://en.wikipedia.org/wiki/National_Archives_and_Records_Administration">National Archives and Records Administration</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0033-1031">0033-1031</a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a> <a href="https://search.worldcat.org/oclc/321015582">321015582</a><span>. Retrieved <span>April 13,</span> 2013</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.census.gov/history/www/genealogy/decennial_census_records/availability_of_1890_census.html">&quot;Availability of 1890 Census – History&quot;</a>. <i>U.S. Census Bureau</i><span>. Retrieved <span>March 28,</span> 2017</span>.</cite></span> </li> <li><span><b>^</b></span> <span>Including <a href="https://en.wikipedia.org/wiki/Indian_Territory">Indian Territory</a>, which was yet to be combined with <a href="https://en.wikipedia.org/wiki/Oklahoma_Territory">Oklahoma Territory</a> to form the state of Oklahoma.</span> </li> <li><span><b>^</b></span> <span>The District of Columbia is not a state but was created with the passage of the <a href="https://en.wikipedia.org/wiki/Residence_Act">Residence Act</a> of 1790.</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.census.gov/library/working-papers/1998/demo/POP-twps0027.html"><i>Population of the 100 Largest Cities and Other Urban Places in the United States: 1790 to 1990</i></a>, U.S. Census Bureau, 1998</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://web.archive.org/web/20161203020637/http://www.census.gov/econ/census/help/geography/regions_and_divisions.html">&quot;Regions and Divisions&quot;</a>. U.S. Census Bureau. Archived from <a href="https://www.census.gov/econ/census/help/geography/regions_and_divisions.html">the original</a> on December 3, 2016<span>. Retrieved <span>September 9,</span> 2016</span>.</cite></span> </li> </ol></div></div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=1890_United_States_census&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Richmond_Mayo-Smith">Mayo-Smith, Richmond</a> (1891), &quot;<a href="https://en.wikisource.org/wiki/The_Eleventh_Census_of_the_United_States">The Eleventh Census of the United States</a>&quot;. In: <a href="https://en.wikisource.org/wiki/The_Economic_Journal/Volume_1"><i>The Economic Journal</i> (<i>EJ</i>), Vol. 1</a>, pp. 43–58 (in <span><a href="https://en.wikipedia.org/wiki/File:Wikisource-logo.svg"></a></span> <a href="https://en.wikipedia.org/wiki/Wikisource">Wikisource</a>)</li> <li>Walker, Francis A. (1888). &quot;<a href="https://www.jstor.org/stable/1879486">The Eleventh Census of the United States</a>&quot;. <i>The Quarterly Journal of Economics</i>. <b>2</b> (2): 135–161.</li> <li><a href="http://www2.census.gov/prod2/statcomp/documents/1891-02.pdf">1891 U.S Census Report</a> Contains 1890 census results</li> <li><a href="https://www.census.gov/population/www/censusdata/hiscendata.html">Historical US Census data</a> from the U.S. Census Bureau website</li> <li><a href="http://www.columbia.edu/cu/computinghistory/census-tabulator.html"><i>Hollerith 1890 Census Tabulator</i> by Columbia University</a></li> <li><a href="https://www.archives.gov/publications/prologue/1996/spring/1890-census-1.html">&quot;The Fate of the 1890 Population Census&quot;</a> from the National Archives website</li></ul><div><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q2095711#identifiers"></a></span></div></th></tr><tr><th>National</th><td><div><ul><li><span><a href="https://id.loc.gov/authorities/sh2007100396">United States</a></span></li><li><span><a href="https://www.nli.org.il/en/authorities/987007561785605171">Israel</a></span></li></ul></div></td></tr><tr><th>Other</th><td><div><ul><li><span><a href="https://lux.collections.yale.edu/view/concept/a18a786e-e72e-41e6-8057-54934e030921">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div> Flow (psychology) - Wikipedia https://en.wikipedia.org/wiki/Flow_(psychology) OMY32CVtrsaOHZhBbW_PmM62eMOE89n_QzMeUA== Mon, 11 May 2026 06:11:31 +0000 Full immersion in an activity <div>Full immersion in an activity</div><div>&quot;Flow state&quot; redirects here. For the album, see <a href="https://en.wikipedia.org/wiki/Flow_State"><i>Flow State</i></a>.</div><table><tbody><tr><td><div><span><a href="https://en.wikipedia.org/wiki/File:OOjs_UI_icon_robot.svg"></a></span></div></td><td><div>Parts of this article <b>may incorporate text from a <a href="https://en.wikipedia.org/wiki/Wikipedia:Large_language_models">large language model</a>, which is <a href="https://en.wikipedia.org/wiki/Wikipedia:LLM">prohibited in Wikipedia articles</a></b>.<span> It may include <a href="https://en.wikipedia.org/wiki/Hallucination_(artificial_intelligence)">hallucinated</a> information, <a href="https://en.wikipedia.org/wiki/Wikipedia:COPYVIO">copyright violations</a>, claims not <a href="https://en.wikipedia.org/wiki/Wikipedia:V">verified</a> in cited sources, <a href="https://en.wikipedia.org/wiki/Wikipedia:OR">original research</a>, or <a href="https://en.wikipedia.org/wiki/Wikipedia:Fictitious_references">fictitious references</a>. Any such material should be <a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit">removed</a>. The reason given is: <b>Text added in <a href="https://en.wikipedia.org/wiki/Special:Diff/1167941571">this 2023 edit</a>; note <a href="https://en.wikipedia.org/wiki/Wikipedia:AISIGNS">WP:AISIGNS</a> in superficial analyses, vocab distribution typical of 2023 LLMs, title case etc</b></span> <span><i>(<span>February 2026</span>)</i></span><span><i> (<small><a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table><figure><a href="https://en.wikipedia.org/wiki/File:Scout_Girl_in_Concentration.jpg"></a><figcaption>Concentrating on a task, one aspect of flow</figcaption></figure><p><b>Flow</b> in <a href="https://en.wikipedia.org/wiki/Positive_psychology">positive psychology</a>, also known colloquially as being <b>in</b> <b>the zone</b> or focused, is the <a href="https://en.wikipedia.org/wiki/Mental_state">mental state</a> in which a person performing some activity is fully immersed in a feeling of energized <a href="https://en.wikipedia.org/wiki/Attention">focus</a>, full involvement, and enjoyment in the process of the activity. In essence, flow is characterized by the complete absorption in what one does, and a resulting transformation in one&#39;s sense of time.<sup><span>[</span>1<span>]</span></sup> Flow is the melting together of action and <a href="https://en.wikipedia.org/wiki/Consciousness">consciousness</a>; the state of finding a balance between a skill and how challenging that task is. It requires a high level of concentration. Flow is used as a <a href="https://en.wikipedia.org/wiki/Coping">coping</a> skill for stress and anxiety when productively pursuing a form of leisure that matches one&#39;s skill set.<sup><span>[</span>2<span>]</span></sup> </p><p>First presented in the 1975 book <i>Beyond Boredom and Anxiety</i> by the Hungarian-American psychologist <a href="https://en.wikipedia.org/wiki/Mihaly_Csikszentmihalyi">Mihály Csíkszentmihályi</a>,<sup><span>[</span>3<span>]</span></sup><sup><span>[</span>4<span>]</span></sup> the concept has been widely referred to across a variety of fields (and is particularly well recognized in <a href="https://en.wikipedia.org/wiki/Occupational_therapy">occupational therapy</a>). </p><p>The flow state shares many characteristics with <a href="https://en.wikipedia.org/wiki/Hyperfocus">hyperfocus</a>.<sup><span>[</span>5<span>]</span></sup> However, hyperfocus is not always described in a positive light. Some examples include spending &quot;too much&quot; time playing video games or becoming pleasurably absorbed by one aspect of an assignment or task to the detriment of the overall assignment. In some cases, hyperfocus can &quot;capture&quot; a person, perhaps causing them to appear unfocused or to start several <a href="https://en.wikipedia.org/wiki/Project">projects</a>, but complete few. Hyperfocus is often mentioned &quot;in the context of <a href="https://en.wikipedia.org/wiki/Autism">autism</a>, <a href="https://en.wikipedia.org/wiki/Schizophrenia">schizophrenia</a>, and <a href="https://en.wikipedia.org/wiki/Attention_deficit_hyperactivity_disorder">attention deficit hyperactivity disorder</a> – conditions that have consequences on attentional abilities.&quot;<sup><span>[</span>5<span>]</span></sup> </p><p>Flow is an individual experience and the idea behind flow originated from the <a href="https://en.wikipedia.org/wiki/Sport_psychology">sport psychology</a> theory about an Individual Zone of Optimal Functioning. The individuality of the concept of flow suggests that each person has their subjective area of flow, where they would function best given the situation. One is most likely to experience flow at moderate levels of psychological <a href="https://en.wikipedia.org/wiki/Arousal">arousal</a>, as one is unlikely to be overwhelmed, but not understimulated to the point of boredom.<sup><span>[</span>6<span>]</span></sup> </p><div><h2>Etymology</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>Flow is so named because, during Csíkszentmihályi&#39;s 1975 interviews, several people described their &quot;flow&quot; experiences using the metaphor of a water current carrying them along: </p><blockquote> <p>We have called this state the flow experience, because this is the term many of the people we interviewed had used in their descriptions of how it felt to be in top form: &quot;It was like floating,&quot; &quot;I was carried on by the flow.&quot; </p> </blockquote><div><p>— Csikszentmihályi, Flow (1990)<sup><span>[</span>7<span>]</span></sup></p></div><div><h2>History</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p><a href="https://en.wikipedia.org/wiki/Mihaly_Csikszentmihalyi">Mihaly Csikszentmihályi</a> and others began researching flow after he became fascinated by artists who would essentially get lost in their work.<sup><span>[</span>8<span>]</span></sup> Artists, especially painters, got so immersed in their work that they would disregard their need for food, water and even sleep. The theory of flow came about when Csikszentmihályi tried to understand the phenomenon experienced by these artists. Flow research became prevalent in the 1980s and 1990s, with Csikszentmihályi and his colleagues in Italy still at the forefront. Researchers grew interested in optimal experiences and emphasizing positive experiences, especially in places such as schools and the business world.<sup><span>[</span>9<span>]</span></sup> They also began studying the theory of flow at this time.<sup><span>[</span>10<span>]</span></sup> </p><p>The <a href="https://en.wikipedia.org/wiki/Cognitive_science">cognitive science</a> of flow has been studied under the rubric of effortless attention.<sup><span>[</span>11<span>]</span></sup> </p><div><h2>Components</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Jeanne Nakamura and Csíkszentmihályi identify the following six factors as encompassing an experience of flow:<sup><span>[</span>10<span>]</span></sup> </p><ol><li>Intense and focused <a href="https://en.wikipedia.org/wiki/Attentional_control">concentration</a> on <a href="https://en.wikipedia.org/wiki/The_present">the present</a> moment</li> <li>Merging of <a href="https://en.wikipedia.org/wiki/Action_(philosophy)">action</a> and <a href="https://en.wikipedia.org/wiki/Awareness">awareness</a></li> <li>A loss of <a href="https://en.wikipedia.org/wiki/Self-reflection#Modern_era">reflective</a> <a href="https://en.wikipedia.org/wiki/Self-consciousness">self-consciousness</a></li> <li>A sense of personal control or agency over the situation or activity</li> <li>A distortion of temporal experience, as one&#39;s <a href="https://en.wikipedia.org/wiki/Sense_of_time">subjective experience of time</a> is altered</li> <li>Experience of the activity as intrinsically <a href="https://en.wikipedia.org/wiki/Reward_system">rewarding</a>, also referred to as <a href="https://en.wiktionary.org/wiki/autotelic">autotelic</a> experience</li></ol><p>Those aspects can appear independently of each other, but only in combination do they constitute a so-called <i>flow experience</i>. Additionally, psychology writer Kendra Cherry has mentioned three other components that Csíkszentmihályi lists as being a part of the flow experience:<sup><span>[</span>12<span>]</span></sup> </p><ol><li>Immediate feedback</li> <li>Feeling the potential to succeed</li> <li>Feeling so engrossed in the experience that other needs become negligible</li></ol><p>Just as with the conditions listed above, these conditions can be independent of one another. </p><p>In 2021, Cameron Norsworthy and colleagues aimed to address the inconsistencies and concerns of many of the flow-related models and studies, and proposed a framework that differentiated the flow antecedents and experiential dimensions.<sup><span>[</span>13<span>]</span></sup> Norsworthy et al. identified a core experience of flow including overarching antecedent constructs: </p><ol><li>Optimal challenge: A perceived capability to meet the challenging demands of the situation</li> <li>High motivation: A high motivational force</li></ol><p>And recurring characteristics of the flow experience itself included: </p><ol><li>Absorption: A state of absorption in the task characterized by focused, undistracted attention, and a merging of action and awareness</li> <li>Effort-less control: A high sense of control in which the task feels less effortful than is typical for that person, characterized by fluidity of performance and an absence of concern over losing control</li> <li>Intrinsic reward: An intrinsically rewarding experience characterized by positive valence and optimal levels of arousal</li></ol><p>The proposed definition of flow: Flow is an intrinsically rewarding state of absorption in a task in which a high degree of control feels more effort-less than normal. </p><div><h2>Mechanism</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>In any given moment, a great deal of information is made available to each individual. Psychologists have found that one&#39;s mind can attend to only a certain amount of information at a time. According to Csikszentmihályi&#39;s 2004 <a href="https://en.wikipedia.org/wiki/TED_(conference)">TED</a> talk, that number is about &quot;110 <a href="https://en.wikipedia.org/wiki/Baud">bits of information per second</a>.&quot;<sup><span>[</span>14<span>]</span></sup> That may seem like a lot of information, but simple daily tasks take quite a lot of information. Just decoding speech takes about 40–60 bits of information per second,<sup><span>[</span>15<span>]</span></sup> which is why when having a conversation, one cannot focus as much <a href="https://en.wikipedia.org/wiki/Attention">attention</a> on other things.<sup><span>[</span>16<span>]</span></sup> </p><p>Generally, people have the ability to decide what they will give their full attention to. This excludes basic distinctive feelings, such as hunger and pain. However, when one is in the flow state, they are completely engrossed with the one task at hand and, without making the conscious decision to do so, lose awareness of all other things: time, people, distractions, and even basic bodily needs.<sup><span>[</span>17<span>]</span></sup><sup><span>[</span>18<span>]</span></sup> According to Csikszentmihályi, this event occurs because all of the attention of the person in the flow state is on the task at hand; there is no more attention to be allocated.<sup><span>[</span>19<span>]</span></sup> </p><p>The flow state has been described by Csikszentmihályi as the &quot;optimal experience&quot; in that one gets to a level of high gratification from the experience.<sup><span>[</span>20<span>]</span></sup> Achieving this experience is considered to be personal and &quot;depends on the ability&quot; of the individual.<sup><span>[</span>20<span>]</span></sup> One&#39;s capacity and desire to overcome challenges in order to achieve their ultimate goals leads not only to the optimal experience but also to a sense of <a href="https://en.wikipedia.org/wiki/Life_satisfaction">life satisfaction</a> overall.<sup><span>[</span>20<span>]</span></sup> </p><div><h3>Operationalizing flow</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>Despite the attraction of flow and the varying flow interventions (e.g., mindfulness, goal-setting, visualisation) there has existed no gold standard intervention to promote flow experiences. Recently, Norsworthy et al. found continued evidence that it may be possible to &#39;train&#39; flow through an educational intervention of flow.<sup><span>[</span>21<span>]</span></sup><sup><span>[</span>22<span>]</span></sup> </p><div><h2>Measurement</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>There are three common ways to measure flow experiences: the flow questionnaire (FQ), the experience sampling method (ESM), and the &quot;standardized scales of the componential approach.&quot;<sup><span>[</span>23<span>]</span></sup> </p><div><h3>Flow questionnaire</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>The FQ requires individuals to identify definitions of flow and situations in which they believe that they have experienced flow, followed by a section that asks them to evaluate their personal experiences in these flow-inducing situations. The FQ identifies flow as multiple constructs, therefore allowing the results to be used to estimate differences in the likelihood of experiencing flow across a variety of factors. Another strength of the FQ is that it does not assume that everyone&#39;s flow experiences are the same. Because of this, the FQ is the ideal measure for estimating the prevalence of flow.<sup><span>[</span>24<span>]</span></sup> However, the FQ has some weaknesses that more recent methods have set out to address. The FQ does not allow for a measurement of the intensity of flow during specific activities. This method also does not measure the influence of the ratio of challenge to skill on the flow state.<sup><span>[</span>23<span>]</span></sup> </p><div><h3>Experience sampling method</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>The ESM requires individuals to fill out the experience sampling form (ESF) at eight randomly chosen time intervals throughout the day. The purpose of this is to understand subjective experiences by estimating the time intervals that individuals spend in specific states during everyday life. The ESF is made up of 13 categorical items and 29 scaled items. The purpose of the categorical items is to determine the context and <a href="https://en.wikipedia.org/wiki/Motivation">motivational</a> aspects of the current actions (these items include: time, location, companionship/desire for companionship, activity being performed, reason for performing activity). Because these are <a href="https://en.wikipedia.org/wiki/Open-ended_question">open-ended questions</a>, the answers need to be coded by researchers. This needs to be done carefully so as to avoid any biases in the statistical analysis. The scaled items are intended to measure the levels of a variety of subjective feelings that the individual may be experiencing. The ESM is more complex than the FQ and contributes to understanding how flow plays out in a variety of situations. However, the possible biases make it a risky choice.<sup><span>[</span>23<span>]</span></sup> </p><div><h3>Standardized scales</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>Jackson and colleagues<sup><span>[</span>25<span>]</span></sup><sup><span>[</span>26<span>]</span></sup><sup><span>[</span>27<span>]</span></sup><sup><span>[</span>28<span>]</span></sup><sup><span>[</span>29<span>]</span></sup> have created several scales that have been proven to be psychometrically valid and reliable: the Flow State Scale-2 (FSS-2)<sup><span>[</span>25<span>]</span></sup><sup><span>[</span>26<span>]</span></sup><sup><span>[</span>27<span>]</span></sup><sup><span>[</span>29<span>]</span></sup> (which measures flow as a state), and the Dispositional Flow Scale-2 (DFS-2)<sup><span>[</span>25<span>]</span></sup><sup><span>[</span>26<span>]</span></sup><sup><span>[</span>27<span>]</span></sup><sup><span>[</span>29<span>]</span></sup> (designed to measure flow as a trait, either general or domain-specific), being the most widely known. The statistical analysis of the DFS-2 and FSS-2 scales gives a more complete understanding of flow from a dimensional perspective than the ESM or the FQ.<sup><span>[</span>30<span>]</span></sup> Jackson and colleagues also created short versions of the FSS-2 and DFS-2, and an additional brief scale that assesses the subjective experience of flow, called the Core Flow Scales.<sup><span>[</span>28<span>]</span></sup><sup><span>[</span>29<span>]</span></sup> More recently, the Psychological Flow Scale (PFS) that was designed to be used across domains and scientific disciplines was validated and offers a parsimonious alternative model of flow.<sup><span>[</span>31<span>]</span></sup> </p><div><h2>Characteristics</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><p>The flow state can be entered while performing any activity; however, it is more likely to occur when the task or activity is wholeheartedly engaged for <a href="https://en.wikipedia.org/wiki/Motivation#Types_of_motivation">intrinsic purposes</a>.<sup><span>[</span>19<span>]</span></sup><sup><span>[</span>33<span>]</span></sup> Passive activities such as taking a bath or even watching TV usually do not elicit a flow experience because active engagement is prerequisite to entering the flow state.<sup><span>[</span>34<span>]</span></sup><sup><span>[</span>35<span>]</span></sup> While the activities that induce flow vary and may be multifaceted, Csikszentmihályi asserts that the experience of flow is similar whatever the activity.<sup><span>[</span>36<span>]</span></sup> </p><p>Flow theory postulates that three conditions must be met to achieve flow: </p><ol><li>The activity must have clear goals and progress. This establishes structure and direction.<sup><span>[</span>37<span>]</span></sup></li> <li>The task must provide clear and immediate feedback. This helps to negotiate any changing demands and allows adjusting performance to maintain the flow state.<sup><span>[</span>37<span>]</span></sup></li> <li>Good balance is required between the <i>perceived</i> challenges of the task and one&#39;s <i>perceived</i> skills. Confidence in the ability to complete the task is required.<sup><span>[</span>37<span>]</span></sup></li></ol><p>It has been argued that the antecedent factors of flow are interrelated, and as such, a balance between perceived challenges and skills requires that the goals are clear and feedback is effective. Thus, such balance can be identified as the central precondition of flow experience.<sup><span>[</span>38<span>]</span></sup> </p><p>In 1987, Massimini, Csíkszentmihályi and Carli published the eight-channel (or eight-sector) model of flow.<sup><span>[</span>39<span>]</span></sup> (See Figure.) Antonella Delle Fave, who worked with Fausto Massimini at the <a href="https://en.wikipedia.org/wiki/University_of_Milan">University of Milan</a>, calls this graph the Experience Fluctuation Model.<sup><span>[</span>40<span>]</span></sup> The model depicts the channels of experience that result from different levels of perceived challenges and perceived skills. The graph illustrates another aspect of flow: it is more likely to occur when the activity is a higher-than-average challenge (above the center point) and the individual has above-average skills (to the right of the center point).<sup><span>[</span>19<span>]</span></sup> The center of the graph where the sectors meet represents the average level of challenge and skill across all individual daily activities. The further from the center an experience is, the greater the intensity of that state of being, whether it is flow or anxiety or boredom or relaxation.<sup><span>[</span>33<span>]</span></sup> </p><p>Several problems of the model have been discussed in the literature.<sup><span>[</span>38<span>]</span></sup><sup><span>[</span>41<span>]</span></sup> One is that it does not ensure the perceived balance between challenges and skills, which is said to be the central precondition of flow experience. Individuals with a low average level of skills and a high average level of challenges (or the converse) do not necessarily experience a match between skills and challenges when both are above their individual average.<sup><span>[</span>42<span>]</span></sup> Another study found that low challenge situations which were surpassed by skill were associated with enjoyment, relaxation, and happiness, which, they claim, is contrary to flow theory.<sup><span>[</span>43<span>]</span></sup> </p><p>Schaffer (2013) proposed seven flow conditions: </p><ol><li>Knowing what to do</li> <li>Knowing how to do it</li> <li>Knowing how well one is doing</li> <li>Knowing where to go (if navigation is involved)</li> <li>High perceived challenges</li> <li>High perceived skills</li> <li>Freedom from distractions</li></ol><p>Schaffer published a flow condition questionnaire (FCQ), to measure each of these seven flow conditions for any given task or activity.<sup><span>[</span>44<span>]</span></sup> </p><div><h3>Challenges to maintaining flow</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><p>Some of the challenges to staying in flow include states of <a href="https://en.wikipedia.org/wiki/Apathy">apathy</a>, <a href="https://en.wikipedia.org/wiki/Boredom">boredom</a>, and <a href="https://en.wikipedia.org/wiki/Anxiety">anxiety</a>. The state of apathy is characterized by easy challenges and low skill level requirements, resulting in a general lack of interest in the activity. Boredom is a slightly different state that occurs when challenges are few, but one&#39;s skill level exceeds those challenges causing one to seek higher challenges. A state of anxiety occurs when challenges are high enough to exceed perceived skill level, causing distress and uneasiness. These states in general prevent achieving the balance necessary for flow.<sup><span>[</span>45<span>]</span></sup> Csíkszentmihályi has said, &quot;If challenges are too low, one gets back to flow by increasing them. If challenges are too great, one can return to the flow state by learning new skills.&quot;<sup><span>[</span>12<span>]</span></sup> </p><div><h3>The autotelic personality</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><p>Csíkszentmihályi hypothesized that people with certain personality traits may be better able to achieve flow than the average person. These traits include curiosity, persistence, low egotism, and a high propensity to perform activities for intrinsic reasons. People with most of these personality traits are said to have an <i>autotelic personality</i>, i.e. a disposition to actively seek challenges and flow experiences.<sup><span>[</span>33<span>]</span></sup><sup><span>[</span>46<span>]</span></sup> The term &quot;autotelic&quot; derives from two <a href="https://en.wikipedia.org/wiki/Ancient_Greek">Greek</a> words, <i>autos</i> (&quot;self&quot;) and <i>telos</i> (&quot;end&quot; or &quot;goal&quot;). </p><p>There is scant research on the <i>autotelic personality</i>, but results of the few studies that have been conducted suggest that indeed some people are more likely to experience flow than others. One researcher (Abuhamdeh, 2000) found that people with an autotelic personality have a greater preference for &quot;high-action-opportunity, high-skills situations that stimulate them and encourage growth&quot; compared to those without an autotelic personality.<sup><span>[</span>33<span>]</span></sup> It is in such high-challenge, high-skills situations that people are most likely to experience flow. </p><p>Experimental evidence shows that a balance between individual skills and demands of the task (compared to boredom and overload) only elicits the flow experience in individuals having an internal <a href="https://en.wikipedia.org/wiki/Locus_of_control">locus of control</a><sup><span>[</span>47<span>]</span></sup> or a habitual action orientation.<sup><span>[</span>48<span>]</span></sup> Several correlational studies found <a href="https://en.wikipedia.org/wiki/Need_for_achievement">need for achievement</a> to be a personal characteristic that fosters flow experiences.<sup><span>[</span>49<span>]</span></sup><sup><span>[</span>50<span>]</span></sup><sup><span>[</span>51<span>]</span></sup> </p><p>Autotelic Personality also has been shown in studies to correlate and show overlapping of flow in personal life and the <a href="https://en.wikipedia.org/wiki/Big_Five_personality_traits">Big Five Personality Traits</a> of Extraversion, Agreeableness, <a href="https://en.wikipedia.org/wiki/Conscientiousness">Conscientiousness</a>, Neuroticism, and Openness to Experience, especially the traits of agreeableness and extraversion. Study of Autotelic Personality is difficult as most studies are performed through self-evaluation, a <a href="https://en.wikipedia.org/wiki/Big_Five_personality_traits#Limitations_of_self-report">recognized difficulty</a> for Big Five questionnaires.<sup><span>[</span>52<span>]</span></sup><sup><span>[</span>53<span>]</span></sup> </p><div><h2>Group</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><div>See also: <a href="https://en.wikipedia.org/wiki/Crowd_psychology">Crowd psychology</a></div><p>More than one type of flow exists. Group flow (or <b>team flow</b>) is notably different from independent flow, as it is inherently mutual. Group flow is attainable when the performance unit is a group, such as a team or musical group. When groups cooperate to agree on goals and patterns, social flow, commonly known as group cohesion, is much more likely to occur. If a group still has not entered flow, a team-level challenge may stimulate the group to harmonize.<sup><span>[</span>54<span>]</span></sup> Group flow is different from synchronized solitary flow, in which a group is simultaneously experiencing individual flow. Group Flow occurs in an interpersonal manner, in which the act of others being present is inherent to the cause of the state of flow.<sup><span>[</span>55<span>]</span></sup> </p><p>In research presented in a review written by <a href="https://en.wikipedia.org/wiki/PLOS_One">PLoS ONE</a>,<sup><span>[</span>55<span>]</span></sup> Pels <i>et al.</i> stated, &quot;Group contexts introduce many additional variables that cause individuals to act, think, and feel differently during group situations compared to solitary situations.&quot; Due to these additional variables, the cause and effect of flow are vastly different and unique to the experience of individual flow, hence providing evidence for the existence of a separate flow state: group flow. </p><div><h3>Physiology of group flow</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><p>Snijdewint<sup><span>[</span>56<span>]</span></sup> studies the correlation of the physiological effect of a group that simultaneously reports a &quot;flow&quot; state. This research concludes that between many similar studies when a participant reports a feeling of flow state (in synchronization or due to a group environment), there are similarities in the cardiovascular triggers<sup><span>[</span>57<span>]</span></sup> that the participants experience<b>.</b> </p><div><h2>Applications</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div><div><h3>Applications suggested by Csíkszentmihályi versus other practitioners</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div><p>Only Csíkszentmihályi seems to have published suggestions for <a href="https://en.wikipedia.org/wiki/Extrinsic">extrinsic</a> applications of the flow concept, such as <a href="https://en.wikipedia.org/wiki/Design">design</a> methods for playgrounds to elicit the flow experience. Other practitioners of Csíkszentmihályi&#39;s flow concept focus on <a href="https://en.wikipedia.org/wiki/Intrinsic_and_extrinsic_properties_(philosophy)">intrinsic</a> applications, such as <a href="https://en.wikipedia.org/wiki/Spirituality">spirituality</a>, <a href="https://en.wikipedia.org/wiki/Performance_improvement">performance improvement</a>, or <a href="https://en.wikipedia.org/wiki/Self-help">self-help</a>. </p><div><h3>Education</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=17"><span>edit</span></a><span>]</span></span></div><table><tbody><tr><td></td><td><div>This section <b>is written like a <a href="https://en.wikipedia.org/wiki/Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_publisher_of_original_thought">personal reflection, personal essay, or argumentative essay</a></b> that states a Wikipedia editor&#39;s personal feelings or presents an original argument about a topic.<span> Please <a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit">help improve it</a> by rewriting it in an <a href="https://en.wikipedia.org/wiki/Wikipedia:Writing_better_articles#Information_style_and_tone">encyclopedic style</a>.</span> <span><i>(<span>August 2023</span>)</i></span><span><i> (<small><a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table><p>Flow state theory suggests that when individuals are in a state of flow, they experience deep immersion, focus, and intrinsic motivation in their activities.<sup><span>[</span>58<span>]</span></sup> In the context of education, flow has been associated with increased student engagement, which is a key determinant of learning success. </p><p>Numerous studies have examined the relationship between flow and student engagement, demonstrating positive associations. For example, Csikszentmihalyi and Larson (1984) found that students who reported experiencing flow during their academic tasks exhibited higher levels of engagement, concentration, and enjoyment. Similarly, Cho and Lee (2017) discovered that flow experiences positively correlated with student engagement in a college classroom setting.<sup><span>[</span>59<span>]</span></sup> </p><p>Flow state research has also explored its impact on learning outcomes, such as <a href="https://en.wikipedia.org/wiki/Knowledge_acquisition">knowledge acquisition</a>, skill development, and creativity. When students are in a state of flow, they are more likely to experience a heightened sense of focus, concentration, and <a href="https://en.wikipedia.org/wiki/Motivation">intrinsic motivation</a>, which can lead to improved <a href="https://en.wikipedia.org/wiki/Educational_aims_and_objectives">learning outcomes</a>.<sup><span>[</span>60<span>]</span></sup> </p><p>Studies have shown that flow experiences can enhance cognitive processes related to learning. For instance, Schüler and Brunner (2009) found that university students who reported being in a state of flow while studying demonstrated better <a href="https://en.wikipedia.org/wiki/Recall_(memory)">information recall</a> and <a href="https://en.wikipedia.org/wiki/Problem_solving">problem-solving abilities</a>. In addition, studies by Simons and Dewitte (2004) and Jackson and Csikszentmihalyi (1999) revealed that flow experiences positively influenced creativity and innovation among students.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><div><h4>Applications</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=18"><span>edit</span></a><span>]</span></span></div><p>The concept of flow has been applied to various educational settings and practices, offering valuable insights for teaching and learning. Here are a few notable applications: </p><ul><li>Skill development: Flow state theory can inform the design of <a href="https://en.wikipedia.org/wiki/Curriculum">curricula</a> and learning activities that promote the development of specific skills.<sup><span>[</span>61<span>]</span></sup> By structuring tasks to align with students&#39; skill levels and providing immediate feedback, educators can facilitate skill acquisition and mastery.</li> <li>Optimal <a href="https://en.wikipedia.org/wiki/Learning_environment">learning environments</a>: Flow state research suggests that the design of learning environments can significantly impact student engagement and learning outcomes.<sup><span>[</span>62<span>]</span></sup> Creating environments that are challenging, supportive, and tailored to students&#39; interests can facilitate flow experiences and foster deep learning.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup></li> <li><a href="https://en.wikipedia.org/wiki/Motivation">Motivation</a> and <a href="https://en.wikipedia.org/wiki/Well-being">well-being</a>: Flow state theory emphasizes the role of intrinsic motivation in optimal performance and well-being. Educators can encourage students&#39; intrinsic motivation by promoting <a href="https://en.wikipedia.org/wiki/Autonomy">autonomy</a>, competence, and relatedness in the learning process, thus facilitating flow experiences.<sup><span>[</span>63<span>]</span></sup></li> <li><a href="https://en.wikipedia.org/wiki/Classroom_management">Classroom management</a>: Understanding flow state dynamics can help educators manage classroom activities more effectively.<sup><span>[</span>64<span>]</span></sup> By providing clear instructions, structuring tasks, and offering appropriate challenges, educators can create conditions conducive to flow, leading to improved classroom experiences.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup></li></ul><p> These applications demonstrate the potential benefits of integrating flow state theory into educational practices. However, further research is needed to explore the specific strategies and <a href="https://en.wikipedia.org/wiki/Intervention_(counseling)">interventions</a> that effectively foster flow in educational settings.</p><figure><a href="https://en.wikipedia.org/wiki/File:South-Goodwin.jpg"></a><figcaption>Young child, painting a model</figcaption></figure><div><h4>History</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=19"><span>edit</span></a><span>]</span></span></div><p>In <a href="https://en.wikipedia.org/wiki/Education">education</a>, the concept of <a href="https://en.wikipedia.org/wiki/Overlearning">overlearning</a> plays a role in a student&#39;s ability to achieve flow. Csíkszentmihályi<sup><span>[</span>20<span>]</span></sup> states that overlearning enables the mind to concentrate on visualizing the desired performance as a singular, integrated action instead of a set of actions. Challenging assignments that (slightly) stretch one&#39;s skills lead to flow.<sup><span>[</span>65<span>]</span></sup> </p><p>In the 1950s British cybernetician <a href="https://en.wikipedia.org/wiki/Gordon_Pask">Gordon Pask</a> designed an adaptive teaching machine called SAKI, an early example of &quot;e-learning&quot;. The machine is discussed in some detail in Stafford Beer&#39;s book &quot;Cybernetics and Management&quot;.<sup><span>[</span>66<span>]</span></sup> In the patent application for SAKI (1956),<sup><span>[</span>67<span>]</span></sup> Pask&#39;s comments (some of which are included below) indicate an awareness of the pedagogical importance of balancing student competence with didactic challenge, which is quite consistent with flow theory: </p><blockquote><p>If the operator is receiving data at too slow a rate, he is likely to become bored and attend to other irrelevant data. </p><p>If the data given indicates too precisely what responses the operator is required to make, the skill becomes too easy to perform and the operator again tends to become bored. </p><p>If the data given is too complicated or is given at too great a rate, the operator is unable to deal with it. He is then liable to become discouraged and lose interest in performing or learning the skill. </p><p> Ideally, for an operator to perform a skill efficiently, the data presented to him should always be of sufficient complexity to maintain his interest and maintain a competitive situation, but not so complex as to discourage the operator. Similarly these conditions should obtain at each stage of a learning process if it is to be efficient. A tutor teaching one pupil seeks to maintain just these conditions.</p></blockquote><p>Around 2000, it came to the attention of Csíkszentmihályi that the principles and practices of the <a href="https://en.wikipedia.org/wiki/Montessori_Method">Montessori Method</a> of education seemed to purposefully set up continuous flow opportunities and experiences for students. Csíkszentmihályi and psychologist Kevin Rathunde embarked on a multi-year study of student experiences in Montessori settings and traditional educational settings. The research supported observations that students achieved flow experiences more frequently in Montessori settings.<sup><span>[</span>68<span>]</span></sup><sup><span>[</span>69<span>]</span></sup><sup><span>[</span>70<span>]</span></sup> </p><div><h3>Music</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=20"><span>edit</span></a><span>]</span></span></div><p>Musicians, especially <a href="https://en.wikipedia.org/wiki/Musical_improvisation">improvisational</a> <a href="https://en.wikipedia.org/wiki/Solo_(music)">soloists</a>, may experience a state of flow while playing their instrument.<sup><span>[</span>71<span>]</span></sup> Research has shown that performers in a flow state have a heightened quality of performance as opposed to when they are not in a flow state.<sup><span>[</span>72<span>]</span></sup> In a study performed with professional classical pianists who played piano pieces several times to induce a flow state, a significant relationship was found between the flow state of the pianist and the pianist&#39;s heart rate, blood pressure, and major facial muscles. As the pianist entered the flow state, heart rate and blood pressure decreased, and the major facial muscles relaxed. This study further emphasized that flow is a state of effortless attention. In spite of the effortless attention and overall relaxation of the body, the performance of the pianist during the flow state improved.<sup><span>[</span>73<span>]</span></sup> </p><p>Groups of drummers go through a state of flow when they sense a collective energy that drives the beat, something they refer to as <i>getting into the groove</i> or <a href="https://en.wikipedia.org/wiki/Entrainment_(biomusicology)">entrainment</a>. Likewise, drummers and bass guitarists often describe a state of flow when they are feeling the downbeat together as being <i>in the pocket.</i><sup><span>[</span>74<span>]</span></sup> Researchers have measured flow through subscales; challenge-skill balance, merging of action and awareness, clear goals, unambiguous feedback, total concentration, sense of control, loss of self-consciousness, transformation of time and autotelic experience.<sup><span>[</span>75<span>]</span></sup> </p><div><h3>Sports</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=21"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Concentration.jpg"></a><figcaption>Flow may occur in challenging sports such as <a href="https://en.wikipedia.org/wiki/Eventing">eventing</a>.</figcaption></figure><p>The concept of <i>being in the zone</i> during an athletic performance fit within Csíkszentmihályi&#39;s description of the flow experience. Theories and applications of <i>being in the zone</i> and its relationship with an athletic competitive advantage are topics studied in the field of <a href="https://en.wikipedia.org/wiki/Sport_psychology">sport psychology</a>.<sup><span>[</span>76<span>]</span></sup> Flow experience has received considerable attention within sport psychology, with Jackson conducting qualitative research on the flow experience in elite athletes.<sup><span>[</span>77<span>]</span></sup><sup><span>[</span>78<span>]</span></sup><sup><span>[</span>79<span>]</span></sup> Jackson co-authored with Csikszentmihalyi the book, <i>Flow in Sports</i>.<sup><span>[</span>80<span>]</span></sup> In a qualitative study of NCAA Division I athletes on the experience of flow, 94% of the athletes described flow state as causing a merging of action and awareness, and that it was effortless and automatic.<sup><span>[</span>81<span>]</span></sup> </p><p><a href="https://en.wikipedia.org/wiki/Timothy_Gallwey">Timothy Gallwey</a>&#39;s influential works on the &quot;inner game&quot; of sports, such as <a href="https://en.wikipedia.org/wiki/Golf">golf</a> and <a href="https://en.wikipedia.org/wiki/Tennis">tennis</a>, described the mental coaching and attitudes required to &quot;get in the zone&quot; and fully internalize mastery of the sport.<sup><span>[</span>82<span>]</span></sup> </p><p>Roy Palmer suggests that &quot;being in the zone&quot; may also influence movement patterns as better integration of the conscious and subconscious reflex functions improves coordination. Many athletes describe the effortless nature of their performance while achieving personal bests.<sup><span>[</span>83<span>]</span></sup><sup><span>[</span>84<span>]</span></sup><sup><span>[</span>85<span>]</span></sup> </p><p>Many <a href="https://en.wikipedia.org/wiki/Martial_arts">martial arts</a> such as Japanese <a href="https://en.wikipedia.org/wiki/Bud%C5%8D">budō</a> contain aspects of psychological flow.<sup><span>[</span>86<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Mixed_martial_arts">Mixed martial arts</a> champion and <a href="https://en.wikipedia.org/wiki/Karate">Karate</a> master <a href="https://en.wikipedia.org/wiki/Lyoto_Machida">Lyoto Machida</a> uses meditation techniques before fights to attain <a href="https://en.wikipedia.org/wiki/Mushin_(mental_state)">mushin</a>, a concept that, by his description, is in all respects equal to flow. </p><p><a href="https://en.wikipedia.org/wiki/Formula_One">Formula One</a> driver <a href="https://en.wikipedia.org/wiki/Ayrton_Senna">Ayrton Senna</a>, during qualifying for the <a href="https://en.wikipedia.org/wiki/1988_Monaco_Grand_Prix">1988 Monaco Grand Prix</a>, explained: &quot;I was already on pole, [...] and I just kept going. Suddenly I was nearly two seconds faster than anybody else, including my team mate with the same car. And suddenly I realised that I was no longer driving the car consciously. I was driving it by a kind of instinct, only I was in a different dimension. It was like I was in a tunnel.&quot;<sup><span>[</span>87<span>]</span></sup> </p><p>Former <a href="https://en.wikipedia.org/wiki/Grand_Prix_motorcycle_racing">500 GP</a> rider <a href="https://en.wikipedia.org/wiki/Wayne_Gardner">Wayne Gardner</a> talking about his victory at the <a href="https://en.wikipedia.org/wiki/1990_Australian_motorcycle_Grand_Prix">1990 Australian Grand Prix</a> on <i>The Unrideables 2</i> documentary said: &quot;During these last five laps I had this sort of above body experience where actually raised up above and I could see myself racing. It was kind of a remote control and it&#39;s the weirdest thing I&#39;ve ever had in my life. [...]&quot; After the race <a href="https://en.wikipedia.org/wiki/Mick_Doohan">Mick [Doohan]</a> and in fact <a href="https://en.wikipedia.org/wiki/Wayne_Rainey">Wayne Rainey</a> said: &quot;How the hell did you do that?&quot; and I said: &quot;I have no idea.&quot;<sup><span>[</span>88<span>]</span></sup> </p><div><h3>Religion and spirituality</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=22"><span>edit</span></a><span>]</span></span></div><p>In <a href="https://en.wikipedia.org/wiki/Yoga">yogic</a> traditions such as <a href="https://en.wikipedia.org/wiki/Raja_Yoga">Raja Yoga</a>, reference is made to a state of <i>flow</i><sup><span>[</span>89<span>]</span></sup> in the practice of <a href="https://en.wikipedia.org/wiki/Samyama">Samyama</a>, a psychological absorption in the object of meditation.<sup><span>[</span>90<span>]</span></sup> </p><div><h3>Games and gaming</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=23"><span>edit</span></a><span>]</span></span></div><p>Flow in <a href="https://en.wikipedia.org/wiki/Game">games</a> and gaming has been linked to the <a href="https://en.wikipedia.org/wiki/Laws_of_learning">laws of learning</a> as a part of the explanation for why learning-games (the use of games to introduce material, improve understanding, or increase retention) have the potential to be effective.<sup><span>[</span>91<span>]</span></sup><sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Verifiability"><span>failed verification</span></a></i>]</sup> In particular, flow is intrinsically motivating, which is a part of the law of readiness. The condition of feedback, required for flow, is associated with the feedback aspects of the law of exercise. This is exhibited in well designed games, in particular, where players perform at the edge of their competency as they are guided by clear goals and feedback.<sup><span>[</span>92<span>]</span></sup> The positive emotions associated with flow are associated with the law of effect. The intense experiences of being in a state of flow are directly associated with the law of intensity. Thus, the experience of gaming can be so engaging and motivating as it meets many of the laws of learning, which are inextricably connected to creating flow. </p><p>In games often much can be achieved thematically through an imbalance between challenge level and skill level. Horror games often keep challenges significantly above the player&#39;s level of competency in order to foster a continual feeling of anxiety. Conversely, so called &quot;relaxation games&quot; keep the level of challenges significantly below the player&#39;s competency level, in order to achieve an opposite effect.<sup><span>[</span>93<span>]</span></sup> The video game <i><a href="https://en.wikipedia.org/wiki/Flow_(video_game)">Flow</a></i> was designed as part of <a href="https://en.wikipedia.org/wiki/Jenova_Chen">Jenova Chen</a>&#39;s master&#39;s thesis for exploring the design decisions that allow players to achieve the flow state, by adjusting the difficulty dynamically during play.<sup><span>[</span>94<span>]</span></sup> </p><p>It improves performance; calling the phenomenon &quot;TV trance,&quot; a 1981 <i><a href="https://en.wikipedia.org/wiki/BYTE">BYTE</a></i> article discussed how &quot;the best seem to enter a trance where they play but don&#39;t pay attention to the details of the game.&quot;<sup><span>[</span>95<span>]</span></sup> The primary goal of games is to create entertainment through <a href="https://en.wikipedia.org/wiki/Motivation#Types_of_motivation">intrinsic motivation</a>, which is related to flow; that is, without intrinsic motivation it is virtually impossible to establish flow.<sup><span>[</span>96<span>]</span></sup> Through the balance of skill and challenge, the player&#39;s brain is aroused, with attention engaged and motivation high.<sup><span>[</span>92<span>]</span></sup> Thus, the use of flow in games helps foster an enjoyable experience, which in turn increases motivation and draws players to continue playing. As such, game designers strive to integrate flow principles into their projects.<sup><span>[</span>97<span>]</span></sup> Overall, the experience of play is fluid and is intrinsically psychologically rewarding independent of scores or in-game successes in the flow state.<sup><span>[</span>92<span>]</span></sup> </p><div><h3>Pain modulation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=24"><span>edit</span></a><span>]</span></span></div><p>Flow has recently been discussed as a psychological state potentially associated with modulation of pain perception, with emerging conceptual frameworks suggesting a possible reduction in pain during states of deep task engagement. This phenomenon, referred to as flow-induced analgesia, highlights the role of cognitive-emotional processes in central pain modulation.<sup><span>[</span>98<span>]</span></sup> </p><div><h3>Design of intrinsically motivated computer systems</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=25"><span>edit</span></a><span>]</span></span></div><p>A simplified modification to flow has been combined with the <a href="https://en.wikipedia.org/wiki/Technology_acceptance_model">technology acceptance model</a> (TAM) to help guide the design of and explain the adoption of intrinsically motivated computer systems. This model, the hedonic-motivation system adoption model (HMSAM) is modelled to improve the understanding of hedonic-motivation systems (HMS) adoption.<sup><span>[</span>96<span>]</span></sup> HMS are systems used primarily to fulfill users&#39; intrinsic motivations, such for online gaming, virtual worlds, online shopping, learning/education, online dating, digital music repositories, social networking, online pornography, gamified systems, and for general gamification. Instead of a minor, TAM extension, HMSAM is an HMS-specific system acceptance model based on an alternative theoretical perspective, which is in turn grounded in flow-based concept of cognitive absorption (CA). The HMSAM further builds on van der Heijden&#39;s (2004) model of hedonic system adoption<sup><span>[</span>99<span>]</span></sup> by including CA as a key mediator of perceived ease of use (PEOU) and of behavioral intentions to use (BIU) hedonic-motivation systems. Typically, models simplistically represent &quot;intrinsic motivations&quot; by mere perceived enjoyed. Instead, HMSAM uses the more complex, rich construct of CA, which includes joy, control, curiosity, focused immersion, and temporal dissociation. CA is a construct grounded in the seminal flow literature, yet CA has traditionally been used as a static construct, as if all five of its subconstructs occur at the same time—in direct contradiction to the flow literature. Thus, part of HMSAM&#39;s contribution is to return CA closer to its flow roots by re-ordering these CA subconstructs into more natural process-variance order as predicted by flow. Empirical data collection along with mediation tests further support this modeling approach. </p><div><h3>Workplace</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=26"><span>edit</span></a><span>]</span></span></div><p>Conditions of flow, defined as a state in which challenges and skills are equally matched, play an important role in the workplace.<sup><span>[</span>100<span>]</span></sup> Because flow is associated with achievement, its development may have specific implications for increased workplace satisfaction and achievement. Flow researchers, such as Csikszentmihályi, believe that certain interventions may be performed to enhance and increase flow in the workplace, through which people would gain &#39;intrinsic rewards that encourage persistence&quot; and provide benefits. In his consultation work, Csikszentmihályi emphasizes finding activities and environments that are conducive to flow, and then identifying and developing personal characteristics to increase experiences of flow. Applying these methods in the workplace can improve morale by fostering a sense of greater happiness and accomplishment, which may be correlated with increased performance. In his review of Mihály Csikszentmihályi&#39;s book &quot;Good Business: Leadership, Flow, and the Making of Meaning,&quot; Coert Visser introduces the ideas presented by Csikszentmihályi, including &quot;good work&quot; in which one &quot;enjoys doing your best while at the same time contributing to something beyond yourself.&quot;<sup><span>[</span>101<span>]</span></sup> He then provides tools by which managers and employees can create an atmosphere that encourages good work. Some consultants suggest that the experience sampling form (EMS) method be used for individuals and teams in the workplace in order to identify how time is currently being spent, and where focus should be redirected to in order to maximize flow experiences.<sup><span>[</span>102<span>]</span></sup> </p><p>In order to achieve flow, Csikszentmihályi lays out the following three conditions: </p><ul><li>Goals are clear</li> <li>Feedback is immediate</li> <li>A balance exists between opportunity and capacity</li></ul><p>Csikszentmihályi argues that with increased experiences of flow, people experience &quot;growth towards complexity&quot;. People flourish as their achievements grow and with that comes development of increasing &quot;emotional, cognitive, and social complexity.&quot;<sup><span>[</span>101<span>]</span></sup> Creating a workplace atmosphere that allows for flow and growth, Csikszentmihályi argues, can increase the happiness and achievement of employees. An increasingly popular way of promoting greater flow in the workplace is using the &quot;<a href="https://en.wikipedia.org/wiki/Serious_Play">serious play</a>&quot; facilitation methods.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><div><h3>Implications</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=27"><span>edit</span></a><span>]</span></span></div><p>In the study &quot;Predicting flow at work: Investigating the activities and job characteristics that predict flow states at work&quot;, Karina Nielsen and Bryan Cleal used a 9-item flow scale to examine predictors of flow at two levels: activity level (such as brainstorming, problem solving, and evaluation) and at a more stable level (such as role clarity, influence, and cognitive demands). They found that activities such as planning, problem solving, and evaluation predicted transient flow states, but that more stable job characteristics were not found to predict flow at work. This study can help us identify which task at work can be cultivated and emphasized in order to help employees experience flow on the job.<sup><span>[</span>103<span>]</span></sup> In her article in <i>Positive Psychology News Daily</i>, Kathryn Britton examines the importance of experiencing flow in the workplace beyond the individual benefits it creates. She writes, &quot;Flow isn&#39;t just valuable to individuals; it also contributes to organizational goals. For example, frequent experiences of flow at work lead to higher productivity, innovation, and employee development (Csikszentmihályi, 1991, 2004). So finding ways to increase the frequency of flow experiences can be one way for people to work together to increase the effectiveness of their workplaces.&quot;<sup><span>[</span>104<span>]</span></sup> </p><div><h2>Effects</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=28"><span>edit</span></a><span>]</span></span></div><table><tbody><tr><td></td><td><div>This section <b>is written like a <a href="https://en.wikipedia.org/wiki/Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_publisher_of_original_thought">personal reflection, personal essay, or argumentative essay</a></b> that states a Wikipedia editor&#39;s personal feelings or presents an original argument about a topic.<span> Please <a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit">help improve it</a> by rewriting it in an <a href="https://en.wikipedia.org/wiki/Wikipedia:Writing_better_articles#Information_style_and_tone">encyclopedic style</a>.</span> <span><i>(<span>August 2023</span>)</i></span><span><i> (<small><a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table><p>Books by Csikszentmihályi suggest that enhancing the time spent in flow makes our lives more happy and successful. Flow experiences are predicted to lead to positive affect as well as to better performance.<sup><span>[</span>20<span>]</span></sup><sup><span>[</span>105<span>]</span></sup> For example, delinquent behavior was reduced in adolescents after two years of enhancing flow through activities.<sup><span>[</span>45<span>]</span></sup> </p><p>People who have experienced flow, describe the following feeling: </p><ol><li>Completely involved in what we are doing – focused, concentrated.</li> <li>A sense of ecstasy – of being outside everyday reality.</li> <li>Great inner clarity – knowing what needs to be done, and how well we are doing.</li> <li>Knowing that the activity is doable – that our skills are adequate to the task.</li> <li>A sense of serenity – no worries about oneself, and a feeling of growing beyond the boundaries of the ego.</li> <li>Timelessness – thoroughly focused on the present, hours seem to pass by the minute.</li> <li>Intrinsic motivation – whatever produces flow becomes its own reward.<sup><span>[</span>106<span>]</span></sup></li></ol><p>However, further empirical evidence is required<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions"><span>according to whom?</span></a></i>]</sup> to substantiate these preliminary indications, as flow researchers continue to explore the problem of how to directly investigate causal consequences of flow experiences using modern scientific instrumentation to observe the neuro-physiological correlates of the flow state.<sup><span>[</span>107<span>]</span></sup> </p><div><h3>Satisfaction</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=29"><span>edit</span></a><span>]</span></span></div><p>Flow is an innately positive experience known to &quot;produce intense feelings of enjoyment&quot;.<sup><span>[</span>19<span>]</span></sup> An experience that is so enjoyable should lead to positive <a href="https://en.wikipedia.org/wiki/Affect_(psychology)">affect</a> and <a href="https://en.wikipedia.org/wiki/Happiness">happiness</a> in the long run. Also, Csikszentmihályi stated that happiness is derived from personal development and growth– and flow situations permit the experience of personal development.<sup><span>[</span>105<span>]</span></sup> </p><p>Several studies found that flow experiences and positive affect go hand in hand,<sup><span>[</span>50<span>]</span></sup><sup><span>[</span>108<span>]</span></sup> and that challenges and skills above the individual&#39;s average foster positive affect.<sup><span>[</span>109<span>]</span></sup><sup><span>[</span>110<span>]</span></sup><sup><span>[</span>111<span>]</span></sup> However, the causal processes underlying those relationships remain unclear at present. </p><div><h3>Performance and learning</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=30"><span>edit</span></a><span>]</span></span></div><p>Flow experiences imply a growth principle. When one is in a flow state, they are working to master the activity at hand. To maintain that flow state, one must seek increasingly greater challenges. Attempting these new, difficult challenges stretches one&#39;s skills. One emerges from such a flow experience with a bit of personal growth and great &quot;feelings of competence and efficacy&quot;.<sup><span>[</span>37<span>]</span></sup> By increasing time spent in flow, intrinsic motivation and self-directed learning also increases.<sup><span>[</span>112<span>]</span></sup> </p><p>Flow has a documented correlation with high performance in the fields of artistic and scientific creativity,<sup><span>[</span>113<span>]</span></sup><sup><span>[</span>114<span>]</span></sup> teaching,<sup><span>[</span>105<span>]</span></sup> learning,<sup><span>[</span>115<span>]</span></sup> and sports;<sup><span>[</span>116<span>]</span></sup><sup><span>[</span>117<span>]</span></sup> Looking at the sports side of being in a Flow State to help in learning different techniques, there has been research conducted by <a href="https://en.wikipedia.org/wiki/Alexandria_University">Alexandria University</a>, <a href="https://en.wikipedia.org/wiki/Alexandria">Alexandria</a>, <a href="https://en.wikipedia.org/wiki/Egypt">Egypt</a>. Their research revolved around tennis and field hockey players, specifically 24 students who are novices in the respective sports and were between the ages 19-20 years old.<sup><span>[</span>118<span>]</span></sup> The experiment itself consisted of putting a group of students learning the sports through the process of mental training. The participants do this by watching the clips of athletes in slow motion.<sup><span>[</span>118<span>]</span></sup> They did this over the course of 16 sessions with it being split in 8 sessions for each of the sports being tested.<sup><span>[</span>118<span>]</span></sup> These sessions also lasted for 40 minutes 3 times a week, alternating sports every session.<sup><span>[</span>118<span>]</span></sup> Overall the reliability of the experiment was shown to be very good. The results of the experiment also indicated that the participants were in fact able to perform at a higher level than if they didn&#39;t do the mental training/relaxation.<sup><span>[</span>118<span>]</span></sup> Specifically looking at the forehand, backhand in tennis and push pass in field hockey, there was a spike in performance.<sup><span>[</span>118<span>]</span></sup> </p><p>Flow has been linked to persistence and achievement in activities while also helping to lower anxiety during various activities and raise self-esteem.<sup><span>[</span>45<span>]</span></sup> An article that was produced by José A. Domínguez-González, Rafael E. Reigal, Verónica Morales-Sánchez and Antonio Hernández-Mendo at the <a href="https://en.wikipedia.org/wiki/University_of_M%C3%A1laga">University of Málaga</a>, in Spain show more benefits to using flow state in young football (soccer) players. The experiment was to show if there was a &quot;correlation between sports psychological profile, competitive anxiety, self-confidence and the flow state.&quot;<sup><span>[</span>119<span>]</span></sup> Their sample was 328 people that were split into 2 different groups.<sup><span>[</span>119<span>]</span></sup> The first group contained 172 people and the second group contained 156 people.<sup><span>[</span>119<span>]</span></sup> The mean ages of group 1 was 14.72 and 17.11 for group 2. The first group also had higher status in different leagues for certain sports while the second group had many lower league status.<sup><span>[</span>119<span>]</span></sup>The experiment was questionnaire based and was used to determine whether there was a correlation between sports psychological profile, competitive anxiety, self-confidence and the flow state.<sup><span>[</span>119<span>]</span></sup> The conclusion was that athletes with high skill had less anxiety and higher sports psychological profile, self-confidence and the flow state on average than the athletes in lower leagues of football(soccer).<sup><span>[</span>119<span>]</span></sup> It also shows the positive correlation between psychological sports profile to self-confidence and the flow state.<sup><span>[</span>119<span>]</span></sup> While also showing the <a href="https://en.wikipedia.org/wiki/Negative_correlation">negative correlation</a> between competitive anxiety to psychological sports profile, self confidence, and the flow state.<sup><span>[</span>119<span>]</span></sup> </p><p>However, evidence regarding better performance in flow situations is mixed.<sup><span>[</span>107<span>]</span></sup> For sure, the association between the two is a reciprocal one. That is, flow experiences may foster better performance but, on the other hand, good performance makes flow experiences more likely. Results of a longitudinal study in the academic context indicate that the causal effect of flow on performance is only of small magnitude and the strong relationship between the two is driven by an effect of performance on flow.<sup><span>[</span>49<span>]</span></sup> In the long run, flow experiences in a specific activity may lead to higher performance in that activity as flow is positively correlated with a higher subsequent motivation to perform and to perform well.<sup><span>[</span>37<span>]</span></sup> </p><div><h2>Criticism</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=31"><span>edit</span></a><span>]</span></span></div><table><tbody><tr><td></td><td><div>This section <b>is written like a <a href="https://en.wikipedia.org/wiki/Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_publisher_of_original_thought">personal reflection, personal essay, or argumentative essay</a></b> that states a Wikipedia editor&#39;s personal feelings or presents an original argument about a topic.<span> Please <a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit">help improve it</a> by rewriting it in an <a href="https://en.wikipedia.org/wiki/Wikipedia:Writing_better_articles#Information_style_and_tone">encyclopedic style</a>.</span> <span><i>(<span>August 2023</span>)</i></span><span><i> (<small><a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table><p>Research on flow experiences is well established, however there are still unresolved, critical issues with the universal definitions and measurements associated with the concept.<sup><span>[</span>120<span>]</span></sup> In recent years, the language, definitions, measurement approaches, and models of flow state in the research community continually increased. A comprehensive review of flow state studies conducted from 2012 to 2019 took one of the first steps towards determining a potential universalization of terminology for future use in research of flow.<sup><span>[</span>121<span>]</span></sup> Despite the varied approaches to flow evident in this review, a common set of overarching antecedent constructs included &quot;optimal challenge&quot; and &quot;high motivation,&quot; and recurring characteristics of the flow experience itself included &quot;absorption,&quot; &quot;effort-less control,&quot; and &quot;intrinsic reward.&quot; By separating the antecedents of flow from the experience of flow itself, and utilising a language accessible to all scientific disciplines, Norsworthy et al.&#39;s three dimensional conceptualsiation of flow offers a contemporary framework that can be used for the study of flow across scientific disciplines. </p><p>Psychological flow state research has made significant strides in understanding the concept and its implications. However, like any scientific field, it is not without its <a href="https://en.wikipedia.org/wiki/Criticism_of_science">criticisms</a> and areas that require further investigation. </p><p>This section explores the criticisms of flow state research and highlights the potential directions for future research. </p><ol><li>Lack of Clarity and <a href="https://en.wikipedia.org/wiki/Operationalization">Operationalization</a>: One common criticism of Csikszentmihalyi&#39;s flow theory pertains to the lack of clarity and operationalization of its components. Flow is described as a state of complete immersion, but there is ongoing debate regarding the specific dimensions and criteria that constitute flow experiences. Some researchers argue that the theory lacks clear and consistent guidelines for measuring flow, which limits comparability across studies and hinders the establishment of a standardized framework</li> <li><a href="https://en.wikipedia.org/wiki/Homogeneity_and_heterogeneity_(statistics)">Homogeneity</a> of flow experiences: Critics have raised concerns about the assumption that flow experiences have consistent qualities and outcomes across different individuals and activities. While Csikszentmihalyi&#39;s theory posits a universal nature of flow, some argue that flow experiences might vary depending on personal characteristics, cultural factors, and situational contexts. This criticism highlights the need for a more nuanced understanding of the diversity and contextual nuances of flow experiences. Keller and Landhäußer advocate for a flow intensity model because many models of flow have trouble predicting the intensity of flow experiences that can occur under various circumstances where skill and task demands fit together to produce flow.<sup><span>[</span>122<span>]</span></sup> Cowley found that because self-reported flow happens after-the-fact, it does not really capture the aspect of flow that happens in the moment. Furthermore, that aspect of flow is prone to change, so the self-reported experience of flow cannot be trusted as much.<sup><span>[</span>123<span>]</span></sup></li> <li>Limited attention to negative aspects: Csikszentmihalyi&#39;s flow theory primarily focuses on positive aspects of the flow experience, emphasizing enjoyment, intrinsic motivation, and optimal performance. However, some researchers argue that neglecting the potential negative aspects of flow, such as potential conflicts, negative emotions, or overuse leading to burnout, limits the comprehensiveness of the theory. Critics call for a more balanced approach that considers both positive and negative dimensions of flow experiences.</li></ol><p>The lack of standardized definitions, measurement approaches, and terminologies hampers the cumulative progress of flow state research and poses challenges in synthesizing and comparing findings across studies.<sup><span>[</span>124<span>]</span></sup> It also limits the development of comprehensive <a href="https://en.wikipedia.org/wiki/Theory">theoretical models</a> that can encompass the complexity and nuances of flow experiences. Addressing these critical issues is essential to enhance the scientific rigor and <a href="https://en.wikipedia.org/wiki/Validity_scale">validity</a> of flow state research, enabling a deeper understanding of this intriguing psychological phenomenon. Despite these criticisms and challenges, the study of flow states continues to evolve and expand. Researchers are actively working towards refining the conceptualization, measurement, and theoretical frameworks of flow. Through ongoing efforts to establish consensus and develop standardized guidelines, the field aims to overcome these limitations, paving the way for more robust and comprehensive investigations into the nature and significance of psychological flow states.<sup><span>[</span>125<span>]</span></sup> </p><p> Csikszentmihályi writes about the dangers of flow himself:</p><blockquote><p>...enjoyable activities that produce flow have a potentially negative effect: while they are capable of improving the quality of existence by creating order in the mind, they can become addictive, at which point the self becomes captive of a certain kind of order, and is then unwilling to cope with the ambiguities of life.</p></blockquote><p> Further, he writes:</p><blockquote><p> The flow experience, like everything else, is not &quot;good&quot; in an absolute sense. It is good only in that it has the potential to make life more rich, intense, and meaningful; it is good because it increases the strengths and complexity of the self. But whether the consequence of any particular instance of flow is good in a larger sense needs to be discussed and evaluated in terms of more inclusive social criteria.<sup><span>[</span>126<span>]</span></sup></p></blockquote><p>Keller and Landhäußer (2012, p. 56) advocate for a flow intensity model because many models of flow have trouble predicting the intensity of flow experiences that can occur under various circumstances where skill and task demands fit together to produce flow.<sup><span>[</span>38<span>]</span></sup> </p><p>Cowley et al. found that because self-reported flow happens after-the-fact, it does not really capture the aspect of flow that happens in the moment. Furthermore, that aspect of flow is prone to change, so the self-reported experience of flow cannot be trusted as much.<sup><span>[</span>127<span>]</span></sup> </p><p>Cameron et al. found that there is not a lot of information on group flow, and this may be hindering development in managerial and theoretical contributions.<sup><span>[</span>128<span>]</span></sup> </p><p>Goddard et al. found that interventions such as hypnosis, mindfulness, and imagery were found to be unsuccessful in stimulating flow experiences in individuals; however, these strategies were found to increase the state of flow.<sup><span>[</span>129<span>]</span></sup> </p><p>Braxton Soderman&#39;s 2021 monograph <i>Against Flow: Video Games and the Flowing Subject</i> points out that flow exists on ideological grounds as an individualist counterpoint to socialism. Furthermore, the application of flow via gamification has brought work and play into ever closer relationship. Play is, therefore, converted into a form of unpaid labor.<sup><span>[</span>130<span>]</span></sup> </p><p>Norsworthy et al. proposed a parsimonious model of three core dimensions of flow, reflecting the findings from the largest review on flow science to date, synthesising flow research across scientific disciplines and addressing conceptual criticisms of flow science regarding construct validity, theoretical compatibility, relational ambiguity, and definitional inconsistency. A new Psychological Flow Scale (PFS) to measure the core aspects of the flow state that could be utilized across domains and scientific disciplines was validated.<sup><span>[</span>131<span>]</span></sup> </p><div><h2>Global-cultural perspectives</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=32"><span>edit</span></a><span>]</span></span></div><p>In a global context, there is a gap in understanding how flow manifests within various socio-cultural contexts. Cross-cultural comparative studies, as suggested by Engeser and Rheinberg (2008), could delve into how flow experiences differ across societies, deepening our understanding of the concept&#39;s universality or cultural specificity.<sup><span>[</span>132<span>]</span></sup> </p><p>Longitudinal studies, capable of tracking flow experiences over extended periods, could offer insights into the sustained effects of flow on personal development, well-being, and performance. As Seligman and Csikszentmihalyi (2000) have suggested, such research could offer a more nuanced understanding of the concept&#39;s long-term impact.<sup><span>[</span>133<span>]</span></sup> </p><div><h2>Technology</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=33"><span>edit</span></a><span>]</span></span></div><table><tbody><tr><td></td><td><div>This section <b>is written like a <a href="https://en.wikipedia.org/wiki/Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_publisher_of_original_thought">personal reflection, personal essay, or argumentative essay</a></b> that states a Wikipedia editor&#39;s personal feelings or presents an original argument about a topic.<span> Please <a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit">help improve it</a> by rewriting it in an <a href="https://en.wikipedia.org/wiki/Wikipedia:Writing_better_articles#Information_style_and_tone">encyclopedic style</a>.</span> <span><i>(<span>August 2023</span>)</i></span><span><i> (<small><a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table><p>The impact of technological advancements on flow experiences represents another noteworthy research direction. As digital technology increasingly permeates our lives, exploring how immersive technologies such as virtual reality or augmented reality facilitate or hinder flow states could be an enlightening line of study. The potential of such research has been discussed by Csikszentmihalyi and Csikszentmihalyi (2014), emphasizing the need to understand how digital distractions may disrupt flow and how these effects could be mitigated. Another critical avenue for future research is the role of flow in online learning. The rise of digital education platforms, as discussed by Csíkszentmihályi and Nakamura (2018), necessitates investigations into how flow can be fostered in these contexts and how it might influence learning outcomes.<sup><span>[</span>134<span>]</span></sup> </p><figure><a href="https://en.wikipedia.org/wiki/File:FMRI_scan_during_working_memory_tasks.jpg"></a><figcaption>This specific FMRI scan determined which areas of the brain are activated during working memory tasks, but this type of imaging could also determine the areas of brain activated during flow experiences.</figcaption></figure><p>The neuroscientific underpinnings of flow are a developing field with significant potential. With advancements in neuroimaging technologies, as highlighted by Linden (2021), the opportunity to correlate psychological experiences of flow with their physiological counterparts becomes increasingly feasible.<sup><span>[</span>135<span>]</span></sup> </p><div><h3>Ethics</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=34"><span>edit</span></a><span>]</span></span></div><p>Additional research into how flow impacts ethical decision-making across professional fields could have extensive implications. An exploratory study by Nielsen and Cleal (2010) hints at the potential role of flow in influencing ethical judgments, suggesting the necessity more extensive research in this domain.<sup><span>[</span>136<span>]</span></sup> </p><div><h3>Other areas of research</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=35"><span>edit</span></a><span>]</span></span></div><p>Cameron et al. proposed a research program that focuses on how group flow is different from individual flow, and how group flow affects group performance. These ideas will address some of the issues in group flow research such as poor data collection and interpretation.<sup><span>[</span>137<span>]</span></sup> Sridhar &amp; Lyngdoh suggested that research should investigate how mobility affects the ethical performance of sales professionals. Furthermore, there should be longitudinal studies done in various fields to understand the ethical implications of flow in sales.<sup><span>[</span>138<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=36"><span>edit</span></a><span>]</span></span></div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=37"><span>edit</span></a><span>]</span></span></div><div><h3>Citations</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=38"><span>edit</span></a><span>]</span></span></div><div><ol> <li><span><b>^</b></span> <span><cite>Ellis, Gary D.; Voelkl, Judith E.; Morris, Catherine (September 1994). &quot;Measurement and Analysis Issues with Explanation of Variance in Daily Experience Using the Flow Model&quot;. <i>Journal of Leisure Research</i>. <b>26</b> (4): <span>337–</span>356. <a href="https://en.wikipedia.org/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1994JLeiR..26..337E">1994JLeiR..26..337E</a>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1080%2F00222216.1994.11969966">10.1080/00222216.1994.11969966</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0022-2216">0022-2216</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Mirvis, Philip H. (July 1991). &quot;Flow: The Psychology of Optimal Experience, by Csikszentmihalyi Michael. New York: Harper &amp; Row, 1990, 303 pp., $19.95, cloth&quot;. <i>Academy of Management Review</i>. <b>16</b> (3): <span>636–</span>640. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.5465%2Famr.1991.4279513">10.5465/amr.1991.4279513</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0363-7425">0363-7425</a>.</cite></span> </li> <li><span><b>^</b></span> <span>Csikszentmihályi (1975), pp. 11–12, 36–37.</span> </li> <li><span><b>^</b></span> <span>Csikszentmihályi 1990, p. 242: &quot;The original research and the theoretical model of the flow experience were first fully reported in <i>Beyond Boredom and Anxiety</i> (Csikszentmihalyi 1975).&quot;</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Ashinoff, Brandon K.; Abu-Akel, Ahmad (2021-02-01). <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7851038">&quot;Hyperfocus: the forgotten frontier of attention&quot;</a>. <i>Psychological Research</i>. <b>85</b> (1): <span>1–</span>19. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2Fs00426-019-01245-8">10.1007/s00426-019-01245-8</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1430-2772">1430-2772</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a> <span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7851038">7851038</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/31541305">31541305</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Sanderson, Catherine (2016). <i>Sport Psychology</i>. Oxford University Press. pp. <span>164–</span>165. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-991744-0"><bdi>978-0-19-991744-0</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span>Csikszentmihályi (1990), p. 40.</span> </li> <li><span><b>^</b></span> <span><cite>Barrett, Nathaniel F. (2011). <a href="https://web.archive.org/web/20170810124108/http://enlight.lib.ntu.edu.tw/FULLTEXT/JR-PHIL/phil390582.pdf">&quot;<i>Wuwei</i> and Flow: Comparative Reflections on Spirituality, Transcendence, and Skill in the <i>Zhuangzi</i>&quot;</a> <span>(PDF)</span>. <i>Philosophy East and West</i>. <b>61</b> (4): <span>679–</span>706. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1353%2Fpew.2011.0051">10.1353/pew.2011.0051</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1529-1898">1529-1898</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <span><a href="https://api.semanticscholar.org/CorpusID:56222168">56222168</a></span>. 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Cambridge, UK: Cambridge University Press. pp. <span>15–</span>35. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-521-43809-4"><bdi>978-0-521-43809-4</bdi></a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup> <sup><i><b>e</b></i></sup></span> <span><cite><a href="https://en.wikipedia.org/wiki/Mihaly_Csikszentmihalyi">Csikszentmihályi M</a> (1990). <a href="https://web.archive.org/web/20150225201519/http://www.psy-flow.com/sites/psy-flow/files/docs/flow.pdf"><i>FLOW: The Psychology of Optimal Experience</i></a> <span>(PDF)</span>. Harper and Row. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-06-016253-5"><bdi>978-0-06-016253-5</bdi></a>. Archived from <a href="http://www.psy-flow.com/sites/psy-flow/files/docs/flow.pdf">the original</a> <span>(PDF)</span> on 25 February 2015<span>. Retrieved <span>2 April</span> 2015</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Norsworthy, C.; Thelwell, R.; Weston, N.; A. Jackson, S. (2018). <a href="http://www.ijsp-online.com/abstract/view/49/134">&quot;Flow training, flow states, and performance in elite athletes&quot;</a>. <i>International Journal of Sport Psychology</i>. <b>49</b> (2): <span>134–</span>152. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.7352%2Fijsp.2018.49.134">10.7352/ijsp.2018.49.134</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Norsworthy, Cameron; Dimmock, James A.; Nicholas, Joanna; Krause, Amanda; Jackson, Ben (2023-12-01). <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10204032">&quot;Psychological Flow Training: Feasibility and Preliminary Efficacy of an Educational Intervention on Flow&quot;</a>. <i>International Journal of Applied Positive Psychology</i>. <b>8</b> (3): <span>531–</span>554. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2Fs41042-023-00098-2">10.1007/s41042-023-00098-2</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/2364-5059">2364-5059</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a> <span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10204032">10204032</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/37361627">37361627</a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>Moneta G (2012). &quot;On the Measurement and Conceptualization of Flow&quot;. 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Proceedings of the Gmunden Retreat on NeuroIS. p. 13.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Goddard, Scott G.; Stevens, Christopher J.; Jackman, Patricia C.; Swann, Christian (2023-12-31). <span><a href="https://www.tandfonline.com/doi/full/10.1080/1750984X.2021.1923055">&quot;A systematic review of flow interventions in sport and exercise&quot;</a></span>. <i>International Review of Sport and Exercise Psychology</i>. <b>16</b> (1): <span>657–</span>692. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1080%2F1750984X.2021.1923055">10.1080/1750984X.2021.1923055</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1750-984X">1750-984X</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Christian, Haines (16 March 2022). <a href="https://criticalinquiry.uchicago.edu/christian_haines_reviews_against_flow/">&quot;Christian Haines reviews Against Flow&quot;</a>. <i>Critical Inquiry</i><span>. Retrieved <span>5 April</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Norsworthy, Cameron; Dimmock, James A.; Miller, Daniel J.; Krause, Amanda; Jackson, Ben (2023-08-01). <a href="https://doi.org/10.1007%2Fs41042-023-00092-8">&quot;Psychological Flow Scale (PFS): Development and Preliminary Validation of a New Flow Instrument that Measures the Core Experience of Flow to Reflect Recent Conceptual Advancements&quot;</a>. <i>International Journal of Applied Positive Psychology</i>. <b>8</b> (2): <span>309–</span>337. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1007%2Fs41042-023-00092-8">10.1007/s41042-023-00092-8</a></span>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/2364-5059">2364-5059</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Rheinberg, F; Engeser, S (2008). &quot;Flow, performance and moderators of challenge-skill balance&quot;. <i>Motivation and Emotion</i>: 179.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Seligman, Martin E. P.; Csikszentmihalyi, Mihaly (2000). &quot;Positive psychology: An introduction&quot;. <i>American Psychologist</i>. <b>55</b> (1): <span>5–</span>14. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1037%2F0003-066x.55.1.5">10.1037/0003-066x.55.1.5</a>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/11392865">11392865</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:14783574">14783574</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Nakamura, Jeanne; Csikszentmihalyi, Mihaly (2014). &quot;The Concept of Flow&quot;. <i>Flow and the Foundations of Positive Psychology</i>. Flow and the Foundations of Positive Psychology: The Collected Works of Mihaly Csikszentmihalyi. pp. <span>239–</span>263. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2F978-94-017-9088-8_16">10.1007/978-94-017-9088-8_16</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-94-017-9087-1"><bdi>978-94-017-9087-1</bdi></a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:30035071">30035071</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>van der Linden, Dimitri; Tops, Mattie; Bakker, Arnold B. (2021). &quot;The Neuroscience of the Flow State: Involvement of the Locus Coeruleus Norepinephrine System&quot;. <i>Frontiers in Psychology</i>. <b>12</b>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Nielsen, Karina; Cleal, Bryan (2010). &quot;Predicting flow at work: Investigating the activities and job characteristics that predict flow states at work&quot;. <i>Journal of Occupational Health Psychology</i>. <b>15</b> (2): <span>180–</span>190. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1037%2Fa0018893">10.1037/a0018893</a>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/20364915">20364915</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Léger PM, Sénécal S, Aubé C, Cameron AF, de Guinea AO, Brunelle E (June 2013). <a href="https://www.researchgate.net/publication/252931290"><i>The Influence of Group Flow on Group Performance: a Research Program</i></a>. Proceedings of the Gmunden Retreat on NeuroIS. p. 13.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Sridhar G, Lyngdoh T (2019-09-01). &quot;Flow and Information Sharing as Predictors of Ethical Selling Behavior&quot;. <i>Journal of Business Ethics</i>. <b>158</b> (3): <span>807–</span>823. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2Fs10551-017-3743-8">10.1007/s10551-017-3743-8</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1573-0697">1573-0697</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:158513460">158513460</a>.</cite></span> </li> </ol></div><div><h3>Sources</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=39"><span>edit</span></a><span>]</span></span></div><div> <ul><li><cite>Csikszentmihályi, Mihály (1975). <i>Beyond Boredom and Anxiety</i>. San Francisco, Calif.: Jossey-Bass. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-87589-261-2"><bdi>0-87589-261-2</bdi></a>.</cite></li> <li><cite>Csíkszentmihályi M (1996), <i>Creativity: Flow and the Psychology of Discovery and Invention</i>, New York: Harper Perennial, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-06-092820-9"><bdi>978-0-06-092820-9</bdi></a></cite></li> <li><cite>Csíkszentmihályi M (1996), <i>Finding Flow: The Psychology of Engagement With Everyday Life</i>, Basic Books, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-465-02411-7"><bdi>978-0-465-02411-7</bdi></a></cite> (a popular exposition emphasizing technique)</li> <li><cite>Csíkszentmihályi M (2003), <i>Good Business: Leadership, Flow, and the Making of Meaning</i>, New York: Penguin Books, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-14-200409-8"><bdi>978-0-14-200409-8</bdi></a></cite></li> <li><cite>Egbert J (2003), &quot;A Study of Flow Theory in the Foreign Language Classroom&quot;, <i>The Modern Language Journal</i>, <b>87</b> (4): <span>499–</span>518, <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1111%2F1540-4781.00204">10.1111/1540-4781.00204</a></cite></li> <li><cite>Jackson SA, Csíkszentmihályi M (1999), <i>Flow in Sports: The Keys to Optimal Experiences and Performances</i>, Champaign, Illinois: Human Kinetics Publishers, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-88011-876-7"><bdi>978-0-88011-876-7</bdi></a></cite></li> <li><cite>Mainemelis C (2001), &quot;When the Muse Takes It All: A Model for the Experience of Timelessness in Organizations&quot;, <i>The Academy of Management Review</i>, <b>26</b> (4): <span>548–</span>565, <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F3560241">10.2307/3560241</a>, <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/3560241">3560241</a></cite></li> <li><cite>Shainberg L (1989-04-09), <a href="https://www.nytimes.com/1989/04/09/magazine/finding-the-zone.html">&quot;Finding &#39;The Zone&#39;&quot;</a>, <i>The New York Times Magazine</i></cite></li></ul> </div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Flow_(psychology)&amp;action=edit&amp;section=40"><span>edit</span></a><span>]</span></span></div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Wiktionary-logo-en-v2.svg"></a></span></div> <div>Look up <i><b><a href="https://en.wiktionary.org/wiki/flow">flow</a></b></i> in Wiktionary, the free dictionary.</div></div> </div><ul><li><a href="http://positivepsychology.org.uk/pp-theory/flow/30-living-in-flow.html">&quot;Living in the Flow&quot;</a> <a href="https://web.archive.org/web/20161013112825/http://positivepsychology.org.uk/pp-theory/flow/30-living-in-flow.html">Archived</a> 2016-10-13 at the <a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a></li> <li><a href="https://www.youtube.com/watch?v=fXIeFJCqsPs"><span>Mihaly Csikszentmihalyi: Creativity, fulfillment and flow</span></a> on <a href="https://en.wikipedia.org/wiki/YouTube_video_(identifier)">YouTube</a>; presentation at the February, 2004 <a href="https://en.wikipedia.org/wiki/TED_(conference)">TED conference</a></li> <li><a href="http://web.cs.wpi.edu/~gogo/courses/imgd5100/papers/FlowQuestionnaire.pdf">Schaffer, Owen (2013), Crafting Fun User Experiences: A Method to Facilitate Flow</a></li></ul><div><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a>: National <span><a href="https://www.wikidata.org/wiki/Q750449#identifiers"></a></span></th><td><div><ul><li><span><span><a href="https://aleph.nkp.cz/F/?func=find-c&amp;local_base=aut&amp;ccl_term=ica=ph1084572&amp;CON_LNG=ENG">Czech Republic</a></span></span></li></ul></div></td></tr></tbody></table></div> Ananda Coomaraswamy - Wikipedia https://en.wikipedia.org/wiki/Ananda_Coomaraswamy LZ2I3yvIvNFUEx_e0artAphpRTdUTgTHv72B7g== Sat, 09 May 2026 12:02:05 +0000 Sri Lankan Tamil metaphysician (1877–1947) <div>Sri Lankan Tamil metaphysician (1877–1947)</div><p> </p><table><tbody><tr><th colspan="2"><div>Ananda Coomaraswamy</div></th></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Coomaraswamy.jpg"></a></span><div>Coomaraswamy in 1916</div></td></tr><tr><th>Born</th><td><span>(<span>1877-08-22</span>)</span>22 August 1877<br/><div><a href="https://en.wikipedia.org/wiki/Colombo">Colombo</a>, <a href="https://en.wikipedia.org/wiki/British_Ceylon">British Ceylon</a></div></td></tr><tr><th>Died</th><td>9 September 1947<span>(1947-09-09)</span> (aged 70)<br/><div><a href="https://en.wikipedia.org/wiki/Needham,_Massachusetts">Needham, Massachusetts</a>, U.S.</div></td></tr><tr><th>Spouses</th><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Ethel_Mairet">Ethel Mairet</a> (m. 1902–1913)</li><li><a href="https://en.wikipedia.org/wiki/Alice_Coomaraswamy">Ratna Devi</a> (m. 1913–1922)</li><li><a href="https://en.wikipedia.org/wiki/Stella_Bloch">Stella Bloch</a> (m. 1922–1930)</li><li>Luisa Runstein (m. 1930–1947, his death)</li></ul></div></td></tr><tr><td colspan="2"></td></tr><tr><th colspan="2">Philosophical work</th></tr><tr><th>Era</th><td><a href="https://en.wikipedia.org/wiki/Modern_philosophy">Modern philosophy</a><br/> <a href="https://en.wikipedia.org/wiki/20th-century_philosophy">20th-century philosophy</a></td></tr><tr><th>Region</th><td><a href="https://en.wikipedia.org/wiki/Indian_philosophy">Indian philosophy</a><br/><a href="https://en.wikipedia.org/wiki/Western_philosophy">Western philosophy</a></td></tr><tr><th><div><a href="https://en.wikipedia.org/wiki/List_of_schools_of_philosophy">School</a></div></th><td><a href="https://en.wikipedia.org/wiki/Perennialism">Perennialism</a><br/><a href="https://en.wikipedia.org/wiki/Traditionalist_School">Traditionalist School</a></td></tr><tr><th><div>Main interests</div></th><td><a href="https://en.wikipedia.org/wiki/Metaphysics">Metaphysics</a>, <a href="https://en.wikipedia.org/wiki/Philosophy_of_art">philosophy of art</a>, <a href="https://en.wikipedia.org/wiki/History">history</a></td></tr><tr><th><div>Notable works</div></th><td><i>The Dance of Shiva</i> (1918), <i>Hinduism and Buddhism</i> (1943)</td></tr><tr><td colspan="2"> </td></tr></tbody></table><p><b>Ananda Kentish Muthu Coomaraswamy</b> (<a href="https://en.wikipedia.org/wiki/Tamil_language">Tamil</a>: <span>ஆனந்த குமாரசுவாமி</span>, <i>Āṉanta Kumāracuvāmi</i>; <a href="https://en.wikipedia.org/wiki/Sinhala_language">Sinhala</a>: <span>ආනන්ද කුමාරස්වාමි</span> <i>Ānanda Kumārasvāmī</i>; 22 August 1877 − 9 September 1947) was a <a href="https://en.wikipedia.org/wiki/Sri_Lanka">Ceylonese</a> <a href="https://en.wikipedia.org/wiki/Metaphysics">metaphysician</a>, historian and a <a href="https://en.wikipedia.org/wiki/Aesthetics#Indian_aesthetics">philosopher of Indian art</a> who was an early interpreter of <a href="https://en.wikipedia.org/wiki/Indian_culture">Indian culture</a> to the West.<sup><span>[</span>1<span>]</span></sup> He has been described as &quot;the groundbreaking theorist who was largely responsible for introducing ancient Indian art to the West&quot;.<sup><span>[</span>2<span>]</span></sup> </p><div><h2>Life</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><div>See also: <a href="https://en.wikipedia.org/wiki/Ponnambalam%E2%80%93Coomaraswamy_family">Ponnambalam–Coomaraswamy family</a></div><p>Ananda Kentish Coomaraswamy was born in <a href="https://en.wikipedia.org/wiki/Colombo">Colombo</a>, British Ceylon, now <a href="https://en.wikipedia.org/wiki/Sri_Lanka">Sri Lanka</a>, to the <a href="https://en.wikipedia.org/wiki/Sri_Lankan_Tamils">Ceylon Tamil</a> legislator and philosopher Sir <a href="https://en.wikipedia.org/wiki/Muthu_Coomaraswamy">Muthu Coomaraswamy</a> of the <a href="https://en.wikipedia.org/wiki/Ponnambalam%E2%80%93Coomaraswamy_family">Ponnambalam–Coomaraswamy family</a> and his English wife Elizabeth Beeby.<sup><span>[</span>3<span>]</span></sup><sup><span>[</span>4<span>]</span></sup><sup><span>[</span>5<span>]</span></sup> His father died when Ananda was two years old, and Ananda spent much of his childhood and education abroad.<sup><span>[</span>6<span>]</span></sup> </p><p>Coomaraswamy moved to England in 1879 and attended <a href="https://en.wikipedia.org/wiki/Wycliffe_College_(Gloucestershire)">Wycliffe College</a>, a preparatory school in <a href="https://en.wikipedia.org/wiki/Stroud,_Gloucestershire">Stroud, Gloucestershire</a>, at the age of twelve. In 1900, he graduated from <a href="https://en.wikipedia.org/wiki/University_College_London">University College London</a> (UCL), with a degree in geology and botany. On 19 June 1902, Coomaraswamy married <a href="https://en.wikipedia.org/wiki/Ethel_Mary_Partridge">Ethel Mary Partridge</a>, an English photographer, who then traveled with him to Ceylon. Their marriage lasted until 1913. Coomaraswamy&#39;s field work between 1902 and 1906 earned him a <a href="https://en.wikipedia.org/wiki/Doctor_of_science">doctor of science</a> for his study of <a href="https://en.wikipedia.org/wiki/Ceylon">Ceylonese</a> <a href="https://en.wikipedia.org/wiki/Mineralogy">mineralogy</a>, and prompted the formation of the Geological Survey of Ceylon which he initially directed.<sup><span>[</span>7<span>]</span></sup> While in Ceylon, the couple collaborated on <i>Mediaeval Sinhalese Art</i>; Coomaraswamy wrote the text and Ethel provided the photographs. His work in Ceylon fueled Coomaraswamy&#39;s anti-<a href="https://en.wikipedia.org/wiki/Westernisation">Westernisation</a> sentiments.<sup><span>[</span>8<span>]</span></sup> After their divorce, Partridge returned to England, where she became a famous weaver and later married the writer <a href="https://en.wikipedia.org/wiki/Philip_Mairet">Philip Mairet</a>. </p><p>By 1906, Coomaraswamy had made it his mission to educate the West about Indian art, and was back in London with a large collection of photographs, actively seeking out artists to try to influence. He knew he could not rely on museum curators or other members of the cultural establishment – in 1908 he wrote &quot;The main difficulty so far seems to have been that Indian art has been studied so far only by archaeologists. It is not archaeologists, but artists ... who are the best qualified to judge of the significance of works of art considered as art.&quot; By 1909, he was firmly acquainted with <a href="https://en.wikipedia.org/wiki/Jacob_Epstein">Jacob Epstein</a> and <a href="https://en.wikipedia.org/wiki/Eric_Gill">Eric Gill</a>, the city&#39;s two most important early Modernists, and soon both of them had begun to incorporate Indian aesthetics into their work. The curiously hybrid sculptures that were produced as a result can be seen to form the very roots of what is now considered British Modernism.<sup><span>[</span>9<span>]</span></sup><sup><span>[</span>10<span>]</span></sup> </p><figure><a href="https://en.wikipedia.org/wiki/File:Roshanara,_and_Alice_Coomara_as_Ratan_Devi_on_March_17,_1917_in_Manhattan.jpg"></a><figcaption>His second wife: Alice Coomaraswamy (Ratan Devi) with <a href="https://en.wikipedia.org/wiki/Roshanara">Roshanara</a> </figcaption></figure><p>Coomaraswamy then met and married a British woman <a href="https://en.wikipedia.org/wiki/Ratan_Devi">Alice Ethel Richardson</a> and together they stayed on a houseboat in <a href="https://en.wikipedia.org/wiki/Srinagar">Srinagar</a> in Kashmir. Commaraswamy studied Rajput painting while his wife studied Indian music with Abdul Rahim of Kapurthala. When they returned to England, Alice performed Indian song under the stage name <a href="https://en.wikipedia.org/wiki/Ratan_Devi">Ratan Devi</a>. Alice was successful and both went to America when Ratan Devi did a concert tour.<sup><span>[</span>11<span>]</span></sup> While they were there, Coomaraswamy was invited to serve as the first Keeper of Indian art in the <a href="https://en.wikipedia.org/wiki/Museum_of_Fine_Arts,_Boston">Boston Museum of Fine Arts</a> in 1917.<sup><span>[</span>12<span>]</span></sup> The couple had two children, a son, Narada, and daughter, Rohini. </p><figure><a href="https://en.wikipedia.org/wiki/File:AnandaCoomaraswamy.jpg"></a><figcaption>Portrait of Ananda Coomaraswamy, published 1907.</figcaption></figure><p>Coomaraswamy divorced his second wife after they arrived in America.<sup><span>[</span>12<span>]</span></sup> He married the American artist <a href="https://en.wikipedia.org/wiki/Stella_Bloch">Stella Bloch</a>, 20 years his junior, in November 1922. Through the 1920s, Coomaraswamy and his wife were part of the <a href="https://en.wikipedia.org/wiki/Bohemianism">bohemian</a> art circles in New York City, Coomaraswamy befriended <a href="https://en.wikipedia.org/wiki/Alfred_Stieglitz">Alfred Stieglitz</a> and the artists who exhibited at Stieglitz&#39;s gallery. At the same time, he studied Sanskrit and Pali religious literature as well as Western religious works. He wrote catalogues for the Boston Museum of Fine Arts and published his <i>History of Indian and Indonesian Art</i> in 1927. </p><p>After the couple divorced in 1930, they remained friends. Shortly thereafter, on 18 November 1930, Coomaraswamy married <a href="https://en.wikipedia.org/wiki/Argentina">Argentine</a> <a href="https://en.wikipedia.org/w/index.php?title=Luisa_Runstein&amp;action=edit&amp;redlink=1">Luisa Runstein</a>, 28 years younger, who was working as a society photographer under the professional name Xlata Llamas. They had a son, Coomaraswamy&#39;s third child, Rama Ponnambalam (1929-2006), who became a physician and convert at age 22 to the <a href="https://en.wikipedia.org/wiki/Roman_Catholic_Church">Roman Catholic Church</a>. Following <a href="https://en.wikipedia.org/wiki/Vatican_II">Vatican II</a>, Rama became a critic of the reforms and author of Catholic <a href="https://en.wikipedia.org/wiki/Traditionalist_School">Traditionalist</a> works.<sup><span>[</span>13<span>]</span></sup> He was also ordained a Traditionalist Roman Catholic priest, despite the fact that he was married and had a living wife.<sup><span>[</span>14<span>]</span></sup> Rama Coomaraswamy studied in England and then in India, learning <a href="https://en.wikipedia.org/wiki/Hindi">Hindi</a> and <a href="https://en.wikipedia.org/wiki/Sanskrit">Sanskrit</a>.<sup><span>[</span>15<span>]</span></sup> Became a <a href="https://en.wikipedia.org/wiki/Psychiatrist">psychiatrist</a> in the United States, he was an opponent of <a href="https://en.wikipedia.org/wiki/Pope_John_Paul_II#Relations_with_other_Christian_denominations">Pope John Paul II</a><sup><span>[</span>15<span>]</span></sup> and remain a wider correspondent of mother <a href="https://en.wikipedia.org/wiki/Teresa_of_Calcutta">Teresa of Calcutta</a>, whose first healing attribution was recognised by John Paul II in 2002.<sup><span>[</span>16<span>]</span></sup> </p><p>During his long career, Coomaraswamy was instrumental in bringing Eastern art to the West. While at the Boston Museum of Fine Arts, he built the first substantial collection of Indian art in the United States.<sup><span>[</span>17<span>]</span></sup> In 1933, Coomaraswamy&#39;s title there changed from <a href="https://en.wikipedia.org/wiki/Curator">curator</a> to Fellow for Research in Indian, <a href="https://en.wikipedia.org/wiki/Persian_art">Persian</a>, and <a href="https://en.wikipedia.org/wiki/Mohammedan">Mohammedan</a> Art.<sup><span>[</span>8<span>]</span></sup> </p><p>After Coomaraswamy&#39;s death, his widow, Doña Luisa Runstein, acted as a guide and resource for students of his work.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><div><h2>Contributions</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>Coomaraswamy made important contributions to the philosophy of art, literature, and religion. In Ceylon, he applied the lessons of <a href="https://en.wikipedia.org/wiki/William_Morris">William Morris</a> to Ceylonese culture <sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> and, with his wife Ethel, produced a groundbreaking study of Ceylonese crafts and culture. While in India, he was part of the literary circle around <a href="https://en.wikipedia.org/wiki/Rabindranath_Tagore">Rabindranath Tagore</a>, and he contributed to the &quot;<a href="https://en.wikipedia.org/wiki/Swadeshi">Swadeshi</a>&quot; movement, an early phase of the struggle for Indian independence.<sup><span>[</span>18<span>]</span></sup> In the 1920s, he made discoveries in the history of Indian art, particularly some distinctions between <a href="https://en.wikipedia.org/wiki/Rajput">Rajput</a> and <a href="https://en.wikipedia.org/wiki/Mughal_Empire">Moghul</a> painting, and published his book <i>Rajput Painting</i>. At the same time, he amassed an unmatched collection of Rajput and Moghul paintings, which he took with him to the Museum of Fine Arts, Boston, when he joined its curatorial staff in 1917. Through 1932, from his base in Boston, he produced two kinds of publications: brilliant scholarship in his curatorial field but also graceful introductions to Indian and Asian art and culture, typified by <i>The Dance of Shiva</i>, a collection of essays that remain in print to this day. Deeply influenced by <a href="https://en.wikipedia.org/wiki/Ren%C3%A9_Gu%C3%A9non">René Guénon</a>, he became one of the founders of the <a href="https://en.wikipedia.org/wiki/Traditionalist_School">Traditionalist School</a>. His books and essays on art and culture, symbolism and metaphysics, scripture, folklore and myth, and still other topics, offer a remarkable education to readers who accept the challenges of his resolutely cross-cultural perspective and insistence on tying every point he makes back to sources in multiple traditions. He once remarked, &quot;I actually think in both Eastern and Christian terms—Greek, Latin, Sanskrit, Pali, and to some extent Persian and Chinese.&quot;<sup><span>[</span>19<span>]</span></sup> Alongside the deep and not infrequently difficult writings of this period, he also delighted in polemical writings created for a larger audience—essays such as &quot;Why exhibit works of art?&quot; (1943).<sup><span>[</span>20<span>]</span></sup> </p><p>In his book <i>The Information Society: An Introduction</i> (Sage, 2003, p. 44), Armand Mattelart credits Coomaraswamy for coining the term &#39;post-industrial&#39; in 1913. </p><div><h2>Methodology</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Coomaraswamy was a firm believer in the comparative method. The analysis of both texts and symbols across a wide variety of cultures and time periods allowed him to see below the surface of local interpretations and religious exclusivism to locate the bedrock of tradition. By tradition, he meant that which has been handed down from time beyond memory. </p><blockquote> <p>The folk has thus preserved, without understanding, the remains of old traditions that go back sometimes to the indeterminably distant past, to which we can only refer as “prehistoric”.<sup><span>[</span>21<span>]</span></sup> Had the folk beliefs not indeed been once understood, we could not now speak of them as metaphysically intelligible, or explain the accuracy of their formulations.<sup><span>[</span>22<span>]</span></sup> </p> </blockquote><p>His extensive knowledge of ancient languages allowed him access to primary sources and his understanding of metaphysics helped him discern the deeper meanings that other scholars often missed. Given the specialisation and compartmentation of knowledge that was part of the Western academic tradition, his efforts were not always appreciated. He expressed some of his feelings in a letter to Graham Carey: </p><blockquote> <p>What the secular mind does is to assert that we (symbolists) are reading meaning into things that originally had none: our assertion is that they are reading out the meaning. The proof of our contention lies in the perfection, consistency and universality of the pattern in which these meanings are united.<sup><span>[</span>23<span>]</span></sup> </p> </blockquote><p>His criticism of the academic world was centered around a number of related issues. First, the academic method, by itself, was ill-equipped to deal with the way in which ideas where transmitted in non-literate cultures, due to an over-reliance on written documentation. Too much was left out. </p><blockquote> <p>By “folklore” we mean the whole and consistent body of culture which has been handed down, not in books but by word of mouth and in practice, from time beyond the reach of historical research, in the form of legends, fairy tales, ballads, games, toys, crafts, medicine, agriculture, and other rites, and forms of social organisation, especially those that we call “tribal.” This is a cultural complex independent of national and even racial boundaries, and of remarkable similarity throughout the world.<sup><span>[</span>24<span>]</span></sup> </p> </blockquote><p>A second point of conflict was the obsessive tendency of Western scholarship to divide cultures, religions, and time periods into discrete categories in order to fit into academic organisational and mental structures. </p><blockquote> <p>It is equally surprising that so many scholars, meeting with some universal doctrine in a given context, so often think of it as a local peculiarity.<sup><span>[</span>25<span>]</span></sup> </p> </blockquote><p>As a traditionalist, Coomaraswamy emphasised the continuity of culture. He was well aware of historical change but he felt that the connecting elements had been lost by the extreme emphasis placed on change and “progress”. Conflict between a new religion and an older one often obscured the commonalities that linked them. </p><blockquote> <p>The opposition of religion to folklore is often a kind of rivalry set up as between a new dispensation and an older tradition, the gods of the older cult becoming the evil spirits of the newer.<sup><span>[</span>26<span>]</span></sup> </p> </blockquote><p>He pointed out that the Greek word <i>daimon</i>, which at root indicates something given, was synonymous with the Christian Holy Spirit, God&#39;s gift of life. If Christian propagandists chose to emphasise the demonic at the expense of the <i>daimon</i> it was only to further their own cause. Ideas like this did not go over well with other scholars and his correspondence has its share of angry or condescending responses to his work which he deflected with a combination of erudition, tact, and humor.<sup><span>[</span>27<span>]</span></sup> </p><p>A third issue that raised his ire was the racism inherent in the Western world&#39;s criticism and misinterpretation of traditional and tribal cultures, attitudes tied closely to literacy and the attendant idea of progress. </p><blockquote> <p>It was possible for Aristotle, starting from the premise that a man, being actually cultured, may also become literate, to ask whether there is a necessary or merely an accidental connection of literacy with culture. Such a question can hardly arise for those to whom illiteracy implies, as a matter of course, ignorance, backwardness, unfitness for self-government: for you, unlettered people are uncivilised peoples and vice versa—as a recent publisher&#39;s blurb expresses it: “The greatest force in civilisation is the collective wisdom of a literate people.&quot;<sup><span>[</span>28<span>]</span></sup> </p> </blockquote><p>Like Franz Boas and a handful of others, Coomaraswamy waged a constant war against racism with the press and academic world. He was a strong advocate for Indian independence and was pressured to leave England for publicly suggesting that Indians not fight in the First World War.<sup><span>[</span>29<span>]</span></sup> </p><p>Unlike Rene Guenon and others who shared many of his understandings, Coomaraswamy was not content to describe traditional ideas from the inside out, in metaphysical terms alone.. He did not believe that science and metaphysics were in opposition, but were two different ways of looking at the world.<sup><span>[</span>30<span>]</span></sup> </p><p>Coomaraswamy was critical of the writings of Carl Jung and of Theosophy, which he believed distorted the meaning of traditional ideas.<sup><span>[</span>31<span>]</span></sup> The comparative method has achieved a good deal of success in linguistics but its application to culture had rarely gone beyond mere documentation before Ananda Coomaraswamy.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><div><h2>Traditional symbolism</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>One of Coomaraswamy&#39;s most important contributions was in his study of the language of symbolism contained in images. </p><blockquote> <p>To have lost the art of thinking in images is precisely to have lost the proper linguistic of metaphysics and to have descended to the verbal logic of “philosophy.<sup><span>[</span>32<span>]</span></sup> </p> </blockquote><p>His study of traditional symbols had taught him that symbols were meant to express <i>ideas</i> and not <i>emotions</i> and that a study of “styles” and “influences” would reveal little of significance. </p><blockquote> <p>An adequate knowledge of theology and cosmology is then indispensable to an understanding of the history of art, insofar as the actual shapes and structures of works of art are determined by their real content. Christian art, for example, begins with the representation of deity by abstract symbols, which may be geometrical, vegetable, or theriomorphic, and are devoid of any sentimental appeal whatever. An anthropomorphic symbol follows, but this is still a form and not a figuration; not made as though to function biologically or as if to illustrate a text book of anatomy or dramatic expression. Still later, the form is sentimentalised; the features of the crucified are made to exhibit human suffering, the type is completely humanised, and where we began with the shape of humanity as an analogical representation of the idea of God, we end with the portrait of the artist&#39;s mistress posing as the Madonna and a representation of an all-too-human baby; the Christ is no longer a man-God, but the sort of man we can approve of.<sup><span>[</span>33<span>]</span></sup> </p> </blockquote><p>In keeping with his traditionalist stance, he saw this process as one of gradual decay in which the human life world began to encroach gradually on the divine with an attendant growth of sentimentality and loss of meaning. He was fond of quoting the curator, John Lodge: “From the Stone Age until now, <i>quelle dégringolade</i>.”<sup><span>[</span>34<span>]</span></sup> </p><p>Coomaraswamy spent a lot of his time documenting themes and images that appeared to be very old, given their widespread distribution. Major areas of study included: </p><ul><li>Solar symbolism</li> <li>Symbolism of the wheel</li> <li>The Flood story</li> <li>The “Water Cosmology” and the “Plant Style”</li> <li>Soma and the Water of Life</li> <li>Traditional cosmologies (the three worlds)</li> <li>The symbolism of snakes and reptiles</li> <li>The symbolism of birds and other “psychopomps” (soul carriers)</li> <li>The heavenly ladder</li> <li>The cosmic dome and the hole in the sky with its guardian figure</li> <li>The Thread-spirit (<i>sutratman</i>) doctrine that underlies the symbolism of the fiber arts</li> <li>The concept of ether and the symbolism of fire</li> <li>Divine bi-unity (male/female) as one</li> <li>The inverted tree and arboreal symbolism</li> <li>The Symplegades (Clashing Rocks) and the Coincidence of Opposites</li></ul><p>Coomaraswamy observed these symbols in different cultures and time periods, both in religious writings and in folklore. He saw little opposition between religion and folklore. Folklore was transmitted in the vernacular as compared to the sacred languages in which scripture was delivered and interpreted. Folklore was less moralistic but its themes shared a common source with those of religion; Jack&#39;s beanstalk was Jacob&#39;s ladder. Religion was not “contaminated” by folklore but used it to express the same ideas in a more rationalised and moralised setting, just as Plato used myths to explain his philosophy.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>The designs we found in Neolithic times were derived from older images. Thus the continuity of tradition reveals itself best in art, which expresses ideas. Even when religious philosophies developed with writing, a continuity of meaning could be observed often because the change was gradual and the old and the new existed side by side. </p><blockquote> <p>In the Vedas, the belief {that all life began in the “Waters”} appears in the form of an old popular theory, for which are substituted the successively more philosophical concepts of Space Cosmology, of a belief in the origin of the world in Non-being, in an origin of the world from Being, and finally in the conception of Brahman (the Absolute) as world-ground. The Water Cosmology, it is true, persists side by side with, and linked with these deeper views, even in post-Vedic literature; but it is typically not a creation of the Vedas and seems to belong to an even older stratum of ideas than that which is developed in the Vedas.<sup><span>[</span>35<span>]</span></sup> </p> </blockquote><p>The ideas expressed by images were made explicit by writing, which allowed for a greater degree of abstraction and elaboration but since the concrete preceded the abstract, all philosophy started with images. In the absence of writing, the tribal cultures of the world have preserved a good deal of this older symbolism.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>Coomaraswamy also maintained that traditional technologies (like the needle or the fire drill) were applications of metaphysical ideas, just as modern technology is an expression of scientific principles. </p><blockquote> <p>Primitive man knew nothing of a possible divorce of function and meaning: all his inventions were applied meaning.<sup><span>[</span>36<span>]</span></sup> </p> </blockquote><p>The American art historian, <a href="https://en.wikipedia.org/wiki/Carl_Schuster">Carl Schuster</a>, who corresponded with Coomarawamy and learned much from him, would go on to identify some of the Paleolithic sources of this symbolism.<sup><span>[</span>37<span>]</span></sup> </p><div><h2>Perennial philosophy</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Ananda_Coomaraswamy.jpg"></a><figcaption>Portrait of Coomaraswamy printed in the April 1916 issue of <i>The Hindusthanee Student</i>.</figcaption></figure><p>He was described by <a href="https://en.wikipedia.org/wiki/Heinrich_Zimmer">Heinrich Zimmer</a> as &quot;That noble scholar upon whose shoulders we are still standing.&quot;<sup><span>[</span>38<span>]</span></sup> While serving as a curator to the Boston Museum of Fine Arts in the latter part of his life, he devoted his work to the explication of traditional metaphysics and symbolism. His writings of this period are filled with references to <a href="https://en.wikipedia.org/wiki/Plato">Plato</a>, <a href="https://en.wikipedia.org/wiki/Plotinus">Plotinus</a>, <a href="https://en.wikipedia.org/wiki/Clement_of_Alexandria">Clement</a>, <a href="https://en.wikipedia.org/wiki/Philo">Philo</a>, <a href="https://en.wikipedia.org/wiki/Augustine_of_Hippo">Augustine</a>, <a href="https://en.wikipedia.org/wiki/Aquinas">Aquinas</a>, <a href="https://en.wikipedia.org/wiki/Adi_Shankara">Shankara</a>, <a href="https://en.wikipedia.org/wiki/Meister_Eckhart">Eckhart</a>, <a href="https://en.wikipedia.org/wiki/Rumi">Rumi</a> and other mystics. When asked how he defined himself foremost, Coomaraswamy said he was a &quot;metaphysician&quot;, referring to the concept of <a href="https://en.wikipedia.org/wiki/Perennial_philosophy">perennial philosophy</a>, or <i>sophia perennis</i>.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>Along with <a href="https://en.wikipedia.org/wiki/Ren%C3%A9_Gu%C3%A9non">René Guénon</a> and <a href="https://en.wikipedia.org/wiki/Frithjof_Schuon">Frithjof Schuon</a>, Coomaraswamy is regarded as one of the three founders of <a href="https://en.wikipedia.org/wiki/Integral_Traditionalism">Perennialism</a>, also called the <a href="https://en.wikipedia.org/wiki/Traditionalist_School">Traditionalist School</a>. Several articles by Coomaraswamy on the subject of <a href="https://en.wikipedia.org/wiki/Hinduism">Hinduism</a> and the perennial philosophy were <a href="https://en.wikipedia.org/wiki/List_of_works_published_posthumously">published posthumously</a> in the quarterly journal <i><a href="https://en.wikipedia.org/wiki/Studies_in_Comparative_Religion">Studies in Comparative Religion</a></i> alongside articles by Schuon and Guénon among others. </p><p>Although he agrees with Guénon on the universal principles, Coomaraswamy&#39;s works are very different in form. By vocation, he was a scholar who dedicated the last decades of his life to &quot;searching the Scriptures&quot;.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Please_clarify"><span>clarification needed</span></a></i>]</sup> He offers a perspective on the tradition that complements Guénon&#39;s.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Please_clarify"><span>clarification needed</span></a></i>]</sup> He was extremely perceptive regarding aesthetics and wrote dozens of articles on traditional arts and mythology. His works are also finely balanced intellectually. Although born in the <a href="https://en.wikipedia.org/wiki/Hindu">Hindu</a> tradition, he had a deep knowledge of the <a href="https://en.wikipedia.org/wiki/Western_world">Western</a> tradition as well as a great expertise in, and love for, Greek metaphysics, especially that of Plotinus, the founder of <a href="https://en.wikipedia.org/wiki/Neoplatonism">Neoplatonism</a>.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>Coomaraswamy built a bridge between East and West that was designed to be two-way: among other things, his metaphysical writings aimed at demonstrating the unity of the Vedanta and Platonism. His works also sought to rehabilitate <a href="https://en.wikipedia.org/wiki/Original_Buddhism">original Buddhism</a>, as he believed that the distance (i.e. differences) between Buddhism and Hinduism was artificially created by Western Indologists. In his book, <i>Hinduism and Buddhism</i>, he wrote: </p><blockquote><p>The more superficially one studies Buddhism, the more it seems to differ from the Brahmanism in which it originated; the more profound our study, the more difficult it becomes to distinguish Buddhism from Brahmanism, or to say in what respects, if any, Buddhism is really unorthodox.<sup><span>[</span>39<span>]</span></sup></p></blockquote><div><h2>Thought and major works</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>Coomaraswamy’s intellectual work spanned Indian art, symbolism, religion, and philosophy. He emphasised the metaphysical and spiritual foundations of traditional cultures and critiqued modern industrial and materialist perspectives in contrast to what he saw as the integrated worldview of traditional societies. His major writings include <i>The Dance of Shiva</i>, <i>Hinduism and Buddhism</i>, and the address <i>The Religious Basis of the Forms of Indian Society</i> (1946), in which he articulated his understanding of Indian social institutions in religious and philosophical terms.<sup><span>[</span>40<span>]</span></sup> </p><div><h3>Views on caste and social order</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>In <i>The Religious Basis of the Forms of Indian Society</i>, Coomaraswamy interpreted the traditional Indian social order, including caste (varṇa), not merely as a hierarchy of status but as an expression of metaphysical principles and vocational responsibilities. He described caste divisions as “born of the Sacrifice” and linked them to the idea that qualities and operations are distributed according to divine or cosmic order, rather than racial or purely economic logic.<sup><span>[</span>41<span>]</span></sup> He framed the notion of <i>sva-dharma</i> (one’s own duty) as the basis for social roles and argued that institutions reflect an application of metaphysical doctrine and are stable because they encode an accepted cosmic pattern.<sup><span>[</span>42<span>]</span></sup> Coomaraswamy criticised modern conceptions of equality and criticised reducing human vocation to jobs determined by economics, asserting that abolishing caste in favour of such models would “not be a solution, but much rather a dissolution.”<sup><span>[</span>43<span>]</span></sup> </p><div><h2>Works</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>For a complete bibliography, see James S. Crouch, <i>A Bibliography of Ananda Kentish Coomarswamy</i>. <a href="https://en.wikipedia.org/wiki/Indira_Gandhi_National_Center_for_the_Arts">Indira Gandhi National Center for the Arts</a>, Manohar, New Delhi, (2002). Corrigenda to the above volume see at <a href="https://docs.google.com/document/d/e/2PACX-1vTxAageyFJX44YmJJ_mSyPK0kWVs80tJpRyBq2fLrm4onpprfJltaVGutUTNXPGiV5vG6OxrLxgML9x/pub">Corrigenda to A Bibliography of Ananda Kentish Coomaraswamy</a>. </p><p>Extensive bibliography was also compiled by the author&#39;s son: </p><p><i>Ananda Kentish Coomaraswamy: A Working Bibliography</i>, compiled by Dr. Rama P. Coomaraswamy (New Delhi: Lalit Kala Academi, n.d.) <a href="https://cdn.aaa.org.hk/_source/gms-corr-akccent-pub-akcworkingbibliography.pdf">[1]</a> </p><dl> <dt>Traditional art</dt></dl><ul><li>&quot;A Plea for the Teaching of Indian Music in Ceylon&quot;, <i>Journal of the Ceylon University Association, I, No.2</i> (Colombo 1906)</li> <li><i>Elements of Buddhist Iconography</i>, Harvard University Press, 1935.</li> <li><i>Figures of Speech or Figures of Thought?: The Traditional View of Art</i>, (World Wisdom 2007)</li> <li><i>Introduction To Indian Art</i>, (Kessinger Publishing, 2007)</li> <li><i>Buddhist Art</i>, (Kessinger Publishing, 2005)</li> <li><i>Guardians of the Sundoor: Late Iconographic Essays</i>, (<a href="https://en.wikipedia.org/wiki/Fons_Vitae_Publishing">Fons Vitae</a>, 2004)</li> <li><i>History of Indian and Indonesian Art</i>, (Kessinger Publishing, 2003)</li> <li><i>Teaching of Drawing in Ceylon</i> (1906, Colombo Apothecaries)</li> <li><i>The Indian Craftsman</i> (1909, <a href="https://en.wikipedia.org/wiki/Probsthain">Probsthain</a>: London)</li> <li><i><a href="http://www.germanicmythology.com/PoeticEdda/VSPCooms.html">Voluspa; The Sibyl&#39;s Saying</a></i> (1909, <a href="https://en.wikipedia.org/wiki/Essex_House_Press">Essex House Press</a>, London)</li> <li><i><a href="https://archive.org/details/cu31924022942993">Viśvakarmā; Examples of Indian Architecture, Sculpture, Painting, Handicraft</a></i> (1914, London)</li> <li><i><a href="https://en.wikipedia.org/wiki/Vidyapati">Vidyāpati</a></i>: <i>Bangīya Padābali; Songs of the Love of Rādhā and Krishna</i>, (1915, The Old Bourne press: London)</li> <li><i>The Mirror of Gesture: Being the Abhinaya Darpaṇa of Nandikeśvara</i> (with <a href="https://en.wikipedia.org/wiki/Duggir%C4%81la_G%C5%8Dp%C4%81lakr%CC%A5%E1%B9%A3%E1%B9%87a">Duggirāla Gōpālakr̥ṣṇa</a>) (1917, Harvard University Press; 1997, South Asia Books,)</li> <li><i>Indian Music</i> (1917, G. Schirmer; 2006, <a href="https://en.wikipedia.org/wiki/Kessinger_Publishing">Kessinger Publishing</a>,</li> <li><i>A Catalog of Sculptures by John Mowbray-Clarke: Shown at the Kevorkian Galleries, New York, from May the seventh to June the seventh, 1919.</i> (1919, New York: Kevorkian Galleries, co-authored with <a href="https://en.wikipedia.org/wiki/John_Frederick_Mowbray-Clarke">Mowbray-Clarke, John</a>, H. Kevorkian, and Amy Murray)</li> <li><i>Rajput Painting</i>, (B.R. Publishing Corp., 2003)</li> <li><i>Early Indian Architecture: Cities and City-Gates</i>, (South Asia Books, 2002) I</li> <li><i>The Origin of the Buddha Image</i>, (Munshiram Manoharlal Pub Pvt Ltd, 2001)</li> <li><i>The Transformation of Nature in Art</i>, (Sterling Pub Private Ltd, 1996)</li> <li><i>Bronzes from Ceylon, chiefly in the Colombo Museum</i>, (Dept. of Govt. Print, 1978)</li> <li><i>Early Indian Architecture: Palaces</i>, (<a href="https://en.wikipedia.org/wiki/Munshiram_Manoharlal">Munshiram Manoharlal</a>, 1975)</li> <li><i><a href="https://archive.org/details/cu31924022942985">The Arts &amp; Crafts of India &amp; Ceylon</a></i>, (<a href="https://en.wikipedia.org/wiki/Farrar,_Straus">Farrar, Straus</a>, 1964)</li> <li><i>Christian and Oriental Philosophy of Art</i>, (<a href="https://en.wikipedia.org/wiki/Dover_Publications">Dover Publications</a>, 1956)</li> <li><i>Archaic Indian Terracottas</i>, (Klinkhardt &amp; Biermann, 1928)</li> <li><i>Yaksas</i>, (Munshiram Manoharlal Pub Pvt Ltd, 1998) <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-81-215-0230-6"><bdi>978-81-215-0230-6</bdi></a></li></ul><dl><dt>Metaphysics</dt></dl><ul><li><i>Hinduism and Buddhism</i>, (Kessinger Publishing, 2007; Golden Elixir Press, 2011)</li> <li><i><a href="https://en.wikipedia.org/wiki/Myths_of_the_Hindus_%26_Buddhists">Myths of the Hindus &amp; Buddhists</a></i> (with <a href="https://en.wikipedia.org/wiki/Sister_Nivedita">Sister Nivedita</a>) (1914, H. Holt; 2003, Kessinger Publishing)</li> <li><i><a href="https://archive.org/details/buddhagospelofbu00coom">Buddha and the Gospel of Buddhism</a></i> (1916, G. P. Putnam&#39;s sons; 2006, Obscure Press,)</li> <li><i>A New Approach to the Vedas: An Essay in Translation and Exegesis</i>, (South Asia Books, 1994)</li> <li><i>The Living Thoughts of Gotama the Buddha</i>, (<a href="https://en.wikipedia.org/wiki/Fons_Vitae_Publishing">Fons Vitae</a>, 2001)</li> <li><i>Time and Eternity</i>, (<a href="https://en.wikipedia.org/wiki/Artibus_Asiae">Artibus Asiae</a>, 1947)</li> <li><i>Perception of the Vedas</i>, (Manohar Publishers and Distributors, 2000)</li> <li><i>Coomaraswamy: Selected Papers, Volume 2, Metaphysics</i>, (Princeton University Press, 1977)</li></ul><dl><dt>Social criticism</dt></dl><ul><li><i>Am I My Brothers Keeper</i>, (Ayer Co, 1947)</li> <li><i><a href="https://archive.org/details/danceofsivafourt01coomuoft">The Dance of Shiva – Fourteen Indian Essays</a></i> Turn Inc., New York; 2003, Kessinger Publishing,</li> <li><i>The village community and modern progress</i> (12 pages) (Colombo Apothecaries, 1908)</li> <li><i>Essays in National Idealism</i> (Colombo Apothecaries, 1910)</li> <li><i>Bugbear of Literacy</i>, (Sophia Perennis, 1979)</li> <li><i>What is Civilisation?: and Other Essays</i>. Golgonooza Press, (UK),</li> <li><i>Spiritual Authority and Temporal Power in the Indian Theory of Government</i>, (<a href="https://en.wikipedia.org/wiki/Oxford_University_Press">Oxford University Press</a>, 1994)</li> <li><i>The Religious Basis of the Forms of Indian Society</i>, (Orientalia, 1946)</li></ul><dl><dt>Posthumous collections</dt></dl><ul><li><i>The Door in the Sky. Coomaraswamy on Myth and Meaning</i>, (Princeton University Press, 1997)</li> <li><i>Coomaraswamy: Selected Papers, 3 volumes: Traditional Art and Symbolism, Metaphysics, His Life and Work</i>, (Princeton University Press, 1977)</li> <li><i>The Essential Ananda K. Coomaraswamy</i>, (2003, <a href="https://en.wikipedia.org/wiki/World_Wisdom">World Wisdom</a>)</li> <li><i>Guardians of the Sun-Door</i>, (<a href="https://en.wikipedia.org/wiki/Fons_Vitae_Publishing">Fons Vitae</a>, 2004)</li></ul><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><div><ol> <li><span><b>^</b></span> <span>Murray Fowler, &quot;In Memoriam: Ananda Kentish Coomaraswamy&quot;, <i>Artibus Asiae,</i> Vol. 10, No. 3 (1947), pp. 241-244</span> </li> <li><span><b>^</b></span> <span><a href="https://web.archive.org/web/20090201093042/http://mfa.org/collections/sub.asp?key=22&amp;subkey=133">MFA: South Asian Art</a>. Archived from <a href="http://www.mfa.org/collections/sub.asp?key=22&amp;subkey=133">the original</a> <a href="https://web.archive.org/web/20100615042318/http://www.mfa.org/collections/sub.asp?key=22&amp;subkey=133">Archived</a> 15 June 2010 at the <a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://kataragama.org/centers/akc_oration99.htm">&quot;The Annual Ananda Coomaraswamy Memorial Oration 1999&quot;</a><span>. Retrieved <span>7 April</span> 2016</span>.</cite></span> </li> <li><span><b>^</b></span> <span>Kathleen Taylor, <i>Sir John Woodroffe Tantra and Bengal</i>, Routledge (2012), p. 63</span> </li> <li><span><b>^</b></span> <span><i>Journal of Comparative Literature &amp; Aesthetics</i>, Volume 16 (1993), p. 61</span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.silumina.lk/2020/12/05/තරංග/දේශීයත්වයේ-පටු-සීමා-විනිවිද-දේශීයත්වයේ-මහිමය-දැකීම">&quot;Seeing the glory of localism that transcends the narrow boundaries of localism&quot;</a>. <i>Silumina</i>. 4 December 2020<span>. Retrieved <span>7 June</span> 2021</span>.</cite></span> </li> <li><span><b>^</b></span> <span><a href="http://www.nybooks.com/articles/article-preview?article_id=7902">Philip Rawson, &quot;A Professional Sage&quot;, <i>The New York Review of Books,</i> v. 26, no. 2 (February 22, 1979)</a></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="http://arks.princeton.edu/ark:/88435/zg64tk96f">&quot;Stella Bloch Papers Relating to Ananda K. Coomaraswamy, 1890-1985 (bulk 1917-1930)&quot;</a>. Princeton University Library Manuscripts Division.</cite></span> </li> <li><span><b>^</b></span> <span>Arrowsmith, Rupert Richard. <a href="https://books.google.com/books?id=MIBNXScRj3QC&amp;dq=modernism%20and%20the%20museum&amp;pg=PP1"><i>Modernism and the Museum: Asian, African and Pacific Art and the London Avant Garde</i></a>. Oxford University Press, 2011, passim. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-959369-9"><bdi>978-0-19-959369-9</bdi></a>.</span> </li> <li><span><b>^</b></span> <span><a href="https://vimeo.com/arrowsmith/cosmopolitanism-and-modernism">Video of a Lecture discussing Coomaraswamy&#39;s role in the introduction of Indian art to Western Modernists</a>, <i><a href="https://en.wikipedia.org/wiki/School_of_Advanced_Study">School of Advanced Study</a></i>, March 2012.</span> </li> <li><span><b>^</b></span> <span><a href="http://www.open.ac.uk/researchprojects/makingbritain/content/alice-richardson">Alice Richardson</a>, Making Britain, Open University, Retrieved 17 October 2015</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>G. R. Seaman, <i><a href="http://www.oxforddnb.com/view/article/55201">Coomaraswamy, Ananda Kentish (1877–1947)</a></i>, Oxford Dictionary of National Biography, Oxford University Press, 2004, accessed 17 Oct 2015</span> </li> <li><span><b>^</b></span> <span><a href="http://www.religioperennis.org/documents/stoddart/On_Rama_Coomaraswamy-by_Stoddart_and_de_Azevedo.pdf">&quot;Rama P.Coomaraswamy (1929-2006)&quot; by William Stoddart and Mateus Soares de Azevedo (3 pdfs)</a></span> </li> <li><span><b>^</b></span> <span><a href="http://www.the-pope.com/validity.html">&quot;On the Validity of My Ordination&quot; by Dr. Rama P. Coomaraswamy</a></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Father Rama Coomaraswamy (1981). <a href="https://www.holyromancatholicchurch.org/CatholicWritings.htm">&quot;&quot;About&quot;&quot;</a>. <i>The Destruction of the Christian Tradition</i> (2nd ed.). <a href="https://web.archive.org/web/20100209025124/https://www.holyromancatholicchurch.org/CatholicWritings.htm">Archived</a> from the original on 9 February 2010. <q>His son, born in Massachusetts in 1932, plays the same role in the catholic resistance guerilla against so-called &#39;II Vatican Council&#39; and so-called &#39;John Paul II&#39;. He studied in England and later in India,</q></cite> <span><code class="cs1-code">{{cite book}}</code>: </span><span><code class="cs1-code">|website=</code> ignored (<a href="https://en.wikipedia.org/wiki/Help:CS1_errors#periodical_ignored">help</a>)</span></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.bbc.com/news/world-asia-india-35130795">&quot;Profile: &#39;Living Saint&#39; Mother Teresa&quot;</a>. <i>BBC.com</i>. 18 December 2015. <a href="https://web.archive.org/web/20051101050306/http://news.bbc.co.uk/onthisday/hi/dates/stories/february/3/newsid_4117000/4117617.stm">Archived</a> from the original on 1 November 2005. <q>In 2002, five years after her death, Pope John Paul II judged that the healing of a woman suffering from an abdominal tumour was the result of Mother Teresa&#39;s supernatural intervention.</q></cite></span> </li> <li><span><b>^</b></span> <span><a href="https://en.wikipedia.org/wiki/Princeton_University_Press">Princeton University Press</a>, <a href="http://press.princeton.edu/titles/6166.html">The Door in the Sky: Coomaraswamy on Myth and Meaning</a></span> </li> <li><span><b>^</b></span> <span><cite>Antliff, Allan (2001). <i>Anarchist Modernism : Art, Politics, and the First American Avant-Garde</i>. Chicago: University of Chicago Press. p. 129. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9780226021041"><bdi>9780226021041</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://web.archive.org/web/20080420053046/http://www.ignca.gov.in/nl001801.htm">&quot;Anand Coomaraswamy A Pen Sketch By - Dr. Rama P. Coomaraswamy&quot;</a>. Archived from <a href="https://www.ignca.gov.in/nl001801.htm">the original</a> on 20 April 2008<span>. Retrieved <span>21 November</span> 2007</span>.</cite></span> </li> <li><span><b>^</b></span> <span><a href="http://www.studiesincomparativereligion.com/public/articles/Why_Exhibit_Works_of_Art-by_Ananda_Coomaraswamy.aspx">Why Exhibit Works of Art?</a> <a href="https://web.archive.org/web/20100828112019/http://www.studiesincomparativereligion.com/public/articles/Why_Exhibit_Works_of_Art-by_Ananda_Coomaraswamy.aspx">Archived</a> 28 August 2010 at the <a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a>, essay. He also published a book of that title.</span> </li> <li><span><b>^</b></span> <span>Ananda Coomaraswamy, <i>Christian and Oriental Philosophy of Art</i>, p. 139; quoting René Guénon</span> </li> <li><span><b>^</b></span> <span>Ananda Coomaraswamy, <i>Christian and Oriental Philosophy of Art</i>, p. 140.</span> </li> <li><span><b>^</b></span> <span>Selected Letters of Ananda Coomaraswamy, p. 213. Graham Carey (1892-1984) was an architect, essayist, lecturer and the co-author, with A. K. Coomaraswamy, of Patron and Artist, Pre-Renaissance and Modern (1936).</span> </li> <li><span><b>^</b></span> <span>The Collected Works of Ananda Coomaraswamy, vol. 1, p. 286.</span> </li> <li><span><b>^</b></span> <span>Ananda Coomaraswamy, The Greek Sphinx in Guardians of the Sun-Door pg. 120 ft. 5</span> </li> <li><span><b>^</b></span> <span>The Collected Works of Ananda Coomaraswamy, vol. 1, p. 286, ft.2.</span> </li> <li><span><b>^</b></span> <span>See Selected Letters of Ananda Coomaraswamy, passim, for many examples.</span> </li> <li><span><b>^</b></span> <span>Ananda Coomaraswamy, The Bugbear of Literacy, p. 23, quoting Aristotle, Metaphysics, VI 2, 4, and XI: 8, 12.</span> </li> <li><span><b>^</b></span> <span>See Selected Letters of Ananda Coomaraswamy, passim, for his stance on Indian independence.</span> </li> <li><span><b>^</b></span> <span>See Ananda Coomaraswamy, What is Civilisation and Other Essays. “Gradation and Evolution” Chapters 7 and 8.</span> </li> <li><span><b>^</b></span> <span>See &quot;Vedanta and Western Tradition&quot; in The Collected Works of Ananda Coomaraswamy, vol. 2, and The Selected Letters of Ananda Coomaraswamy, p. 150 and p. 157.</span> </li> <li><span><b>^</b></span> <span>The Collected Works of Ananda Coomaraswamy, vol. 1, pp. 296-297.</span> </li> <li><span><b>^</b></span> <span>Ananda Coomaraswamy, Christian and Oriental Philosophy of Art, pl. 45.</span> </li> <li><span><b>^</b></span> <span>&quot;From the Stone Age until now, what a downfall.</span> </li> <li><span><b>^</b></span> <span>&quot;Ananda Coomaraswamy, Yaksas, pp. 98-99.</span> </li> <li><span><b>^</b></span> <span>Selected Letters of Ananda Coomaraswamy, p. 291, in a letter to George Sarton.</span> </li> <li><span><b>^</b></span> <span>See Selected Letters of Ananda Coomaraswamy, pp. 220-221, for one example. The two men met in Cambridge, Massachusetts in the 1930s.</span> </li> <li><span><b>^</b></span> <span><a href="http://www.stumbleupon.com/url/www.multiworld.org/m_versity/althinkers/coomara.htm">Multiworld.org/m_versity/althinkers... - StumbleUpon</a></span> </li> <li><span><b>^</b></span> <span><cite>Coomaraswamy, Ananda (1943). <i>Hinduism and Buddhism</i>. Open Road Media. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/1497675847"><bdi>1497675847</bdi></a>.</cite> <span><code class="cs1-code">{{cite book}}</code>: </span><span>ISBN / Date incompatibility (<a href="https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_isbn_date">help</a>)</span></span> </li> <li><span><b>^</b></span> <span><cite>Coomaraswamy, Ananda K. (1946). <a href="https://archive.org/download/religiousbasisof00coom/religiousbasisof00coom.pdf"><i>The Religious Basis of the Forms of Indian Society: An Address to the Student&#39;s Religious Association, Ann Arbor, January 1946; Indian Culture and English Influence; and East and West</i></a> <span>(PDF)</span>. Orientalia<span>. Retrieved <span>26 February</span> 2026</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Coomaraswamy, Ananda K. (1946). <a href="https://archive.org/download/religiousbasisof00coom/religiousbasisof00coom.pdf"><i>The Religious Basis of the Forms of Indian Society: An Address to the Student&#39;s Religious Association, Ann Arbor, January 1946; Indian Culture and English Influence; and East and West</i></a> <span>(PDF)</span>. Orientalia. p. 15<span>. Retrieved <span>26 February</span> 2026</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Coomaraswamy, Ananda K. (1946). <a href="https://archive.org/download/religiousbasisof00coom/religiousbasisof00coom.pdf"><i>The Religious Basis of the Forms of Indian Society: An Address to the Student&#39;s Religious Association, Ann Arbor, January 1946; Indian Culture and English Influence; and East and West</i></a> <span>(PDF)</span>. Orientalia. p. 14<span>. Retrieved <span>26 February</span> 2026</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Coomaraswamy, Ananda K. (1946). <a href="https://archive.org/download/religiousbasisof00coom/religiousbasisof00coom.pdf"><i>The Religious Basis of the Forms of Indian Society: An Address to the Student&#39;s Religious Association, Ann Arbor, January 1946; Indian Culture and English Influence; and East and West</i></a> <span>(PDF)</span>. Orientalia. p. 19<span>. Retrieved <span>26 February</span> 2026</span>.</cite></span> </li> </ol></div><div><h2>Sources</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://web.archive.org/web/20160303171247/http://stateless.freehosting.net/ANANDAkCOOMARASWAMY.htm">T.Wignesan, &quot;Ananda K. Coomaraswamy&#39;s Aesthetics&quot; # Tamil studies Now published in the collection: T.Wignesan. Rama and Ravana at the Altar of Hanuman: On Tamils, Tamil Literature &amp; Tamil Culture. Allahabad:Cyberwit.net, 2008, 750p. &amp; at Chennai: Institute of Asian Studies, 2007, 439p.</a></li> <li><a href="http://tamilnation.co/hundredtamils/coomaraswamy.htm">&quot;Ananda Kentish Coomaraswamy&quot; in <i>One Hundred Tamils of the 20th Century</i></a></li> <li>&quot;Coomaraswamy, Ananda K.&quot;, <i>Encyclopaedia of Indian Literature,</i> vol. 1, ed. Amaresh Dutta, Sahitya Akademi (1987), p. 768. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/81-260-1803-8"><bdi>81-260-1803-8</bdi></a></li> <li>Mattelart, Armand. <i>The Information Society: An Introduction</i>, Sage: London, Thousand Oaks, New Delhi, 2003, p. 44.</li></ul><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><ul><li><i>Ananda Coomaraswamy: Remembering and Remembering Again and Again</i>, by S. Durai Raja Singam. Publisher: Raja Singam, 1974.</li> <li><i>Ananda K. Coomaraswamy</i>, by P. S. Sastri. Arnold-Heinemann Publishers, India, 1974.</li> <li><i>Ananda K. Coomaraswamy: A Handbook</i>, by S. Durai Raja Singam. Publisher s.n., 1979.</li> <li><i>Ananda Coomaraswamy: A Study</i>, by Moni Bagchee. Publisher: Bharata Manisha, 1977.</li> <li><i>Ananda K. Coomaraswamy</i>, by Vishwanath S. Naravane. Twayne Publishers, 1977. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-8057-7722-9"><bdi>0-8057-7722-9</bdi></a>.</li> <li><i>Selected Letters of Ananda Coomaraswamy</i>, Edited by Alvin Moore, Jr; and Rama P. Coomaraswamy (1988).</li> <li><i>Coomaraswamy: Volume I: Selected Papers, Traditional Art and Symbolism</i>, Princeton University Press (1977).</li> <li><i>Coomaraswamy: Volume II: Selected Papers, Metaphysics</i>, Edited by Roger Lipsey, Princeton University Press (1977).</li> <li><i>Coomaraswamy: Volume III: His Life and Work</i>, by Roger Lipsey, Princeton University Press (1977).</li></ul><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Ananda_Coomaraswamy&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><div> <div> <div>Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Ananda_Coomaraswamy">Ananda Coomaraswamy</a></b></i>.</div></div> </div><ul><li><a href="https://www.gutenberg.org/ebooks/author/39295">Works by Ananda Coomaraswamy</a> at <a href="https://en.wikipedia.org/wiki/Project_Gutenberg">Project Gutenberg</a></li> <li><a href="https://archive.org/search.php?query=%28%28subject%3A%22Coomaraswamy%2C%20Ananda%20Kentish%22%20OR%20subject%3A%22Coomaraswamy%2C%20Ananda%20K%2E%22%20OR%20subject%3A%22Coomaraswamy%2C%20A%2E%20K%2E%22%20OR%20subject%3A%22Ananda%20Kentish%20Coomaraswamy%22%20OR%20subject%3A%22Ananda%20K%2E%20Coomaraswamy%22%20OR%20subject%3A%22A%2E%20K%2E%20Coomaraswamy%22%20OR%20subject%3A%22Coomaraswamy%2C%20Ananda%22%20OR%20subject%3A%22Ananda%20Coomaraswamy%22%20OR%20creator%3A%22Ananda%20Kentish%20Coomaraswamy%22%20OR%20creator%3A%22Ananda%20K%2E%20Coomaraswamy%22%20OR%20creator%3A%22A%2E%20K%2E%20Coomaraswamy%22%20OR%20creator%3A%22A%2E%20Kentish%20Coomaraswamy%22%20OR%20creator%3A%22Coomaraswamy%2C%20Ananda%20Kentish%22%20OR%20creator%3A%22Coomaraswamy%2C%20Ananda%20K%2E%22%20OR%20creator%3A%22Coomaraswamy%2C%20A%2E%20K%2E%22%20OR%20creator%3A%22Coomaraswamy%2C%20A%2E%20Kentish%22%20OR%20creator%3A%22Ananda%20Coomaraswamy%22%20OR%20creator%3A%22Coomaraswamy%2C%20Ananda%22%20OR%20title%3A%22Ananda%20Kentish%20Coomaraswamy%22%20OR%20title%3A%22Ananda%20K%2E%20Coomaraswamy%22%20OR%20title%3A%22A%2E%20K%2E%20Coomaraswamy%22%20OR%20title%3A%22Ananda%20Coomaraswamy%22%20OR%20description%3A%22Ananda%20Kentish%20Coomaraswamy%22%20OR%20description%3A%22Ananda%20K%2E%20Coomaraswamy%22%20OR%20description%3A%22A%2E%20K%2E%20Coomaraswamy%22%20OR%20description%3A%22Coomaraswamy%2C%20Ananda%20Kentish%22%20OR%20description%3A%22Coomaraswamy%2C%20Ananda%20K%2E%22%20OR%20description%3A%22Ananda%20Coomaraswamy%22%20OR%20description%3A%22Coomaraswamy%2C%20Ananda%22%29%20OR%20%28%221877-1947%22%20AND%20Coomaraswamy%29%29%20AND%20%28-mediatype:software%29">Works by or about Ananda Coomaraswamy</a> at the <a href="https://en.wikipedia.org/wiki/Internet_Archive">Internet Archive</a></li> <li><a href="https://web.archive.org/web/20051211184940/http://www.fonsvitae.com/coomaraswamyseries.html">Books by Coomaraswamy</a> – <a href="https://en.wikipedia.org/wiki/Fons_Vitae_Publishing">Fons Vitae</a> Series</li> <li><a href="http://kataragama.org/centers/akc_oration99.htm">1999 Coomaraswamy lecture by Sandrasagra</a></li> <li><a href="http://www.worldcat.org/search?q=au%3AAnanda+K.+Coomaraswamy&amp;qt=advanced&amp;dblist=638">Ananda K. Coomaraswamy at WorldCat</a></li> <li><a href="http://www.religioperennis.org/Bibliography.html#Coomaraswamy">Coomaraswamy bibliography at religioperennis.org</a></li> <li><a href="https://web.archive.org/web/20091011202349/http://www.worldwisdom.com/public/authors/Ananda-K-Coomaraswamy.aspx">&quot;Ananda K. Coomaraswamy&#39;s Life and Work&quot; at World Wisdom publishers</a></li> <li><a href="https://web.archive.org/web/20071228093929/http://www.museindia.com/showfocus4.asp?id=698">The Colonial Context and Aesthetic Identity Formation: Coomaraswamy, A Case Study by Binda Paranjpe</a></li> <li><a href="https://www.rootsweb.ancestry.com/~lkawgw/anandac.htm">Coomaraswamy&#39;s Impetus to Eastern Spirit</a></li> <li><a href="http://arthistorians.info/coomaraswamya">Coomarswamy</a> in Dictionary of Art Historians</li> <li><a href="http://www.saadigitalarchive.org/entity/ananda-coomaraswamy">Ananda Coomaraswamy materials in the South Asian American Digital Archive (SAADA)</a></li></ul><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Aesthetics"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Aesthetics"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Aesthetics"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Aesthetics">Aesthetics</a></div></th></tr><tr><th>Areas</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/African_aesthetic">African</a></li> <li><a href="https://en.wikipedia.org/wiki/Ancient_aesthetics">Ancient</a></li> <li><a href="https://en.wikipedia.org/wiki/Indian_aesthetics">Indian</a></li> <li><a href="https://en.wikipedia.org/wiki/Japanese_aesthetics">Japanese</a></li> <li><a href="https://en.wikipedia.org/wiki/Mathematics_and_art">Mathematics</a></li> <li><a href="https://en.wikipedia.org/wiki/Medieval_aesthetics">Medieval</a></li> <li><a href="https://en.wikipedia.org/wiki/Aesthetics_of_music">Music</a></li> <li><a href="https://en.wikipedia.org/wiki/Aesthetics_of_nature">Nature</a></li> <li><a href="https://en.wikipedia.org/wiki/Aesthetics_of_science">Science</a></li> <li><a href="https://en.wikipedia.org/wiki/Theological_aesthetics">Theology</a></li></ul> </div></td></tr><tr><th>Schools</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Aestheticism">Aestheticism</a></li> <li><a href="https://en.wikipedia.org/wiki/Classicism">Classicism</a></li> <li><a href="https://en.wikipedia.org/wiki/Fascism#Aesthetics">Fascism</a></li> <li><a href="https://en.wikipedia.org/wiki/Feminist_aesthetics">Feminism</a></li> <li><a href="https://en.wikipedia.org/wiki/Formalism_(art)">Formalism</a></li> <li><a href="https://en.wikipedia.org/wiki/Historicism_(art)">Historicism</a></li> <li><a href="https://en.wikipedia.org/wiki/Marxist_aesthetics">Marxism</a></li> <li><a href="https://en.wikipedia.org/wiki/Modernism">Modernism</a></li> <li><a href="https://en.wikipedia.org/wiki/Postmodernism">Postmodernism</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychoanalytic_theory">Psychoanalysis</a></li> <li><a href="https://en.wikipedia.org/wiki/Aesthetic_Realism">Realism</a></li> <li><a href="https://en.wikipedia.org/wiki/Romanticism">Romanticism</a></li> <li><a href="https://en.wikipedia.org/wiki/Symbolism_(movement)">Symbolism</a></li> <li><a href="https://en.wikipedia.org/wiki/Theosophy_and_visual_arts">Theosophy</a></li> <li><i><a href="https://en.wikipedia.org/wiki/List_of_art_movements">more...</a></i></li></ul> </div></td></tr><tr><th>Philosophers</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Abhinavagupta">Abhinavagupta</a></li> <li><a href="https://en.wikipedia.org/wiki/Theodor_W._Adorno">Adorno</a></li> <li><a href="https://en.wikipedia.org/wiki/Leon_Battista_Alberti">Alberti</a></li> <li><a href="https://en.wikipedia.org/wiki/Mirza_Fatali_Akhundov">Akhundov</a></li> <li><a href="https://en.wikipedia.org/wiki/Ibn_Arabi">Ibn Arabi</a></li> <li><a href="https://en.wikipedia.org/wiki/Aristotle">Aristotle</a></li> <li><a href="https://en.wikipedia.org/wiki/Thomas_Aquinas">Aquinas</a></li> <li><a href="https://en.wikipedia.org/wiki/B%C3%A9la_Bal%C3%A1zs">Balázs</a></li> <li><a href="https://en.wikipedia.org/wiki/Hans_Urs_von_Balthasar">Balthasar</a></li> <li><a href="https://en.wikipedia.org/wiki/Georges_Bataille">Bataille</a></li> <li><a href="https://en.wikipedia.org/wiki/Charles_Baudelaire">Baudelaire</a></li> <li><a href="https://en.wikipedia.org/wiki/Jean_Baudrillard">Baudrillard</a></li> <li><a href="https://en.wikipedia.org/wiki/Alexander_Gottlieb_Baumgarten">Baumgarten</a></li> <li><a href="https://en.wikipedia.org/wiki/Clive_Bell">Bell</a></li> <li><a href="https://en.wikipedia.org/wiki/Walter_Benjamin">Benjamin</a></li> <li><a href="https://en.wikipedia.org/wiki/Edmund_Burke">Burke</a></li> <li><a href="https://en.wikipedia.org/wiki/Samuel_Taylor_Coleridge">Coleridge</a></li> <li><a href="https://en.wikipedia.org/wiki/R._G._Collingwood">Collingwood</a></li> <li>Coomaraswamy</li> <li><a href="https://en.wikipedia.org/wiki/Arthur_Danto">Danto</a></li> <li><a href="https://en.wikipedia.org/wiki/Gilles_Deleuze">Deleuze</a></li> <li><a href="https://en.wikipedia.org/wiki/John_Dewey">Dewey</a></li> <li><a href="https://en.wikipedia.org/wiki/Gustave_Flaubert">Flaubert</a></li> <li><a href="https://en.wikipedia.org/wiki/Michel_Foucault">Foucault</a></li> <li><a href="https://en.wikipedia.org/wiki/Roger_Fry">Fry</a></li> <li><a href="https://en.wikipedia.org/wiki/Johann_Wolfgang_von_Goethe">Goethe</a></li> <li><a href="https://en.wikipedia.org/wiki/Nelson_Goodman">Goodman</a></li> <li><a href="https://en.wikipedia.org/wiki/Antonio_Gramsci">Gramsci</a></li> <li><a href="https://en.wikipedia.org/wiki/Clement_Greenberg">Greenberg</a></li> <li><a href="https://en.wikipedia.org/wiki/Eduard_Hanslick">Hanslick</a></li> <li><a href="https://en.wikipedia.org/wiki/Georg_Wilhelm_Friedrich_Hegel">Hegel</a></li> <li><a href="https://en.wikipedia.org/wiki/Martin_Heidegger">Heidegger</a></li> <li><a href="https://en.wikipedia.org/wiki/David_Hume">Hume</a></li> <li><a href="https://en.wikipedia.org/wiki/Francis_Hutcheson_(philosopher)">Hutcheson</a></li> <li><a href="https://en.wikipedia.org/wiki/Immanuel_Kant">Kant</a></li> <li><a href="https://en.wikipedia.org/wiki/S%C3%B8ren_Kierkegaard">Kierkegaard</a></li> <li><a href="https://en.wikipedia.org/wiki/Paul_Klee">Klee</a></li> <li><a href="https://en.wikipedia.org/wiki/Susanne_Langer">Langer</a></li> <li><a href="https://en.wikipedia.org/wiki/Theodor_Lipps">Lipps</a></li> <li><a href="https://en.wikipedia.org/wiki/Liu_Xie">Liu</a></li> <li><a href="https://en.wikipedia.org/wiki/Gy%C3%B6rgy_Luk%C3%A1cs">Lukács</a></li> <li><a href="https://en.wikipedia.org/wiki/Jean-Fran%C3%A7ois_Lyotard">Lyotard</a></li> <li><a href="https://en.wikipedia.org/wiki/Paul_de_Man">de Man</a></li> <li><a href="https://en.wikipedia.org/wiki/Herbert_Marcuse">Marcuse</a></li> <li><a href="https://en.wikipedia.org/wiki/Jacques_Maritain">Maritain</a></li> <li><a href="https://en.wikipedia.org/wiki/Maurice_Merleau-Ponty">Merleau-Ponty</a></li> <li><a href="https://en.wikipedia.org/wiki/Friedrich_Nietzsche">Nietzsche</a></li> <li><a href="https://en.wikipedia.org/wiki/Jos%C3%A9_Ortega_y_Gasset">Ortega y Gasset</a></li> <li><a href="https://en.wikipedia.org/wiki/George_Orwell">Orwell</a></li> <li><a href="https://en.wikipedia.org/wiki/Walter_Pater">Pater</a></li> <li><a href="https://en.wikipedia.org/wiki/Petrarch">Petrarch</a></li> <li><a href="https://en.wikipedia.org/wiki/Plato">Plato</a></li> <li><a href="https://en.wikipedia.org/wiki/Pythagoras">Pythagoras</a></li> <li><a href="https://en.wikipedia.org/wiki/Quintilian">Quintilian</a></li> <li><a href="https://en.wikipedia.org/wiki/Jacques_Ranci%C3%A8re">Rancière</a></li> <li><a href="https://en.wikipedia.org/wiki/Ayn_Rand">Rand</a></li> <li><a href="https://en.wikipedia.org/wiki/I._A._Richards">Richards</a></li> <li><a href="https://en.wikipedia.org/wiki/John_Ruskin">Ruskin</a></li> <li><a href="https://en.wikipedia.org/wiki/Edward_Said">Said</a></li> <li><a href="https://en.wikipedia.org/wiki/George_Santayana">Santayana</a></li> <li><a href="https://en.wikipedia.org/wiki/Friedrich_Schiller">Schiller</a></li> <li><a href="https://en.wikipedia.org/wiki/Arthur_Schopenhauer">Schopenhauer</a></li> <li><a href="https://en.wikipedia.org/wiki/Roger_Scruton">Scruton</a></li> <li><a href="https://en.wikipedia.org/wiki/Susan_Sontag">Sontag</a></li> <li><a href="https://en.wikipedia.org/wiki/Rabindranath_Tagore">Tagore</a></li> <li><a href="https://en.wikipedia.org/wiki/Jun%27ichir%C5%8D_Tanizaki">Tanizaki</a></li> <li><a href="https://en.wikipedia.org/wiki/J._R._R._Tolkien">Tolkien</a></li> <li><a href="https://en.wikipedia.org/wiki/Giorgio_Vasari">Vasari</a></li> <li><a href="https://en.wikipedia.org/wiki/Oscar_Wilde">Wilde</a></li> <li><a href="https://en.wikipedia.org/wiki/Johann_Joachim_Winckelmann">Winckelmann</a></li> <li><a href="https://en.wikipedia.org/wiki/Virginia_Woolf">Woolf</a></li> <li><a href="https://en.wikipedia.org/wiki/%C3%89mile_Zola">Zola</a></li> <li><i><a href="https://en.wikipedia.org/wiki/List_of_philosophers_of_art">more...</a></i></li></ul> </div></td></tr><tr><th>Concepts</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Apollonian_and_Dionysian">Apollonian and Dionysian</a></li> <li><a href="https://en.wikipedia.org/wiki/Appropriation_(art)">Appropriation</a></li> <li><a href="https://en.wikipedia.org/wiki/Art_for_art%27s_sake">Art for art&#39;s sake</a></li> <li><a href="https://en.wikipedia.org/wiki/Art_manifesto">Art manifesto</a></li> <li><a href="https://en.wikipedia.org/wiki/Artistic_merit">Artistic merit</a></li> <li><a href="https://en.wikipedia.org/wiki/Authenticity_in_art">Authenticity</a></li> <li><a href="https://en.wikipedia.org/wiki/Avant-garde">Avant-garde</a></li> <li><a href="https://en.wikipedia.org/wiki/Beauty">Beauty</a> <ul><li><a href="https://en.wikipedia.org/wiki/Feminine_beauty_ideal">Feminine</a></li> <li><a href="https://en.wikipedia.org/wiki/Masculine_beauty_ideal">Masculine</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Cool_(aesthetic)">Cool</a></li> <li><a href="https://en.wikipedia.org/wiki/Camp_(style)">Camp</a></li> <li><a href="https://en.wikipedia.org/wiki/Comedy">Comedy</a></li> <li><a href="https://en.wikipedia.org/wiki/Creativity">Creativity</a></li> <li><a href="https://en.wikipedia.org/wiki/Cuteness">Cuteness</a></li> <li><a href="https://en.wikipedia.org/wiki/Depiction">Depiction</a></li> <li><a href="https://en.wikipedia.org/wiki/Disgust">Disgust</a></li> <li><a href="https://en.wikipedia.org/wiki/Ecstasy_(philosophy)">Ecstasy</a></li> <li><a href="https://en.wikipedia.org/wiki/Elegance">Elegance</a></li> <li><a href="https://en.wikipedia.org/wiki/Aesthetic_emotions">Emotions</a></li> <li><a href="https://en.wikipedia.org/wiki/Entertainment">Entertainment</a></li> <li><a href="https://en.wikipedia.org/wiki/Eroticism">Eroticism</a></li> <li><a href="https://en.wikipedia.org/wiki/Exoticism">Exoticism</a></li> <li><a href="https://en.wikipedia.org/wiki/Fashion">Fashion</a></li> <li><a href="https://en.wikipedia.org/wiki/Gaze">Gaze</a></li> <li><a href="https://en.wikipedia.org/wiki/Harmony">Harmony</a></li> <li><a href="https://en.wikipedia.org/wiki/Cultural_hegemony">Hegemony</a> <ul><li><a href="https://en.wikipedia.org/wiki/Cultural_imperialism">Imperialism</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Humour">Humour</a></li> <li><a href="https://en.wikipedia.org/wiki/Iconography">Iconography</a> <ul><li><a href="https://en.wikipedia.org/wiki/Aniconism">Aniconism</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Artistic_integrity">Integrity</a></li> <li><a href="https://en.wikipedia.org/wiki/Aesthetic_interpretation">Interpretation</a></li> <li><a href="https://en.wikipedia.org/wiki/Judgment">Judgment</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Kama">Kama</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Kitsch">Kitsch</a></li> <li><a href="https://en.wikipedia.org/wiki/Life_imitating_art">Life imitating art</a></li> <li><a href="https://en.wikipedia.org/wiki/Magnificence_(history_of_ideas)">Magnificence</a></li> <li><a href="https://en.wikipedia.org/wiki/Mimesis">Mimesis</a></li> <li><a href="https://en.wikipedia.org/wiki/Art_and_morality">Morality</a></li> <li><a href="https://en.wikipedia.org/wiki/Perception">Perception</a></li> <li><a href="https://en.wikipedia.org/wiki/Picturesque">Picturesque</a></li> <li><a href="https://en.wikipedia.org/wiki/Quality_(philosophy)">Quality</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Rasa_(aesthetics)">Rasa</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Recreation">Recreation</a> <ul><li><a href="https://en.wikipedia.org/wiki/Leisure">Leisure</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Reverence_(emotion)">Reverence</a></li> <li><a href="https://en.wikipedia.org/wiki/Satire">Satire</a></li> <li><a href="https://en.wikipedia.org/wiki/Style_(visual_arts)">Style</a></li> <li><a href="https://en.wikipedia.org/wiki/Sublime_(philosophy)">Sublime</a></li> <li><a href="https://en.wikipedia.org/wiki/Taste_(sociology)">Taste</a></li> <li><a href="https://en.wikipedia.org/wiki/Tragedy">Tragedy</a></li> <li><a href="https://en.wikipedia.org/wiki/Work_of_art">Work of art</a></li></ul> </div></td></tr><tr><th>Works</th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Hippias_Major">Hippias Major</a></i> <span>(c. 390 BCE)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Poetics_(Aristotle)">Poetics</a></i> <span>(c. 335 BCE)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Ars_Poetica_(Horace)">Ars Poetica</a></i> <span>(c. 19 BCE)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/The_Literary_Mind_and_the_Carving_of_Dragons">The Literary Mind and the Carving of Dragons</a></i> <span>(c. 100)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/On_the_Sublime">On the Sublime</a></i> <span>(c. 500)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Asrar_al-Balagha">Asrar al-Balagha</a></i> <span>(11th century)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Mumy%C5%8Dz%C5%8Dshi">Mumyōzōshi</a></i> <span>(13th century)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/On_the_Sublime_and_Beautiful">On the Sublime and Beautiful</a></i> <span>(1757)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Lectures_on_Aesthetics">Lectures on Aesthetics</a></i> <span>(1835)</span></li> <li>&quot;<a href="https://en.wikipedia.org/wiki/The_Critic_as_Artist">The Critic as Artist</a>&quot; <span>(1891)</span></li> <li>&quot;<a href="https://en.wikipedia.org/wiki/A_Room_of_One%27s_Own">A Room of One&#39;s Own</a>&quot; <span>(1929)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/In_Praise_of_Shadows">In Praise of Shadows</a></i> <span>(1933)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Art_as_Experience">Art as Experience</a></i> <span>(1934)</span></li> <li>&quot;<a href="https://en.wikipedia.org/wiki/The_Work_of_Art_in_the_Age_of_Mechanical_Reproduction">The Work of Art in the Age of Mechanical Reproduction</a>&quot; <span>(1935)</span></li> <li>&quot;<a href="https://en.wikipedia.org/wiki/Avant-Garde_and_Kitsch">Avant-Garde and Kitsch</a>&quot; <span>(1939)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Prison_Notebooks">Prison Notebooks</a></i> (Gramsci) <span>1947</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Critical_Essays_(Orwell)">Critical Essays</a></i> <span>(1946)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Against_Interpretation">Against Interpretation</a></i> <span>(1966)</span> <ul><li>&quot;<a href="https://en.wikipedia.org/wiki/Notes_on_%22Camp%22">Notes on &#39;Camp&#39;</a>&quot; <span>(1964)</span></li></ul></li> <li><i><a href="https://en.wikipedia.org/wiki/The_Aesthetic_Dimension">The Aesthetic Dimension</a></i> <span>(1977)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Orientalism_(book)">Orientalism</a></i> <span>(1978)</span></li> <li><i><a href="https://en.wikipedia.org/wiki/Why_Beauty_Matters">Why Beauty Matters</a></i> <span>(2009)</span></li></ul> </div></td></tr><tr><th>Related</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Applied_aesthetics">Applied aesthetics</a></li> <li><a href="https://en.wikipedia.org/wiki/Arts_criticism">Arts criticism</a> <ul><li><a href="https://en.wikipedia.org/wiki/Art_criticism">Art criticism</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/The_arts_and_politics">The arts and politics</a> <ul><li><a href="https://en.wikipedia.org/wiki/Aestheticization_of_politics">Aestheticization of politics</a></li> <li><a href="https://en.wikipedia.org/wiki/Artistic_freedom">Artistic freedom</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Axiology">Axiology</a></li> <li><a href="https://en.wikipedia.org/wiki/Economics_of_the_arts_and_literature">Economics of the arts and literature</a> <ul><li><a href="https://en.wikipedia.org/wiki/Patronage#Arts">Artistic patronage</a></li> <li><a href="https://en.wikipedia.org/wiki/Cultural_economics">Cultural economics</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Evolutionary_aesthetics">Evolutionary aesthetics</a></li> <li><a href="https://en.wikipedia.org/wiki/Mathematical_beauty">Mathematical beauty</a></li> <li><a href="https://en.wikipedia.org/wiki/Neuroesthetics">Neuroesthetics</a></li> <li><a href="https://en.wikipedia.org/wiki/Patterns_in_nature">Patterns in nature</a></li> <li><a href="https://en.wikipedia.org/wiki/Philosophy_of_design">Philosophy of design</a></li> <li><a href="https://en.wikipedia.org/wiki/Philosophy_of_film">Philosophy of film</a></li> <li><a href="https://en.wikipedia.org/wiki/Philosophy_of_language">Philosophy of language</a> <ul><li><a href="https://en.wikipedia.org/wiki/Semantics">Semantics</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Philosophy_of_music">Philosophy of music</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychology_of_art">Psychology of art</a></li> <li><a href="https://en.wikipedia.org/wiki/Religious_art">Religious art</a></li> <li><a href="https://en.wikipedia.org/wiki/Theory_of_art">Theory of art</a></li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Outline_of_aesthetics">Outline</a></li> <li><a href="https://en.wikipedia.org/wiki/Category:Aesthetics">Category</a></li> <li> <a href="https://en.wikipedia.org/wiki/Portal:Philosophy">Philosophy portal</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Modern_Hindu_writers"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Modern_Hindu_writers"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Modern_Hindu_writers"><abbr>e</abbr></a></li></ul></div><div>Modern <a href="https://en.wikipedia.org/wiki/Hinduism">Hindu</a> writers <small><span>(<a href="https://en.wikipedia.org/wiki/India#Modern_India">1848</a> to date)</span></small></div></th></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Hinduism">Hinduism</a></li> <li><a href="https://en.wikipedia.org/wiki/Hinduism_in_the_West">Hinduism in the West</a></li> <li><a href="https://en.wikipedia.org/wiki/Indian_philosophy">Indian philosophy</a></li> <li><a href="https://en.wikipedia.org/wiki/Indian_religions">Indian religions</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Hindu_denominations">Religious writers</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Mirra_Alfassa">Mirra Alfassa (The Mother)</a></li> <li><a href="https://en.wikipedia.org/wiki/Sri_Anirvan">Sri Anirvan</a></li> <li><a href="https://en.wikipedia.org/wiki/Sri_Aurobindo">Sri Aurobindo</a></li> <li>Ananda Coomaraswamy</li> <li><a href="https://en.wikipedia.org/wiki/Eknath_Easwaran">Eknath Easwaran</a></li> <li><a href="https://en.wikipedia.org/wiki/Satsvarupa_dasa_Goswami">Satsvarupa dasa Goswami</a></li> <li><a href="https://en.wikipedia.org/wiki/Mahendranath_Gupta">Mahendranath Gupta</a></li> <li><a href="https://en.wikipedia.org/wiki/Jiddu_Krishnamurti">Jiddu Krishnamurti</a></li> <li><a href="https://en.wikipedia.org/wiki/Nisargadatta_Maharaj">Nisargadatta Maharaj</a></li> <li><a href="https://en.wikipedia.org/wiki/Ramana_Maharshi">Ramana Maharshi</a></li> <li><a href="https://en.wikipedia.org/wiki/A._G._Mohan">A. G. Mohan</a></li> <li><a href="https://en.wikipedia.org/wiki/Sister_Nivedita">Sister Nivedita</a></li> <li><a href="https://en.wikipedia.org/wiki/Swami_Prabhavananda">Swami Prabhavananda</a></li> <li><a href="https://en.wikipedia.org/wiki/A._C._Bhaktivedanta_Swami_Prabhupada">A. C. Bhaktivedanta Swami Prabhupada</a></li> <li><a href="https://en.wikipedia.org/wiki/Krishna_Prem">Krishna Prem</a></li> <li><a href="https://en.wikipedia.org/wiki/Swami_Rama">Swami Rama</a></li> <li><a href="https://en.wikipedia.org/wiki/Srivatsa_Ramaswami">Srivatsa Ramaswami</a></li> <li><a href="https://en.wikipedia.org/wiki/Swami_Ramdas">Swami Ramdas</a></li> <li><a href="https://en.wikipedia.org/wiki/Chinmayananda_Saraswati">Chinmayananda Saraswati</a></li> <li><a href="https://en.wikipedia.org/wiki/Dayananda_Saraswati">Dayananda Saraswati (Arya Samaj)</a></li> <li><a href="https://en.wikipedia.org/wiki/Dayananda_Saraswati_(Arsha_Vidya)">Dayananda Saraswati (Arsha Vidya)</a></li> <li><a href="https://en.wikipedia.org/wiki/Krishnananda_Saraswati">Krishnananda Saraswati</a></li> <li><a href="https://en.wikipedia.org/wiki/Sivananda_Saraswati">Sivananda Saraswati</a></li> <li><a href="https://en.wikipedia.org/wiki/Swami_Satprakashananda">Swami Satprakashananda</a></li> <li><a href="https://en.wikipedia.org/wiki/Swami_Shraddhanand">Swami Shraddhanand</a></li> <li><a href="https://en.wikipedia.org/wiki/Swami_Vivekananda">Swami Vivekananda</a></li> <li><a href="https://en.wikipedia.org/wiki/Paramahansa_Yogananda">Paramahansa Yogananda</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Hindu_politics">Political writers</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Mahatma_Gandhi">Mahatma Gandhi</a></li> <li><a href="https://en.wikipedia.org/wiki/Sarvepalli_Radhakrishnan">Sarvepalli Radhakrishnan</a></li> <li><a href="https://en.wikipedia.org/wiki/Bal_Gangadhar_Tilak">Bal Gangadhar Tilak</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Indian_literature">Literary writers</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Bankim_Chandra_Chattopadhyay">Bankim Chandra Chattopadhyay</a></li> <li><a href="https://en.wikipedia.org/wiki/Ramdhari_Singh_Dinkar">Ramdhari Singh Dinkar</a></li> <li><a href="https://en.wikipedia.org/wiki/C._Rajagopalachari">C. Rajagopalachari</a></li> <li><a href="https://en.wikipedia.org/wiki/K._D._Sethna">K. D. Sethna</a></li> <li><a href="https://en.wikipedia.org/wiki/Amish_Tripathi">Amish Tripathi</a></li></ul> </div></td></tr><tr><th>Westerners influenced<br/> by Hinduism</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Annie_Besant">Annie Besant</a></li> <li><a href="https://en.wikipedia.org/wiki/Helena_Blavatsky">Helena Blavatsky</a></li> <li><a href="https://en.wikipedia.org/wiki/Deepak_Chopra">Deepak Chopra</a></li> <li><a href="https://en.wikipedia.org/wiki/Aleister_Crowley">Aleister Crowley</a></li> <li><a href="https://en.wikipedia.org/wiki/Ram_Dass">Ram Dass</a></li> <li><a href="https://en.wikipedia.org/wiki/Wayne_Dyer">Wayne Dyer</a></li> <li><a href="https://en.wikipedia.org/wiki/T._S._Eliot">T. S. Eliot</a></li> <li><a href="https://en.wikipedia.org/wiki/Ralph_Waldo_Emerson">R.W. Emerson</a></li> <li><a href="https://en.wikipedia.org/wiki/Allen_Ginsberg">Allen Ginsberg</a></li> <li><a href="https://en.wikipedia.org/wiki/Ren%C3%A9_Gu%C3%A9non">René Guénon</a></li> <li><a href="https://en.wikipedia.org/wiki/George_Harrison">George Harrison</a></li> <li><a href="https://en.wikipedia.org/wiki/Aldous_Huxley">Aldous Huxley</a></li> <li><a href="https://en.wikipedia.org/wiki/Christopher_Isherwood">Christopher Isherwood</a></li> <li><a href="https://en.wikipedia.org/wiki/David_Lynch">David Lynch</a></li> <li><a href="https://en.wikipedia.org/wiki/Andr%C3%A9_Malraux">André Malraux</a></li> <li><a href="https://en.wikipedia.org/wiki/Henry_Miller">Henry Miller</a></li> <li><a href="https://en.wikipedia.org/wiki/Maria_Montessori">Maria Montessori</a></li> <li><a href="https://en.wikipedia.org/wiki/Henry_Steel_Olcott">H.S. Olcott</a></li> <li><a href="https://en.wikipedia.org/wiki/J._Robert_Oppenheimer">Oppenheimer</a></li> <li><a href="https://en.wikipedia.org/wiki/Helena_Roerich">Helena Roerich</a></li> <li><a href="https://en.wikipedia.org/wiki/Romain_Rolland">Romain Rolland</a></li> <li><a href="https://en.wikipedia.org/wiki/Arthur_Schopenhauer">Arthur Schopenhauer</a></li> <li><a href="https://en.wikipedia.org/wiki/Erwin_Schr%C3%B6dinger">Erwin Schrödinger</a></li> <li><a href="https://en.wikipedia.org/wiki/Henry_David_Thoreau">Thoreau</a></li> <li><a href="https://en.wikipedia.org/wiki/Leo_Tolstoy">Leo Tolstoy</a></li> <li><a href="https://en.wikipedia.org/wiki/Voltaire">Voltaire</a></li> <li><a href="https://en.wikipedia.org/wiki/Alan_Watts">Alan Watts</a></li> <li><a href="https://en.wikipedia.org/wiki/Ken_Wilber">Ken Wilber</a></li> <li><a href="https://en.wikipedia.org/wiki/W._B._Yeats">W. B. Yeats</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Indology">Scholars</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Alain_Dani%C3%A9lou">Alain Daniélou</a></li> <li><a href="https://en.wikipedia.org/wiki/S._N._Balagangadhara">S. N. Balagangadhara</a></li> <li><a href="https://en.wikipedia.org/wiki/Paul_Deussen">Paul Deussen</a></li> <li><a href="https://en.wikipedia.org/wiki/Dharampal">Dharampal</a></li> <li><a href="https://en.wikipedia.org/wiki/Mircea_Eliade">Mircea Eliade</a></li> <li><a href="https://en.wikipedia.org/wiki/Sister_Gargi">Sister Gargi</a></li> <li><a href="https://en.wikipedia.org/wiki/Georg_Feuerstein">Georg Feuerstein</a></li> <li><a href="https://en.wikipedia.org/wiki/Klaus_Klostermaier">Klaus Klostermaier</a></li> <li><a href="https://en.wikipedia.org/wiki/Hajime_Nakamura">Hajime Nakamura</a></li> <li><a href="https://en.wikipedia.org/wiki/Anantanand_Rambachan">Anantanand Rambachan</a></li> <li><a href="https://en.wikipedia.org/wiki/Graham_Schweig">Graham Schweig</a></li></ul> </div></td></tr><tr><th>Lists</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_modern_Eastern_religions_writers">List of modern Eastern religions writers</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_writers_on_Hinduism">List of writers on Hinduism</a></li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Portal:Hinduism">Hinduism Portal</a></li> <li><a href="https://en.wikipedia.org/wiki/Portal:India">India Portal</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Traditionalism_(perennialism)"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/w/index.php?title=Template_talk:Traditionalism_(perennialism)&amp;action=edit&amp;redlink=1"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Traditionalism_(perennialism)"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Traditionalism_(perennialism)">Traditionalism</a></div></th></tr><tr><th><div>Associated<br/>people</div></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Kurt_Almqvist">Kurt Almqvist</a></li> <li><a href="https://en.wikipedia.org/wiki/Muhammed_Amin_Andrabi">Muhammed Amin Andrabi</a></li> <li><a href="https://en.wikipedia.org/wiki/Jean_Bi%C3%A8s">Jean Biès</a></li> <li><a href="https://en.wikipedia.org/wiki/Jean_Borella">Jean Borella</a></li> <li><a href="https://en.wikipedia.org/wiki/A._K._Brohi">A. K. Brohi</a></li> <li><a href="https://en.wikipedia.org/wiki/Titus_Burckhardt">Titus Burckhardt</a></li> <li>Ananda Coomaraswamy</li> <li><a href="https://en.wikipedia.org/wiki/James_Cutsinger">James Cutsinger</a></li> <li><a href="https://en.wikipedia.org/wiki/Gai_Eaton">Gai Eaton</a></li> <li><a href="https://en.wikipedia.org/wiki/Julius_Evola">Julius Evola</a></li> <li><a href="https://en.wikipedia.org/wiki/Ren%C3%A9_Gu%C3%A9non">René Guénon</a></li> <li><a href="https://en.wikipedia.org/wiki/Jean_Hani">Jean Hani</a></li> <li><a href="https://en.wikipedia.org/wiki/Jean-Pierre_LaFouge">Jean-Pierre LaFouge</a></li> <li><a href="https://en.wikipedia.org/wiki/Ali_Lakhani">Ali Lakhani</a></li> <li><a href="https://en.wikipedia.org/wiki/Tage_Lindbom">Tage Lindbom</a></li> <li><a href="https://en.wikipedia.org/wiki/Martin_Lings">Martin Lings</a></li> <li><a href="https://en.wikipedia.org/wiki/Donald_Macleod_Matheson">Donald Macleod Matheson</a></li> <li><a href="https://en.wikipedia.org/wiki/Jean-Louis_Michon">Jean-Louis Michon</a></li> <li><a href="https://en.wikipedia.org/wiki/Seyyed_Hossein_Nasr">Seyyed Hossein Nasr</a></li> <li><a href="https://en.wikipedia.org/wiki/Walter_James,_4th_Baron_Northbourne">Lord Northbourne</a></li> <li><a href="https://en.wikipedia.org/wiki/Harry_Oldmeadow">Harry Oldmeadow</a></li> <li><a href="https://en.wikipedia.org/wiki/Marco_Pallis">Marco Pallis</a></li> <li><a href="https://en.wikipedia.org/wiki/Whitall_Perry">Whitall Perry</a></li> <li><a href="https://en.wikipedia.org/wiki/A._K._Saran">A. K. Saran</a></li> <li><a href="https://en.wikipedia.org/wiki/Frithjof_Schuon">Frithjof Schuon</a></li> <li><a href="https://en.wikipedia.org/wiki/Wolfgang_Smith">Wolfgang Smith</a></li> <li><a href="https://en.wikipedia.org/wiki/William_Stoddart">William Stoddart</a></li> <li><a href="https://en.wikipedia.org/wiki/Charles_Upton_(poet)">Charles Upton</a></li> <li><a href="https://en.wikipedia.org/wiki/Algis_U%C5%BEdavinys">Algis Uždavinys</a></li> <li><a href="https://en.wikipedia.org/wiki/Michel_Valsan">Michel Valsan</a></li></ul> </div></td></tr><tr><th>Concepts</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Desacralization_of_knowledge">Desacralization of knowledge</a></li> <li><a href="https://en.wikipedia.org/wiki/Resacralization_of_knowledge">Resacralization of knowledge</a></li> <li><a href="https://en.wikipedia.org/wiki/Scientia_sacra">Scientia sacra</a></li> <li><a href="https://en.wikipedia.org/wiki/Tradition_(Perennialism)">Tradition</a></li></ul> </div></td></tr><tr><th>Publications</th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Revolt_Against_the_Modern_World">Revolt Against the Modern World</a></i> (1934)</li> <li><i><a href="https://en.wikipedia.org/wiki/The_Reign_of_Quantity_and_the_Signs_of_the_Times">The Reign of Quantity and the Signs of the Times</a></i> (1945)</li> <li><i><a href="https://en.wikipedia.org/wiki/Knowledge_and_the_Sacred">Knowledge and the Sacred</a></i> (1981)</li></ul> </div></td></tr><tr><th>Related</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Ivan_Agu%C3%A9li">Ivan Aguéli</a></li> <li><a href="https://en.wikipedia.org/wiki/The_Matheson_Trust">The Matheson Trust</a></li> <li><a href="https://en.wikipedia.org/wiki/World_Wisdom">World Wisdom</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q379589#identifiers"></a></span></div></th></tr><tr><th>International</th><td><div><ul><li><span><a href="https://isni.org/isni/0000000120954037">ISNI</a></span></li><li><span><a href="https://viaf.org/viaf/9231">VIAF</a></span></li><li><span><a href="https://d-nb.info/gnd/119436655">GND</a></span></li><li><span><a href="https://id.worldcat.org/fast/37737">FAST</a></span></li><li><span><a href="https://id.oclc.org/worldcat/entity/E39PBJvxyWfDdyvdrRc8Pp3PcP">WorldCat</a></span></li></ul></div></td></tr><tr><th>National</th><td><div><ul><li><span><a href="https://id.loc.gov/authorities/n79066552">United States</a></span></li><li><span><a href="https://catalogue.bnf.fr/ark:/12148/cb11897585t">France</a></span></li><li><span><a href="https://data.bnf.fr/ark:/12148/cb11897585t">BnF data</a></span></li><li><span><a href="https://id.ndl.go.jp/auth/ndlna/00520835">Japan</a></span></li><li><span><span><a href="https://opac.sbn.it/nome/CFIV038739">Italy</a></span></span></li><li><span><a href="https://aleph.nkp.cz/F/?func=find-c&amp;local_base=aut&amp;ccl_term=ica=xx0092133&amp;CON_LNG=ENG">Czech Republic</a></span></li><li><span><a href="https://datos.bne.es/resource/XX4579489">Spain</a></span></li><li><span><a href="http://id.bnportugal.gov.pt/aut/catbnp/45315">Portugal</a></span></li><li><span><a href="http://data.bibliotheken.nl/id/thes/p068784783">Netherlands</a></span></li><li><span><a href="https://authority.bibsys.no/authority/rest/authorities/html/90375085">Norway</a></span></li><li><span><a href="https://kopkatalogs.lv/F?func=direct&amp;local_base=lnc10&amp;doc_number=000187922&amp;P_CON_LNG=ENG">Latvia</a></span></li><li><span><a href="http://katalog.nsk.hr/F/?func=direct&amp;doc_number=000116583&amp;local_base=nsk10">Croatia</a></span></li><li><span><a href="https://catalogue.nlg.gr/cgi-bin/koha/opac-authoritiesdetail.pl?authid=66114">Greece</a></span></li><li><span><a href="https://dbn.bn.org.pl/descriptor-details/9810636992305606">Poland</a></span></li><li><span><a href="https://wikidata-externalid-url.toolforge.org/?p=8034&amp;url_prefix=https://opac.vatlib.it/auth/detail/&amp;id=495/109557">Vatican</a></span></li><li><span><a href="https://www.nli.org.il/en/authorities/987007297360805171">Israel</a></span></li><li><span><a href="https://cantic.bnc.cat/registre/981058521264106706">Catalonia</a></span></li></ul></div></td></tr><tr><th>Academics</th><td><div><ul><li><span><a href="https://ci.nii.ac.jp/author/DA01456268?l=en">CiNii</a></span></li><li><span><a href="https://zbmath.org/authors/?q=ai:coomaraswamy.a-k">zbMATH</a></span></li></ul></div></td></tr><tr><th>Artists</th><td><div><ul><li><span><a href="https://www.getty.edu/vow/ULANFullDisplay?find=&amp;role=&amp;nation=&amp;subjectid=500122911">ULAN</a></span></li><li><span><a href="https://pic.nypl.org/constituents/335927">Photographers&#39; Identities</a></span></li></ul></div></td></tr><tr><th>People</th><td><div><ul><li><span><a href="https://trove.nla.gov.au/people/1310110">Trove</a></span></li><li><span><a href="https://www.deutsche-biographie.de/119436655.html?language=en">Deutsche Biographie</a></span></li><li><span><a href="https://www.deutsche-digitale-bibliothek.de/person/gnd/119436655">DDB</a></span></li></ul></div></td></tr><tr><th>Other</th><td><div><ul><li><span><a href="https://www.idref.fr/026798077">IdRef</a></span></li><li><span><a href="https://openlibrary.org/works/OL102871A?mode=all">Open Library</a></span></li><li><span><a href="https://snaccooperative.org/ark:/99166/w6d50pfc">SNAC</a></span></li><li><span><a href="https://lux.collections.yale.edu/view/person/7e06bb78-7517-45d3-93ea-65b7eeaf0f94">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div> Disability - Wikipedia https://en.wikipedia.org/wiki/Disability W0xwH_4LXuSH8PQ9KpFDuR0BWEXKof0ZM4qmBw== Sat, 09 May 2026 12:00:08 +0000 Impairments, activity limitations, and participation restrictions <div>Impairments, activity limitations, and participation restrictions</div><div>&quot;Impaired&quot; redirects here. For other uses, see <a href="https://en.wikipedia.org/wiki/Impairment_(disambiguation)">Impairment (disambiguation)</a>.</div><p> </p><div><div><div><div><div><span><a href="https://en.wikipedia.org/wiki/File:Pictograms-nps-accessibility-wheelchair-accessible.svg"></a></span></div></div><div><div><span><a href="https://en.wikipedia.org/wiki/File:Pictograms-nps-accessibility-low_vision_access.svg"></a></span></div></div><div><div><span><a href="https://en.wikipedia.org/wiki/File:Pictograms-nps-accessibility-sign_language_interpretation.svg"></a></span></div></div></div><div><div>Pictographs used by the United States <a href="https://en.wikipedia.org/wiki/National_Park_Service">National Park Service</a> for <a href="https://en.wikipedia.org/wiki/Wheelchair">wheelchair</a> accessibility, <a href="https://en.wikipedia.org/wiki/Low_vision">low vision</a> access and <a href="https://en.wikipedia.org/wiki/Sign_language">sign language</a> interpretation.</div></div></div></div><table><tbody><tr><th>Disability</th></tr><tr><td> <div><div>Theory and models</div><div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Curb_cut_effect">Curb cut effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_studies">Disability theory</a></li> <li><a href="https://en.wikipedia.org/wiki/Ableism">Ableism / Disablism</a></li> <li><a href="https://en.wikipedia.org/wiki/Medical_model_of_disability">Medical model</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_model_of_disability">Social model</a></li> <li><a href="https://en.wikipedia.org/wiki/Models_of_disability">Other models</a></li></ul> </div></div></div></td> </tr><tr><td> <div><div>Education</div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Mainstreaming_(education)">Mainstreaming</a></li> <li><a href="https://en.wikipedia.org/wiki/Individualized_Education_Program">Individualized Education Program (IEP)</a></li></ul> <div> <ul><li><a href="https://en.wikipedia.org/wiki/Special_needs">Special needs</a></li> <li><a href="https://en.wikipedia.org/wiki/Special_education#Special_schools">Special school</a></li> <li><a href="https://en.wikipedia.org/wiki/Special_education">Special education</a></li> <li><a href="https://en.wikipedia.org/wiki/Learning_disability">Learning disability</a></li></ul> </div></div></div></td> </tr><tr><td> <div><div>Therapy</div><div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Physical_therapy">Physical</a></li> <li><a href="https://en.wikipedia.org/wiki/Occupational_therapy">Occupational</a></li> <li><a href="https://en.wikipedia.org/wiki/Speech%E2%80%93language_pathology">Speech</a></li></ul> </div></div></div></td> </tr><tr><td> <div><div>Societal implications</div><div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_rights_movement">Disability rights movement</a></li> <li><a href="https://en.wikipedia.org/wiki/Inclusion_(disability_rights)">Inclusion</a></li> <li><a href="https://en.wikipedia.org/wiki/Normalization_(people_with_disabilities)">Normalization</a></li> <li><a href="https://en.wikipedia.org/wiki/People-first_language">People-first language</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_disability-related_terms_with_negative_connotations">Pejorative terms</a></li> <li><a href="https://en.wikipedia.org/wiki/Sexuality_and_disability">Sexuality and disability</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_and_women%27s_health">Women&#39;s health</a></li></ul> </div></div></div></td> </tr><tr><td> <div><div>Personal assistance</div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Accessibility">Accessibility</a></li> <li><a href="https://en.wikipedia.org/wiki/Unlicensed_assistive_personnel">Unlicensed assistive personnel</a> (<a href="https://en.wikipedia.org/wiki/Activities_of_daily_living">ADLs</a>)</li></ul> <div> <ul><li><a href="https://en.wikipedia.org/wiki/Accessible_toilet">Accessible toilet</a></li> <li><a href="https://en.wikipedia.org/wiki/Assistive_technology">Assistive technology</a></li> <li><a href="https://en.wikipedia.org/wiki/Assisted_living">Assisted living</a></li> <li><a href="https://en.wikipedia.org/wiki/Inclusive_design">Inclusive design</a></li> <li><a href="https://en.wikipedia.org/wiki/Mobility_aid">Mobility aid</a></li> <li><a href="https://en.wikipedia.org/wiki/Orthotics">Orthotics and braces</a></li> <li><a href="https://en.wikipedia.org/wiki/Accessibility">Physical accessibility</a></li> <li><a href="https://en.wikipedia.org/wiki/Prosthesis">Prosthetics</a></li> <li><a href="https://en.wikipedia.org/wiki/Universal_design">Universal design</a></li> <li><a href="https://en.wikipedia.org/wiki/Web_accessibility">Web accessibility</a></li></ul> </div></div></div></td> </tr><tr><td> <div><div>Socioeconomic assistance</div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Social_Security_Disability_Insurance">Social Security Disability Insurance</a></li> <li><a href="https://en.wikipedia.org/wiki/Supplemental_Security_Income">Supplemental Security Income</a></li> <li><a href="https://en.wikipedia.org/wiki/Ticket_to_Work">Ticket to Work</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_pension">Disability pension</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_Living_Allowance">Disability Living Allowance</a></li> <li><a href="https://en.wikipedia.org/wiki/Disabled_Students%27_Allowance">Disabled Students&#39; Allowance</a></li> <li><a href="https://en.wikipedia.org/wiki/Disabled_Persons_Railcard">Disabled Persons Railcard</a></li> <li><a href="https://en.wikipedia.org/wiki/Freedom_Pass">Freedom Pass</a></li> <li><div><a href="https://en.wikipedia.org/wiki/Assured_Income_for_the_Severely_Handicapped">Assured Income for<br/>the Severely Handicapped</a></div></li> <li><a href="https://en.wikipedia.org/wiki/Ontario_Disability_Support_Program">Ontario Disability Support Program</a></li></ul></div></div></td> </tr><tr><td> <div><div><div><ul><li>Groups</li><li>Organizations</li></ul></div></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/National_Telecommuting_Institute">National Telecommuting Institute</a></li> <li><a href="https://en.wikipedia.org/wiki/Society_for_Disability_Studies">Society for Disability Studies</a></li> <li><a href="https://en.wikipedia.org/wiki/Disabled_Peoples%27_International">Disabled Peoples&#39; International (DPI)</a></li> <li><a href="https://en.wikipedia.org/wiki/Visitability">Visitability</a></li> <li><a href="https://en.wikipedia.org/wiki/WeThe15">WeThe15</a></li></ul></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Parasports">Parasports</a></div><div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Special_Olympics">Special Olympics</a></li> <li><a href="https://en.wikipedia.org/wiki/Paralympic_Games">Paralympic Games</a></li> <li><a href="https://en.wikipedia.org/wiki/Deaflympics">Deaflympics</a></li> <li><a href="https://en.wikipedia.org/wiki/Invictus_Games">Invictus Games</a></li></ul> </div></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Disability_culture">Culture</a></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_in_the_arts">Disability in the arts</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_art">Disability art</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_the_media">Disability in the media</a></li></ul></div></div></td> </tr><tr><td> <ul><li><div><ul><li> <a href="https://en.wikipedia.org/wiki/Category:Disability">Disability</a></li><li><a href="https://en.wikipedia.org/wiki/Category:Disability-related_lists">Lists</a></li></ul></div></li></ul></td></tr><tr><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Disability_sidebar"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Disability_sidebar"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Disability_sidebar"><abbr>e</abbr></a></li></ul></div></td></tr></tbody></table><p><b>Disability</b> is the experience of any condition that makes it more difficult for a person to do certain activities or have equitable access within a given society.<sup><span>[</span>1<span>]</span></sup> Disabilities may be <a href="https://en.wikipedia.org/wiki/Cognitive_disability">cognitive</a>, <a href="https://en.wikipedia.org/wiki/Developmental_disability">developmental</a>, <a href="https://en.wikipedia.org/wiki/Intellectual_disability">intellectual</a>, <a href="https://en.wikipedia.org/wiki/Mental_disorder#Disability">mental</a>, <a href="https://en.wikipedia.org/wiki/Physical_disability">physical</a>, <a href="https://en.wikipedia.org/wiki/Sense">sensory</a>, or a combination of multiple factors. Disabilities can be <a href="https://en.wikipedia.org/wiki/Birth_defect">present from birth</a> or can be acquired during a person&#39;s lifetime. Historically, disabilities have only been recognized based on a narrow set of criteria—however, disabilities are not binary and can present uniquely depending on the individual.<sup><span>[</span>2<span>]</span></sup> A disability may be easily visible, or <a href="https://en.wikipedia.org/wiki/Invisible_disability">invisible</a> in nature. The <a href="https://en.wikipedia.org/wiki/United_Nations">United Nations</a> <a href="https://en.wikipedia.org/wiki/Convention_on_the_Rights_of_Persons_with_Disabilities">Convention on the Rights of Persons with Disabilities</a> defines disability as including: </p><blockquote><p>long-term physical, mental, intellectual or sensory impairments which in interaction with various barriers may hinder [a person&#39;s] full and effective participation in society on an equal basis with others.<sup><span>[</span>3<span>]</span></sup></p></blockquote><p>Disabilities have been perceived differently throughout history, through a variety of different theoretical lenses. There are two main models that attempt to explain disability in our society: the <a href="https://en.wikipedia.org/wiki/Medical_model_of_disability">medical model</a> and the <a href="https://en.wikipedia.org/wiki/Social_model_of_disability">social model</a>.<sup><span>[</span>4<span>]</span></sup> The medical model serves as a theoretical framework that considers disability as an undesirable medical condition that requires specialized treatment. Those who ascribe to the medical model tend to focus on finding the root causes of disabilities, as well as any cures—such as assistive technology. The social model centers disability as a societally-created limitation on individuals who do not have the same ability as the majority of the population. Those who ascribe to the social model tend to focus on accessibility and social/cultural attitudes toward disability. Although the medical model and social model are the most common frames for disability, there are a multitude of other models that theorize disability.<sup><span>[</span>5<span>]</span></sup> </p><p>Like many social categories, the concept of &quot;disability&quot; is under heavy discussion amongst academia, the medical and legal worlds, and the disability community. There are many terms that explain aspects of disability. While some terms solely exist to describe phenomena pertaining to disability, others have been centered around stigmatizing and ostracizing those with disabilities. Some terms have such a negative connotation that they are considered to be slurs.<sup><span>[</span>6<span>]</span></sup> A point of contention is whether it is appropriate to use person-first language (i.e. a person who is disabled) or identity-first language (i.e. a disabled person) when referring to disability and an individual. </p><p>Due to the <a href="https://en.wikipedia.org/wiki/Marginalization">marginalization</a> of disabled people, there have been several activist causes that push for equitable treatment and access in society. Disability activists have fought to receive equal and equitable rights under the law—though there are still political issues that enable or advance the oppression of disabled people. Although disability activism serves to dismantle <a href="https://en.wikipedia.org/wiki/Ableist">ableist</a> systems, social norms relating to the perception of disabilities are often reinforced by <a href="https://en.wikipedia.org/wiki/Trope_(literature)">tropes</a> used by the media. Since negative perceptions of disability are pervasive in modern society, disabled people have turned to self-advocacy in an attempt to push back against their marginalization. The recognition of disability as an identity that is experienced differently based on the other multi-faceted identities of the individual is one often pointed out by disabled self-advocates. The ostracization of disability from mainstream society has created the opportunity for a disability culture to emerge. While disabled activists still promote the integration of disabled people into mainstream society, several disabled-only spaces have been created to foster a disability community—such as with art, social media, and sports. </p><div><h2>History</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>Contemporary understandings of disability derive from concepts that arose during the scientific <a href="https://en.wikipedia.org/wiki/Age_of_Enlightenment">Enlightenment</a> in the West; prior to the Enlightenment, physical differences were viewed through a different lens.<sup><span>[</span>7<span>]</span></sup> </p><div><h3>Antiquity</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>Historically, scholars have often assumed that disabled individuals were unsupported and marginalized within their communities, based on the belief that ancient agricultural societies had to be strategic with their limited resources for survival.<sup><span>[</span>8<span>]</span></sup> For instance, some historians argue that ancient Greeks actively practiced ableism through <a href="https://en.wikipedia.org/wiki/Infanticide">infanticide</a>, as suggested in the writings of <a href="https://en.wikipedia.org/wiki/Plutarch">Plutarch</a>, <a href="https://en.wikipedia.org/wiki/Plato">Plato</a>, and <a href="https://en.wikipedia.org/wiki/Aristotle">Aristotle</a>.<sup><span>[</span>8<span>]</span></sup> Despite this, ancient Greeks demonstrated notable empathy and acceptance toward their disabled peers, contrary to the views presented in the writings of Plato and Aristotle. Literary accounts from Hippocratic physicians and archaeological evidence support the idea that the Greeks made efforts to cure and assist disabled individuals, including deformed infants, whom Plutarch claimed were promptly killed in Sparta. Since disability was not uncommon, it was frequently mentioned in literature and poetry. Disabled individuals, regardless of social rank, were largely integrated into society thanks to the variety of roles and duties available in personal life, the economy, and the military. As a result, these writings represent the philosophical ideals of Greek thinkers and do not necessarily reflect the actual practices of ancient Greece, as neither work was intended to serve as factual records.<sup><span>[</span>9<span>]</span></sup> </p><p>In &quot;The Life of Lycurgus&quot; of <i><a href="https://en.wikipedia.org/wiki/Parallel_Lives">Parallel Lives</a></i>, Plutarch&#39;s describes infanticide as a common practice in <a href="https://en.wikipedia.org/wiki/Sparta">Sparta</a>, where the lawgiver decreed that newborn infants be taken to the <i><a href="https://en.wikipedia.org/wiki/Lesche">lesche</a></i>, likely a public building, for examination by elders.<sup><span>[</span>10<span>]</span></sup> If an infant was &quot;ill-bred and deformed&quot;, it would be sent to the <i>apothetai</i>, meaning &quot;exposure places&quot;, a pit beneath <a href="https://en.wikipedia.org/wiki/Mount_Taygetus">Mount Taygetus</a>.<sup><span>[</span>10<span>]</span></sup> Plutarch suggested this practice occurred because a deformed infant would be seen as a liability to Sparta, a city-state known for its strict martial ethos.<sup><span>[</span>9<span>]</span></sup> While Plutarch&#39;s account provides valuable insights into Spartan society, its reliability is questionable, as he lived 700 years after the events he described. Even Plutarch acknowledged that his accounts were open to dispute for this very reason.<sup><span>[</span>11<span>]</span></sup> In <i><a href="https://en.wikipedia.org/wiki/Republic_(Plato)">Republic</a></i>, Plato argues that in an ideal state rulers must ensure the breeding of the best men and women while discouraging those deemed inferior from reproducing.<sup><span>[</span>12<span>]</span></sup> He asserts that if the children of inferior parents, or any other parents, were deformed, they should be &quot;hidden away in a secret and unknown place, as is fitting&quot;.<sup><span>[</span>12<span>]</span></sup> In <i><a href="https://en.wikipedia.org/wiki/Politics_(Aristotle)">Politics</a></i>, Aristotle advocates that &quot;the bodies of offspring should conform to the wishes of the lawgiver&quot;, ideally being healthy and strong, which implies a similarly ableist stance to that of Plato.<sup><span>[</span>13<span>]</span></sup> He further proposes that a law should exist to prevent the raising of deformed infants, implying his endorsement of killing disabled infants.<sup><span>[</span>14<span>]</span></sup> </p><figure><a href="https://en.wikipedia.org/wiki/File:FL_Titusville_Windover_Arch_Site_marker03.jpg"></a><figcaption>Windover Archeological Site, location of the 15-year-old with spina bifida who was taken care of in a hunter-gather community</figcaption></figure><p>There is considerable evidence suggesting that individuals with deformities were well cared for in antiquity. At the <a href="https://en.wikipedia.org/wiki/Windover_Archeological_Site">Windover Archeological Site</a>, one of the skeletons was a male about 15 years old who had <a href="https://en.wikipedia.org/wiki/Spina_bifida">spina bifida</a>. The condition meant that the boy, probably paralyzed below the waist, was taken care of in a <a href="https://en.wikipedia.org/wiki/Hunter-gatherer">hunter-gatherer</a> community.<sup><span>[</span>15<span>]</span></sup><sup><span>[</span>16<span>]</span></sup> Disability was not viewed as a means of divine punishment and therefore disabled individuals were neither exterminated nor discriminated against for their impairments. Many were instead employed in different levels of Mesopotamian society including working in religious temples as servants of the gods.<sup><span>[</span>17<span>]</span></sup> In <a href="https://en.wikipedia.org/wiki/Ancient_Egypt">Ancient Egypt</a>, staffs were frequently used in society. A common usage for them was for older persons with disabilities to help them walk.<sup><span>[</span>18<span>]</span></sup> </p><p>In <a href="https://en.wikipedia.org/wiki/Ancient_Greece">Ancient Greece</a>, regardless of gender, age, or rank, deformed citizens were largely acknowledged, embraced, and accommodated in various aspects of society. This is illustrated in the <i><a href="https://en.wikipedia.org/wiki/Hippocratic_Corpus">Hippocratic Corpus</a></i>, a collection of treatises written by physicians during the late 5th and 4th centuries BCE as a practical manual.<sup><span>[</span>8<span>]</span></sup> Therefore, it offers a more accurate depiction of how the Greeks treated disabled people. For instance, many of the treatises describe the conditions and treatments for infants with congenital anomalies or impairments, such as weasel-arm, <a href="https://en.wikipedia.org/wiki/Clubfoot">clubfoot</a>, and <a href="https://en.wikipedia.org/wiki/Cleft_lip_and_cleft_palate">cleft conditions</a>.<sup><span>[</span>19<span>]</span></sup><sup><span>[</span>20<span>]</span></sup><sup><span>[</span>21<span>]</span></sup> Ironically, among these, the practice of infanticide or the harming of deformed infants is never mentioned.<sup><span>[</span>8<span>]</span></sup> In fact, these Hippocratic physicians treated a wide range of patients throughout the Greek-speaking world from the 5th century BCE onwards. This suggests that it may not have been normal in ancient Greece to kill deformed infants, presenting a reality that contrasts with the views of Plato, Aristotle, and other ancient philosophers. Many of them expressed neutrality, if not optimism, toward deformed infants, striving to cure them while documenting their conditions.<sup><span>[</span>8<span>]</span></sup> </p><p>The depiction of disabled adults or gods was common in the literature of ancient Greece. In <a href="https://en.wikipedia.org/wiki/Homer">Homer</a>&#39;s <i><a href="https://en.wikipedia.org/wiki/Iliad">Iliad</a></i> and <i><a href="https://en.wikipedia.org/wiki/Odyssey">Odyssey</a></i>, <a href="https://en.wikipedia.org/wiki/Hephaistos">Hephaistos</a>, a god and renowned craftsman, is described as being &quot;lame in both legs&quot;, and he is mentioned 41 times in the <i>Iliad</i> and 19 times in the <i>Odyssey</i>.<sup><span>[</span>9<span>]</span></sup> In Book 2 of the <i>Iliad</i>, Homer provides a detailed description of <a href="https://en.wikipedia.org/wiki/Thersites">Thersites</a>&#39; deformity, including his bandy legs, lame foot, hunched shoulders, and balding pate, calling him &quot;the ugliest man who came beneath <a href="https://en.wikipedia.org/wiki/Ilion,_Greece">Ilion</a>&quot;.<sup><span>[</span>22<span>]</span></sup> This suggests that ancient Greeks acknowledged disabled adult civilians, as disability, whether congenital or acquired, was common due to the harsh realities of ancient life and warfare.<sup><span>[</span>9<span>]</span></sup> In addition to literary evidence, archaeological evidence is crucial in unfolding ancient Greeks&#39; attitude towards deformed individuals. One that is most related to the discussion of infanticide in Ancient Greece is the <a href="https://en.wikipedia.org/wiki/Agora">Agora</a> Bone Well, in which archaeologists found a large number of skeletons, including those of infants.<sup><span>[</span>23<span>]</span></sup> Since the median age at death for these infants was only eight days old, it gives rise to the assumption that infanticide could be a possible explanation;<sup><span>[</span>23<span>]</span></sup> however, scholars cannot determine whether the infants were intentionally killed or whether they died of natural causes, which was particularly common, especially during the first eight days after birth.<sup><span>[</span>8<span>]</span></sup> </p><p>Archaeologists have discovered a significant number of feeding bottles throughout the <a href="https://en.wikipedia.org/wiki/Hellenic_world">Hellenic world</a>, dating back to the <a href="https://en.wikipedia.org/wiki/Bronze_Age">Late Bronze Age</a>.<sup><span>[</span>9<span>]</span></sup> Many of these were found in the tombs of infants and young children. While scholars debate whether these bottles were used as aids for weaning infants or as symbols of condolence with no practical purpose, the shape of the bottles is particularly suited for feeding infants with cleft conditions.<sup><span>[</span>9<span>]</span></sup> Depending on the severity, such infants would have had difficulty extracting milk from a nipple.<sup><span>[</span>9<span>]</span></sup> This suggests that the ancient Greeks may have invested extra care and resources in raising disabled infants, rather killing them. Contrary to previous beliefs, Greek men with disabilities or physical infirmities were generally exempt from military campaigns and battles.<sup><span>[</span>8<span>]</span></sup> In <i><a href="https://en.wikipedia.org/wiki/Memorabilia_(Xenophon)">Memorabilia</a></i>, <a href="https://en.wikipedia.org/wiki/Xenophon">Xenophon</a> suggests that men with bodily weakness or illness were considered liabilities in battle.<sup><span>[</span>24<span>]</span></sup> Additionally, during the <a href="https://en.wikipedia.org/wiki/Battle_of_Thermopylae">Battle of Thermopylae</a>, the Spartan king and commander <a href="https://en.wikipedia.org/wiki/Leonidas_I">Leonidas</a> excused <a href="https://en.wikipedia.org/wiki/Eurytus">Eurytus</a> and <a href="https://en.wikipedia.org/wiki/Aristodemus_(died_479_BC)">Aristodemus</a> from fighting, as both of them were suffering from severe eye sickness, demonstrating that men unfit for war were not forced to participate.<sup><span>[</span>25<span>]</span></sup> In exceptional cases, disabled or injured men might be called upon to take on suitable roles that would contribute to the war effort.<sup><span>[</span>8<span>]</span></sup> </p><p>In terms of personal life, there is no evidence to suggest that disabled Greeks were barred from marriage or reproduction. This likely stemmed from the belief that deformed parents did not necessarily produce deformed offspring;<sup><span>[</span>26<span>]</span></sup> however, disabled individuals may have faced greater challenges in finding a suitable partner, as they were sometimes rejected by the family of a potential spouse.<sup><span>[</span>8<span>]</span></sup> Regarding their economic situation, disabled Greeks—regardless of gender or social rank—worked in a variety of positions and professions. According to <a href="https://en.wikipedia.org/wiki/Lysias">Lysias</a>, a disabled man who uses two canes to walk &quot;plies a craft&quot; and runs a shop, demonstrating that disabled individuals were not deprived of the ability to support themselves.<sup><span>[</span>27<span>]</span></sup> In <i>On Joints,</i> <a href="https://en.wikipedia.org/wiki/Hippocrates">Hippocrates</a> describes people with arm disabilities also being engaged in &quot;handiwork&quot;, provided they were still able to operate tools.<sup><span>[</span>19<span>]</span></sup> Plato also mentions in <i><a href="https://en.wikipedia.org/wiki/The_Laws_(Plato)">Laws</a></i> that slaves who acquired disabilities later in life could be reassigned to other suitable roles, a principle that logically should also apply to free individuals in Greece.<sup><span>[</span>28<span>]</span></sup> </p><p>Ancient Greeks were subjected to a wide range of physical consequences of aging, causing impairments and disabilities.<sup><span>[</span>9<span>]</span></sup> Therefore, ancient Greeks put great effort into assisting elderly people in their communities. In some Greek states, children were legally required to care for their elderly parents, which might have included parents who were physically or mentally impaired.<sup><span>[</span>9<span>]</span></sup> According to Aristotle, people who failed to do so would be imprisoned.<sup><span>[</span>29<span>]</span></sup> Provisions that enabled individuals with impaired mobility to access temples and healing sanctuaries were made in ancient Greece.<sup><span>[</span>30<span>]</span></sup> Specifically, by 370 BC, at the most important healing sanctuary in the wider area, the <a href="https://en.wikipedia.org/wiki/Temple_of_Asclepius,_Epidaurus">Sanctuary of Asclepius</a> at <a href="https://en.wikipedia.org/wiki/Epidaurus">Epidaurus</a>, there were at least 11 permanent stone ramps that provided access to mobility-impaired visitors to nine different structures.<sup><span>[</span>31<span>]</span></sup> On top of this, disabled Athenians who were unable to support themselves received monetary assistance from the state, sufficient to cover their basic needs.<sup><span>[</span>32<span>]</span></sup> This indicates that some forms of charity and social welfare existed in <a href="https://en.wikipedia.org/wiki/Athens">Athens</a>. Disability was also common among individuals of high status in ancient Greece. In the 6th century BCE, <a href="https://en.wikipedia.org/wiki/Croesus">Croesus</a>, the King of Lydia, had two sons, one of whom was either deaf or mute.<sup><span>[</span>33<span>]</span></sup> He spent a considerable amount of wealth in an unsuccessful attempt to cure this son, even consulting the oracle of <a href="https://en.wikipedia.org/wiki/Apollo">Apollo</a> at <a href="https://en.wikipedia.org/wiki/Delphi">Delphi</a>.<sup><span>[</span>33<span>]</span></sup> Eventually, Croesus rejected the disabled son, choosing to favor only his able-bodied son, Atys, instead.<sup><span>[</span>33<span>]</span></sup> Similarly, <a href="https://en.wikipedia.org/wiki/Agesilaus_II">Agesilaus</a>, a Spartan king in the 4th century BCE, was lame in one leg but still became a general and fought in major battles.<sup><span>[</span>34<span>]</span></sup> The Macedonian king, <a href="https://en.wikipedia.org/wiki/Philip_II_of_Macedon">Philip II</a>, also suffered from multiple physical impairments during his conquests; he lost one eye, fractured his collarbone, and shattered one hand and leg.<sup><span>[</span>35<span>]</span></sup> </p><div><h3>Middle Ages and After</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>During the <a href="https://en.wikipedia.org/wiki/Middle_Ages">Middle Ages</a>, madness and other conditions were thought to be caused by demons. They were also thought to be part of the natural order, especially during and in the fallout of the <a href="https://en.wikipedia.org/wiki/Black_Death">Black Death</a>, which wrought impairments throughout the general population.<sup><span>[</span>36<span>]</span></sup> In the <a href="https://en.wikipedia.org/wiki/Early_modern_period">early modern period</a> there was a shift to seeking biological causes for physical and mental differences, as well as heightened interest in demarcating categories: for example, Ambroise Pare, in the sixteenth century, wrote of &quot;monsters&quot;, &quot;prodigies&quot;, and &quot;the maimed&quot;.<sup><span>[</span>37<span>]</span></sup> The <a href="https://en.wikipedia.org/wiki/European_Enlightenment">European Enlightenment</a>&#39;s emphases on knowledge derived from reason and on the value of natural science to human progress helped spawn the birth of <a href="https://en.wikipedia.org/wiki/Institutionalisation">institutions</a> and associated knowledge systems that observed and categorized human beings; among these, the ones significant to the development of today&#39;s concepts of disability were <a href="https://en.wikipedia.org/wiki/Psychiatric_hospital">asylums</a>, <a href="https://en.wikipedia.org/wiki/Clinic">clinics</a>, and <a href="https://en.wikipedia.org/wiki/Prison">prisons</a>.<sup><span>[</span>36<span>]</span></sup> </p><p>Contemporary concepts of disability are rooted in eighteenth- and nineteenth-century developments. Foremost among these was the development of clinical medical discourse, which made the human body visible as a thing to be manipulated, studied, and transformed. These worked in tandem with scientific discourses that sought to classify and categorize and, in so doing, became methods of <a href="https://en.wikipedia.org/wiki/Normalization_(people_with_disabilities)">normalization</a>.<sup><span>[</span>38<span>]</span></sup> The concept of the &quot;norm&quot; developed in this time period, and is signaled in the work of the Belgian <a href="https://en.wikipedia.org/wiki/Statistician">statistician</a>, <a href="https://en.wikipedia.org/wiki/Sociology">sociologist</a>, <a href="https://en.wikipedia.org/wiki/Mathematician">mathematician</a>, and <a href="https://en.wikipedia.org/wiki/Astronomer">astronomer</a> <a href="https://en.wikipedia.org/wiki/Adolphe_Quetelet">Adolphe Quetelet</a>, who wrote in the 1830s of <span><i>l&#39;homme moyen</i></span> – the average man. Quetelet postulated that one could take the sum of all people&#39;s attributes in a given population (such as their height or weight) and find their average and that this figure should serve as a statistical norm toward which all should aspire.<sup><span>[</span>39<span>]</span></sup> This idea of the statistical norm threads through the rapid take-up of statistics gathering by Britain, the United States, and the Western European states during this time period, and it is tied to the rise of <a href="https://en.wikipedia.org/wiki/Eugenics">eugenics</a>.<sup><span>[</span>39<span>]</span></sup> Disability, as well as the concepts of abnormal, non-normal, and normalcy, came from this.<sup><span>[</span>40<span>]</span></sup> The circulation of these concepts is evident in the popularity of the <a href="https://en.wikipedia.org/wiki/Freak_show">freak show</a>, where showmen profited from exhibiting people who deviated from those norms.<sup><span>[</span>41<span>]</span></sup> </p><p>With the rise of eugenics in the latter part of the nineteenth century, such deviations were viewed as dangerous to the health of entire populations. With disability viewed as part of a person&#39;s biological make-up and thus their genetic inheritance, scientists turned their attention to notions of weeding such as &quot;deviations&quot; out of the gene pool. Various metrics for assessing a person&#39;s genetic fitness were determined and were then used to <a href="https://en.wikipedia.org/wiki/Deportation">deport</a>, sterilize, or institutionalize those deemed unfit. People with disabilities were one of the groups targeted by the <a href="https://en.wikipedia.org/wiki/Nazi_Germany">Nazi regime</a> in Germany, resulting in approximately 250,000 disabled people being killed during <a href="https://en.wikipedia.org/wiki/The_Holocaust">the Holocaust</a>.<sup><span>[</span>42<span>]</span></sup> At the end of the <a href="https://en.wikipedia.org/wiki/World_War_II">Second World War</a>, with the example of <a href="https://en.wikipedia.org/wiki/Nazi_eugenics">Nazi eugenics</a>, eugenics faded from <a href="https://en.wikipedia.org/wiki/Public_sphere">public discourse</a>, and increasingly disability cohered into a set of attributes to which medicine could attend – whether through augmentation, rehabilitation, or treatment. In both contemporary and modern history, disability was often viewed as a by-product of <a href="https://en.wikipedia.org/wiki/Incest">incest</a> between <a href="https://en.wikipedia.org/wiki/First-degree_relatives">first-degree relatives</a> or <a href="https://en.wikipedia.org/wiki/Second-degree_relatives">second-degree relatives</a>.<sup><span>[</span>43<span>]</span></sup> </p><figure><figcaption>A short government advisory animation on the <a href="https://en.wikipedia.org/wiki/Social_model_of_disability">social model of disability</a></figcaption></figure><p>Disability scholars have also pointed to the <a href="https://en.wikipedia.org/wiki/Industrial_Revolution">Industrial Revolution</a>, along with the economic shift from <a href="https://en.wikipedia.org/wiki/Feudalism">feudalism</a> to <a href="https://en.wikipedia.org/wiki/Capitalism">capitalism</a>, as prominent historical moments in the understanding of disability. Although there was a certain amount of religious superstition surrounding disability during the <a href="https://en.wikipedia.org/wiki/Middle_Ages">Middle Ages</a>, disabled people were still able to play significant roles in the rural production based economy, allowing them to make genuine contributions to daily economic life.<sup><span>[</span>44<span>]</span></sup> The Industrial Revolution and the advent of capitalism made it so that people were no longer tied to the land and were then forced to find work that would pay a wage in order to survive. The wage system, in combination with industrialized production, transformed the way bodies were viewed as people were increasingly valued for their ability to produce like machines.<sup><span>[</span>45<span>]</span></sup> Capitalism and the industrial revolution effectively solidified this class of &quot;disabled&quot; people who could not conform to the standard <a href="https://en.wikipedia.org/wiki/Working_class">worker</a>&#39;s body or level of work power. As a result, disabled people came to be regarded as a problem, to be solved or erased.<sup><span>[</span>44<span>]</span></sup> </p><p>In the early 1970s, the <a href="https://en.wikipedia.org/wiki/Disability_rights_movement">disability rights movement</a> became established, when disability activists began to challenge how society treated disabled people and the medical approach to disability. Due to this work, physical <a href="https://en.wikipedia.org/wiki/Accessibility">barriers to access</a> were identified. These conditions functionally disabled them, and what is now known as the <a href="https://en.wikipedia.org/wiki/Social_model_of_disability">social model of disability</a> emerged. Coined by Mike Oliver in 1983, this phrase distinguishes between the <a href="https://en.wikipedia.org/wiki/Medical_model_of_disability">medical model of disability</a> – under which an impairment needs to be fixed – and the social model of disability – under which the society that limits a person needs to be fixed.<sup><span>[</span>46<span>]</span></sup> </p><div><h2>Theory</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><div><h3>Disability studies</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>The academic discipline focused on theorizing disability is <a href="https://en.wikipedia.org/wiki/Disability_studies">disability studies</a>, which has been expanding since the late twentieth century. The field investigates the past, present, and future constructions of disability, along with advancing the viewpoint that disability is a complex social identity from which we can all gain insight. As disabilities scholar Claire Mullaney puts it, &quot;At its broadest, disability studies encourages scholars to value disability as a form of cultural difference.&quot;<sup><span>[</span>47<span>]</span></sup> Scholars of the field focus on a range of disability-related topics, such as ethics, policy and legislation, history, art of the disability community, and more. Notable scholars from the field include <a href="https://en.wikipedia.org/wiki/Marta_Russell">Marta Russell</a>, <a href="https://en.wikipedia.org/wiki/Robert_McRuer">Robert McRuer</a>, <a href="https://en.wikipedia.org/wiki/Johanna_Hedva">Johanna Hedva</a>, <a href="https://en.wikipedia.org/wiki/Laura_Hershey">Laura Hershey</a>, <a href="https://en.wikipedia.org/wiki/Irving_Zola">Irving Zola</a>, and many more. Prominent disability scholar <a href="https://en.wikipedia.org/wiki/Lennard_J._Davis">Lennard J. Davis</a> notes that disability studies should not be considered a niche or specialized discipline, but instead is applicable to a wide range of fields and topics.<sup><span>[</span>47<span>]</span></sup> </p><div><h3>International Classification</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>The <a href="https://en.wikipedia.org/wiki/International_Classification_of_Functioning,_Disability_and_Health">International Classification of Functioning, Disability and Health</a> (ICF), produced by the <a href="https://en.wikipedia.org/wiki/World_Health_Organization">World Health Organization</a>, distinguishes between body functions (including physiological, cognitive and psychological functioning) and body structures (anatomical parts, such as the eye and related structures). Impairment in bodily structure or function is defined as involving an anomaly, defect, loss or other significant deviation from certain generally accepted population standards, which may fluctuate over time. Activity is defined as the execution of a task or action. The ICF lists nine broad domains of functioning which can be affected: </p><ul><li>Learning and applying knowledge</li> <li>General tasks and demands</li> <li>Communication</li> <li>Basic physical mobility, domestic life, and self-care (<a href="https://en.wikipedia.org/wiki/Activities_of_daily_living">activities of daily living</a>)</li> <li>Interpersonal interactions and relationships</li> <li>Community, social and civic life (<a href="https://en.wikipedia.org/wiki/Employment">employment</a>, <a href="https://en.wikipedia.org/wiki/Self_determination">political participation</a>, etc.)</li> <li>Other major life areas</li></ul><p>In concert with disability scholars, the introduction to the ICF states that a variety of <a href="https://en.wikipedia.org/wiki/Conceptual_model">conceptual models</a> have been proposed to understand and explain disability and functioning, which it seeks to integrate. These models include the following: </p><div><h3>Medical model</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Medical_model_of_disability">Medical model of disability</a></div><p>The <a href="https://en.wikipedia.org/wiki/Medical_model">medical model</a> views disability as a problem of the person, directly caused by disease, trauma, or other health conditions which therefore requires sustained medical care in the form of individual treatment by professionals. The medical model focuses on finding causes and cures for disabilities. In the medical model, management of the disability is aimed at a &quot;cure&quot;, or the individual&#39;s adjustment and behavioral change that would lead to an &quot;almost-cure&quot; or effective cure. The individual, in this case, must overcome their disability by medical care. In the medical model, medical care is viewed as the main issue, and at the political level, the principal response is that of modifying or reforming <a href="https://en.wikipedia.org/wiki/Healthcare">healthcare</a> policy.<sup><span>[</span>48<span>]</span></sup><sup><span>[</span>49<span>]</span></sup> </p><div><h4>Causes</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>There are many causes of disability that often affect basic <a href="https://en.wikipedia.org/wiki/Activities_of_daily_living">activities of daily living</a>, such as eating, dressing, transferring, and maintaining <a href="https://en.wikipedia.org/wiki/Personal_hygiene">personal hygiene</a>; or advanced activities of daily living such as shopping, food preparation, driving, or working; however, causes of disability are usually determined by a person&#39;s capability to perform the activities of daily life. As Marta Russell and Ravi Malhotra argue, &quot;The &#39;<a href="https://en.wikipedia.org/wiki/Medicalization">medicalization</a>&#39; of disablement and the tools of classification clearly played an important role in establishing divisions between the &#39;disabled&#39; and the &#39;able-bodied.<span>&#39;</span>&quot;<sup><span>[</span>50<span>]</span></sup> This positions disability as a problem to be solved via medical intervention, which hinders our understanding about what disability can mean.<sup><span>[</span>51<span>]</span></sup> </p><p>There is not a fully exhaustive list and many injuries and medical problems cause disability. Some causes of disability, such as injuries, may resolve over time and are considered <i><dfn>temporary disabilities</dfn></i>. An <i><dfn>acquired disability</dfn></i> is the result of impairments that occur suddenly or chronically during the lifespan, as opposed to being born with the impairment. <i><dfn><a href="https://en.wikipedia.org/wiki/Invisible_disabilities">Invisible disabilities</a></dfn></i> may not be obviously noticeable. For the purposes of the <a href="https://en.wikipedia.org/wiki/Americans_with_Disabilities_Act_of_1990">Americans with Disabilities Act of 1990</a>, the US <a href="https://en.wikipedia.org/wiki/Equal_Employment_Opportunity_Commission">Equal Employment Opportunity Commission</a> regulations provide a list of conditions that should easily<sup><span>[</span>52<span>]</span></sup> be concluded to be disabilities: <a href="https://en.wikipedia.org/wiki/Amputation">amputation</a>, <a href="https://en.wikipedia.org/wiki/Attention_deficit_hyperactivity_disorder">attention deficit hyperactivity disorder</a> (ADHD), <a href="https://en.wikipedia.org/wiki/Autism">autism</a>, <a href="https://en.wikipedia.org/wiki/Bipolar_disorder">bipolar disorder</a>, <a href="https://en.wikipedia.org/wiki/Blindness">blindness</a>, <a href="https://en.wikipedia.org/wiki/Cancer">cancer</a>, <a href="https://en.wikipedia.org/wiki/Cerebral_palsy">cerebral palsy</a>, <a href="https://en.wikipedia.org/wiki/Deafness">deafness</a>, <a href="https://en.wikipedia.org/wiki/Diabetes">diabetes</a>, <a href="https://en.wikipedia.org/wiki/Epilepsy">epilepsy</a>, <a href="https://en.wikipedia.org/wiki/HIV/AIDS">HIV/AIDS</a>, <a href="https://en.wikipedia.org/wiki/Intellectual_disability">intellectual disability</a>, <a href="https://en.wikipedia.org/wiki/Major_depressive_disorder">major depressive disorder</a>, <a href="https://en.wikipedia.org/wiki/Mobility_impairment">mobility impairments</a> requiring a wheelchair, <a href="https://en.wikipedia.org/wiki/Multiple_sclerosis">multiple sclerosis</a>, <a href="https://en.wikipedia.org/wiki/Muscular_dystrophy">muscular dystrophy</a>, <a href="https://en.wikipedia.org/wiki/Obsessive%E2%80%93compulsive_disorder">obsessive–compulsive disorder</a> (OCD), <a href="https://en.wikipedia.org/wiki/Post-traumatic_stress_disorder">post-traumatic stress disorder</a> (PTSD), <a href="https://en.wikipedia.org/wiki/Spina_bifida">spina bifida</a>, and <a href="https://en.wikipedia.org/wiki/Schizophrenia">schizophrenia</a>.<sup><span>[</span>53<span>]</span></sup> </p><div><h4>Cures</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>The medical model focuses heavily on finding treatments, cures, or rehabilitative practices for disabled people.<sup><span>[</span>54<span>]</span></sup> </p><div><h5>Assistive technology</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Assistive_technology">Assistive technology</a></div><p>Assistive technology is a generic term for devices and modifications (for a person or within a society) that help overcome or remove a disability. The first recorded example of the use of a <a href="https://en.wikipedia.org/wiki/Prosthesis">prosthesis</a> dates to at least 1800 BC.<sup><span>[</span>55<span>]</span></sup> The <a href="https://en.wikipedia.org/wiki/Wheelchair">wheelchair</a> dates from the 17th century.<sup><span>[</span>56<span>]</span></sup> The <a href="https://en.wikipedia.org/wiki/Curb_cut">curb cut</a> is a related structural innovation. Other examples are <a href="https://en.wikipedia.org/wiki/Standing_frames">standing frames</a>, text <a href="https://en.wikipedia.org/wiki/Telephones">telephones</a>, accessible <a href="https://en.wikipedia.org/wiki/Keyboard_(computing)">keyboards</a>, <a href="https://en.wikipedia.org/wiki/Large_print">large print</a>, <a href="https://en.wikipedia.org/wiki/Braille">braille</a>, and <a href="https://en.wikipedia.org/wiki/Speech_recognition">speech recognition</a> <a href="https://en.wikipedia.org/wiki/Software">software</a>. Disabled people often develop adaptations which can be personal (e.g. strategies to suppress tics in public) or community (e.g. <a href="https://en.wikipedia.org/wiki/Sign_language">sign language</a> in d/Deaf communities). </p><p>As the <a href="https://en.wikipedia.org/wiki/Personal_computer">personal computer</a> has become more ubiquitous, various organizations have formed to <a href="https://en.wikipedia.org/wiki/Software_development">develop software</a> and <a href="https://en.wikipedia.org/wiki/Computer_hardware">hardware</a> to make computers more accessible for disabled people. Some software and hardware, such as <a href="https://en.wikipedia.org/wiki/Voice_Finger">Voice Finger</a>, <a href="https://en.wikipedia.org/wiki/Freedom_Scientific">Freedom Scientific</a>&#39;s <i><a href="https://en.wikipedia.org/wiki/JAWS_(screen_reader)">JAWS</a></i>, the Free and Open Source alternative <i><a href="https://en.wikipedia.org/wiki/Orca_(assistive_technology)">Orca</a></i> etc. have been specifically designed for disabled people while other software and hardware, such as <a href="https://en.wikipedia.org/wiki/Nuance_Communications">Nuance</a>&#39;s <a href="https://en.wikipedia.org/wiki/Dragon_NaturallySpeaking">Dragon NaturallySpeaking</a>, were not developed specifically for disabled people, but can be used to increase accessibility.<sup><span>[</span>57<span>]</span></sup> The <a href="https://en.wikipedia.org/wiki/LOMAK">LOMAK</a> keyboard was designed in New Zealand specifically for persons with disabilities.<sup><span>[</span>58<span>]</span></sup> The World Wide Web consortium recognized a need for International Standards for Web Accessibility for persons with disabilities and created the <a href="https://en.wikipedia.org/wiki/Web_Accessibility_Initiative">Web Accessibility Initiative</a> (WAI).<sup><span>[</span>59<span>]</span></sup> As at Dec 2012 the standard is WCAG 2.0 (WCAG = Web Content Accessibility Guidelines).<sup><span>[</span>60<span>]</span></sup> </p><div><h3>Social model</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Social_model_of_disability">Social model of disability</a></div><p>The social model of disability sees &quot;disability&quot; as a socially created problem and a matter of the full <a href="https://en.wikipedia.org/wiki/Inclusion_(disability_rights)">integration of individuals into society</a>. In this model, disability is not an attribute of an individual, but rather a complex collection of conditions, created by the social environment. The management of the problem requires <a href="https://en.wikipedia.org/wiki/Social_activist">social action</a> and it is the collective responsibility of society to create a society in which limitations for disabled people are minimal. Disability is both <a href="https://en.wikipedia.org/wiki/Cultural">cultural</a> and <a href="https://en.wikipedia.org/wiki/Ideological">ideological</a> in creation. According to the social model, equal access for someone with an impairment/disability is a human rights concern.<sup><span>[</span>61<span>]</span></sup><sup><span>[</span>49<span>]</span></sup> The social model of disability has come under criticism. While recognizing the importance played by the social model in stressing the responsibility of society, scholars, including <a href="https://en.wikipedia.org/wiki/Tom_Shakespeare">Tom Shakespeare</a>, point out the limits of the model and urge the need for a new model that will overcome the &quot;medical vs. social&quot; dichotomy.<sup><span>[</span>62<span>]</span></sup> The limitations of this model mean that often the vital services and information persons with disabilities face are simply not available, often due to limited economic returns in supporting them.<sup><span>[</span>63<span>]</span></sup> Some say <a href="https://en.wikipedia.org/wiki/Medical_humanities">medical humanities</a> is a fruitful field where the gap between the medical and the social model of disability might be bridged.<sup><span>[</span>64<span>]</span></sup> </p><div><h4>Social construction</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><p>The social construction of disability is the idea that disability is constructed by social expectations and institutions rather than biological differences. Highlighting the ways society and institutions construct disability is one of the main focuses of this idea.<sup><span>[</span>65<span>]</span></sup> In the same way that race and gender are not biologically fixed, neither is disability. Around the early 1970s, sociologists, notably Eliot Friedson, began to argue that <a href="https://en.wikipedia.org/wiki/Labeling_theory">labeling theory</a> and <a href="https://en.wikipedia.org/wiki/Social_deviance">social deviance</a> could be applied to disability studies. This led to the creation of the <a href="https://en.wikipedia.org/wiki/Social_construction_of_disability">social construction of disability</a> theory. The social construction of disability is the idea that disability is constructed as the social response to a deviance from the norm. The medical industry is the creator of the ill and disabled social role. Medical professionals and institutions, who wield expertise over health, have the ability to define health and physical and mental norms. When an individual has a feature that creates an impairment, restriction, or limitation from reaching the social definition of health, the individual is labeled as disabled. Under this idea, disability is not defined by the physical features of the body but by a deviance from the <a href="https://en.wikipedia.org/wiki/Social_convention">social convention</a> of health.<sup><span>[</span>66<span>]</span></sup> The social construction of disability would argue that the <a href="https://en.wikipedia.org/wiki/Medical_model_of_disability">medical model of disability</a>&#39;s view that a disability is an impairment, restriction, or limitation is wrong. Instead what is seen as a disability is just a difference in the individual from what is considered &quot;normal&quot; in society.<sup><span>[</span>67<span>]</span></sup> </p><div><h3>Other models</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><ul><li>The political/relational model is an alternative to and critical engagement with both the social and medical models. This analytic posed by Alison Kafer shows not only how the &quot;problem&quot; of disability &quot;is located in inaccessible buildings, discriminatory attitudes, and ideological systems that attribute normalcy and deviance to particular minds and bodies&quot; but also how mind and bodily impairments can still have disabling effects. Furthermore, the political/relational model frames the medicalization of disabled folks as political in nature given it should always be interrogated.<sup><span>[</span>68<span>]</span></sup></li> <li>The spectrum model refers to the range of audibility, sensibility, and visibility under which people function. The model asserts that disability does not necessarily mean a reduced spectrum of operations. Rather, disability is often defined according to thresholds set on a continuum of disability.<sup><span>[</span>69<span>]</span></sup></li> <li>The moral model refers to the attitude that people are <i>morally responsible</i> for their own disability.<sup><span>[</span>70<span>]</span></sup> For example, disability may be seen as a result of bad actions of parents if <a href="https://en.wikipedia.org/wiki/Congenital">congenital</a>, or as a result of practicing witchcraft if not.<sup><span>[</span>71<span>]</span></sup> Echoes of this can be seen in the doctrine of <a href="https://en.wikipedia.org/wiki/Karma">karma</a> in Eastern and New Age religions. It also includes notions that a disability gives a person &quot;special abilities to perceive, reflect, transcend, be spiritual&quot;.<sup><span>[</span>72<span>]</span></sup></li> <li>The expert/professional model has provided a traditional response to disability issues and can be seen as an offshoot of the medical model. Within its framework, professionals follow a process of identifying the impairment and its limitations (using the medical model), and taking the necessary action to improve the position of the disabled person. This has tended to produce a system in which an authoritarian, over-active service provider prescribes and acts for a passive client.<sup><span>[</span>73<span>]</span></sup></li> <li>The tragedy/charity model depicts disabled people as victims of circumstance who are deserving of pity. This, along with the medical model, are the models used by most people with no acknowledged disability to define and explain disability.<sup><span>[</span>74<span>]</span></sup></li> <li>The legitimacy model views disability as a value-based determination about which explanations for the atypical are legitimate for membership in the disability category. This viewpoint allows for multiple explanations and models to be considered as purposive and viable.<sup><span>[</span>75<span>]</span></sup></li> <li>The social adapted model states although a person&#39;s disability poses some limitations in an able-bodied society, often the surrounding society and environment are more limiting than the disability itself.<sup><span>[</span>76<span>]</span></sup></li> <li>The economic model defines disability in terms of reduced ability to work, the related loss of productivity and economic effects on the individual, employer and society in general.<sup><span>[</span>77<span>]</span></sup></li> <li>The empowering model (also, customer model or <a href="https://en.wikipedia.org/wiki/Supported_decision_making">supported decision making</a>) allows for the person with a disability and their family to decide the course of their treatment. This turns the professional into a service provider whose role is to offer guidance and carry out the client&#39;s decisions. This model &quot;empowers&quot; the individual to pursue their own goals.<sup><span>[</span>76<span>]</span></sup></li> <li>The market model of disability is minority rights and consumerist model of disability that recognizing disabled people and their stakeholders as representing a large group of consumers, employees, and voters. This model looks to personal identity to define disability and empowers people to chart their own destiny in everyday life, with a particular focus on economic empowerment. Based on US Census data, this model shows that there are 1.2 billion people in the world who consider themselves to have a disability. &quot;This model states that due to the size of the demographic, companies and governments will serve the desires, pushed by demand as the message becomes prevalent in the cultural mainstream.&quot;<sup><span>[</span>49<span>]</span></sup></li> <li>The consumer model of disability is based upon the &quot;rights-based&quot; model and claims that disabled people should have equal rights and access to products, goods, and services offered by businesses. The consumer model extends the rights-based model by proposing that businesses, not only accommodate customers with disabilities under the requirements of legislation but that businesses actively seek, market to, welcome and fully engage disabled people in all aspects of business service activities. The model suggests that all business operations, for example, websites, policies, procedures, mission statements, emergency plans, programs, and services, should integrate access and inclusion practices. Furthermore, these access and inclusion practices should be based on established customer service access and inclusion standards that embrace and support the active engagement of people of all abilities in business offerings.<sup><span>[</span>78<span>]</span></sup> In this regard, specialized products and specialized services become important, such as auxiliary means, prostheses, special foods, domestic help, and assisted living.<sup><span>[</span>79<span>]</span></sup></li> <li>Different theories revolve around prejudice, stereotyping, discrimination, and stigma related to disability. One of the more popular ones, as put by Weiner, Perry, and Magnusson&#39;s (1988) work with <a href="https://en.wikipedia.org/wiki/Attribution_(psychology)">attribution theory</a>, physical stigmas are perceived as to be uncontrollable and elicit pity and desire to help, whereas, mental-behavioral stigmas are considered to be controllable and therefore elicit anger and desire to neglect the individuals with disabilities.<sup><span>[</span>80<span>]</span></sup></li> <li>The <a href="https://en.wikipedia.org/wiki/Just-world_fallacy">just-world fallacy</a> talks about how a person is viewed as deserving the disability. And because it is the fault of that person, an observer does not feel obligated to feel bad for them or to help them.<sup><span>[</span>81<span>]</span></sup></li></ul><div><h2>Terminology</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><div><h3>People-first language</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/People-first_language">People-first language</a></div><p>People-first language is one way to talk about disability which some people prefer. Using people-first language is said to put the person before the disability. Those individuals who prefer people-first language would prefer to be called, &quot;a person with a disability&quot;. This style is reflected in major legislation on disability rights, including the <a href="https://en.wikipedia.org/wiki/Americans_with_Disabilities_Act_of_1990">Americans with Disabilities Act</a> and the <a href="https://en.wikipedia.org/wiki/Convention_on_the_Rights_of_Persons_with_Disabilities">UN Convention on the Rights of Persons with Disabilities</a>. &quot;Cerebral Palsy: A Guide for Care&quot; at the <a href="https://en.wikipedia.org/wiki/University_of_Delaware">University of Delaware</a> describes people-first language:<sup><span>[</span>82<span>]</span></sup> </p><blockquote><p>The <a href="https://en.wikipedia.org/wiki/APA_style">American Psychological Association style guide</a> states that, when identifying a person with a disability, the person&#39;s name or pronoun should come first, and descriptions of the disability should be used so that the disability is identified, but is not modifying the person. Acceptable examples included &quot;a woman with <a href="https://en.wikipedia.org/wiki/Down_syndrome">Down syndrome</a>&quot; or &quot;a man who has <a href="https://en.wikipedia.org/wiki/Schizophrenia">schizophrenia</a>&quot;. It also states that a person&#39;s adaptive equipment should be described functionally as something that assists a person, not as something that limits a person, for example, &quot;a woman who uses a wheelchair&quot; rather than &quot;a woman in/confined to a wheelchair&quot;.</p></blockquote><p>People-first terminology is used in the UK in the form &quot;people with impairments&quot; (such as &quot;people with visual impairments&quot;); however other individuals and groups prefer identity-first language to emphasize how a disability can impact people&#39;s identities. Which style of language used varies between different countries, groups and individuals. In the UK, identity-first language is generally preferred over people-first language. The use of people-first terminology has given rise to the use of the acronym PWD to refer to person(s) (or people) with disabilities (or disability);<sup><span>[</span>83<span>]</span></sup><sup><span>[</span>84<span>]</span></sup><sup><span>[</span>85<span>]</span></sup> </p><div><h3>Identity-first language</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div><p>Identity-first language describes the person as &quot;disabled&quot;. Some people prefer this and argue that this fits the social model of disability better than people-first language, as it emphasizes that the person is disabled not by their body, but by a world that does not accommodate them.<sup><span>[</span>86<span>]</span></sup> This is especially true in the UK, where it is argued under the <a href="https://en.wikipedia.org/wiki/Social_model_of_disability">social model</a> that while someone&#39;s impairment (for example, having a <a href="https://en.wikipedia.org/wiki/Spinal_cord_injury">spinal cord injury</a>) is an individual property, &quot;disability&quot; is something created by external societal factors such as a lack of accessibility.<sup><span>[</span>87<span>]</span></sup> This distinction between the individual property of impairment and the social property of disability is central to the <a href="https://en.wikipedia.org/wiki/Social_model_of_disability">social model</a>. The term &quot;disabled people&quot; as a political construction is also widely used by international organizations of disabled people, such as <a href="https://en.wikipedia.org/wiki/Disabled_Peoples%27_International">Disabled Peoples&#39; International</a>. Using the identity-first language also parallels how people talk about other aspects of identity and diversity. For example:<sup><span>[</span>88<span>]</span></sup> </p><blockquote><p>In the autism community, many self-advocates and their allies prefer terminology such as &#39;Autistic,&#39; &#39;Autistic person,&#39; or &#39;Autistic individual&#39; because we understand autism as an inherent part of an individual&#39;s identity – the same way one refers to &#39;Muslims,&#39; &#39;African-Americans,&#39; &#39;Lesbian/Gay/Bisexual/Transgender/Queer,&#39; &#39;Chinese,&#39; &#39;gifted,&#39; &#39;athletic,&#39; or &#39;Jewish.&#39;</p></blockquote><p>Similarly, <a href="https://en.wikipedia.org/wiki/Deaf_culture">Deaf communities</a> in the US reject people-first language in favor of identity-first language.<sup><span>[</span>89<span>]</span></sup> In 2021, the US <a href="https://en.wikipedia.org/w/index.php?title=Association_on_Higher_Education_and_Disability&amp;action=edit&amp;redlink=1">Association on Higher Education and Disability</a> (AHEAD) announced their decision to use identity-first language in their materials, explaining: &quot;Identity-first language challenges negative connotations by claiming disability directly. Identity-first language references the variety that exists in how our bodies and brains work with a myriad of conditions that exist, and the role of inaccessible or oppressive systems, structures, or environments in making someone disabled.&quot;<sup><span>[</span>90<span>]</span></sup> </p><div><h3>Neurodiversity</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=17"><span>edit</span></a><span>]</span></span></div><p>In the 2020s, the term &quot;<a href="https://en.wikipedia.org/wiki/Neurodiversity">neurodiversity</a>&quot; has been embraced by many adults with various neurological differences. In the original conceptualization, “neurodiversity” refers to the belief that &quot;no two brains or minds function in exactly the same way.&quot;<sup><span>[</span>91<span>]</span></sup> &quot;Neurodivergent&quot;, often contrasted with &quot;neurotypical&quot;, refers to a brain or mind that functions in a way that deviates from culturally normative expectations.<sup><span>[</span>92<span>]</span></sup> Neuroscientist Mo Costandi views terms like <i>neurotypical</i> and <i>neurodiversity</i> as not being of use in neuroscience, and that those terms are in no way valid.<sup><span>[</span>93<span>]</span></sup> </p><p>Many sources attribute the term neurodiversity as having first been seen in print in a 1991 chapter in a work by <a href="https://en.wikipedia.org/wiki/Judy_Singer">Judy Singer</a>, an Australian sociologist. In 2024, a group of autistic academics challenged this concept by suggesting that the term had evolved collectively since the mid-1990s, led primarily by autism self-advocates.<sup><span>[</span>94<span>]</span></sup> Like the <a href="https://en.wikipedia.org/wiki/Social_model_of_disability">social model of disability</a>, the neurodiversity movement, as a <a href="https://en.wikipedia.org/wiki/Civil_rights_movement">civil rights movement</a>, seeks to fight stigma associated with seeing neurological differences as a disability.<sup><span>[</span>95<span>]</span></sup> This conceptualization does not come without controversy, as some academics have challenged whether or not an extreme view of neurodiversity suggests that neurodevelopmental disorders &quot;are not disorders or illnesses at all.&quot;<sup><span>[</span>96<span>]</span></sup> </p><div><h3>Handicap</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=18"><span>edit</span></a><span>]</span></span></div><dl><dd>The term <i>handicap</i> derives from the medieval game <a href="https://en.wikipedia.org/wiki/Hand-in-cap">hand-in-cap</a>, in which two players trade possessions, and a third, neutral person judges the difference of value between the possessions.<sup><span>[</span>97<span>]</span></sup> The concept of a neutral person evening up the odds was extended to <a href="https://en.wikipedia.org/wiki/Handicap_(horse_racing)">handicap racing</a> in the mid-18th century, where horses carry different weights based on the umpire&#39;s estimation of what would make them run equally. In the early 20th century the word gained the additional meaning of describing a disability, in the sense that a person with a handicap was carrying a heavier burden than normal.<sup><span>[</span>98<span>]</span></sup> This concept, then, adds to the conception of disability as a burden, or individual problem, rather than a societal problem.<sup><span>[</span>99<span>]</span></sup> The UK government advises civil servants to avoid this term.<sup><span>[</span>100<span>]</span></sup></dd></dl><div><h3>Accessibility</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=19"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Taiwan_Accessibility.jpg"></a><figcaption>A sign in Taiwan showing a wheelchair accessibility ramp</figcaption></figure><dl><dd><a href="https://en.wikipedia.org/wiki/Accessibility">Accessibility</a> is the degree to which a product, service or environment is available for use to the people that need it. People with certain types of disabilities struggle to get equal access to some things in society. For example, a blind person cannot read printed <a href="https://en.wikipedia.org/wiki/Ballot">paper ballots</a>, and therefore does not have access to voting that requires paper ballots. Another example can be that a person in a wheelchair cannot ascend stairs and therefore does not have access to buildings without ramps. Accessible access to health clubs and fitness centers has been observed to be especially problematic.<sup><span>[</span>101<span>]</span></sup><sup><span>[</span>102<span>]</span></sup></dd></dl><div><h3>Accommodation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=20"><span>edit</span></a><span>]</span></span></div><dl><dd>A change that improves access. For example, if voting ballots are available in <a href="https://en.wikipedia.org/wiki/Braille">braille</a> or on a <a href="https://en.wikipedia.org/wiki/Text_to_Speech">text-to-speech</a> machine, or if another person reads the ballot to the blind person and recorded the choices, then the blind person would have access to voting.</dd></dl><div><h3>Invisible disability</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=21"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Invisible_disability">Invisible disability</a></div><p>Invisible disabilities, also known as hidden disabilities or non-visible disabilities (NVD), are disabilities that are not immediately apparent, or seeable. They are often <a href="https://en.wikipedia.org/wiki/Chronic_illnesses">chronic illnesses</a> and conditions that significantly impair normal activities of daily living. Invisible disabilities can hinder a person&#39;s efforts to go to school, work, socialize, and more. Some examples of invisible disabilities include <a href="https://en.wikipedia.org/wiki/Intellectual_disabilities">intellectual disabilities</a>, <a href="https://en.wikipedia.org/wiki/Autism_spectrum_disorder">autism spectrum disorder</a>, <a href="https://en.wikipedia.org/wiki/Attention_deficit_hyperactivity_disorder">attention deficit hyperactivity disorder</a>, <a href="https://en.wikipedia.org/wiki/Fibromyalgia">fibromyalgia</a>, <a href="https://en.wikipedia.org/wiki/Mental_disorder">mental disorders</a>, <a href="https://en.wikipedia.org/wiki/Asthma">asthma</a>, <a href="https://en.wikipedia.org/wiki/Epilepsy">epilepsy</a>, <a href="https://en.wikipedia.org/wiki/Allergies">allergies</a>, <a href="https://en.wikipedia.org/wiki/Migraine">migraines</a>, <a href="https://en.wikipedia.org/wiki/Arthritis">arthritis</a>, and <a href="https://en.wikipedia.org/wiki/Chronic_fatigue_syndrome">chronic fatigue syndrome</a>.<sup><span>[</span>103<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Employment_discrimination">Employment discrimination</a> is reported to play a significant part in the high rate of <a href="https://en.wikipedia.org/wiki/Unemployment">unemployment</a> among those with a diagnosis of mental illness.<sup><span>[</span>104<span>]</span></sup> </p><div><h3>Episodic disability</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=22"><span>edit</span></a><span>]</span></span></div><p>People with health conditions such as <a href="https://en.wikipedia.org/wiki/Arthritis">arthritis</a>, <a href="https://en.wikipedia.org/wiki/Bipolar_disorder">bipolar disorder</a>, <a href="https://en.wikipedia.org/wiki/HIV">HIV</a>, or <a href="https://en.wikipedia.org/wiki/Multiple_sclerosis">multiple sclerosis</a> may have periods of wellness between episodes of illness. During the illness episodes people&#39;s ability to perform normal tasks, such as work, can be intermittent.<sup><span>[</span>105<span>]</span></sup> </p><div><h2>Disability activism</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=23"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Museum_of_disABILITY_History_Buffalo_NY.jpg"></a><figcaption>Museum of disABILITY History, <a href="https://en.wikipedia.org/wiki/Buffalo,_New_York">Buffalo, New York</a></figcaption></figure><figure><a href="https://en.wikipedia.org/wiki/File:Autism_spectrum_infinity_awareness_symbol.svg"></a><figcaption>Disability activists have drawn attention to several issues. Disability activism itself has led to the revision of appropriate language, when discussing disability and disabled people. For example, the medical classification of &quot;retarded&quot; has since been disregarded due to its negative implications. Moreover, disability activism has also led to pejorative language being reclaimed by disabled people. Mairs (1986) explained how disabled people may choose to self-describe themselves as a &quot;cripple&quot;. This may appear surprising that they are using stereotypically negative language associated with disability to describe themselves; however, the purpose is to reclaim the &quot;disabled identity&quot; from medical professionals, and realign it with the preferred language of disabled people. The reclamation of language demonstrated above positions itself within the social model, as it highlights how as a society we construct concepts and perceptions of disability.<sup><span>[</span>106<span>]</span></sup> The rainbow-colored <a href="https://en.wikipedia.org/wiki/Infinity">infinity</a> symbol represents the diversity of the autism spectrum as well as the greater <a href="https://en.wikipedia.org/wiki/Neurodiversity">neurodiversity</a> movement.<sup><span>[</span>107<span>]</span></sup></figcaption></figure><div><h3>Rights and policies</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=24"><span>edit</span></a><span>]</span></span></div><div><h4>Rights movement</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=25"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Disability_rights_movement">Disability rights movement</a></div><p>The disability rights movement aims to secure equal opportunities and equal rights for disabled people. The specific goals and demands of the movement are <a href="https://en.wikipedia.org/wiki/Accessibility">accessibility</a> and <a href="https://en.wikipedia.org/wiki/Safety">safety</a> in transportation, architecture, and the physical environment; equal opportunities in <a href="https://en.wikipedia.org/wiki/Independent_living">independent living</a>, employment, education, and housing; and freedom from abuse, neglect, and violations of <a href="https://en.wikipedia.org/wiki/Patients%27_rights">patients&#39; rights</a>.<sup><span>[</span>108<span>]</span></sup> Effective civil rights legislation is sought to secure these opportunities and rights.<sup><span>[</span>108<span>]</span></sup><sup><span>[</span>109<span>]</span></sup><sup><span>[</span>110<span>]</span></sup> </p><p>The early disability rights movement was dominated by the medical model of disability, where emphasis was placed on curing or treating disabled people so that they would adhere to the social norm, but starting in the 1960s, rights groups began shifting to the social model of disability, where disability is interpreted as an issue of discrimination, thereby paving the way for rights groups to achieve equality through legal means.<sup><span>[</span>111<span>]</span></sup> Advocacy for disability issues and accessibility in the republics of the former Soviet Union has become more organized and influential in policymaking.<sup><span>[</span>112<span>]</span></sup> </p><div><h4>Disability Justice movement</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=26"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Disability_justice">Disability Justice</a></div><p>Evolving from the disability rights movement is the Disability Justice movement. The term &quot;Disability Justice&quot; was coined in 2005 by <a href="https://en.wikipedia.org/wiki/LGBTQ">LGBTQ</a> disabled women of color <a href="https://en.wikipedia.org/wiki/Mia_Mingus">Mia Mingus</a>, <a href="https://en.wikipedia.org/wiki/Patricia_Berne">Patricia Berne</a>, and <a href="https://en.wikipedia.org/wiki/Stacey_Milbern">Stacey Milbern</a>, who sought to build an anti-ableist movement with a larger emphasis on <a href="https://en.wikipedia.org/wiki/Intersectionality">intersectionality</a> than mainstream disability rights, as to center marginalized voices. Their group, the Disability Justice Collective, also included notable disability activists such as Sebastian Margaret; <a href="https://en.wikipedia.org/wiki/Leroy_F._Moore_Jr.">Leroy F. Moore Jr.</a>, well known for his poetry and founding of the <a href="https://en.wikipedia.org/wiki/Krip_Hop">Krip Hop</a> movement; and <a href="https://en.wikipedia.org/wiki/Eli_Clare">Eli Clare</a>, well known for popularizing the <a href="https://en.wikipedia.org/wiki/Bodymind">bodymind</a> concept within disability studies. The Disability Justice movement aims to improve the lives of disabled people through prioritizing collective liberation, as opposed to prioritizing legislative change and traditional civil rights. This framework, dubbed the &quot;second wave&quot; of disability rights, seeks to examine the many systems of oppression that are intertwined with ableism, such as colonialism, <a href="https://en.wikipedia.org/wiki/White_supremacy">white supremacy</a>, and heteropatriarchal capitalism.<sup><span>[</span>113<span>]</span></sup> </p><div><h4>Convention on the Rights of Persons with Disabilities</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=27"><span>edit</span></a><span>]</span></span></div><p>On December 13, 2006, the <a href="https://en.wikipedia.org/wiki/United_Nations">United Nations</a> formally agreed on the <a href="https://en.wikipedia.org/wiki/Convention_on_the_Rights_of_Persons_with_Disabilities">Convention on the Rights of Persons with Disabilities</a>, the first human rights treaty of the 21st century, to protect and enhance the rights and opportunities of the world&#39;s estimated 650 million disabled people.<sup><span>[</span>114<span>]</span></sup> As of December 2025<sup><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit">[update]</a></sup>, 193 nations have ratified or accepted accession to the convention.<sup><span>[</span>115<span>]</span></sup> Countries that sign the convention are required to adopt national laws, and remove old ones, so that persons with disabilities will, for example, have equal rights to education, employment, and cultural life; to the right to own and inherit property; to not be discriminated against in marriage, etc.; and to not be unwilling subjects in medical experiments. UN officials, including the High Commissioner for Human Rights, have characterized the bill as representing a paradigm shift in attitudes toward a more rights-based view of disability in line with the social model.<sup><span>[</span>114<span>]</span></sup> </p><div><h4>International Year of Disabled Persons</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=28"><span>edit</span></a><span>]</span></span></div><p>In 1976, the <a href="https://en.wikipedia.org/wiki/United_Nations">United Nations</a> began planning for its <a href="https://en.wikipedia.org/wiki/International_Year_of_Disabled_Persons">International Year of Disabled Persons</a> (1981),<sup><span>[</span>116<span>]</span></sup> later renamed the <a href="https://en.wikipedia.org/wiki/International_Year_of_Disabled_Persons">International Year of Disabled Persons</a>. Some disability activists used the Year to highlight various injustices, such as in Australia where beauty pageants were targeted in order to, in the words of activist Leslie Hall, &quot;challenge the notion of beauty&quot; and &quot;reject the charity ethic.<sup><span>[</span>117<span>]</span></sup> The UN Decade of Disabled Persons (1983–1993) featured a World Programme of Action Concerning Disabled Persons. In 1979, <a href="https://en.wikipedia.org/wiki/Frank_Bowe">Frank Bowe</a> was the only person with a disability representing any country in the planning of IYDP-1981. Today, many countries have named representatives who are themselves individuals with disabilities. The decade was closed in an address before the General Assembly by <a href="https://en.wikipedia.org/wiki/Robert_Davila">Robert Davila</a>. Both Bowe and Davila are <a href="https://en.wikipedia.org/wiki/Deaf">deaf</a>. In 1984, <a href="https://en.wikipedia.org/wiki/UNESCO">UNESCO</a> accepted <a href="https://en.wikipedia.org/wiki/Sign_language">sign language</a> for use in the education of deaf children and youth. </p><div><h4>Policies in former Soviet Union republics</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=29"><span>edit</span></a><span>]</span></span></div><p>UN programs and OSCE work to align policy and programs in countries that were part of the former Soviet Union with the <a href="https://en.wikipedia.org/wiki/Convention_on_the_Rights_of_Persons_with_Disabilities">Convention on the Rights of Persons with Disabilities</a>.<sup><span>[</span>118<span>]</span></sup> </p><div><h3>Political issues</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=30"><span>edit</span></a><span>]</span></span></div><div>See also: <a href="https://en.wikipedia.org/wiki/Ableism">Ableism</a></div><figure><a href="https://en.wikipedia.org/wiki/File:USMC-00772.jpg"></a><figcaption>A 28-year-old Iraqi woman who lost both of her legs during the <a href="https://en.wikipedia.org/wiki/Iraq_War">Iraq War</a> in 2005</figcaption></figure><p><a href="https://en.wikipedia.org/wiki/Political_rights">Political rights</a>, <a href="https://en.wikipedia.org/wiki/Social_inclusion">social inclusion</a> and <a href="https://en.wikipedia.org/wiki/Citizenship">citizenship</a> have come to the fore in developed and some developing countries.<sup><span>[</span>119<span>]</span></sup><sup><span>[</span>120<span>]</span></sup> The debate has, some instances, moved beyond a concern about the perceived cost of maintaining dependent disabled people to finding effective ways to ensure that disabled people can participate in and contribute to society in all spheres of life.<sup><span>[</span>121<span>]</span></sup><sup><span>[</span>122<span>]</span></sup> </p><p>In developing nations, where the vast bulk of the estimated 650 million disabled people reside, a great deal of work is needed to address concerns ranging from accessibility and education to self-empowerment, self-supporting employment, and beyond.<sup><span>[</span>123<span>]</span></sup> Into the 21st century, the efforts of disability rights activists around the world who focused on obtaining full citizenship for disabled people have come under academic study and gained some level of public recognition in many places, such as in the United States.<sup><span>[</span>124<span>]</span></sup><sup><span>[</span>125<span>]</span></sup> There are obstacles in many countries in getting full employment and public perception of disabled people varies.<sup><span>[</span>126<span>]</span></sup> </p><div><h4>Abuse</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=31"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Disability_abuse">Disability abuse</a></div><p>Disability abuse happens when a person is abused physically, financially, verbally or mentally due to the person having a disability. As many disabilities are not visible (for example, asthma, learning disabilities) some abusers cannot rationalize the non-physical disability with a need for understanding, support, and so on.<sup><span>[</span>127<span>]</span></sup><sup><span>[</span>128<span>]</span></sup> As the prevalence of disability and the cost of supporting disability increases with medical advancement and longevity in general, this aspect of society becomes of greater political importance. How political parties treat their disabled constituents may become a measure of a political party&#39;s understanding of disability, particularly in the social model of disability.<sup><span>[</span>129<span>]</span></sup> </p><div><h4>Insurance</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=32"><span>edit</span></a><span>]</span></span></div><p>Disability benefit, or <a href="https://en.wikipedia.org/wiki/Disability_pension">disability pension</a>, is a major kind of <a href="https://en.wikipedia.org/wiki/Disability_insurance">disability insurance</a> that is provided by government agencies to people who are temporarily or permanently unable to work due to a disability. In the US, the disability benefit is provided in the category of <a href="https://en.wikipedia.org/wiki/Supplemental_Security_Income">Supplemental Security Income</a>. In Canada, it is within the <a href="https://en.wikipedia.org/wiki/Canada_Pension_Plan">Canada Pension Plan</a>.<sup><span>[</span>130<span>]</span></sup> Following a long nationwide campaign involving hundreds of thousands of people the <a href="https://en.wikipedia.org/wiki/National_Disability_Insurance_Scheme">National Disability Insurance Scheme</a> was introduced in Australia in 2013 to fund a number of supports.In other countries, disability benefits may be provided under <a href="https://en.wikipedia.org/wiki/Social_security">social security</a> systems.<sup><span>[</span>131<span>]</span></sup> Costs of disability pensions are steadily growing in Western countries, mainly in Europe and the United States. It was reported that, in the UK, expenditure on disability pensions accounted for 0.9% of <a href="https://en.wikipedia.org/wiki/Gross_domestic_product">gross domestic product</a> (GDP) in 1980; two decades later it had reached 2.6% of GDP.<sup><span>[</span>128<span>]</span></sup><sup><span>[</span>132<span>]</span></sup> Several studies have reported a link between increased absence from work due to sickness and elevated risk of future disability pension.<sup><span>[</span>133<span>]</span></sup> </p><p>A study by researchers in Denmark suggests that information on self-reported days of absence due to sickness can be used to effectively identify future potential groups for disability pension.<sup><span>[</span>132<span>]</span></sup> These studies may provide useful information for policymakers, case managing authorities, employers, and physicians. In Switzerland, social policies in the field of disability have been significantly reshaped over the last two decades by reducing the number of allowances awarded and by increasing the recourse to vocational rehabilitation measures. Drawing on interviews conducted with individuals who have been involved in programs set up by Swiss disability insurance, a study highlights their uncertainties and concerns relating to their place in society, as well as their reactions to disability insurance&#39;s interventions.<sup><span>[</span>134<span>]</span></sup><sup><span>[</span>135<span>]</span></sup> Private, for-profit disability insurance plays a role in providing incomes to disabled people, but the nationalized programs are the safety net that catch most claimants. </p><div><h4>Employment</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=33"><span>edit</span></a><span>]</span></span></div><p>Studies have illustrated a correlation between <a href="https://en.wikipedia.org/wiki/Disability_and_poverty">disability and poverty</a>. Notably, jobs offered to disabled people are scarce. Marta Russell notes that &quot;[a] primary basis for oppression of disabled persons (those who could work with accommodations) is their exclusion from exploitation as wage laborers.&quot;<sup><span>[</span>136<span>]</span></sup> </p><div><h5>Intellectual disability</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=34"><span>edit</span></a><span>]</span></span></div><p>Many countries have programs which aid <a href="https://en.wikipedia.org/wiki/Intellectual_disabled">intellectually disabled</a> (ID) people to acquire skills needed in the workforce.<sup><span>[</span>137<span>]</span></sup> Such programs include sheltered workshops and adult day care programs. Sheltered programs consist of daytime activities such as gardening, manufacturing, and assembling. These activities facilitate routine-oriented tasks that in turn allow ID people to gain experience before entering the workforce. Similarly, adult day care programs also include day time activities; however, these activities are based in an educational environment where ID people are able to engage in educational, physical, and communication-based tasks which helps facilitate communication, memory, and general living skills. In addition, adult day care programs arranged community activities by scheduling field trips to public places (e.g. zoos and movie theaters). Despite both programs providing essential skills for intellectually disabled people prior to entering the workforce, researchers have found that ID people prefer to be involved with <a href="https://en.wikipedia.org/wiki/Community_integration">community-integrated employment</a>.<sup><span>[</span>137<span>]</span></sup> Community-integrated employment opportunities are offered to ID people at minimum or higher wages in a variety of occupations ranging from customer service, clerical, janitorial, hospitality, and manufacturing positions. ID employees work alongside employees without disabilities who are able to assist them with training. All three options allow intellectually disabled people to develop and exercise social skills that are vital to everyday life; however, it is not guaranteed that ID employees receive the same treatment as employees without ID; according to Lindstrom et al., community-integrated employees are less likely to receive raises, and only 26% are able to retain full-time status.<sup><span>[</span>138<span>]</span></sup> </p><p>Finding a stable workforce poses additional challenges. A study published in the <i>Journal of Applied Research in Intellectual Disability</i> indicated that although finding a job may be difficult, stabilizing a job is even harder.<sup><span>[</span>139<span>]</span></sup> Chadsey-Rusch proposed that securing employment for ID people requires adequate production skills and effective social skills.<sup><span>[</span>139<span>]</span></sup> Other underlying factors for job loss include structural factors and worker-workplace integration. As stated by Kilsby, limited structural factors can affect a multitude of factors in a job, such as a restricted number of hours an ID person is allowed to work. This in return, according to Fabian et al., leads to a lack of opportunity to develop relationships with coworkers or to better integrate within the workplace. Nevertheless, those who are unable to stabilize a job often are left discouraged. According to the same study conducted by JARID, many who had participated found that they had made smaller incomes when compared to their co-workers, had an excess of time throughout their days because they did not have work. This renders ID people unable to provide for themselves, including basic necessities such as food, medical care, transportation, and housing. They also had feelings of hopelessness and failure. According to the US National Organization on Disability, not only ID people face constant discouragement but many live below the poverty line because they are unable to find or stabilize employment and because of employee restricting factors placed on ID workers.<sup><span>[</span>138<span>]</span></sup> </p><div><h4>Poverty</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=35"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Disability_and_poverty">Disability and poverty</a></div><figure><a href="https://en.wikipedia.org/wiki/File:Pieter_Bruegel_the_Elder_-_The_Beggars_(1568).jpg"></a><figcaption><i><a href="https://en.wikipedia.org/wiki/The_Beggars">The Cripples</a></i>, <a href="https://en.wikipedia.org/wiki/Pieter_Bruegel_the_Elder">Pieter Bruegel</a>, 1568</figcaption></figure><p>The poverty rate for working-age people with disabilities is nearly two and a half times higher than that for people without disabilities. Disability and poverty may form a vicious circle, in which physical barriers and stigma of disability make it more difficult to get income, which in turn diminishes access to health care and other necessities for a healthy life.<sup><span>[</span>140<span>]</span></sup> In societies without state funded health and social services, living with a disability could require spending on medication and frequent health care visits, in-home personal assistance, and adaptive devices and clothing, along with the usual costs of living. The <a href="https://en.wikipedia.org/wiki/World_report_on_disability">World report on disability</a> indicates that half of all disabled people cannot afford health care, compared to a third of abled people.<sup><span>[</span>141<span>]</span></sup> In countries without public services for adults with disabilities, their families may be impoverished.<sup><span>[</span>142<span>]</span></sup> </p><div><h4>Disasters</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=36"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Disability_and_disasters">Disability and disasters</a></div><p>There is limited research knowledge, but many anecdotal reports, on what happens when disasters impact disabled people.<sup><span>[</span>143<span>]</span></sup><sup><span>[</span>144<span>]</span></sup> Individuals with disabilities are greatly affected by disasters.<sup><span>[</span>143<span>]</span></sup><sup><span>[</span>145<span>]</span></sup> Those with physical disabilities can be at risk when evacuating if assistance is not available. Individuals with <a href="https://en.wikipedia.org/wiki/Cognitive_impairments">cognitive impairments</a> may struggle with understanding instructions that must be followed in the event a disaster occurs.<sup><span>[</span>145<span>]</span></sup><sup><span>[</span>146<span>]</span></sup><sup><span>[</span>147<span>]</span></sup> All of these factors can increase the degree of variation of risk in disaster situations with disabled individuals.<sup><span>[</span>148<span>]</span></sup> Research studies have consistently found discrimination against individuals with disabilities during all phases of a disaster cycle.<sup><span>[</span>143<span>]</span></sup> The most common limitation is that people cannot physically access buildings or <a href="https://en.wikipedia.org/wiki/Transportation">transportation</a>, as well as access disaster-related services.<sup><span>[</span>143<span>]</span></sup> The exclusion of these individuals is caused in part by the lack of disability-related training provided to emergency planners and <a href="https://en.wikipedia.org/wiki/Disaster_relief">disaster relief</a> personnel.<sup><span>[</span>149<span>]</span></sup> </p><div><h2>Disability in society</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=37"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Disability_Rights_protest.jpg"></a><figcaption>Protest for the recognition of Irish Sign Language</figcaption></figure><div>See also: <a href="https://en.wikipedia.org/wiki/Ableism">Ableism</a> and <a href="https://en.wikipedia.org/wiki/Epistemic_injustice">Epistemic injustice</a></div><div><h3>Aging</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=38"><span>edit</span></a><span>]</span></span></div><p>To a certain degree, physical impairments and changing mental states are almost ubiquitously experienced by people as they age. Aging populations are often stigmatized for having a high prevalence of disability. <a href="https://en.wikipedia.org/wiki/Kathleen_Woodward">Kathleen Woodward</a>, writing in <i>Key Words for Disability Studies</i>, explains the phenomenon as follows: </p><blockquote><p>Aging is invoked rhetorically – at times ominously – as a pressing reason why disability should be of crucial interest to all of us (we are all getting older, we will all be disabled eventually), thereby inadvertently reinforcing the damaging and dominant stereotype of aging as solely an experience of decline and deterioration. But little attention has been given to the imbrication of aging and disability.<sup><span>[</span>150<span>]</span></sup></p></blockquote><p>In <i>Feminist, Queer, Crip</i>, <a href="https://en.wikipedia.org/wiki/Alison_Kafer">Alison Kafer</a> mentions aging and the anxiety associated with it. According to Kafer, this anxiety stems from ideas of normalcy. She says: </p><blockquote><p>Anxiety about aging, for example, can be seen as a symptom of compulsory able-bodiedness/able-mindedness, as can attempts to &quot;treat&quot; children who are slightly shorter than average with growth hormones; in neither case are the people involved necessarily disabled, but they are certainly affected by cultural ideals of normalcy and ideal form and function.<sup><span>[</span>151<span>]</span></sup></p></blockquote><div><h3>Societal norms</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=39"><span>edit</span></a><span>]</span></span></div><p>In contexts where their differences are visible, persons with disabilities often face <a href="https://en.wikipedia.org/wiki/Social_stigma">stigma</a>. People frequently react to disabled presence with fear, pity, patronization, intrusive gazes, <a href="https://en.wikipedia.org/wiki/Disgust">revulsion</a>, or disregard. These reactions can, and often do, exclude persons with disabilities from accessing social spaces along with the benefits and resources these spaces provide.<sup><span>[</span>152<span>]</span></sup> Disabled writer/researcher Jenny Morris describes how stigma functions to marginalize persons with disabilities:<sup><span>[</span>153<span>]</span></sup> </p><blockquote><p>Going out in public so often takes courage. How many of us find that we can&#39;t dredge up the strength to do it day after day, week after week, year after year, a lifetime of rejection and revulsion? It is not only physical limitations that restrict us to our homes and those whom we know. It is the knowledge that each entry into the public world will be dominated by stares, by condescension, by pity, and by hostility.</p></blockquote><p>Additionally, facing stigma can cause harm to the psycho-emotional well-being of the person being stigmatized. One of the ways in which the psycho-emotional health of persons with disabilities is adversely affected is through the internalization of the oppression they experience, which can lead to feeling that they are weak, crazy, worthless or any number of other negative attributes that may be associated with their conditions. Internalization of oppression damages the self-esteem of the person affected and shapes their behaviors in ways that are compliant with dominance of those with no acknowledged disability.<sup><span>[</span>152<span>]</span></sup> Ableist ideas are frequently internalized when disabled people are pressured by the people and institutions around them to hide and downplay their disabled difference, or &quot;pass&quot;. The media play a significant role in creating and reinforcing stigma associated with disability. Media portrayals of disability usually cast disabled presence as necessarily <a href="https://en.wikipedia.org/wiki/Social_exclusion">marginal</a> within society at large. These portrayals simultaneously reflect and influence the popular perception of disabled difference. According to writer Simi Linton, the act of passing takes a deep emotional toll by causing disabled individuals to experience loss of community, anxiety and self-doubt.<sup><span>[</span>154<span>]</span></sup> </p><div><h4>Tropes</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=40"><span>edit</span></a><span>]</span></span></div><div>Further information: <a href="https://en.wikipedia.org/wiki/Disability_in_the_media">Disability in the media</a></div><p>There are distinct tactics that the media frequently employ in representing disability. These common ways of framing disability are heavily criticized for being dehumanizing and failing to place importance on the perspectives of persons with disabilities. As outlined by <a href="https://en.wikipedia.org/wiki/Disability_studies">disability theorist</a> and <a href="https://en.wikipedia.org/wiki/Rhetoric">rhetorician</a> <a href="https://en.wikipedia.org/wiki/Jay_Timothy_Dolmage">Jay Timothy Dolmage</a>, ableist media tropes can reflect and continue to perpetuate societal myths about disabled people.<sup><span>[</span>155<span>]</span></sup> </p><div><h5>Inspiration porn</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=41"><span>edit</span></a><span>]</span></span></div><p><a href="https://en.wikipedia.org/wiki/Inspiration_porn">Inspiration porn</a> refers to portrayals of persons with disabilities in which they are presented as being inspiring simply because the person has a disability. These portrayals are criticized because they are created with the intent of making viewers with no acknowledged disability feel better about themselves in comparison to the individual portrayed. Rather than recognizing the humanity of persons with disabilities, inspiration porn turns them into objects of inspiration for an audience composed of those with no acknowledged disability.<sup><span>[</span>156<span>]</span></sup> </p><div><h5>Supercrip</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=42"><span>edit</span></a><span>]</span></span></div><p>The supercrip trope refers to instances when the media reports on or portray a disabled person who has made a noteworthy achievement but centers on their disability rather than what they actually did. They are portrayed as awe-inspiring for being exceptional compared to others with the same or similar conditions. This trope is widely used in reporting on disabled athletes as well as in portrayals of autistic savants.<sup><span>[</span>157<span>]</span></sup><sup><span>[</span>158<span>]</span></sup> These representations, notes disability scholar Ria Cheyne, &quot;are widely assumed to be inherently regressive&quot;,<sup><span>[</span>159<span>]</span></sup> reducing people to their condition rather than viewing them as full people. Furthermore, supercrip portrayals are criticized for creating the unrealistic expectation that disability should be accompanied by some type of special talent, genius, or insight.<sup><span>[</span>160<span>]</span></sup> </p><p>Examples of this trope in the media include Dr. <a href="https://en.wikipedia.org/wiki/Shaun_Murphy_(The_Good_Doctor)">Shaun Murphy</a> from <i><a href="https://en.wikipedia.org/wiki/The_Good_Doctor_(American_TV_series)">The Good Doctor</a></i>, Marvel&#39;s <a href="https://en.wikipedia.org/wiki/Daredevil_(Marvel_Comics_character)">Daredevil</a>, and others. Scholar <a href="https://en.wikipedia.org/wiki/Sami_Schalk">Sami Schalk</a> argues that the term supercrip has a narrow definition given how widely used the term is. As a result, Schlak provides three categories of supercrip narratives used:<sup><span>[</span>160<span>]</span></sup> </p><ol><li>The regular supercrip narrative in which a disabled person gains regulation for completing mundane tacts. This is commonly seen as a disabled person being able to accomplish something despite their disability.</li> <li>The glorified supercrip narrative in which a disabled person is praised for succeeding at something even a non-disabled person would not be able to do. This narrative form is commonly used to talk about disabled <a href="https://en.wikipedia.org/wiki/Paralympic_sports">Paralympic athletes</a>.</li> <li>The superpowered supercrip narrative which appears in functionalized representations of disabled characters. Characters of this narrative type gain superpowers due to their disability. Common examples of this narrative form in action are prosthetics limbs that make one more powerful than expected or have futuristic technology that makes one a <a href="https://en.wikipedia.org/wiki/Cyborg">cyborg</a>.<sup><span>[</span>160<span>]</span></sup></li></ol><div><h5>Disabled villain</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=43"><span>edit</span></a><span>]</span></span></div><p>Characters in fiction that bear physical or mental markers of difference from perceived societal norms are frequently positioned as villains within a text. Lindsey Row-Heyveld shares ways students should be taught to begin to further analyze this issue.<sup><span>[</span>161<span>]</span></sup> Disabled people&#39;s visible differences from the abled majority are meant to evoke fear in audiences that can perpetuate the mindset of disabled people being a threat to individual or public interests and well-being. </p><div><h5>Disability drop</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=44"><span>edit</span></a><span>]</span></span></div><p>The &quot;disability drop&quot; <a href="https://en.wikipedia.org/wiki/Trope_(literature)">trope</a> is when a supposedly disabled character is revealed to have been faking, embellishing, or otherwise not actually embodying their claimed disability. <a href="https://en.wikipedia.org/wiki/Jay_Dolmage">Jay Dolmage</a> offers <a href="https://en.wikipedia.org/wiki/Kevin_Spacey">Kevin Spacey</a>&#39;s character, Verbal Kint, in the film <i><a href="https://en.wikipedia.org/wiki/Usual_Suspects">Usual Suspects</a></i> as an example of this, and depictions like this can reflect able-bodied society&#39;s mistrust of disabled people.<sup><span>[</span>155<span>]</span></sup> In addition, this reveal of a character&#39;s nondisabledness often serves as the narrative climax of a story, and the use of disability as a source of conflict in the plot, narrative obstacle, or a device of characterization aligns with other disability studies scholars&#39; theory of &quot;Narrative <a href="https://en.wikipedia.org/wiki/Prosthesis">Prosthesis</a>&quot;, a term coined by David T. Mitchell and Sharon Snyder.<sup><span>[</span>162<span>]</span></sup> </p><div><h5>Disabled victim</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=45"><span>edit</span></a><span>]</span></span></div><p>Another frequent occurrence is when someone with a disability is assumed to be miserable or helpless.<sup><span>[</span>163<span>]</span></sup> <i><a href="https://en.wikipedia.org/wiki/The_Hunchback_of_Notre_Dame_(1996_film)">The Hunchback of Notre Dame&#39;s</a></i> <a href="https://en.wikipedia.org/wiki/Quasimodo">Quasimodo</a>, <i><a href="https://en.wikipedia.org/wiki/The_Elephant_Man_(1980_film)">The Elephant Man&#39;s</a></i> <a href="https://en.wikipedia.org/wiki/Joseph_Merrick">John Merrick</a>, <i><a href="https://en.wikipedia.org/wiki/A_Christmas_Carol_(2009_film)">A Christmas Carol&#39;s</a></i> <a href="https://en.wikipedia.org/wiki/Tiny_Tim_(A_Christmas_Carol)">Tiny Tim</a>, and even news broadcasts that refer to people as &quot;victims&quot; or &quot;sufferers&quot; are a few examples of this stereotype.<sup><span>[</span>164<span>]</span></sup> </p><div><h5>Eternally innocent</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=46"><span>edit</span></a><span>]</span></span></div><p>Characters with disabilities are frequently portrayed in movies as being angelic or childish. These films include <i><a href="https://en.wikipedia.org/wiki/Rain_Man">Rain Man</a></i> (1988), <i><a href="https://en.wikipedia.org/wiki/Forrest_Gump">Forrest Gump</a></i> (1994) and <i><a href="https://en.wikipedia.org/wiki/I_Am_Sam">I Am Sam</a></i> (2001).<sup><span>[</span>165<span>]</span></sup><sup><span>[</span>166<span>]</span></sup> The innocent and endearing person with a disability often points out the inadequacies of their &quot;normal&quot; adult peers, which helps them achieve salvation.<sup><span>[</span>165<span>]</span></sup><sup><span>[</span>167<span>]</span></sup> Like all the others, this stereotype perpetuates patronizing perceptions that are simply untrue and are therefore damaging.<sup><span>[</span>168<span>]</span></sup> While there are many disability tropes, disability aesthetics attempts to dispel them by accurately depicting disabled bodies in art and media.<sup><span>[</span>169<span>]</span></sup> </p><div><h4>Self-advocacy</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=47"><span>edit</span></a><span>]</span></span></div><p>Some disabled people have attempted to resist <a href="https://en.wikipedia.org/wiki/Marginalization">marginalization</a> through the use of the social model in opposition to the medical model; with the aim of shifting criticism away from their bodies and impairments and towards the social institutions that oppress them relative to their abled peers. Disability activism that demands many grievances be addressed, such as lack of <a href="https://en.wikipedia.org/wiki/Accessibility">accessibility</a>, poor representation in media, general disrespect, and <a href="https://en.wikipedia.org/wiki/Ignorance">lack of recognition</a>, originates from a social model framework.<sup><span>[</span>170<span>]</span></sup> The creation of &quot;disability culture&quot; stemmed from the shared experience of stigmatization in broader society.<sup><span>[</span>171<span>]</span></sup> Embracing disability as a positive identity by becoming involved in disabled communities and participating in disability culture can be an effective way to combat internalized prejudice; and can challenge dominant narratives about disability.<sup><span>[</span>172<span>]</span></sup> </p><div><h4>Intersections</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=48"><span>edit</span></a><span>]</span></span></div><table><tbody><tr><td><span><a href="https://en.wikipedia.org/wiki/File:Wiki_letter_w_cropped.svg"></a></span></td><td><div>This section <b>needs expansion</b>. You can help by <a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=">adding missing information</a>. <span><i>(<span>February 2018</span>)</i></span></div></td></tr></tbody></table><figure><a href="https://en.wikipedia.org/wiki/File:Disabled_BIPOC_in_front_of_pride_flag.jpg"></a><figcaption>Three Black and disabled people in front of a <a href="https://en.wikipedia.org/wiki/Pride_flag">pride flag</a></figcaption></figure><p>The experiences that disabled people have to navigate social institutions vary greatly as a function of what other social categories they may belong to. For example, a disabled man and a disabled woman experience disability differently.<sup><span>[</span>173<span>]</span></sup> This speaks to the concept of <a href="https://en.wikipedia.org/wiki/Intersectionality">intersectionality</a>, which explains that different aspects of a person&#39;s identity (such as their gender, race, sexuality, religion, or social class) intersect and create unique experiences of oppression and privilege.<sup><span>[</span>174<span>]</span></sup> Many intersections exist. Disability is defined differently by each person; it may be visible or invisible, and multiple intersections often arise from overlapping identity categories. The United Nations <a href="https://en.wikipedia.org/wiki/Convention_on_the_Rights_of_Persons_with_Disabilities">Convention on the Rights of Persons with Disabilities</a> differentiates between a few kinds of disability intersections, such as the age-disability, race-disability, and gender-disability intersection.<sup><span>[</span>175<span>]</span></sup><sup><span>[</span>176<span>]</span></sup> </p><div><h5>Race</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=49"><span>edit</span></a><span>]</span></span></div><p>Incidence of disability is reported to be greater among several minority communities across the globe, according to a systematic analysis of the <a href="https://en.wikipedia.org/wiki/Global_Burden_of_Disease_Study">Global Burden of Disease Study</a>.<sup><span>[</span>177<span>]</span></sup> Disabled people who are also racial <a href="https://en.wikipedia.org/wiki/Minority_group">minorities</a> generally have less access to support and are more vulnerable to <a href="https://en.wikipedia.org/wiki/Police_brutality">violent discrimination.</a><sup><span>[</span>178<span>]</span></sup> A study in the journal <i>Child Development</i> indicated that minority disabled children are more likely to receive punitive discipline in low and middle income countries.<sup><span>[</span>179<span>]</span></sup> Due to the fact that children with disabilities are mistreated more often than those without disability; racialized children in this category are at an even higher risk.<sup><span>[</span>180<span>]</span></sup><sup><span>[</span>181<span>]</span></sup><sup><span>[</span>182<span>]</span></sup><sup><span>[</span>183<span>]</span></sup><sup><span>[</span>184<span>]</span></sup> With respect to <a href="https://en.wikipedia.org/wiki/Disability_in_the_United_States">disability in the United States</a>, Camille A. Nelson, writing for the <i><a href="https://en.wikipedia.org/wiki/Berkeley_Journal_of_Criminal_Law">Berkeley Journal of Criminal Law</a></i>, notes the dual discrimination that racial minorities with disabilities experience from the criminal justice system, expressing that for &quot;people who are negatively racialized, that is people who are perceived as being non-white, and for whom mental illness is either known or assumed, interaction with police is precarious and potentially dangerous.&quot;<sup><span>[</span>185<span>]</span></sup> </p><div><h5>Gender</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=50"><span>edit</span></a><span>]</span></span></div><p>The marginalization of people with disabilities can leave persons with disabilities unable to actualize what society expects of gendered existence. This lack of recognition for their gender identity can leave persons with disabilities with feelings of inadequacy. Thomas J. Gerschick of <a href="https://en.wikipedia.org/wiki/Illinois_State_University">Illinois State University</a> describes why this denial of gendered identity occurs:<sup><span>[</span>186<span>]</span></sup> </p><blockquote><p>Bodies operate socially as canvases on which gender is displayed and kinesthetically as the mechanisms by which it is physically enacted. Thus, the bodies of people with disabilities make them vulnerable to being denied recognition as women and men.</p></blockquote><p>To the extent that women and men with disabilities are gendered, the interactions of these two identities lead to different experiences. Women with disabilities face a sort of &quot;double <a href="https://en.wikipedia.org/wiki/Social_stigma">stigmatization</a>&quot; in which their membership to both of these marginalized categories simultaneously exacerbates the negative stereotypes associated with each as they are ascribed to them. According to the framework of intersectionality, gender and disability intersect to create a unique experience that is not simply the coincidence of being a woman and having a disability separately, but the unique experience of being a woman with a disability. It follows that the more marginalized groups one belongs to, their experience of privilege or oppression changes: in short, a black woman and a white woman will experience disability differently.<sup><span>[</span>187<span>]</span></sup> </p><p>According to The UN Woman Watch, &quot;Persistence of certain cultural, legal and institutional barriers makes women and girls with disabilities the victims of two-fold discrimination: as women and as persons with disabilities.&quot;<sup><span>[</span>188<span>]</span></sup> As Rosemarie Garland-Thomson puts it, &quot;Women with disabilities, even more intensely than women in general, have been cast in the collective cultural imagination as inferior, lacking, excessive, incapable, unfit, and useless.&quot;<sup><span>[</span>189<span>]</span></sup> </p><div><h5>Socio-economic background</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=51"><span>edit</span></a><span>]</span></span></div><p>Similar to the intersections of race and disability or gender and disability, a person&#39;s socio-economic background will also change their experience of disability. A disabled person with a low socio-economic status will experience the world differently, with more obstacles and fewer opportunities, than a disabled person with a high socio-economic status.<sup><span>[</span>190<span>]</span></sup><sup><span>[</span>191<span>]</span></sup> A good example of the <a href="https://en.wikipedia.org/wiki/Socioeconomic_status_and_mental_health">intersection</a> between disability and <a href="https://en.wikipedia.org/wiki/Socioeconomic_status">socio-economic status</a> is access to education, as we know that there are direct links between poverty and disability,<sup><span>[</span>191<span>]</span></sup><sup><span>[</span>192<span>]</span></sup><sup><span>[</span>193<span>]</span></sup> often working in a vicious cycle.<sup><span>[</span>194<span>]</span></sup> The costs of special education and caring for a disabled child are higher than for a child with no acknowledged disability, which poses an immense barrier in accessing appropriate education.<sup><span>[</span>195<span>]</span></sup> The inaccessibility of appropriate education (at any stage), can lead to difficulties in finding employment, which often results in the vicious cycle of being &#39;bound&#39; by one&#39;s experience as a poor and disabled person to remain in the same social structure and experience socio-economic exclusion.<sup><span>[</span>196<span>]</span></sup><sup><span>[</span>197<span>]</span></sup> In short, this vicious cycle exacerbates the lack of <a href="https://en.wikipedia.org/wiki/Economic_capital">economic</a>, <a href="https://en.wikipedia.org/wiki/Social_capital">social</a>, and <a href="https://en.wikipedia.org/wiki/Cultural_capital">cultural capital</a> for disabled people with a low socio-economic background. On the other hand, a disabled person of a high socio-economic status, may have an easier time accessing appropriate (special) education or treatment - for example by having access to better aids, resources, or programmes that can help them succeed.<sup><span>[</span>198<span>]</span></sup><sup><span>[</span>199<span>]</span></sup> </p><div><h2>Disability culture</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=52"><span>edit</span></a><span>]</span></span></div><div><h3>Sport</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=53"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Disability_sports">Disability sports</a></div><figure><a href="https://en.wikipedia.org/wiki/File:Wheelchair_basketball_at_the_2008_Summer_Paralympics.jpg"></a><figcaption><a href="https://en.wikipedia.org/wiki/Wheelchair_basketball">Wheelchair basketball</a> match between South Africa and Iran at the <a href="https://en.wikipedia.org/wiki/Wheelchair_basketball_at_the_2008_Summer_Paralympics">2008 Summer Paralympics</a></figcaption></figure><p>The <a href="https://en.wikipedia.org/wiki/Paralympic_Games">Paralympic Games</a> (meaning &quot;alongside the Olympics&quot;) are held after the (<a href="https://en.wikipedia.org/wiki/Summer_Olympic_Games">Summer</a> and <a href="https://en.wikipedia.org/wiki/Winter_Olympic_Games">Winter</a>) <a href="https://en.wikipedia.org/wiki/Olympic_Games">Olympic Games</a>. The Paralympic Games include athletes with a wide range of physical disabilities. In member countries, organizations exist to organize competition in the Paralympic sports on levels ranging from recreational to elite (for example, <a href="https://en.wikipedia.org/wiki/Disabled_Sports_USA">Disabled Sports USA</a> and <a href="https://en.wikipedia.org/wiki/BlazeSports_America">BlazeSports America</a> in the United States). The Paralympics developed from a rehabilitation program for British war veterans with spinal injuries. In 1948, Sir Ludwig Guttman, a neurologist working with World War II veterans with spinal injuries at <a href="https://en.wikipedia.org/wiki/Stoke_Mandeville_Hospital">Stoke Mandeville Hospital</a> in <a href="https://en.wikipedia.org/wiki/Aylesbury">Aylesbury</a> in the UK, began using sport as part of the rehabilitation programs of his patients. In 2006, the <a href="https://en.wikipedia.org/w/index.php?title=Extremity_Games&amp;action=edit&amp;redlink=1">Extremity Games</a> were formed for physically disabled people, specifically limb loss or limb difference, to be able to compete in <a href="https://en.wikipedia.org/wiki/Extreme_sports">extreme sports</a>.<sup><span>[</span>200<span>]</span></sup> </p><div><h2>Demographics</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=54"><span>edit</span></a><span>]</span></span></div><p>Estimates of worldwide and country-wide numbers of disabled people are problematic. The varying approaches taken to defining disability notwithstanding, demographers agree that the world population of individuals with disabilities is very large. For example, in 2012, the <a href="https://en.wikipedia.org/wiki/World_Health_Organization">World Health Organization</a> estimated a world population of 6.5 billion people. Of those, nearly 650 million people, or 10%, were estimated to be moderately or severely disabled.<sup><span>[</span>201<span>]</span></sup> In 2018 the <a href="https://en.wikipedia.org/wiki/International_Labour_Organization">International Labour Organization</a> estimated that about a billion people, one-seventh of the world population, had disabilities, 80% of them in developing countries, and 80% of working age. Excluding disabled people from the workforce was reckoned to cost up to 7% of <a href="https://en.wikipedia.org/wiki/Gross_domestic_product">gross domestic product</a>.<sup><span>[</span>202<span>]</span></sup> </p><div><h3>United States</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=55"><span>edit</span></a><span>]</span></span></div><p>According to the <a href="https://en.wikipedia.org/wiki/Centers_for_Disease_Control_and_Prevention">Centers for Disease Control</a>&#39;s Morbidity and Mortality weekly report, one-fourth of people in the United States are reported to be disabled as of 2016. 10% of young adults were reported to have mental disabilities. The rates of mobility-related issues were highest among middle-aged people and elderly people, with 18.1% and 26.9%, respectively.<sup><span>[</span>203<span>]</span></sup> In terms of race or ethnicity, Asians have the lowest reported rate of disability at around 10%, while Native Americans, the ethnic group with the highest reported incidence, are reported to have a disability rate at an estimated 30% of adults. African Americans had a higher reported disability rate of 25%, compared to 16% for white adults and 17% for Hispanic people.<sup><span>[</span>204<span>]</span></sup> </p><div><h3>Canada</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=56"><span>edit</span></a><span>]</span></span></div><p>22.3% of Canadians over 15 are reported to have a disability, or 6,246,640 people, according to the 2017 Canadian Survey on Disability Reports. In Canada, women and older people are more likely to be disabled than working-class men. In comparison to working-age persons between 25 and 65, seniors over 65 reported a disability rate of 38%, which is nearly twice as high. In Canada, women over 15 had a reported disability rate of 24.3%, compared to men&#39;s 20%.<sup><span>[</span>205<span>]</span></sup> According to reports from the 2017 Canadian Survey of Disability, South Asians over the age of 15 in Canada had the greatest proportion of disability at 4%, while Latin Americans had a lower rate at 1%.<sup><span>[</span>206<span>]</span></sup> </p><div><h3>Australia</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=57"><span>edit</span></a><span>]</span></span></div><p>Nearly one in five Australians, or 4.4 million people, were estimated by the <a href="https://en.wikipedia.org/wiki/Australian_Bureau_of_Statistics">Australian Bureau of Statistics</a> to have a disability. A mental or behavioral issue was reported in over 25% of Australians with disabilities. Male prevalence was 17.6 million, while female prevalence was somewhat higher at 17.8 million between the sexes. Age-wise, 11.6% of adults between 0 and 64 in Australia had a disability, compared to 49.6% of seniors 65 and over. 53.4% of Australians aged 15 to 64 who have a disability are employed.<sup><span>[</span>207<span>]</span></sup> </p><div><h3>United Kingdom</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=58"><span>edit</span></a><span>]</span></span></div><p>According to the <a href="https://en.wikipedia.org/wiki/House_of_Commons_Library">House of Commons Library</a>, 14.6 million, or 22%, of the population in the UK, were reported to be disabled in 2020–2021. In the UK, there were 9% of children, 21% of working-age people, and 42% of persons over the state pension age who were disabled or impaired.<sup><span>[</span>208<span>]</span></sup> Approximately 29% of White individuals, 27% of mixed-race people, 22% of Asian people, 21% of Black people, and 19% of people from other ethnic groups were reported as having impairments or disabilities, according to the Life Opportunities Survey, which surveyed 35,875 people in 2011. When compared to men, women are a little more likely than men to have a disability, with 31% of women reportedly having one as opposed to 26% of men, according to results of another survey taken the same year.<sup><span>[</span>209<span>]</span></sup> </p><div><h3>China</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=59"><span>edit</span></a><span>]</span></span></div><p>According to Twenty-Year Trends in the Prevalence of Disability in China, a medical publication from the <a href="https://en.wikipedia.org/wiki/United_States_National_Library_of_Medicine">National Library of Medicine</a>, there were an estimated 84.6 million Chinese individuals living with a disability in 2006. In a 2006 poll of 83,342 men and 78,137 women, the age groups with the highest reported rates of disability are 18–44-year-old males (22.5%) and 65–74-year-old females (22.8%), according to polls published in the journal that were representative of the country as a whole. In China, the percentage of people with disabilities varies substantially between urban and rural regions, with men and women having reported rates of 72.4% and 72.2%, respectively, in rural China, compared to reported rates of 27.6% and 27.8%, respectively, in urban China. Hearing and speech disabilities are the most commonly reported in China, with men being more affected than women at rates 39.6% and 36.2% among disabled people, respectively.<sup><span>[</span>210<span>]</span></sup> </p><div><h3>South Korea</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=60"><span>edit</span></a><span>]</span></span></div><p>In South Korea, there were accounted to be 2.517 million people with disabilities in total, or roughly 5.0% of the population, in 2018. When compared to Koreans without disabilities, people with disabilities spent an average of 56.5 days in medical facilities, which was 2.6 more than the national average. 34.9% of the entire workforce was employed in jobs connected to disabilities. Families with disabilities made an average income of 41.53 million won, or 71.3% of total family earnings. According to the Korean 2020 Statistics on the Disabled The majority of persons with disabilities needed help with &quot;cleaning&quot; and &quot;using transportation&quot;, among other everyday tasks.<sup><span>[</span>211<span>]</span></sup> </p><div><h3>Developing nations</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=61"><span>edit</span></a><span>]</span></span></div><p>Disability is more common in developing than in <a href="https://en.wikipedia.org/wiki/Developed_country">developed nations.</a> The connection between <a href="https://en.wikipedia.org/wiki/Disability_and_poverty">disability and poverty</a> is thought to be part of a &quot;vicious cycle&quot; in which these constructs are mutually reinforcing.<sup><span>[</span>212<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=62"><span>edit</span></a><span>]</span></span></div><ul> <li><span><span><a href="https://en.wikipedia.org/wiki/File:Social_sciences.svg"></a></span></span><span><a href="https://en.wikipedia.org/wiki/Portal:Society">Society portal</a></span></li></ul><div> <ul><li><a href="https://en.wikipedia.org/wiki/Assistive_technology">Assistive technology</a></li> <li><a href="https://en.wikipedia.org/wiki/Curb_cut_effect">Curb cut effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_benefits">Disability benefits</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_flag">Disability flag</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_hate_crime">Disability hate crime</a></li> <li><a href="https://en.wikipedia.org/wiki/Disadvantaged">Disadvantaged</a></li> <li><a href="https://en.wikipedia.org/wiki/Conscription_of_people_with_disabilities">Conscription of people with disabilities</a></li> <li><a href="https://en.wikipedia.org/wiki/Epistemic_injustice">Epistemic injustice</a></li> <li><a href="https://en.wikipedia.org/wiki/Frailty_syndrome">Frailty syndrome</a></li> <li><a href="https://en.wikipedia.org/wiki/Hidden_Disabilities_Sunflower">Hidden disability sunflower</a></li> <li><a href="https://en.wikipedia.org/wiki/Nothing_about_us_without_us">Nothing about us without us</a></li> <li><a href="https://en.wikipedia.org/wiki/Parents_with_disabilities">Parents with disabilities</a></li> <li><a href="https://en.wikipedia.org/wiki/Physiological_functional_capacity">Physiological functional capacity</a></li> <li><a href="https://en.wikipedia.org/wiki/Youth_and_disability">Youth and disability</a></li></ul> </div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=63"><span>edit</span></a><span>]</span></span></div><div><h3>Citations</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=64"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span><cite>CDC (April 3, 2024). <a href="https://www.cdc.gov/ncbddd/disabilityandhealth/disability.html">&quot;Disability and Health Overview&quot;</a>. <i>Centers for Disease Control and Prevention</i><span>. Retrieved <span>April 24,</span> 2024</span>.</cite><span><code class="cs1-code">{{cite web}}</code>: CS1 maint: deprecated archival service (<a href="https://en.wikipedia.org/wiki/Category:CS1_maint:_deprecated_archival_service">link</a>)</span></span> </li> <li><span><b>^</b></span> <span><cite>Francis L, Silvers A (October 1, 2016). <a href="https://journalofethics.ama-assn.org/article/perspectives-meaning-disability/2016-10">&quot;Perspectives on the Meaning of &quot;Disability&quot;&quot;</a>. <i>AMA Journal of Ethics</i>. <b>18</b> (10): <span>1025–</span>1033. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1001%2Fjournalofethics.2016.18.10.pfor2-1610">10.1001/journalofethics.2016.18.10.pfor2-1610</a></span>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/2376-6980">2376-6980</a>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/27780027">27780027</a>.</cite></span> </li> <li><span><b>^</b></span> <span><a href="https://www.refworld.org/docid/45f973632.html">Resolution / adopted by the General Assembly, A/RES/61/106</a>. UN General Assembly, Convention on the Rights of Persons with Disabilities. 24 January 2007. [accessed 27 December 2020]</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://odpc.ucsf.edu/clinical/patient-centered-care/medical-and-social-models-of-disability">&quot;Medical and Social Models of Disability&quot;</a>. <i>Office of Developmental Primary Care</i><span>. 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United Kingdom: Liverpool University Press. pp. <span>62–</span>3. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-78962-077-1"><bdi>978-1-78962-077-1</bdi></a>. <a href="https://web.archive.org/web/20240221192952/https://library.oapen.org/bitstream/id/e541dbd4-c418-4250-bf50-4c84e3cbbe54/external_content.pdf">Archived</a> <span>(PDF)</span> from the original on February 21, 2024 – via OAPEN. <q>Although the authors do not expand on their analysis in depth, they do not need to: supercrip representations are widely assumed to be &#39;inherently regressive&#39; (Schalk 75). 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Society</i>. <b>26</b> (7): <span>888–</span>891. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1080%2F09687599.2011.618747">10.1080/09687599.2011.618747</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:144977018">144977018</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Jenkins R (1991). &quot;Disability and Social Stratification&quot;. <i>The British Journal of Sociology</i>. <b>42</b> (4): <span>557–</span>580. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F591447">10.2307/591447</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/591447">591447</a>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/1838293">1838293</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Lukemeyer A, Meyers MK, Smeeding T (2000). &quot;Expensive Children in Poor Families: Out-of-Pocket Expenditures for the Care of Disabled and Chronically Ill Children in Welfare Families&quot;. <i>Journal of Marriage and Family</i>. <b>62</b> (2): <span>399–</span>415. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1111%2Fj.1741-3737.2000.00399.x">10.1111/j.1741-3737.2000.00399.x</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0022-2445">0022-2445</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Barnes C, Sheldon A (December 2010). &quot;Disability, politics and poverty in a majority world context&quot;. <i>Disability &amp; 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Latino Parent Narratives of Struggle in a College Access Program&quot;. <i>Teachers College Record: The Voice of Scholarship in Education</i>. <b>104</b> (7): <span>1369–</span>1392. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1111%2F1467-9620.00207">10.1111/1467-9620.00207</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Perna LW, Titus MA (2005). &quot;The Relationship between Parental Involvement as Social Capital and College Enrollment: An Examination of Racial/Ethnic Group Differences&quot;. <i>The Journal of Higher Education</i>. <b>76</b> (5): <span>485–</span>518. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1353%2Fjhe.2005.0036">10.1353/jhe.2005.0036</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:32290790">32290790</a>. <a href="https://en.wikipedia.org/wiki/Project_Muse">Project MUSE</a> <a href="https://muse.jhu.edu/article/185966">185966</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.oandp.com/articles/2006-08_12.asp">&quot;First Extremity Games was first class success&quot;</a>. oandp.com. <a href="https://web.archive.org/web/20150924054101/http://www.oandp.com/articles/2006-08_12.asp">Archived</a> from the original on September 24, 2015<span>. Retrieved <span>March 6,</span> 2013</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.who.int/disabilities/world_report/2011/report/en/">&quot;Disability World Report&quot;</a>. World Health Organization. 2011. <a href="https://web.archive.org/web/20150119103941/http://www.who.int/disabilities/world_report/2011/report/en/">Archived</a> from the original on January 19, 2015<span>. Retrieved <span>January 8,</span> 2015</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Jack A (May 11, 2018). <a href="https://www.ft.com/content/f4e2dc50-3dab-11e8-bcc8-cebcb81f1f90">&quot;For many, disability is part of what it means to be human&quot;</a> <span>(Special report Modern workplace: Disability)</span>. <i>Financial Times</i>. Bracken House; London: Nikkei. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0307-1766">0307-1766</a>. <a href="https://web.archive.org/web/20180815024712/https://www.ft.com/content/f4e2dc50-3dab-11e8-bcc8-cebcb81f1f90">Archived</a> from the original on August 15, 2018<span>. Retrieved <span>August 14,</span> 2018</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Okoro CA (2018). <a href="https://www.cdc.gov/mmwr/volumes/67/wr/mm6732a3.htm">&quot;Prevalence of Disabilities and Health Care Access by Disability Status and Type Among Adults — United States, 2016&quot;</a>. <i>MMWR. Morbidity and Mortality Weekly Report</i>. <b>67</b> (32): <span>882–</span>887. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.15585%2Fmmwr.mm6732a3">10.15585/mmwr.mm6732a3</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0149-2195">0149-2195</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a> <span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6095650">6095650</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/30114005">30114005</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>CDC (October 25, 2019). <a href="https://www.cdc.gov/ncbddd/disabilityandhealth/materials/infographic-disabilities-ethnicity-race.html">&quot;Infographic: Adults with Disabilities: Ethnicity and Race | CDC&quot;</a>. <i>Centers for Disease Control and Prevention</i><span>. Retrieved <span>September 22,</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Government of Canada SC (November 28, 2018). <a href="https://www150.statcan.gc.ca/n1/pub/89-654-x/89-654-x2018002-eng.htm">&quot;A demographic, employment and income profile of Canadians with disabilities aged 15 years and over, 2017&quot;</a>. <i>www150.statcan.gc.ca</i><span>. Retrieved <span>October 5,</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Government of Canada SC (December 3, 2020). <a href="https://www150.statcan.gc.ca/n1/daily-quotidien/201203/dq201203a-eng.htm">&quot;The Daily — A profile of Canadians with a mobility disability and groups designated as visible minorities with a disability&quot;</a>. <i>www150.statcan.gc.ca</i><span>. Retrieved <span>October 5,</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.abs.gov.au/statistics/health/disability/disability-ageing-and-carers-australia-summary-findings/latest-release">&quot;Disability, Ageing and Carers, Australia: Summary of Findings, 2018 | Australian Bureau of Statistics&quot;</a>. <i>www.abs.gov.au</i>. September 25, 2020<span>. Retrieved <span>October 5,</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.gov.uk/government/statistics/family-resources-survey-financial-year-2020-to-2021">&quot;Family Resources Survey: financial year 2020 to 2021&quot;</a>. <i>GOV.UK</i><span>. Retrieved <span>October 5,</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.gov.uk/government/statistics/life-opportunities-survey-wave-one-results-2009-to-2011">&quot;Life Opportunities Survey: wave 1 results&quot;</a>. <i>GOV.UK</i><span>. Retrieved <span>October 5,</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Zheng X, Chen G, Song X, Liu J, Yan L, Du W, Pang L, Zhang L, Wu J, Zhang B, Zhang J (November 1, 2011). <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3209727">&quot;Twenty-year trends in the prevalence of disability in China&quot;</a>. <i>Bulletin of the World Health Organization</i>. <b>89</b> (11): <span>788–</span>797. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2471%2FBLT.11.089730">10.2471/BLT.11.089730</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0042-9686">0042-9686</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a> <span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3209727">3209727</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/22084524">22084524</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://kostat.go.kr/assist/synap/preview/skin/miri.html?fn=ea190147732590130213133&amp;rs=/assist/synap/preview">&quot;문서뷰어&quot;</a>. <i>kostat.go.kr</i><span>. Retrieved <span>October 8,</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Yeo R., Moore K. (2003). &quot;Including disabled people in poverty reduction work: &#39;Nothing about us, without us&#39;&quot;. <i>World Development</i>. <b>31</b> (3): <span>571–</span>90. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1016%2FS0305-750X%2802%2900218-8">10.1016/S0305-750X(02)00218-8</a>.</cite></span> </li> </ol></div></div><div><h3>Sources</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=65"><span>edit</span></a><span>]</span></span></div><ul><li><cite>DePoy E, Gilson SF (2004). <a href="https://archive.org/details/rethinkingdisabi0000depo"><i>Rethinking Disability: Principles for Professional and Social Change</i></a>. Pacific Grove, CA: Brooks Cole. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-534-54929-9"><bdi>978-0-534-54929-9</bdi></a>.</cite></li> <li><cite>Donovan R (March 1, 2012). <a href="https://web.archive.org/web/20120913222254/http://www.returnondisability.com/pdf-docs/The_Global_Economics_of_Disability_2012.pdf">&quot;The Global Economics of Disability&quot;</a> <span>(PDF)</span>. Return on Disability. Archived from <a href="http://www.returnondisability.com/pdf-docs/The_Global_Economics_of_Disability_2012.pdf">the original</a> <span>(PDF)</span> on September 13, 2012<span>. Retrieved <span>August 11,</span> 2012</span>.</cite></li> <li><cite>McAdams Ducy E, Stough LM, Clark MC (2012). &quot;Choosing Agency in the Midst of Vulnerability: Using Critical Disability Theory to Examine a Disaster Narrative&quot;. In Steinberg SR, Cannella GS (eds.). <i>Critical Qualitative Research Reader</i>. New York: Peter Lang. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-4331-0688-0"><bdi>978-1-4331-0688-0</bdi></a>.</cite></li> <li><cite>Nikora LW, Karapu R, Hickey H, Te Awekotuku N (2004). <a href="https://web.archive.org/web/20200513220653/https://researchcommons.waikato.ac.nz/bitstream/handle/10289/460/content.pdf;jsessionid=CC679321B8E56B193727B2B489F9B94F?sequence=1">&quot;Disabled Maori and Disability Support Options&quot;</a>. Maori &amp; Psychology Research Unit, University of Waikato. Archived from <a href="http://waikato.researchgateway.ac.nz/bitstream/10289/460/1/content.pdf">the original</a> <span>(PDF)</span> on May 13, 2020<span>. Retrieved <span>August 11,</span> 2012</span>.</cite></li> <li><cite>Oliver M (1990). <i>The Politics of Disablement</i>. London: <a href="https://en.wikipedia.org/wiki/St._Martin%27s_Press">St. Martin&#39;s Press</a>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2F978-1-349-20895-1">10.1007/978-1-349-20895-1</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-333-43293-2"><bdi>0-333-43293-2</bdi></a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a> <a href="https://search.worldcat.org/oclc/59098076">59098076</a>.</cite></li> <li><cite>Russell M (2019). Keith Rosenthal (ed.). <i>Capitalism and Disability: Selected Writings by Marta Russell</i>. Haymarket Books. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-60846-686-3"><bdi>978-1-60846-686-3</bdi></a>.</cite></li> <li><cite>Stough LM (2009). <a href="http://oaktrust.library.tamu.edu/bitstream/1969.1/153544/1/The%20effects%20of%20disaster%20on%20the%20mental%20health%20of%20individuals%20with%20disabilities.pdf">&quot;The Effects of Disaster on the Mental Health of Individuals With Disabilities&quot;</a> <span>(PDF)</span>. In Neria Y, Galea S, Norris FH (eds.). <i>Mental Health and Disasters</i>. Cambridge University Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-107-41282-8"><bdi>978-1-107-41282-8</bdi></a>.</cite></li> <li><cite>Yeo R (2005). <a href="https://web.archive.org/web/20110612231627/http://www.dfid.gov.uk/r4d/PDF/Outputs/Disability/RedPov_agenda.pdf">&quot;Disability, poverty, and the new development agenda&quot;</a> <span>(PDF)</span>. <i>Disability Knowledge and Research Programme</i>. Department for International Development (UK Government). Archived from <a href="http://www.dfid.gov.uk/r4d/PDF/Outputs/Disability/RedPov_agenda.pdf">the original</a> <span>(PDF)</span> on June 12, 2011<span>. Retrieved <span>June 19,</span> 2013</span>.</cite></li></ul><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=66"><span>edit</span></a><span>]</span></span></div><ul><li><cite>Albrecht GL, ed. (2006). <a href="https://archive.org/search.php?query=Encyclopedia+of+disability&amp;sin="><i>Encyclopedia of disability</i></a>. Thousand Oaks, CA: <a href="https://en.wikipedia.org/wiki/SAGE_Publications">SAGE Publications</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-7619-2565-1"><bdi>978-0-7619-2565-1</bdi></a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a> <a href="https://search.worldcat.org/oclc/62778255">62778255</a>.</cite></li> <li>Atherton, Martin, ed. 2017. <i>Deafness, Community and Culture in Britain: Leisure and Cohesion, 1945-95</i>. Manchester University Press. https://www.jstor.org/stable/10.2307/j.ctt21216hx.</li> <li><cite>Arditi A, Rosenthal B (1998). <a href="https://web.archive.org/web/20220629204300/https://www.visibilitymetrics.com/sites/default/files/downloads/Developing%20Objective%20Definition%20of%20Visual%20Impairment.pdf">&quot;Developing an objective definition of visual impairment&quot;</a> <span>(PDF)</span>. <i>Vision &#39;96: Proceedings of the International Low Vision Conference</i>. Madrid: <span>331–</span>34. Archived from <a href="https://www.visibilitymetrics.com/sites/default/files/downloads/Developing%20Objective%20Definition%20of%20Visual%20Impairment.pdf">the original</a> <span>(PDF)</span> on June 29, 2022.</cite></li> <li><cite>Bowe F (1978). <span><a href="https://archive.org/details/handicappingamer00bowe"><i>Handicapping America: Barriers to disabled people</i></a></span>. New York: Harper &amp; Row. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-06-010422-1"><bdi>978-0-06-010422-1</bdi></a>.</cite></li> <li>Bohata, Kirsti, Alexandra Jones, Mike Mantin, and Steven Thompson. 2020. <i>Disability in Industrial Britain: A Cultural and Literary History of Impairment in the Coal Industry, 1880-1948</i>. Manchester (UK): Manchester University Press.</li> <li><cite>Charlton JI (1998). <a href="https://archive.org/details/nothingaboutuswi0000char/mode/2up"><i>Nothing about us without us: disability oppression and empowerment</i></a>. Berkeley: Univ. of California Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-520-22481-0"><bdi>978-0-520-22481-0</bdi></a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/10.1525/j.ctt1pnqn9">10.1525/j.ctt1pnqn9</a>.</cite></li> <li><cite>Burkhauser RV, Schmeiser MD, Weathers II RR (January 2012). &quot;The Importance of Anti-Discrimination and Workers&#39; Compensation Laws on the Provision of Workplace Accommodations Following the Onset of a Disability&quot;. <i>Industrial &amp; Labor Relations Review</i>. <b>65</b> (1): <span>161–</span>180. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1177%2F001979391206500109">10.1177/001979391206500109</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:154605646">154605646</a>.</cite></li> <li><cite>Darling P (August 2007). &quot;Disabilities and the Workplace&quot;. <i>Business NH Magazine</i>. <b>24</b> (8). Manchester: EBSCO Masterfile Complete. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1046-9575">1046-9575</a>.</cite></li> <li><cite>Glenn E (1995). Walker, Sylvia (ed.). <a href="https://web.archive.org/web/20090906074019/http://www.dinf.ne.jp/doc/english/Us_Eu/ada_e/pres_com/pres-dd/glenn.html">&quot;African American Women with Disabilities: An Overview&quot;</a>. <i>Disability and Diversity: New Leadership for a New Era</i>: 66. Archived from <a href="http://www.dinf.ne.jp/doc/english/Us_Eu/ada_e/pres_com/pres-dd/glenn.html">the original</a> on September 6, 2009.</cite> <a href="https://eric.ed.gov/?id=ED394233">Alt URL</a></li> <li><cite>Hutchison I, Atherton M, Virdi J, eds. (2020). &quot;Disability and the Victorians: Attitudes, interventions, legacies&quot;. <a href="https://www.manchesterhive.com/view/9781526145727/9781526145727.xml"><i>Disability and the Victorians</i></a>. Manchester University Press. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.7765%2F9781526145727">10.7765/9781526145727</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-5261-4572-7"><bdi>978-1-5261-4572-7</bdi></a>.</cite></li> <li><cite>Johnstone D (2001). <a href="https://archive.org/details/introductiontodi0000john_k7w3"><i>An Introduction to Disability Studies</i></a> (2nd ed.). Internet archive: Fulton. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-85346-726-4"><bdi>978-1-85346-726-4</bdi></a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a> <a href="https://search.worldcat.org/oclc/1244858584">1244858584</a>.</cite></li> <li><cite>Kaushik R (1999). &quot;Access Denied: Can we overcome disabling attitudes&quot;. <i>Museum International</i>. <b>51</b> (3): <span>48–</span>52. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1111%2F1468-0033.00217">10.1111/1468-0033.00217</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1468-0033">1468-0033</a>.</cite></li> <li><cite>Kerr A, Shakespeare T (2002). <a href="https://archive.org/details/geneticpoliticsf0000kerr"><i>Genetic Politics: from Eugenics to Genome</i></a>. Cartoons by Suzy Varty. Internet archive: New Clarion Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-873797-25-9"><bdi>978-1-873797-25-9</bdi></a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a> <a href="https://search.worldcat.org/oclc/1310731470">1310731470</a>.</cite></li> <li>Long, Vicky, Julie Anderson, and Walton Schalick. 2015. <i>Destigmatising Mental Illness?: Professional Politics and Public Education in Britain, 1870-1970</i>. Oxford: Manchester University Press. https://doi.org/10.7765/9781526103253.</li> <li><cite>Masala C, Petretto DR (2008). &quot;From disablement to enablement: conceptual models of disability in the 20th century&quot;. <i>Disability and Rehabilitation</i>. <b>30</b> (17): <span>1233–</span>44. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1080%2F09638280701602418">10.1080/09638280701602418</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0963-8288">0963-8288</a>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/18821191">18821191</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:19377518">19377518</a>.</cite></li> <li><cite>Masala C, Petretto DR (2008). <i>Psicologia dell&#39;Handicap e della Riabilitazione</i> [<i>The Psychology of Handicap and Rehabilitation</i>] (in Italian). Rome: Kappa. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-88-15-06226-0"><bdi>978-88-15-06226-0</bdi></a>.</cite></li> <li>McGuire, Coreen. 2020. <i>Measuring Difference, Numbering Normal Setting the Standards for Disability in the Interwar Period</i>. Manchester, UK: Manchester University Press.</li> <li>Jones, Claire L. 2017. <i>Rethinking Modern Prostheses in Anglo-American Commodity Cultures, 1820-1939</i>. Manchester: Manchester University Press.</li> <li>McDonagh, Patrick, C. F. Goodey, and Timothy Stainton, eds. 2018. <i>Intellectual Disability: A Conceptual History, 1200-1900</i>. Manchester: Manchester University Press.</li> <li>Metzler, Irina. <i>Fools and Idiots?: Intellectual Disability in the Middle Ages</i>. Manchester University Press, 2016.</li> <li>Nielsen, Kim E. 2012. <i>A Disability History of the United States</i>. Boston: Beacon Press.</li> <li>O’Brien, Gerald V. 2016. <i>Framing the Moron: The Social Construction of Feeble-Mindedness in the American Eugenic Era</i>. Manchester: Manchester University Press.</li> <li><cite>Pearson, Charlotte, ed. (2006). <a href="https://archive.org/details/directpaymentspe0000unse"><i>Direct Payments and Personalisation of Care</i></a>. Internet archive: Dunedin Academic Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-903765-62-3"><bdi>978-1-903765-62-3</bdi></a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a> <a href="https://search.worldcat.org/oclc/1280896670">1280896670</a>.</cite></li> <li><cite>Robidoux C (April 7, 2011). <a href="https://www.businessnhmagazine.com/article/an-overlooked-workforce">&quot;An Overlooked Workforce&quot;</a>. <i>Business NH Magazine</i>. Manchester. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1046-9575">1046-9575</a>.</cite></li> <li>Robinson, Michael. 2020. <i>Shell-Shocked British Army Veterans in Ireland, 1918-39: A Difficult Homecoming</i>. Manchester: Manchester University Press.</li> <li><cite>Rose SF (2017). <i>No Right to Be Idle: The Invention of Disability, 1840s–1930s</i>. University of North Carolina Press. pp. xvi, 382. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-4696-2489-1"><bdi>978-1-4696-2489-1</bdi></a>.</cite></li> <li>Wheatcroft, Sue. 2015. <i>Worth Saving: Disabled Children during the Second World War</i>. Manchester University Press.</li> <li>Williamson, Bess (2019). Accessible America. A History of Disability and Design. New York University Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-4798024-94"><bdi>978-1-4798024-94</bdi></a></li> <li>Schmidt, Marion Andrea. 2020. <i>Eradicating Deafness?: Genetics, Pathology, and Diversity in Twentieth-Century America</i>. Manchester: Manchester University Press.</li> <li>Turner, David M., and Daniel Blackie. 2018. <i>Disability in the Industrial Revolution: Physical Impairment in British Coalmining, 1780-1880</i>. Manchester: Manchester University Press.</li> <li><cite><a href="https://web.archive.org/web/20091113152521/https://workwithoutlimits.org/">&quot;Work Without Limits&quot;</a>. Commonwealth Medicine. Shrewsbury, MA: UMASS Chan Medical School. 2021. Archived from <a href="https://workwithoutlimits.org/">the original</a> on November 13, 2009<span>. Retrieved <span>June 28,</span> 2022</span>.</cite></li></ul><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Disability&amp;action=edit&amp;section=67"><span>edit</span></a><span>]</span></span></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Disability_navbox"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Disability_navbox"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Disability_navbox"><abbr>e</abbr></a></li></ul></div><div>Disability</div></th></tr><tr><th>Main topics</th><td><div> <ul><li>Disability</li> <li><a href="https://en.wikipedia.org/wiki/Disability_studies">Disability studies</a></li> <li><a href="https://en.wikipedia.org/wiki/Medical_model_of_disability">Medical model</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_model_of_disability">Social model</a></li></ul> </div></td></tr><tr><th>Approaches</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Individualized_Education_Program">IEP</a></li> <li><a href="https://en.wikipedia.org/wiki/Inclusion_(disability_rights)">Inclusion</a></li> <li><a href="https://en.wikipedia.org/wiki/Learning_disability">Learning disability</a></li> <li><a href="https://en.wikipedia.org/wiki/Mainstreaming_(education)">Mainstreaming</a></li> <li><a href="https://en.wikipedia.org/wiki/Physical_therapy">Physical therapy</a> <ul><li><a href="https://en.wikipedia.org/wiki/Driver_rehabilitation">driver rehabilitation</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Special_needs">Special needs</a> <ul><li><a href="https://en.wikipedia.org/wiki/Special_school">school</a></li> <li><a href="https://en.wikipedia.org/wiki/Special_education">education</a></li></ul></li></ul> </div></td></tr><tr><th>Rights, law, support</th><td><table><tbody><tr><th>Rights</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Ableism">Ableism/disablism</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_rights_movement">Disability rights</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_disability-related_terms_that_developed_negative_connotations">Pejorative terms</a></li> <li><a href="https://en.wikipedia.org/wiki/Right_to_sit">Right to sit</a> <ul><li><a href="https://en.wikipedia.org/wiki/Right_to_sit_in_the_United_States">United States</a></li></ul></li></ul> </div></td></tr><tr><th>Law</th><td><div> <ul><li>Accessibility Act <ul><li><a href="https://en.wikipedia.org/wiki/Accessibility_Act_(Newfoundland_and_Labrador)">NL</a></li> <li><a href="https://en.wikipedia.org/wiki/Accessibility_Act_(Nova_Scotia)">NS</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Accessible_British_Columbia_Act">ABCA</a></li> <li><a href="https://en.wikipedia.org/wiki/Accessible_Canada_Act">ACA</a></li> <li><a href="https://en.wikipedia.org/wiki/Accessibility_for_Manitobans_Act">AMA</a></li> <li><a href="https://en.wikipedia.org/wiki/Accessibility_for_Ontarians_with_Disabilities_Act,_2005">AODA</a></li> <li><a href="https://en.wikipedia.org/wiki/Americans_with_Disabilities_Act_of_1990">ADA</a></li> <li><a href="https://en.wikipedia.org/wiki/Convention_on_the_Rights_of_Persons_with_Disabilities">Convention on the Rights of Persons with Disabilities</a></li> <li><a href="https://en.wikipedia.org/wiki/Declaration_on_the_Rights_of_Disabled_Persons">Declaration on the Rights of Disabled Persons</a></li> <li><a href="https://en.wikipedia.org/wiki/International_Classification_of_Functioning,_Disability_and_Health">International Classification of Functioning, Disability and Health</a></li></ul> </div></td></tr><tr><th>Services</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Services_for_mental_disorders">Services for mental disorders</a></li> <li><a href="https://en.wikipedia.org/wiki/Services_and_supports_for_people_with_disabilities">Services for disabled people</a></li></ul> </div></td></tr><tr><th>Support</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_Living_Allowance">DLA</a></li> <li><a href="https://en.wikipedia.org/wiki/Ontario_Disability_Support_Program">ODSP</a></li> <li><a href="https://en.wikipedia.org/wiki/Disabled_Persons_Railcard">Rail</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_Security_Disability_Insurance">SSDI</a></li> <li><a href="https://en.wikipedia.org/wiki/Supplemental_Security_Income">SSI</a></li> <li><a href="https://en.wikipedia.org/wiki/Disabled_students_allowance">Students</a></li> <li><a href="https://en.wikipedia.org/wiki/CNIB_Foundation">CNIB</a></li></ul> </div></td></tr><tr><th>Activist groups</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Council_for_Canadians_with_Disabilities">CCD</a></li> <li><a href="https://en.wikipedia.org/wiki/Disabled_Peoples%27_International">DPI</a></li> <li><a href="https://en.wikipedia.org/wiki/Movement_for_the_Intellectually_Disabled_of_Singapore">MINDS</a></li> <li><a href="https://en.wikipedia.org/wiki/Reach_Canada">Reach Canada</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Structural and assistive</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Accessible_toilet">Accessible toilet</a></li> <li><a href="https://en.wikipedia.org/wiki/Activities_of_daily_living">Activities of daily living</a></li> <li><a href="https://en.wikipedia.org/wiki/Assistive_technology">Assistive technology</a></li> <li><a href="https://en.wikipedia.org/wiki/Curb_cut">Curb cut</a></li> <li><a href="https://en.wikipedia.org/wiki/Curb_cut_effect">Curb cut effect</a></li> <li><a href="https://en.wikipedia.org/wiki/Inclusive_design">Inclusive design</a></li> <li><a href="https://en.wikipedia.org/wiki/Independent_living">Independent living</a></li> <li><a href="https://en.wikipedia.org/wiki/Mobility_aid">Mobility aid</a></li> <li><a href="https://en.wikipedia.org/wiki/Orthotics">Orthotics and braces</a></li> <li><a href="https://en.wikipedia.org/wiki/Unlicensed_assistive_personnel">Personal Care Assistant</a></li> <li><a href="https://en.wikipedia.org/wiki/Accessibility">Physical accessibility</a></li> <li><a href="https://en.wikipedia.org/wiki/Prosthesis">Prosthetics</a></li> <li><a href="https://en.wikipedia.org/wiki/Redundant_elevators">Redundant elevators</a></li> <li><a href="https://en.wikipedia.org/wiki/Universal_design">Universal design</a></li> <li><a href="https://en.wikipedia.org/wiki/Web_accessibility">Web accessibility</a></li></ul> </div></td></tr><tr><th>Social issues</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Augmentative_and_alternative_communication">Augmentative and alternative communication</a></li> <li><a href="https://en.wikipedia.org/wiki/Conscription_of_people_with_disabilities">Conscription of people with disabilities</a></li> <li><a href="https://en.wikipedia.org/wiki/Emotional_or_behavioral_disability">Emotional or behavioral disability</a></li> <li><a href="https://en.wikipedia.org/wiki/Invisible_disability">Invisible disability</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_and_disasters">Disability and disasters</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_and_LGBT_identities">Disability and LGBT identities</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_and_religion">Disability and religion</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_and_poverty">Disability and poverty</a></li> <li><a href="https://en.wikipedia.org/wiki/Disproportionality_in_special_education">Disproportionality in special education</a></li> <li><a href="https://en.wikipedia.org/wiki/Sexuality_and_disability">Sexuality and disability</a></li> <li><a href="https://en.wikipedia.org/wiki/Youth_and_disability">Youth and disability</a></li></ul> </div></td></tr><tr><th>Disability studies</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Models_of_disability">Models of disability</a></li> <li><a href="https://en.wikipedia.org/wiki/Inspiration_porn">Inspiration porn</a></li> <li><a href="https://en.wikipedia.org/wiki/Bodymind_(disability_studies)">Bodymind</a></li> <li><a href="https://en.wikipedia.org/wiki/Crip_(disability_term)#Crip_theory">Crip as verb</a></li> <li><a href="https://en.wikipedia.org/wiki/Neuroqueer_theory">Neuroqueer theory</a></li> <li><a href="https://en.wikipedia.org/wiki/Deaf_studies">Deaf studies</a></li> <li><a href="https://en.wikipedia.org/wiki/Eugenics">Eugenics</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_anthropology">Anthropology</a></li> <li><a href="https://en.wikipedia.org/wiki/Geography_of_disability">Geography</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_studies_in_education">Education</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_disability_studies_journals">Journals</a></li></ul> </div></td></tr><tr><th>Arts, media, culture, sport</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_culture">Disability culture</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_art">Disability art</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_the_arts">Disability in the arts</a> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_in_children%27s_literature">Disability in children&#39;s literature</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_horror_films">Disability in horror films</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_the_media">Disability in the media</a></li> <li><a href="https://en.wikipedia.org/wiki/Parasports">Parasports</a> <ul><li><a href="https://en.wikipedia.org/wiki/Deaflympics">Deaflympics</a></li> <li><a href="https://en.wikipedia.org/wiki/Paralympic_Games">Paralympics</a></li> <li><a href="https://en.wikipedia.org/wiki/Special_Olympics">Special Olympics</a></li></ul></li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li> <a href="https://en.wikipedia.org/wiki/Category:Disability">Category</a></li> <li> <a href="https://en.wikipedia.org/wiki/Category:Disability-related_lists">Lists</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Disability_by_country"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Disability_by_country"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Disability_by_country"><abbr>e</abbr></a></li></ul></div><div>Disability by country</div></th></tr><tr><th><a href="https://en.wikipedia.org/wiki/Category:Disability_in_Africa">Africa</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_in_Algeria">Algeria</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Angola">Angola</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Benin&amp;action=edit&amp;redlink=1">Benin</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Botswana&amp;action=edit&amp;redlink=1">Botswana</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Burkina_Faso&amp;action=edit&amp;redlink=1">Burkina Faso</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Burundi">Burundi</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Cameroon">Cameroon</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Cape_Verde">Cape Verde</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Central_African_Republic&amp;action=edit&amp;redlink=1">Central African Republic</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Chad&amp;action=edit&amp;redlink=1">Chad</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Comoros&amp;action=edit&amp;redlink=1">Comoros</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_the_Democratic_Republic_of_the_Congo&amp;action=edit&amp;redlink=1">Democratic Republic of the Congo</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_the_Republic_of_the_Congo&amp;action=edit&amp;redlink=1">Republic of the Congo</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Djibouti&amp;action=edit&amp;redlink=1">Djibouti</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Egypt">Egypt</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Equatorial_Guinea&amp;action=edit&amp;redlink=1">Equatorial Guinea</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Eritrea">Eritrea</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Eswatini&amp;action=edit&amp;redlink=1">Eswatini</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Ethiopia&amp;action=edit&amp;redlink=1">Ethiopia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Gabon">Gabon</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_The_Gambia&amp;action=edit&amp;redlink=1">The Gambia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Ghana">Ghana</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Guinea&amp;action=edit&amp;redlink=1">Guinea</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Guinea-Bissau">Guinea-Bissau</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Ivory_Coast&amp;action=edit&amp;redlink=1">Ivory Coast (Côte d&#39;Ivoire)</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Kenya">Kenya</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Lesotho">Lesotho</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Liberia">Liberia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Libya&amp;action=edit&amp;redlink=1">Libya</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Madagascar&amp;action=edit&amp;redlink=1">Madagascar</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Malawi&amp;action=edit&amp;redlink=1">Malawi</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Mali&amp;action=edit&amp;redlink=1">Mali</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Mauritania&amp;action=edit&amp;redlink=1">Mauritania</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Mauritius&amp;action=edit&amp;redlink=1">Mauritius</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Morocco&amp;action=edit&amp;redlink=1">Morocco</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Mozambique&amp;action=edit&amp;redlink=1">Mozambique</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Namibia">Namibia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Niger&amp;action=edit&amp;redlink=1">Niger</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Nigeria">Nigeria</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Rwanda&amp;action=edit&amp;redlink=1">Rwanda</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_S%C3%A3o_Tom%C3%A9_and_Pr%C3%ADncipe&amp;action=edit&amp;redlink=1">São Tomé and Príncipe</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Senegal&amp;action=edit&amp;redlink=1">Senegal</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Seychelles">Seychelles</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Sierra_Leone">Sierra Leone</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Somalia">Somalia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_South_Africa">South Africa</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_South_Sudan">South Sudan</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Sudan">Sudan</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Tanzania&amp;action=edit&amp;redlink=1">Tanzania</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Togo">Togo</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Tunisia&amp;action=edit&amp;redlink=1">Tunisia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Uganda">Uganda</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Zambia">Zambia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Zimbabwe">Zimbabwe</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Category:Disability_in_Asia">Asia</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_in_Afghanistan">Afghanistan</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Armenia">Armenia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Azerbaijan">Azerbaijan</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Bahrain&amp;action=edit&amp;redlink=1">Bahrain</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Bangladesh">Bangladesh</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Bhutan&amp;action=edit&amp;redlink=1">Bhutan</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Brunei">Brunei</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Burma&amp;action=edit&amp;redlink=1">Burma (Myanmar)</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Cambodia">Cambodia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_China">China</a> (<a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Hong_Kong&amp;action=edit&amp;redlink=1">Hong Kong</a>, <a href="https://en.wikipedia.org/wiki/Disability_in_Macau">Macau</a>)</li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_East_Timor&amp;action=edit&amp;redlink=1">East Timor</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_India">India</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Indonesia">Indonesia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Iran">Iran</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Iraq&amp;action=edit&amp;redlink=1">Iraq</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Israel">Israel</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Japan">Japan</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Jordan&amp;action=edit&amp;redlink=1">Jordan</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Kazakhstan&amp;action=edit&amp;redlink=1">Kazakhstan</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Kuwait&amp;action=edit&amp;redlink=1">Kuwait</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Kyrgyzstan">Kyrgyzstan</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Laos&amp;action=edit&amp;redlink=1">Laos</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Lebanon&amp;action=edit&amp;redlink=1">Lebanon</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Malaysia">Malaysia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_the_Maldives&amp;action=edit&amp;redlink=1">Maldives</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Mongolia">Mongolia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Nepal&amp;action=edit&amp;redlink=1">Nepal</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_North_Korea">North Korea</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Oman&amp;action=edit&amp;redlink=1">Oman</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Pakistan">Pakistan</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_the_State_of_Palestine">Palestine</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_the_Philippines">Philippines</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Qatar&amp;action=edit&amp;redlink=1">Qatar</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Russia">Russia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Saudi_Arabia">Saudi Arabia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Singapore">Singapore</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Sri_Lanka">Sri Lanka</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_South_Korea">South Korea</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Syria&amp;action=edit&amp;redlink=1">Syria</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Taiwan">Taiwan</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Tajikistan&amp;action=edit&amp;redlink=1">Tajikistan</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Thailand">Thailand</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Turkey&amp;action=edit&amp;redlink=1">Turkey</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Turkmenistan&amp;action=edit&amp;redlink=1">Turkmenistan</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_the_United_Arab_Emirates&amp;action=edit&amp;redlink=1">United Arab Emirates</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Uzbekistan&amp;action=edit&amp;redlink=1">Uzbekistan</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Vietnam">Vietnam</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Yemen">Yemen</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Category:Disability_in_Europe">Europe</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_in_Albania">Albania</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Andorra&amp;action=edit&amp;redlink=1">Andorra</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Austria&amp;action=edit&amp;redlink=1">Austria</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Belarus">Belarus</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Belgium&amp;action=edit&amp;redlink=1">Belgium</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Bosnia_and_Herzegovina&amp;action=edit&amp;redlink=1">Bosnia and Herzegovina</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Bulgaria&amp;action=edit&amp;redlink=1">Bulgaria</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Croatia&amp;action=edit&amp;redlink=1">Croatia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Cyprus">Cyprus</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_the_Czech_Republic&amp;action=edit&amp;redlink=1">Czech Republic</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Denmark">Denmark</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Estonia&amp;action=edit&amp;redlink=1">Estonia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Finland&amp;action=edit&amp;redlink=1">Finland</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_France">France</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Georgia&amp;action=edit&amp;redlink=1">Georgia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Germany&amp;action=edit&amp;redlink=1">Germany</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Greece&amp;action=edit&amp;redlink=1">Greece</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Hungary&amp;action=edit&amp;redlink=1">Hungary</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Iceland&amp;action=edit&amp;redlink=1">Iceland</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Ireland&amp;action=edit&amp;redlink=1">Ireland</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Italy">Italy</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Kosovo&amp;action=edit&amp;redlink=1">Kosovo</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Latvia&amp;action=edit&amp;redlink=1">Latvia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Liechtenstein&amp;action=edit&amp;redlink=1">Liechtenstein</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Lithuania&amp;action=edit&amp;redlink=1">Lithuania</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Luxembourg">Luxembourg</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Malta&amp;action=edit&amp;redlink=1">Malta</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Moldova">Moldova</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Monaco&amp;action=edit&amp;redlink=1">Monaco</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Montenegro&amp;action=edit&amp;redlink=1">Montenegro</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_the_Netherlands&amp;action=edit&amp;redlink=1">Netherlands</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_North_Macedonia&amp;action=edit&amp;redlink=1">North Macedonia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Norway&amp;action=edit&amp;redlink=1">Norway</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Poland&amp;action=edit&amp;redlink=1">Poland</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Portugal&amp;action=edit&amp;redlink=1">Portugal</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Romania">Romania</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Russia">Russia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_San_Marino&amp;action=edit&amp;redlink=1">San Marino</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Serbia&amp;action=edit&amp;redlink=1">Serbia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Slovakia&amp;action=edit&amp;redlink=1">Slovakia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Slovenia&amp;action=edit&amp;redlink=1">Slovenia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Spain">Spain</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Sweden&amp;action=edit&amp;redlink=1">Sweden</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Switzerland&amp;action=edit&amp;redlink=1">Switzerland</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Turkey&amp;action=edit&amp;redlink=1">Turkey</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Ukraine">Ukraine</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_the_United_Kingdom">United Kingdom</a> (<a href="https://en.wikipedia.org/wiki/Disability_in_Northern_Ireland">Northern Ireland</a>)</li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Vatican_City&amp;action=edit&amp;redlink=1">Vatican City</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Category:Disability_in_North_America">North America</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_in_Antigua_and_Barbuda">Antigua and Barbuda</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_the_Bahamas&amp;action=edit&amp;redlink=1">Bahamas</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Barbados&amp;action=edit&amp;redlink=1">Barbados</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Belize">Belize</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Canada">Canada</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Costa_Rica">Costa Rica</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Cuba">Cuba</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Dominica&amp;action=edit&amp;redlink=1">Dominica</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_the_Dominican_Republic&amp;action=edit&amp;redlink=1">Dominican Republic</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_El_Salvador&amp;action=edit&amp;redlink=1">El Salvador</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Grenada&amp;action=edit&amp;redlink=1">Grenada</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Guatemala&amp;action=edit&amp;redlink=1">Guatemala</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Haiti&amp;action=edit&amp;redlink=1">Haiti</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Honduras&amp;action=edit&amp;redlink=1">Honduras</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Jamaica&amp;action=edit&amp;redlink=1">Jamaica</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Mexico">Mexico</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Nicaragua&amp;action=edit&amp;redlink=1">Nicaragua</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Panama&amp;action=edit&amp;redlink=1">Panama</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Saint_Kitts_and_Nevis&amp;action=edit&amp;redlink=1">Saint Kitts and Nevis</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Saint_Lucia&amp;action=edit&amp;redlink=1">Saint Lucia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Saint_Vincent_and_the_Grenadines&amp;action=edit&amp;redlink=1">Saint Vincent and the Grenadines</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Trinidad_and_Tobago&amp;action=edit&amp;redlink=1">Trinidad and Tobago</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_the_United_States">United States</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Category:Disability_in_Oceania">Oceania</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_in_Australia">Australia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Fiji&amp;action=edit&amp;redlink=1">Fiji</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Kiribati&amp;action=edit&amp;redlink=1">Kiribati</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_the_Marshall_Islands&amp;action=edit&amp;redlink=1">Marshall Islands</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Micronesia&amp;action=edit&amp;redlink=1">Micronesia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Nauru&amp;action=edit&amp;redlink=1">Nauru</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_New_Zealand">New Zealand</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Palau&amp;action=edit&amp;redlink=1">Palau</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Papua_New_Guinea">Papua New Guinea</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Samoa">Samoa</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_the_Solomon_Islands">Solomon Islands</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Tonga">Tonga</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Tuvalu">Tuvalu</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Vanuatu">Vanuatu</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Category:Disability_in_South_America">South America</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Disability_in_Argentina">Argentina</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Bolivia">Bolivia</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Brazil">Brazil</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Chile">Chile</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Colombia&amp;action=edit&amp;redlink=1">Colombia</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Ecuador&amp;action=edit&amp;redlink=1">Ecuador</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Guyana&amp;action=edit&amp;redlink=1">Guyana</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Paraguay">Paraguay</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Peru">Peru</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Suriname&amp;action=edit&amp;redlink=1">Suriname</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_in_Uruguay">Uruguay</a></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Disability_in_Venezuela&amp;action=edit&amp;redlink=1">Venezuela</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q12131#identifiers"></a></span></div></th></tr><tr><th>International</th><td><div><ul><li><span><a href="https://d-nb.info/gnd/4112696-8">GND</a></span></li></ul></div></td></tr><tr><th>National</th><td><div><ul><li><span><span><a href="https://id.loc.gov/authorities/sh2003007662">United States</a></span></span></li><li><span><span><a href="https://catalogue.bnf.fr/ark:/12148/cb13190000m">France</a></span></span></li><li><span><span><a href="https://data.bnf.fr/ark:/12148/cb13190000m">BnF data</a></span></span></li><li><span><span><a href="https://aleph.nkp.cz/F/?func=find-c&amp;local_base=aut&amp;ccl_term=ica=ph121168&amp;CON_LNG=ENG">Czech Republic</a></span></span><ul><li><span><span><a href="https://aleph.nkp.cz/F/?func=find-c&amp;local_base=aut&amp;ccl_term=ica=ph120642&amp;CON_LNG=ENG">2</a></span></span></li><li><span><span><a href="https://aleph.nkp.cz/F/?func=find-c&amp;local_base=aut&amp;ccl_term=ica=ph121167&amp;CON_LNG=ENG">3</a></span></span></li></ul></li><li><span><a href="https://www.nli.org.il/en/authorities/987007561542705171">Israel</a></span></li></ul></div></td></tr><tr><th>Other</th><td><div><ul><li><span><a href="https://catalog.archives.gov/id/10638891">NARA</a></span></li><li><span><a href="http://esu.com.ua/search_articles.php?id=13319">Encyclopedia of Modern Ukraine</a></span></li></ul></div></td></tr></tbody></table></div> Unix time - Wikipedia https://en.wikipedia.org/wiki/Unix_time k5ZycpXx3eRE-1a8ENlguSJMmxwhy6CmEIEEIw== Sat, 09 May 2026 12:00:02 +0000 Date and time representation system widely used in computing <div>Date and time representation system widely used in computing</div><div>&quot;January 1, 1970&quot; redirects here. For the date, see <a href="https://en.wikipedia.org/wiki/January_1,_1970_(date)">January 1, 1970 (date)</a>.</div><div>&quot;Epoch time&quot; redirects here. For other epochs, see <a href="https://en.wikipedia.org/wiki/Epoch_(computing)">Epoch (computing)</a>. For the newspaper, see <a href="https://en.wikipedia.org/wiki/The_Epoch_Times"><i>The Epoch Times</i></a>.</div><p> </p><figure><a href="https://en.wikipedia.org/wiki/File:1000000000seconds.jpg"></a><figcaption>Unix time passed <span>1<span>000</span><span>000</span><span>000</span></span> seconds on 2001-09-09T01:46:40Z.<sup><span>[</span>1<span>]</span></sup> It was celebrated in Copenhagen, Denmark, at a party held by the <a href="https://en.wikipedia.org/wiki/Danish_UNIX_User_Group">Danish UNIX User Group</a>, at 03:46:40 local time.</figcaption></figure><p><b>Unix time</b><sup><span>[</span>a<span>]</span></sup> is a date and time representation widely used in <a href="https://en.wikipedia.org/wiki/Computing">computing</a>. It measures time by the number of <a href="https://en.wikipedia.org/wiki/Leap_second">non-leap</a> <a href="https://en.wikipedia.org/wiki/Seconds">seconds</a> that have elapsed since 00:00:00 <a href="https://en.wikipedia.org/wiki/Coordinated_Universal_Time">UTC</a> on 1 January 1970, the Unix <a href="https://en.wikipedia.org/wiki/Epoch_(computing)">epoch</a>. For example, at midnight on 1 January 2010, Unix time was 1262304000. </p><p>Unix time originated as the <a href="https://en.wikipedia.org/wiki/System_time">system time</a> of <a href="https://en.wikipedia.org/wiki/Unix">Unix</a> operating systems. It has come to be widely used in other computer <a href="https://en.wikipedia.org/wiki/Operating_system">operating systems</a>, <a href="https://en.wikipedia.org/wiki/File_system">file systems</a>, <a href="https://en.wikipedia.org/wiki/Programming_language">programming languages</a>, and <a href="https://en.wikipedia.org/wiki/Database">databases</a>. In modern computing, values are sometimes stored with higher <a href="https://en.wikipedia.org/wiki/Data_granularity">granularity</a>, such as <a href="https://en.wikipedia.org/wiki/Microsecond">microseconds</a> or <a href="https://en.wikipedia.org/wiki/Nanosecond">nanoseconds</a>. </p><div><h2>Definition</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>Unix time is currently defined as the number of non-leap seconds which have passed since 00:00:00<span> </span>UTC on Thursday, 1 January 1970, which is referred to as the <i>Unix <a href="https://en.wikipedia.org/wiki/Epoch_(computing)">epoch</a></i>.<sup><span>[</span>3<span>]</span></sup> Unix time is typically encoded as a <a href="https://en.wikipedia.org/wiki/Integer_(computer_science)#Value_and_representation">signed integer</a>. </p><p>The Unix time <span>0</span> is exactly midnight UTC on 1 January 1970, with Unix time incrementing by 1 for every non-leap second after this. For example, 00:00:00<span> </span>UTC on 1 January 1971 is represented in Unix time as <span>31<span>536</span><span>000</span></span>. Negative values, on systems that support them, indicate times before the Unix epoch, with the value decreasing by 1 for every non-leap second before the epoch. For example, 00:00:00<span> </span>UTC on 1 January 1969 is represented in Unix time as <span>−31<span>536</span><span>000</span></span>. </p><p>Unix time is sometimes referred to as <i>Epoch time</i>. This can be misleading since Unix time is not the only time system based on an epoch and the Unix epoch is not the only epoch used by other time systems.<sup><span>[</span>5<span>]</span></sup> </p><div><h3>Leap seconds</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>Unix time differs from both <a href="https://en.wikipedia.org/wiki/Coordinated_Universal_Time">Coordinated Universal Time</a> (UTC) and <a href="https://en.wikipedia.org/wiki/International_Atomic_Time">International Atomic Time</a> (TAI) in its handling of <a href="https://en.wikipedia.org/wiki/Leap_second">leap seconds</a>. UTC includes leap seconds that adjust for the discrepancy between precise time, as measured by <a href="https://en.wikipedia.org/wiki/Atomic_clock">atomic clocks</a>, and <a href="https://en.wikipedia.org/wiki/Solar_time">solar time</a>, relating to the position of the earth in relation to the sun. <a href="https://en.wikipedia.org/wiki/International_Atomic_Time">International Atomic Time</a> (TAI), in which every day is precisely <span>86<span>400</span></span> seconds long, ignores solar time and gradually loses <a href="https://en.wikipedia.org/wiki/Synchronization">synchronization</a> with the Earth&#39;s rotation as Earth slows at around 1.5 ms per day per <a href="https://en.wikipedia.org/wiki/Century">century</a>. In Unix time, every day contains exactly <span>86<span>400</span></span> seconds. Each leap second uses the <a href="https://en.wikipedia.org/wiki/Timestamp">timestamp</a> of a second that immediately precedes or follows it.<sup><span>[</span>3<span>]</span></sup> </p><p>On a normal UTC day, which has a duration of <span>86<span>400</span></span> seconds, the Unix time number changes in a <a href="https://en.wikipedia.org/wiki/Continuous_function">continuous</a> manner across midnight. For example, at the end of the day used in the examples above, the time representations progress as follows: </p><table> <caption>Unix time across midnight into 17 September 2004 (without leap seconds) </caption> <tbody><tr> <th>TAI (17 September 2004) </th> <th>UTC (16 to 17 September 2004) </th> <th>Unix time </th></tr> <tr> <td>2004-09-17T00:00:30.75 </td> <td>2004-09-16T23:59:58.75 </td> <td><span>1<span>095</span><span>379</span><span>198</span>.75</span> </td></tr> <tr> <td>2004-09-17T00:00:31.00 </td> <td>2004-09-16T23:59:59.00 </td> <td><span>1<span>095</span><span>379</span><span>199</span>.00</span> </td></tr> <tr> <td>2004-09-17T00:00:31.25 </td> <td>2004-09-16T23:59:59.25 </td> <td><span>1<span>095</span><span>379</span><span>199</span>.25</span> </td></tr> <tr> <td>2004-09-17T00:00:31.50 </td> <td>2004-09-16T23:59:59.50 </td> <td><span>1<span>095</span><span>379</span><span>199</span>.50</span> </td></tr> <tr> <th>2004-09-17T00:00:31.75 </th> <th>2004-09-16T23:59:59.75 </th> <th><span>1<span>095</span><span>379</span><span>199</span>.75</span> </th></tr> <tr> <th>2004-09-17T00:00:32.00 </th> <th>2004-09-17T00:00:00.00 </th> <th><span>1<span>095</span><span>379</span><span>200</span>.00</span> </th></tr> <tr> <td>2004-09-17T00:00:32.25 </td> <td>2004-09-17T00:00:00.25 </td> <td><span>1<span>095</span><span>379</span><span>200</span>.25</span> </td></tr> <tr> <td>2004-09-17T00:00:32.50 </td> <td>2004-09-17T00:00:00.50 </td> <td><span>1<span>095</span><span>379</span><span>200</span>.50</span> </td></tr> <tr> <td>2004-09-17T00:00:32.75 </td> <td>2004-09-17T00:00:00.75 </td> <td><span>1<span>095</span><span>379</span><span>200</span>.75</span> </td></tr> <tr> <td>2004-09-17T00:00:33.00 </td> <td>2004-09-17T00:00:01.00 </td> <td><span>1<span>095</span><span>379</span><span>201</span>.00</span> </td></tr> <tr> <td>2004-09-17T00:00:33.25 </td> <td>2004-09-17T00:00:01.25 </td> <td><span>1<span>095</span><span>379</span><span>201</span>.25</span> </td></tr></tbody></table><p>When a <a href="https://en.wikipedia.org/wiki/Leap_second">leap second</a> occurs, the UTC day is not exactly <span>86<span>400</span></span> seconds long and the Unix time number (which always increases by exactly <span>86<span>400</span></span> each day) experiences a <a href="https://en.wikipedia.org/wiki/Discontinuity_(mathematics)">discontinuity</a>. Leap seconds may be positive or negative. No negative leap second has ever been declared, but if one were to be, then at the end of a day with a negative leap second, the Unix time number would jump up by 1 to the start of the next day. During a positive leap second at the end of a day, which occurs about every year and a half on average, the Unix time number increases continuously into the next day during the leap second and then at the end of the leap second jumps back by 1 (returning to the start of the next day). For example, this is what happened on strictly conforming <a href="https://en.wikipedia.org/wiki/POSIX.1">POSIX.1</a> systems at the end of 1998: </p><table> <caption>Unix time across midnight into 1 January 1999 (positive leap second) </caption> <tbody><tr> <th>TAI (1 January 1999) </th> <th>UTC (31 December 1998 to 1 January 1999) </th> <th>Unix time </th></tr> <tr> <td>1999-01-01T00:00:29.75 </td> <td>1998-12-31T23:59:58.75 </td> <td><span>915<span>148</span><span>798</span>.75</span> </td></tr> <tr> <td>1999-01-01T00:00:30.00 </td> <td>1998-12-31T23:59:59.00 </td> <td><span>915<span>148</span><span>799</span>.00</span> </td></tr> <tr> <td>1999-01-01T00:00:30.25 </td> <td>1998-12-31T23:59:59.25 </td> <td><span>915<span>148</span><span>799</span>.25</span> </td></tr> <tr> <td>1999-01-01T00:00:30.50 </td> <td>1998-12-31T23:59:59.50 </td> <td><span>915<span>148</span><span>799</span>.50</span> </td></tr> <tr> <td>1999-01-01T00:00:30.75 </td> <td>1998-12-31T23:59:59.75 </td> <td><span>915<span>148</span><span>799</span>.75</span> </td></tr> <tr> <td>1999-01-01T00:00:31.00 </td> <th>1998-12-31T23:59:60.00 </th> <td><span>915<span>148</span><span>800</span>.00</span> </td></tr> <tr> <td>1999-01-01T00:00:31.25 </td> <th>1998-12-31T23:59:60.25 </th> <td><span>915<span>148</span><span>800</span>.25</span> </td></tr> <tr> <td>1999-01-01T00:00:31.50 </td> <th>1998-12-31T23:59:60.50 </th> <td><span>915<span>148</span><span>800</span>.50</span> </td></tr> <tr> <th>1999-01-01T00:00:31.75 </th> <th>1998-12-31T23:59:60.75 </th> <th><span>915<span>148</span><span>800</span>.75</span> </th></tr> <tr> <th>1999-01-01T00:00:32.00 </th> <th>1999-01-01T00:00:00.00 </th> <th><span>915<span>148</span><span>800</span>.00</span> </th></tr> <tr> <td>1999-01-01T00:00:32.25 </td> <td>1999-01-01T00:00:00.25 </td> <td><span>915<span>148</span><span>800</span>.25</span> </td></tr> <tr> <td>1999-01-01T00:00:32.50 </td> <td>1999-01-01T00:00:00.50 </td> <td><span>915<span>148</span><span>800</span>.50</span> </td></tr> <tr> <td>1999-01-01T00:00:32.75 </td> <td>1999-01-01T00:00:00.75 </td> <td><span>915<span>148</span><span>800</span>.75</span> </td></tr> <tr> <td>1999-01-01T00:00:33.00 </td> <td>1999-01-01T00:00:01.00 </td> <td><span>915<span>148</span><span>801</span>.00</span> </td></tr> <tr> <td>1999-01-01T00:00:33.25 </td> <td>1999-01-01T00:00:01.25 </td> <td><span>915<span>148</span><span>801</span>.25</span> </td></tr></tbody></table><p>Unix time numbers are repeated in the second immediately following a positive leap second. The Unix time number <span>1<span>483</span><span>228</span><span>800</span></span> is thus ambiguous: it can refer either to start of the leap second (2016-12-31 23:59:60) or the end of it, one second later (2017-01-01 00:00:00). In the theoretical case when a negative leap second occurs, no ambiguity is caused, but instead there is a range of Unix time numbers that do not refer to any point in UTC time at all. </p><p>A Unix clock is often implemented with a different type of positive leap second handling associated with the <a href="https://en.wikipedia.org/wiki/Network_Time_Protocol">Network Time Protocol</a> (NTP). This yields a system that does not conform to the POSIX standard. See the section below concerning NTP for details. </p><p>When dealing with periods that do not encompass a UTC leap second, the difference between two Unix time numbers is equal to the duration in seconds of the period between the corresponding points in time. This is a common computational technique. However, where leap seconds occur, such calculations give the wrong answer. In applications where this level of accuracy is required, it is necessary to consult a table of leap seconds when dealing with Unix times, and it is often preferable to use a different time encoding that does not suffer from this problem. </p><p>A Unix time number is easily converted back into a UTC time by taking the quotient and modulus of the Unix time number, modulo <span>86<span>400</span></span>. The quotient is the number of days since the epoch, and the modulus is the number of seconds since midnight UTC on that day. If given a Unix time number that is ambiguous due to a positive leap second, this algorithm interprets it as the time just after midnight. It never generates a time that is during a leap second. If given a Unix time number that is invalid due to a negative leap second, it generates an equally invalid UTC time. If these conditions are significant, it is necessary to consult a table of leap seconds to detect them. </p><div><h4>Non-synchronous Network Time Protocol-based variant</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Commonly a <a href="https://en.wikipedia.org/wiki/David_L._Mills">Mills</a>-style Unix clock is implemented with leap second handling not synchronous with the change of the Unix time number. The time number initially decreases where a leap should have occurred, and then it leaps to the correct time 1 second after the leap. This makes implementation easier, and is described by Mills&#39; paper.<sup><span>[</span>6<span>]</span></sup> This is what happens across a positive leap second: </p><table> <caption>Non-synchronous Mills-style Unix clock<br/>across midnight into 1 January 1999 (positive leap second) </caption> <tbody><tr> <th>TAI (1 January 1999) </th> <th>UTC (31 December 1998 to 1 January 1999) </th> <th>State </th> <th>Unix clock </th></tr> <tr> <td>1999-01-01T00:00:29.75 </td> <td>1998-12-31T23:59:58.75 </td> <td>TIME_INS </td> <td><span>915<span>148</span><span>798</span>.75</span> </td></tr> <tr> <td>1999-01-01T00:00:30.00 </td> <td>1998-12-31T23:59:59.00 </td> <td>TIME_INS </td> <td><span>915<span>148</span><span>799</span>.00</span> </td></tr> <tr> <td>1999-01-01T00:00:30.25 </td> <td>1998-12-31T23:59:59.25 </td> <td>TIME_INS </td> <td><span>915<span>148</span><span>799</span>.25</span> </td></tr> <tr> <td>1999-01-01T00:00:30.50 </td> <td>1998-12-31T23:59:59.50 </td> <td>TIME_INS </td> <td><span>915<span>148</span><span>799</span>.50</span> </td></tr> <tr> <td>1999-01-01T00:00:30.75 </td> <td>1998-12-31T23:59:59.75 </td> <td>TIME_INS </td> <td><span>915<span>148</span><span>799</span>.75</span> </td></tr> <tr> <th>1999-01-01T00:00:31.00 </th> <th>1998-12-31T23:59:60.00 </th> <th>TIME_INS </th> <th><span>915<span>148</span><span>800</span>.00</span> </th></tr> <tr> <th>1999-01-01T00:00:31.25 </th> <th>1998-12-31T23:59:60.25 </th> <th>TIME_OOP </th> <th><span>915<span>148</span><span>799</span>.25</span> </th></tr> <tr> <td>1999-01-01T00:00:31.50 </td> <td>1998-12-31T23:59:60.50 </td> <td>TIME_OOP </td> <td><span>915<span>148</span><span>799</span>.50</span> </td></tr> <tr> <th>1999-01-01T00:00:31.75 </th> <th>1998-12-31T23:59:60.75 </th> <th>TIME_OOP </th> <th><span>915<span>148</span><span>799</span>.75</span> </th></tr> <tr> <th>1999-01-01T00:00:32.00 </th> <th>1999-01-01T00:00:00.00 </th> <th>TIME_OOP </th> <th><span>915<span>148</span><span>800</span>.00</span> </th></tr> <tr> <td>1999-01-01T00:00:32.25 </td> <td>1999-01-01T00:00:00.25 </td> <td>TIME_WAIT </td> <td><span>915<span>148</span><span>800</span>.25</span> </td></tr> <tr> <td>1999-01-01T00:00:32.50 </td> <td>1999-01-01T00:00:00.50 </td> <td>TIME_WAIT </td> <td><span>915<span>148</span><span>800</span>.50</span> </td></tr> <tr> <td>1999-01-01T00:00:32.75 </td> <td>1999-01-01T00:00:00.75 </td> <td>TIME_WAIT </td> <td><span>915<span>148</span><span>800</span>.75</span> </td></tr> <tr> <td>1999-01-01T00:00:33.00 </td> <td>1999-01-01T00:00:01.00 </td> <td>TIME_WAIT </td> <td><span>915<span>148</span><span>801</span>.00</span> </td></tr> <tr> <td>1999-01-01T00:00:33.25 </td> <td>1999-01-01T00:00:01.25 </td> <td>TIME_WAIT </td> <td><span>915<span>148</span><span>801</span>.25</span> </td></tr></tbody></table><p>This can be decoded properly by paying attention to the leap second state variable, which unambiguously indicates whether the leap has been performed yet. The state variable change is synchronous with the leap. </p><p>A similar situation arises with a negative leap second, where the second that is skipped is slightly too late. Very briefly the system shows a nominally impossible time number, but this can be detected by the TIME_DEL state and corrected. </p><p>In this type of system the Unix time number violates POSIX around both types of leap second. Collecting the leap second state variable along with the time number allows for unambiguous decoding, so the correct POSIX time number can be generated if desired, or the full UTC time can be stored in a more suitable format. </p><p>The decoding logic required to cope with this style of Unix clock would also correctly decode a hypothetical POSIX-conforming clock using the same interface. This would be achieved by indicating the TIME_INS state during the entirety of an inserted leap second, then indicating TIME_WAIT during the entirety of the following second while repeating the seconds count. This requires synchronous leap second handling. This is probably the best way to express UTC time in Unix clock form, via a Unix interface, when the underlying clock is fundamentally untroubled by leap seconds. </p><div><h4>Variant that counts leap seconds</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Another, much rarer, non-conforming variant of Unix time keeping involves incrementing the value for all seconds, including leap seconds;<sup><span>[</span>7<span>]</span></sup> some Linux systems are configured this way.<sup><span>[</span>8<span>]</span></sup> Time kept in this fashion is sometimes referred to as &quot;TAI&quot; (although timestamps can be converted to UTC if the value corresponds to a time when the difference between TAI and UTC is known), as opposed to &quot;UTC&quot; (although not all UTC time values have a unique reference in systems that do not count leap seconds).<sup><span>[</span>8<span>]</span></sup> </p><p>Because TAI has no leap seconds, and every TAI day is exactly 86400 seconds long, this encoding is actually a pure linear count of seconds elapsed since 1970-01-01T00:00:10<span> </span>TAI. This makes time interval arithmetic much easier. Time values from these systems do not suffer the ambiguity that strictly conforming POSIX systems or NTP-driven systems have. </p><p>In these systems it is necessary to consult a table of leap seconds to correctly convert between UTC and the pseudo-Unix-time representation. This resembles the manner in which time zone tables must be consulted to convert to and from <a href="https://en.wikipedia.org/wiki/Civil_time">civil time</a>; the <a href="https://en.wikipedia.org/wiki/IANA_time_zone_database">IANA time zone database</a> includes leap second information, and the sample code available from the same source uses that information to convert between TAI-based timestamps and local time. Conversion also runs into definitional problems prior to the 1972 commencement of the current form of UTC (see section UTC basis below). </p><p>This system, despite its superficial resemblance, is not Unix time. It encodes times with values that differ by several seconds from the POSIX time values. A version of this system, in which the epoch was 1970-01-01T00:00:00<span> </span>TAI rather than 1970-01-01T00:00:10<span> </span>TAI, was proposed for inclusion in ISO C&#39;s <a href="https://en.wikipedia.org/wiki/C_date_and_time_functions"><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">time.h</code></a>, but only the UTC part was accepted in 2011.<sup><span>[</span>9<span>]</span></sup> A <code class="mw-highlight mw-highlight-lang-text mw-content-ltr">tai_clock</code> does, however, exist in C++20. </p><div><h3>Representing the number</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>A Unix time number can be represented in any form capable of representing numbers. In some applications the number is simply represented textually as a string of decimal digits, raising only trivial additional problems. However, certain binary representations of Unix times are particularly significant. </p><p>The Unix <code>time_t</code> data type that represents a point in time is, on many platforms, a <a href="https://en.wikipedia.org/wiki/Integer_(computer_science)">signed integer</a>, traditionally of 32<span> </span><a href="https://en.wikipedia.org/wiki/Bit">bits</a> (but see below), directly encoding the Unix time number as described in the preceding section. A signed 32-bit value covers about 68 years before and after the 1970-01-01 epoch. The minimum representable date is Friday 1901-12-13, and the maximum representable date is Tuesday 2038-01-19. One second after 2038-01-19T03:14:07Z this representation will <a href="https://en.wikipedia.org/wiki/Arithmetic_overflow">overflow</a> in what is known as the <a href="https://en.wikipedia.org/wiki/Year_2038_problem">year 2038 problem</a>. </p><p><a href="https://en.wikipedia.org/wiki/UUID">UUIDv</a>7 encodes the Unix epoch timestamp (in milliseconds) in an unsigned 48-bit field. This representation is valid until the year 10889.<sup><span>[</span>10<span>]</span></sup> </p><p>In some newer operating systems, <code>time_t</code> has been widened to 64 bits. This expands the times representable to about <span>292.3 billion years</span> in both directions, which is over twenty times the present <a href="https://en.wikipedia.org/wiki/Age_of_the_universe">age of the universe</a>. </p><p>There was originally some controversy over whether the Unix <code>time_t</code> should be signed or unsigned. If unsigned, its range in the future would be doubled, postponing the 32-bit overflow (by 68 years). However, it would then be incapable of representing times prior to the epoch. The consensus is for <code>time_t</code> to be signed, and this is the usual practice. The software development platform for version 6 of the <a href="https://en.wikipedia.org/wiki/QNX">QNX</a> operating system has an unsigned 32-bit <code>time_t</code>, though older releases used a signed type. </p><p>The <a href="https://en.wikipedia.org/wiki/POSIX">POSIX</a> and <a href="https://en.wikipedia.org/wiki/Open_Group">Open Group</a> Unix specifications include the <a href="https://en.wikipedia.org/wiki/C_standard_library">C standard library</a>, which includes the time types and functions defined in the <a href="https://en.wikipedia.org/wiki/Time.h"><code>&lt;time.h&gt;</code></a> header file. The ISO C standard states that <code>time_t</code> must be an arithmetic type, but does not mandate any specific type or encoding for it. POSIX requires <code>time_t</code> to be an integer type, but does not mandate that it be signed or unsigned. </p><p>Unix has no tradition of directly representing non-integer Unix time numbers as binary fractions. Instead, times with sub-second precision are represented using <a href="https://en.wikipedia.org/wiki/Composite_data_type">composite data types</a> that consist of two integers, the first being a <code>time_t</code> (the integral part of the Unix time), and the second being the fractional part of the time number in millionths (in <code>struct timeval</code>) or billionths (in <code>struct timespec</code>).<sup><span>[</span>11<span>]</span></sup><sup><span>[</span>12<span>]</span></sup> These structures provide a <a href="https://en.wikipedia.org/wiki/Decimal">decimal</a>-based <a href="https://en.wikipedia.org/wiki/Fixed-point_arithmetic">fixed-point</a> data format, which is useful for some applications, and trivial to convert for others. </p><div><h3>UTC basis</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>The present form of UTC, with leap seconds, is defined only starting from 1 January 1972. Prior to that, since 1 January 1961 there was an older form of UTC in which not only were there occasional time steps, which were by non-integer numbers of seconds, but also the UTC second was slightly longer than the SI second, and periodically changed to continuously approximate the Earth&#39;s rotation. Prior to 1961 there was no UTC, and prior to 1958 there was no widespread <a href="https://en.wikipedia.org/wiki/Atomic_clock">atomic timekeeping</a>; in these eras, some approximation of <a href="https://en.wikipedia.org/wiki/GMT">GMT</a> (based directly on the Earth&#39;s rotation) was used instead of an atomic timescale.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>The precise definition of Unix time as an encoding of UTC is only uncontroversial when applied to the present form of UTC. The Unix epoch predating the start of this form of UTC does not affect its use in this era: the number of days from 1 January 1970 (the Unix epoch) to 1 January 1972 (the start of UTC) is not in question, and the number of days is all that is significant to Unix time. </p><p>The meaning of Unix time values below <span>+63<span>072</span><span>000</span></span> (i.e., prior to 1 January 1972) is not precisely defined. The basis of such Unix times is best understood to be an unspecified approximation of UTC. Computers of that era rarely had clocks set sufficiently accurately to provide meaningful sub-second timestamps in any case. Unix time is not a suitable way to represent times prior to 1972 in applications requiring sub-second precision; such applications must, at least, define which form of UT or GMT they use. </p><p>As of 2009<sup><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit">[update]</a></sup>, the possibility of ending the use of leap seconds in civil time is being considered.<sup><span>[</span>13<span>]</span></sup> A likely means to execute this change is to define a new time scale, called <i>International Time</i><sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup>, that initially matches UTC but thereafter has no leap seconds, thus remaining at a constant offset from TAI. If this happens, it is likely that Unix time will be prospectively defined in terms of this new time scale, instead of UTC. Uncertainty about whether this will occur makes prospective Unix time no less predictable than it already is: if UTC were simply to have no further leap seconds the result would be the same. </p><div><h2>History</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>The earliest versions of Unix time had a 32-bit integer incrementing at a rate of 60 <a href="https://en.wikipedia.org/wiki/Hertz">Hz</a>, which was the rate of the system clock on the hardware of the early Unix systems. Timestamps stored this way could only represent a range of a little over two and a quarter years. The epoch being counted from was changed with Unix releases to prevent overflow, with midnight on 1 January 1971 and 1 January 1972 both being used as epochs during Unix&#39;s early development. Early definitions of Unix time also lacked time zones.<sup><span>[</span>14<span>]</span></sup><sup><span>[</span>15<span>]</span></sup> </p><p>The current epoch of 1 January 1970 00:00:00 UTC was selected arbitrarily by Unix engineers because it was considered a convenient date to work with. The precision was changed to count in seconds in order to avoid short-term overflow.<sup><span>[</span>1<span>]</span></sup> </p><p>When <a href="https://en.wikipedia.org/wiki/POSIX#POSIX.1">POSIX.1</a> was written, the question arose of how to precisely define <code>time_t</code> in the face of leap seconds. The POSIX committee considered whether Unix time should remain, as intended, a linear count of seconds since the epoch, at the expense of complexity in conversions with civil time or a representation of civil time, at the expense of inconsistency around leap seconds. Computer clocks of the era were not sufficiently precisely set to form a precedent one way or the other. </p><p>The POSIX committee was swayed by arguments against complexity in the library functions,<sup><span>[</span>16<span>]</span></sup> and firmly defined the Unix time in a simple manner in terms of the elements of UTC time. This definition was so simple that it did not even encompass the entire <a href="https://en.wikipedia.org/wiki/Leap_year">leap year</a> rule of the Gregorian calendar, and would make 2100 a leap year. </p><p>The 2001 edition of POSIX.1 rectified the faulty leap year rule in the definition of Unix time, but retained the essential definition of Unix time as an encoding of UTC rather than a linear time scale. Since the mid-1990s, computer clocks have been routinely set with sufficient precision for this to matter, and they have most commonly been set using the UTC-based definition of Unix time. This has resulted in considerable complexity in Unix implementations, and in the <a href="https://en.wikipedia.org/wiki/Network_Time_Protocol">Network Time Protocol</a>, to execute steps in the Unix time number whenever leap seconds occur.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><div><h2>Usage</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>Unix time is widely adopted in computing beyond its original application as the system time for <a href="https://en.wikipedia.org/wiki/Unix">Unix</a>. Unix time is available in almost all system programming <a href="https://en.wikipedia.org/wiki/API">APIs</a>, including those provided by both Unix-based and non-Unix <a href="https://en.wikipedia.org/wiki/Operating_systems">operating systems</a>. Almost all modern <a href="https://en.wikipedia.org/wiki/Programming_languages">programming languages</a> provide APIs for working with Unix time or converting them to another data structure. Unix time is also used as a mechanism for storing timestamps in a number of <a href="https://en.wikipedia.org/wiki/File_systems">file systems</a>, <a href="https://en.wikipedia.org/wiki/File_formats">file formats</a>, and <a href="https://en.wikipedia.org/wiki/Databases">databases</a>. </p><p>The <a href="https://en.wikipedia.org/wiki/C_standard_library">C standard library</a> uses Unix time for all date and time functions, and Unix time is sometimes referred to as time_t, the name of the <a href="https://en.wikipedia.org/wiki/Data_type">data type</a> used for timestamps in <a href="https://en.wikipedia.org/wiki/C_(programming_language)">C</a> and <a href="https://en.wikipedia.org/wiki/C%2B%2B">C++</a>. C&#39;s Unix time functions are defined as the system time API in the <a href="https://en.wikipedia.org/wiki/POSIX">POSIX</a> specification.<sup><span>[</span>17<span>]</span></sup> The C standard library is used extensively in all modern desktop operating systems, including <a href="https://en.wikipedia.org/wiki/Microsoft_Windows">Microsoft Windows</a> and <a href="https://en.wikipedia.org/wiki/Unix-like">Unix-like</a> systems such as <a href="https://en.wikipedia.org/wiki/MacOS">macOS</a> and <a href="https://en.wikipedia.org/wiki/Linux">Linux</a>, where it is a standard programming interface.<sup><span>[</span>18<span>]</span></sup><sup><span>[</span>19<span>]</span></sup><sup><span>[</span>20<span>]</span></sup> </p><p><a href="https://en.wikipedia.org/wiki/IOS">iOS</a> provides a Swift API which defaults to using an epoch of 1 January 2001 but can also be used with Unix timestamps.<sup><span>[</span>21<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Android_(operating_system)">Android</a> uses Unix time alongside a time zone for its system time API.<sup><span>[</span>22<span>]</span></sup> </p><p>Windows does not use Unix time for storing time internally but does use it in system APIs, which are provided in C++ and implement the C standard library specification.<sup><span>[</span>18<span>]</span></sup> Unix time is used in the <a href="https://en.wikipedia.org/wiki/PE_format">PE format</a> for Windows executables.<sup><span>[</span>23<span>]</span></sup> </p><p>Unix time is typically available in major programming languages and is widely used in desktop, mobile, and web application programming. <a href="https://en.wikipedia.org/wiki/Java_(programming_language)">Java</a> provides an Instant object which holds a Unix timestamp in both seconds and nanoseconds.<sup><span>[</span>24<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Python_(programming_language)">Python</a> provides a time library which uses Unix time.<sup><span>[</span>25<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/JavaScript">JavaScript</a> provides a Date library which provides and stores timestamps in milliseconds since the Unix epoch and is implemented in all modern desktop and mobile <a href="https://en.wikipedia.org/wiki/Web_browsers">web browsers</a> as well as in JavaScript server environments like <a href="https://en.wikipedia.org/wiki/Node.js">Node.js</a>.<sup><span>[</span>26<span>]</span></sup> </p><p><a href="https://en.wikipedia.org/wiki/Free_Pascal">Free Pascal</a> implements UNIX time with the GetTickCount (deprecated unsigned 32 bit) and GetTickCount64 (Unsigned 64 bit) functions to a resolution of 1ms on <a href="https://en.wikipedia.org/wiki/Unix-like">Unix-like</a> platforms. </p><p>Filesystems designed for use with Unix-based operating systems tend to use Unix time. <a href="https://en.wikipedia.org/wiki/APFS">APFS</a>, the file system used by default across all Apple devices, and <a href="https://en.wikipedia.org/wiki/Ext4">ext4</a>, which is widely used on Linux and Android devices, both use Unix time in nanoseconds for file timestamps.<sup><span>[</span>27<span>]</span></sup><sup><span>[</span>28<span>]</span></sup> Several <a href="https://en.wikipedia.org/wiki/Archive_file_format">archive file formats</a> can store timestamps in Unix time, including <a href="https://en.wikipedia.org/wiki/RAR_(file_format)">RAR</a> and <a href="https://en.wikipedia.org/wiki/Tar_(computing)">tar</a>.<sup><span>[</span>29<span>]</span></sup><sup><span>[</span>30<span>]</span></sup> Unix time is also commonly used to store timestamps in databases, including in <a href="https://en.wikipedia.org/wiki/MySQL">MySQL</a> and <a href="https://en.wikipedia.org/wiki/PostgreSQL">PostgreSQL</a>.<sup><span>[</span>31<span>]</span></sup><sup><span>[</span>32<span>]</span></sup> </p><div><h2>Limitations</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>Unix time was designed to encode calendar dates and times in a compact manner intended for use by computers internally. It is not intended to be easily read by humans or to store time-zone-dependent values. It is also limited by default to representing time in seconds, making it unsuited for use when a more precise measurement of time is needed, such as when measuring the execution time of programs.<sup><span>[</span>33<span>]</span></sup> </p><div><h3>Range of representable times</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><div>See also: <a href="https://en.wikipedia.org/wiki/Year_2038_problem">Year 2038 problem</a></div><figure><a href="https://en.wikipedia.org/wiki/File:Year_2038_problem.gif"></a><figcaption>An animated visual of the <a href="https://en.wikipedia.org/wiki/Year_2038_problem">32-bit Unix time overflow which will occur in 2038</a></figcaption></figure><p>Unix time by design does not require a specific size for the storage, but most common implementations of Unix time use a <a href="https://en.wikipedia.org/wiki/Signed_integer">signed integer</a> with the same size as the <a href="https://en.wikipedia.org/wiki/Word_(computer_architecture)">word size</a> of the underlying hardware. As the majority of modern computers are <a href="https://en.wikipedia.org/wiki/32-bit">32-bit</a> or <a href="https://en.wikipedia.org/wiki/64-bit">64-bit</a>, and a large number of programs are still written in 32-bit compatibility mode, this means that many programs using Unix time are using signed 32-bit integer fields. The maximum value of a signed 32-bit integer is <span>2<sup>31</sup> − 1</span>, and the minimum value is <span>−2<sup>31</sup></span>, making it impossible to represent dates before 13 December 1901 (at 20:45:52 UTC) or after 19 January 2038 (at 03:14:07 UTC). The early cutoff can have an impact on databases that are storing historical information; in some databases where 32-bit Unix time is used for timestamps, it may be necessary to store time in a different form of field, such as a string, to represent dates before 1901. The late cutoff is known as the <a href="https://en.wikipedia.org/wiki/Year_2038_problem">Year 2038 problem</a> and has the potential to cause issues as the date approaches, as dates beyond the 2038 cutoff would wrap back around to the start of the representable range in 1901.<sup><span>[</span>33<span>]</span></sup><sup><span>: 60 </span></sup><sup><span>[</span>34<span>]</span></sup> </p><p>Date range cutoffs are not an issue with 64-bit representations of Unix time, as the effective range of dates representable with Unix time stored in a signed 64-bit integer is over 584 billion years, or 292 billion years in either direction of the 1970 epoch.<sup><span>[</span>33<span>]</span></sup><sup><span>: 60-61 </span></sup><sup><span>[</span>35<span>]</span></sup> </p><div><h2>Alternatives</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><p>Unix time is not the only standard for time that counts away from an epoch. The <a href="https://en.wikipedia.org/wiki/C-Sharp_(programming_language)">C# programming language</a>&#39;s <code>DateTime</code> structure, the <code>FILETIME</code> type in <a href="https://en.wikipedia.org/wiki/Microsoft_Windows">Windows</a>, and <a href="https://en.wikipedia.org/wiki/Cosmos_DB">Azure Cosmos DB</a>&#39;s <code>GetCurrentTicks</code> function store time as a count of 100-nanosecond intervals that have elapsed since 0:00 <a href="https://en.wikipedia.org/wiki/GMT">GMT</a> on 1 January <a href="https://en.wikipedia.org/wiki/AD_1">1 AD</a>,<sup><span>[</span>36<span>]</span></sup> 1 January 1601,<sup><span>[</span>37<span>]</span></sup> and 1 January 1970,<sup><span>[</span>38<span>]</span></sup> which will not overflow until the years 29228,<sup><span>[</span>39<span>]</span></sup><sup><span>[</span>40<span>]</span></sup> 30828,<sup><span>[</span>39<span>]</span></sup><sup><span>[</span>41<span>]</span></sup> and 31197,<sup><span>[</span>42<span>]</span></sup> respectively. Windows epoch time is used to store timestamps for files<sup><span>[</span>43<span>]</span></sup> and in protocols such as the <a href="https://en.wikipedia.org/wiki/Active_Directory">Active Directory</a> Time Service<sup><span>[</span>44<span>]</span></sup> and <a href="https://en.wikipedia.org/wiki/Server_Message_Block">Server Message Block</a>. </p><p>The <a href="https://en.wikipedia.org/wiki/Network_Time_Protocol">Network Time Protocol</a> used to coordinate time between computers uses an epoch of 1 January 1900, counted in an unsigned 32-bit integer for seconds and another unsigned 32-bit integer for fractional seconds, which rolls over every 2<sup>32</sup> seconds (about once every 136 years).<sup><span>[</span>45<span>]</span></sup> </p><p>Many applications and programming languages provide methods for storing time with an explicit time zone.<sup><span>[</span>46<span>]</span></sup> There are also a number of time format standards which exist to be readable by both humans and computers, such as <a href="https://en.wikipedia.org/wiki/ISO_8601">ISO 8601</a>. </p><div><h2>Notable events in Unix time</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><p>Unix enthusiasts have a history of holding &quot;time_t parties&quot; (pronounced &quot;time <a href="https://en.wikipedia.org/wiki/Tea_party">tea parties</a>&quot;) to celebrate significant values of the Unix time number.<sup><span>[</span>47<span>]</span></sup><sup><span>[</span>48<span>]</span></sup> These are directly analogous to the <a href="https://en.wikipedia.org/wiki/New_year">new year</a> celebrations that occur at the change of year in many calendars. As the use of Unix time has spread, so has the practice of celebrating its milestones. Usually it is time values that are round numbers in <a href="https://en.wikipedia.org/wiki/Decimal">decimal</a> that are celebrated, following the Unix convention of viewing <code>time_t</code> values in decimal. Among some groups round <a href="https://en.wikipedia.org/wiki/Binary_numeral_system">binary</a> numbers are also celebrated,<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> such as +2<sup>30</sup>, which occurred at 13:37:04 UTC on Saturday, 10 January 2004. </p><p>The events that these celebrate are typically described as &quot;<i>N</i> seconds since the Unix epoch&quot;, but this is inaccurate; as discussed above, due to the handling of leap seconds in Unix time the number of seconds elapsed since the Unix epoch is slightly greater than the Unix time number for times later than the epoch. </p><ul><li>At 18:36:57 UTC on Wednesday, 17 October 1973, the first appearance of the date in <a href="https://en.wikipedia.org/wiki/ISO_8601">ISO 8601</a> format<sup><span>[</span>b<span>]</span></sup> <span>(1973-10-17)</span> within the digits of Unix time (119731017) took place.</li> <li>At 01:46:40 UTC on Sunday, 9 September 2001, the Unix billennium (Unix time number <span>1<span>000</span><span>000</span><span>000</span></span>) was celebrated.<sup><span>[</span>49<span>]</span></sup> The name <i>billennium</i> is a <a href="https://en.wikipedia.org/wiki/Portmanteau">portmanteau</a> of <i><a href="https://en.wikipedia.org/wiki/Billion_(word)">billion</a></i> and <i><a href="https://en.wikipedia.org/wiki/Millennium">millennium</a></i>.<sup><span>[</span>50<span>]</span></sup><sup><span>[</span>51<span>]</span></sup> Some programs which stored timestamps using a text representation encountered sorting errors, as in a text sort, times after the turnover starting with a <i>1</i> digit erroneously sorted before earlier times starting with a <i>9</i> digit. Affected programs included the popular <a href="https://en.wikipedia.org/wiki/Usenet">Usenet</a> reader <a href="https://en.wikipedia.org/wiki/KNode">KNode</a> and <a href="https://en.wikipedia.org/wiki/E-mail">e-mail</a> client <a href="https://en.wikipedia.org/wiki/KMail">KMail</a>, part of the <a href="https://en.wikipedia.org/wiki/KDE">KDE</a> desktop environment. Such bugs were generally cosmetic in nature and quickly fixed once problems became apparent.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> The problem also affected many <i>Filtrix</i> document-format filters provided with <a href="https://en.wikipedia.org/wiki/Linux">Linux</a> versions of <a href="https://en.wikipedia.org/wiki/WordPerfect">WordPerfect</a>; a patch was created by the user community to solve this problem, since <a href="https://en.wikipedia.org/wiki/Corel">Corel</a> no longer sold or supported that version of the program.<sup><span>[</span>52<span>]</span></sup></li> <li>At 23:31:30 UTC on Friday, 13 February 2009, the <a href="https://en.wikipedia.org/wiki/Decimal">decimal</a> representation of Unix time reached <span>1<span>234</span><span>567</span><span>890</span></span> seconds.<sup><span>[</span>53<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Google">Google</a> celebrated this with a <a href="https://en.wikipedia.org/wiki/Google_Doodle">Google Doodle</a>.<sup><span>[</span>54<span>]</span></sup> Parties and other celebrations were held around the world, among various technical subcultures, to celebrate the <span>1<span>234</span><span>567</span><span>890</span></span>th second.<sup><span>[</span>47<span>]</span></sup><sup><span>[</span>55<span>]</span></sup></li></ul><div><h2>In popular culture</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><p><a href="https://en.wikipedia.org/wiki/Vernor_Vinge">Vernor Vinge</a>&#39;s novel <i><a href="https://en.wikipedia.org/wiki/A_Deepness_in_the_Sky">A Deepness in the Sky</a></i> describes a spacefaring trading civilization thousands of years in the future that still uses the Unix epoch. The &quot;<a href="https://en.wikipedia.org/wiki/Software_archaeology">programmer-archaeologist</a>&quot; responsible for finding and maintaining usable code in mature computer systems first believes that the epoch refers to the time when <a href="https://en.wikipedia.org/wiki/Apollo_11">man first walked on the Moon</a>, but then realizes that it is &quot;the 0-second of one of humankind&#39;s first computer operating systems&quot;.<sup><span>[</span>56<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Epoch_(computing)">Epoch (computing)</a></li> <li><a href="https://en.wikipedia.org/wiki/System_time">System time</a></li></ul><div><h2>Notes</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div><div><ol> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Farhad, Manjoo (8 September 2001). <a href="https://www.wired.com/2001/09/unix-tick-tocks-to-a-billion/">&quot;Unix Tick Tocks to a Billion&quot;</a>. <i>Wired</i>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1059-1028">1059-1028</a>. <a href="https://web.archive.org/web/20220911005342/https://www.wired.com/2001/09/unix-tick-tocks-to-a-billion/">Archived</a> from the original on 11 September 2022<span>. Retrieved <span>16 October</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://pubs.opengroup.org/onlinepubs/9699919799/xrat/V4_xbd_chap04.html">&quot;The Open Group Base Specifications Issue 7, Rationale: Base Definitions, section A.4 General Concepts&quot;</a>. <a href="https://en.wikipedia.org/wiki/The_Open_Group">The Open Group</a>. <a href="https://web.archive.org/web/20171115154605/http://pubs.opengroup.org/onlinepubs/9699919799/xrat/V4_xbd_chap04.html">Archived</a> from the original on 15 November 2017<span>. Retrieved <span>9 September</span> 2019</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite><a href="http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1_chap04.html#tag_04_16">&quot;The Open Group Base Specifications Issue 7, section 4.16 Seconds Since the Epoch&quot;</a>. <a href="https://en.wikipedia.org/wiki/The_Open_Group">The Open Group</a>. <a href="https://web.archive.org/web/20171222113543/http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1_chap04.html#tag_04_16">Archived</a> from the original on 22 December 2017<span>. Retrieved <span>22 January</span> 2017</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Matthew, Neil; Stones, Richard (2008). &quot;The Linux Environment&quot;. <i>Beginning Linux Programming</i>. Indianapolis, Indiana, US: Wiley. p. 148. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-14762-7"><bdi>978-0-470-14762-7</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://learn.microsoft.com/en-us/windows/win32/api/minwinbase/ns-minwinbase-filetime">&quot;FILETIME structure (minwinbase.h)&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Microsoft_Docs">Microsoft Docs</a></i>. 2 April 2021.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Mills, David L. (12 May 2012). <a href="https://www.eecis.udel.edu/~mills/leap.html">&quot;The NTP Timescale and Leap Seconds&quot;</a>. <i>eecis.udel.edu</i>. <a href="https://web.archive.org/web/20120515005611/http://www.eecis.udel.edu/~mills/leap.html">Archived</a> from the original on 15 May 2012<span>. Retrieved <span>21 August</span> 2017</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.iana.org/time-zones/repository/tz-link.html#precision">&quot;Precision timekeeping&quot;</a>. <i>Sources for time zone and daylight saving time data</i>. <a href="https://web.archive.org/web/20171016230241/http://www.iana.org/time-zones/repository/tz-link.html#precision">Archived</a> from the original on 16 October 2017<span>. Retrieved <span>30 May</span> 2022</span>. <q>The tz code and data support leap seconds via an optional &quot;right&quot; configuration where a computer&#39;s internal time_t integer clock counts every TAI second, as opposed to the default &quot;posix&quot; configuration where the internal clock ignores leap seconds. The two configurations agree for timestamps starting with 1972-01-01 00:00:00 UTC (time_t 63 072 000) and diverge for timestamps starting with time_t 78 796 800, which corresponds to the first leap second 1972-06-30 23:59:60 UTC in the &quot;right&quot; configuration, and to 1972-07-01 00:00:00 UTC in the &quot;posix&quot; configuration.</q></cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://support.ntp.org/bin/view/Support/TimeScales">&quot;Time Scales&quot;</a>. <i>Network Time Protocol Wiki</i>. 24 July 2019. <a href="https://web.archive.org/web/20200112103701/https://support.ntp.org/bin/view/Support/TimeScales">Archived</a> from the original on 12 January 2020<span>. Retrieved <span>12 January</span> 2020</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Markus Kuhn. <a href="https://www.cl.cam.ac.uk/~mgk25/time/c/">&quot;Modernized API for ISO C&quot;</a>. <i>www.cl.cam.ac.uk</i>. <a href="https://web.archive.org/web/20200926224028/https://www.cl.cam.ac.uk/~mgk25/time/c/">Archived</a> from the original on 26 September 2020<span>. Retrieved <span>31 August</span> 2020</span>.</cite></span> </li> <li><span><b>^</b></span> <span> <a href="https://en.wikipedia.org/wiki/RFC_(identifier)">RFC</a> <a href="https://www.rfc-editor.org/rfc/rfc9562">9562</a></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://netbsd.gw.com/cgi-bin/man-cgi?timespec">&quot;timespec&quot;</a>. <i>NetBSD Manual Pages</i>. 12 April 2011. <a href="https://web.archive.org/web/20190810060329/https://netbsd.gw.com/cgi-bin/man-cgi?timespec">Archived</a> from the original on 10 August 2019<span>. Retrieved <span>5 July</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://man7.org/linux/man-pages/man0/time.h.0p.html">&quot;time.h(0P)&quot;</a>. <i>Linux manual page</i>. <a href="https://web.archive.org/web/20190627152007/http://man7.org/linux/man-pages/man0/time.h.0p.html">Archived</a> from the original on 27 June 2019<span>. Retrieved <span>5 July</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Dennis_McCarthy_(scientist)">McCarthy, D. D.</a>; Seidelmann, P. K. (2009). <i>TIME—From Earth Rotation to Atomic Physics</i>. Weinheim: Wiley–VCH Verlag GmbH &amp; Co. KGaA. p. 232. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-3-527-40780-4"><bdi>978-3-527-40780-4</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.bell-labs.com/usr/dmr/www/pdfs/man22.pdf"><i>Unix Programmer&#39;s Manual</i></a> <span>(PDF)</span> (1st ed.). 3 November 1971. <a href="https://web.archive.org/web/20220305094724/https://www.bell-labs.com/usr/dmr/www/pdfs/man22.pdf">Archived</a> <span>(PDF)</span> from the original on 5 March 2022<span>. Retrieved <span>28 March</span> 2012</span>. <q><i>time</i> returns the time since 00:00:00, Jan. 1, 1971, measured in sixtieths of a second.</q></cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://bitsavers.org/pdf/att/unix/3rd_Edition/UNIX_Programmers_Manual_Third_Edition_Feb73.pdf"><i>Unix Programmer&#39;s Manual</i></a> <span>(PDF)</span> (3rd ed.). 15 March 1972. <a href="https://web.archive.org/web/20230212065854/http://bitsavers.org/pdf/att/unix/3rd_Edition/UNIX_Programmers_Manual_Third_Edition_Feb73.pdf">Archived</a> <span>(PDF)</span> from the original on 12 February 2023<span>. Retrieved <span>11 February</span> 2023</span>. <q><i>time</i> returns the time since 00:00:00, Jan. 1, 1972, measured in sixtieths of a second...The time is stored in 32 bits. This guarantees a crisis every 2.26 years.</q></cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://news.ycombinator.com/item?id=13621623">&quot;Posix Has Become Outdated (2016) [pdf] | Hacker News&quot;</a>. <i>news.ycombinator.com</i>. <a href="https://web.archive.org/web/20250318023606/https://news.ycombinator.com/item?id=13621623">Archived</a> from the original on 18 March 2025<span>. Retrieved <span>23 July</span> 2025</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://pubs.opengroup.org/onlinepubs/9699919799/functions/time.html">&quot;The Open Group Technical Standard Base Specifications Issue 7 (2018 edition)&quot;</a>. IEEE and The Open Group. <a href="https://web.archive.org/web/20230501172931/https://pubs.opengroup.org/onlinepubs/9699919799/functions/time.html">Archived</a> from the original on 1 May 2023<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://learn.microsoft.com/en-us/cpp/c-runtime-library/reference/time-time32-time64?view=msvc-170">&quot;time, _time32, _time64&quot;</a>. <i>learn.microsoft.net</i>. Microsoft Corporation. 13 February 2023. <a href="https://web.archive.org/web/20230501184037/https://learn.microsoft.com/en-us/cpp/c-runtime-library/reference/time-time32-time64?view=msvc-170">Archived</a> from the original on 1 May 2023<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.gnu.org/software/libc/">&quot;The GNU C Library (glibc)&quot;</a>. <i>The GNU Operating Sisyem</i>. Free Software Foundation. <a href="https://web.archive.org/web/20160422061403/http://www.gnu.org/software/libc/">Archived</a> from the original on 22 April 2016<span>. Retrieved <span>1 May</span> 2023</span>. <q>The GNU C Library project provides the core libraries for the GNU system and GNU/Linux systems, as well as many other systems that use Linux as the kernel.</q></cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://developer.apple.com/library/archive/documentation/System/Conceptual/ManPages_iPhoneOS/man3/localtime.3.html">&quot;Mac OS X Manual Page for localtime(3)&quot;</a>. <i>Apple Documentation Archive</i>. Apple Inc. <a href="https://web.archive.org/web/20220722085416/https://developer.apple.com/library/archive/documentation/System/Conceptual/ManPages_iPhoneOS/man3/localtime.3.html">Archived</a> from the original on 22 July 2022<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://developer.apple.com/documentation/foundation/nsdate">&quot;NSDate&quot;</a>. <i>Apple Developer Documentation</i>. Apple Inc. <a href="https://web.archive.org/web/20230501172929/https://developer.apple.com/documentation/foundation/nsdate">Archived</a> from the original on 1 May 2023<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://source.android.com/docs/core/connect/time">&quot;Time Overview&quot;</a>. <i>Android Open Source Project</i>. Google LLC. <a href="https://web.archive.org/web/20230501172931/https://source.android.com/docs/core/connect/time">Archived</a> from the original on 1 May 2023<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://learn.microsoft.com/en-us/windows/win32/debug/pe-format">&quot;PE Format - Win32 apps&quot;</a>. <i>learn.microsoft.com</i>. Microsoft Corporation. 24 March 2023. <a href="https://web.archive.org/web/20230429214701/https://learn.microsoft.com/en-us/windows/win32/debug/pe-format">Archived</a> from the original on 29 April 2023<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://docs.oracle.com/javase/8/docs/api/java/time/Instant.html">&quot;Instant (Java Platform SE 8 )&quot;</a>. <i>docs.oracle.com</i>. Oracle. <a href="https://web.archive.org/web/20161125045518/http://docs.oracle.com/javase/8/docs/api/java/time/Instant.html">Archived</a> from the original on 25 November 2016<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://docs.python.org/3/library/time.html">&quot;time — Time access and conversions&quot;</a>, <i>Python documentation</i>, <a href="https://web.archive.org/web/20220722022415/https://docs.python.org/3/library/time.html">archived</a> from the original on 22 July 2022<span>, retrieved <span>25 July</span> 2022</span></cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Date">&quot;Date - JavaScript | MDN&quot;</a>. <i>developer.mozilla.org</i>. Mozilla. <a href="https://web.archive.org/web/20210721082721/https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Date">Archived</a> from the original on 21 July 2021<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://developer.apple.com/support/downloads/Apple-File-System-Reference.pdf"><i>Apple File System Reference</i></a> <span>(PDF)</span>, p. 57, <a href="https://web.archive.org/web/20221105082749/https://developer.apple.com/support/downloads/Apple-File-System-Reference.pdf">archived</a> <span>(PDF)</span> from the original on 5 November 2022<span>, retrieved <span>19 October</span> 2022</span>, <q>This timestamp is represented as the number of nanoseconds since January 1, 1970 at 0:00 UTC, disregarding leap seconds</q></cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.kernel.org/doc/html/v4.19/filesystems/ext4/ondisk/index.html#inode-timestamps">&quot;Data Structures and Algorithms&quot;</a>. <i>The Linux Kernel documentation</i>. Linux Kernel Organization, Inc. <a href="https://web.archive.org/web/20230501193249/https://www.kernel.org/doc/html/v4.19/filesystems/ext4/ondisk/index.html#inode-timestamps">Archived</a> from the original on 1 May 2023<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.rarlab.com/technote.htm">&quot;RAR 5.0 archive format&quot;</a>. <i>www.rarlab.com</i>. win.rar GmbH. <a href="https://web.archive.org/web/20230501201914/https://www.rarlab.com/technote.htm">Archived</a> from the original on 1 May 2023<span>. Retrieved <span>1 May</span> 2023</span>. <q>Time is stored in Unix time_t format if this flags [sic] is set and in Windows FILETIME format otherwise</q></cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.loc.gov/preservation/digital/formats/fdd/fdd000531.shtml">&quot;Tape Archive (tar) File Format Family&quot;</a>. <i>www.loc.gov</i>. Library of Congress. 7 January 2021. <a href="https://web.archive.org/web/20230501201909/https://www.loc.gov/preservation/digital/formats/fdd/fdd000531.shtml">Archived</a> from the original on 1 May 2023<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://dev.mysql.com/doc/refman/8.0/en/date-and-time-functions.html">&quot;Date and Time Functions&quot;</a>, <i>MySQL 8.0 Reference Manual</i>, <a href="https://web.archive.org/web/20221019165011/https://dev.mysql.com/doc/refman/8.0/en/date-and-time-functions.html">archived</a> from the original on 19 October 2022<span>, retrieved <span>19 October</span> 2022</span></cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.postgresql.org/docs/current/datatype-datetime.html">&quot;8.5. Date/Time Types&quot;</a>. <i>PostgreSQL Documentation</i>. The PostgreSQL Global Development Group. 9 February 2023. <a href="https://web.archive.org/web/20230501123216/https://www.postgresql.org/docs/current/datatype-datetime.html">Archived</a> from the original on 1 May 2023<span>. Retrieved <span>1 May</span> 2023</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>Rochkind, Mark (2004). <i>Advanced UNIX Programing</i> (2nd ed.). Addison-Wesley. pp. <span>56–</span>63. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-13-141154-8"><bdi>978-0-13-141154-8</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://computer.howstuffworks.com/question75.htm">&quot;What is the Year 2038 problem?&quot;</a>. <i>HowStuffWorks</i>. 1 April 2000<span>. Retrieved <span>23 July</span> 2025</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Saxena, Ashutosh; Rawat, Sanjay. <a href="https://web.archive.org/web/20120513133703/http://www.idrbt.ac.in/publications/workingpapers/Working%20Paper%20No.%209.pdf">&quot;IDRBT Working Paper No. 9&quot;</a> <span>(PDF)</span>. Archived from <a href="http://www.idrbt.ac.in/publications/workingpapers/Working%20Paper%20No.%209.pdf">the original</a> <span>(PDF)</span> on 13 May 2012.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://learn.microsoft.com/en-us/dotnet/api/system.datetime?view=net-9.0">&quot;DateTime Struct (System)&quot;</a>. <i>learn.microsoft.com</i><span>. Retrieved <span>14 January</span> 2025</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://learn.microsoft.com/en-us/windows/win32/api/minwinbase/ns-minwinbase-filetime">&quot;FILETIME (minwinbase.h) - Win32 apps&quot;</a>. <i>Microsoft Learn</i>. Microsoft. 2 April 2021. <a href="https://web.archive.org/web/20230310065235/https://learn.microsoft.com/en-us/windows/win32/api/minwinbase/ns-minwinbase-filetime">Archived</a> from the original on 10 March 2023<span>. Retrieved <span>9 March</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://learn.microsoft.com/en-us/azure/cosmos-db/nosql/query/getcurrentticks">&quot;GetCurrentTicks - Azure Cosmos DB for NoSQL&quot;</a>. <i>learn.microsoft.com</i><span>. Retrieved <span>31 August</span> 2025</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="http://people.cs.nycu.edu.tw/~tsaiwn/sisc/runtime_error_200_div_by_0/www.merlyn.demon.co.uk/critdate.htm">&quot;Critical and Significant Dates&quot;</a>. <i>people.cs.nycu.edu.tw</i><span>. Retrieved <span>12 February</span> 2024</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.undocumented-features.com/2023/04/26/working-around-accounts-that-expire-with-aad-connect-redux/">&quot;Working around accounts that expire with AAD Connect: REDUX&quot;</a>. <i>www.undocumented-features.com</i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Thulin, Anders (6 April 2013). <a href="http://articles.forensicfocus.com/2013/04/06/interpretation-of-ntfs-timestamps/">&quot;Interpretation of NTFS Timestamps&quot;</a>. <i>Forensic Focus</i><span>. Retrieved <span>23 July</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://howardhinnant.github.io/date/date.html">&quot;Date&quot;</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://learn.microsoft.com/en-us/windows/win32/sysinfo/file-times">&quot;File Times - Win32 apps&quot;</a>. <i>Microsoft Learn</i>. Microsoft. 7 January 2021. <a href="https://web.archive.org/web/20230308222206/https://learn.microsoft.com/en-us/windows/win32/sysinfo/file-times">Archived</a> from the original on 8 March 2023<span>. Retrieved <span>9 March</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://learn.microsoft.com/en-us/troubleshoot/windows-server/identity/convert-datetime-attributes-to-standard-format#summary">&quot;How to convert date/time attributes in Active Directory to standard time format&quot;</a>. <i>Microsoft Learn</i>. Microsoft. <a href="https://web.archive.org/web/20221020181637/https://learn.microsoft.com/en-us/troubleshoot/windows-server/identity/convert-datetime-attributes-to-standard-format#summary">Archived</a> from the original on 20 October 2022<span>. Retrieved <span>20 October</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>W. Richard Stevens; Bill Fenner; Andrew M. Rudoff (2004). <a href="https://books.google.com/books?id=ptSC4LpwGA0C&amp;pg=PA582"><i>UNIX Network Programming</i></a>. Addison-Wesley Professional. pp. 582–. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-13-141155-5"><bdi>978-0-13-141155-5</bdi></a>. <a href="https://web.archive.org/web/20190330170620/https://books.google.com/books?id=ptSC4LpwGA0C&amp;pg=PA582">Archived</a> from the original on 30 March 2019<span>. Retrieved <span>16 October</span> 2016</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://docs.python.org/3/library/datetime.html#available-types">&quot;datetime — Basic date and time types&quot;</a>. <i>Python Standard Library Reference</i>. Python Software Foundation. <a href="https://web.archive.org/web/20221019115837/https://docs.python.org/3/library/datetime.html#available-types">Archived</a> from the original on 19 October 2022<span>. Retrieved <span>20 October</span> 2022</span>. <q>Attributes: year, month, day, hour, minute, second, microsecond, and tzinfo.</q></cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Tweney, Dylan (12 February 2009). <a href="https://www.wired.com/gadgetlab/2009/02/unix-lovers-to/">&quot;Unix Lovers to Party Like It&#39;s 1234567890&quot;</a>. <i>Wired</i>. <a href="https://web.archive.org/web/20140329022430/http://www.wired.com/gadgetlab/2009/02/unix-lovers-to/">Archived</a> from the original on 29 March 2014<span>. Retrieved <span>12 March</span> 2017</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://slashdot.org/story/05/03/17/169200/date-s-turning-1111111111">&quot;Slashdot | date +%s Turning 1111111111&quot;</a>. 17 March 2005. <a href="https://web.archive.org/web/20200112103650/https://slashdot.org/story/05/03/17/169200/date-s-turning-1111111111">Archived</a> from the original on 12 January 2020<span>. Retrieved <span>12 January</span> 2020</span>.</cite><sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources"><span>unreliable source?</span></a></i>]</sup></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://web.archive.org/web/20171027205157/http://unixtime.info/facts.html">&quot;Unix time facts &amp; trivia – Unix Time . Info&quot;</a>. Archived from <a href="http://unixtime.info/facts.html">the original</a> on 27 October 2017.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.electromagnetic.net/press-releases/unixonebln.php">&quot;UNIX Approaches Ripe Old Age of One Billion&quot;</a>. Electromagnetic.net<span>. Retrieved <span>6 December</span> 2012</span>.</cite><span><code class="cs1-code">{{cite web}}</code>: CS1 maint: deprecated archival service (<a href="https://en.wikipedia.org/wiki/Category:CS1_maint:_deprecated_archival_service">link</a>)</span></span> </li> <li><span><b>^</b></span> <span><cite>Neumann, Peter G. (15 October 2001). <a href="http://catless.ncl.ac.uk/Risks/21.69.html#subj7">&quot;The RISKS Digest, Volume 21 Issue 69&quot;</a>. <i>The Risks Digest</i>. <b>21</b> (69). <a href="https://web.archive.org/web/20151022025543/http://catless.ncl.ac.uk/Risks/21.69.html#subj7">Archived</a> from the original on 22 October 2015<span>. Retrieved <span>6 December</span> 2012</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://linuxmafia.com/wpfaq/problems.html#FITRIX">&quot;Technical Problems&quot;</a>. <i>linuxmafia.com</i>. <a href="https://web.archive.org/web/20121011065555/http://linuxmafia.com/wpfaq/problems.html#FITRIX">Archived</a> from the original on 11 October 2012<span>. Retrieved <span>21 August</span> 2017</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>nixCraft (9 February 2009). <a href="https://www.cyberciti.biz/tips/february-13th-unix-time-will-reach-1234567890.html">&quot;Humor: On Feb, Friday 13, 2009 Unix time Will Be 1234567890&quot;</a>. Cyberciti.biz<span>. Retrieved <span>5 July</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.google.com/logos/unix1234567890.gif">&quot;Google 1234567890 Logo&quot;</a>. Google Inc. <a href="https://web.archive.org/web/20130111012013/http://www.google.com/logos/unix1234567890.gif">Archived</a> from the original on 11 January 2013<span>. Retrieved <span>28 January</span> 2013</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Ahmed, Murad (13 February 2009). <a href="https://web.archive.org/web/20161114122531/http://www.thetimes.co.uk/tto/technology/article1859315.ece">&quot;At the third stroke, the Unix time will be 1234567890&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/The_Times">The Times</a></i>. Archived from <a href="https://www.thetimes.co.uk/tto/technology/article1859315.ece">the original</a> on 14 November 2016<span>. Retrieved <span>12 January</span> 2020</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/John_R._Mashey">Mashey, John R.</a> (27 December 2004). <a href="https://doi.org/10.1145%2F1039511.1039532">&quot;Languages, Levels, Libraries, and Longevity&quot;</a>. <i>ACM Queue</i>. <b>2</b> (9): <span>32–</span>38. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1145%2F1039511.1039532">10.1145/1039511.1039532</a></span>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:28911378">28911378</a>.</cite></span> </li> </ol></div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Unix_time&amp;action=edit&amp;section=17"><span>edit</span></a><span>]</span></span></div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Wikiversity_logo_2017.svg"></a></span></div> <div>Wikiversity has learning resources about <i><b><a href="https://en.wikiversity.org/wiki/JavaScript/Epoch_time_converter">JavaScript/Epoch time converter</a></b></i></div></div> </div><ul><li><a href="https://www.bell-labs.com/usr/dmr/www/1stEdman.html">Unix Programmer&#39;s Manual, first edition</a></li> <li><a href="https://www.mail-archive.com/leapsecs@rom.usno.navy.mil/msg00109.html">Personal account of the POSIX decisions</a> by <a href="https://en.wikipedia.org/wiki/Landon_Curt_Noll">Landon Curt Noll</a></li> <li><a href="https://howardhinnant.github.io/date_algorithms.html">chrono-Compatible Low-Level Date Algorithms</a> – algorithms to convert between Gregorian and Julian dates and the number of days since the start of Unix time</li></ul><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Calendars"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Calendars"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Calendars"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Calendar">Calendars</a></div></th></tr><tr><th>Systems</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Lunar_calendar">Lunar</a></li> <li><a href="https://en.wikipedia.org/wiki/Lunisolar_calendar">Lunisolar</a></li> <li><a href="https://en.wikipedia.org/wiki/Solar_calendar">Solar</a></li></ul> </div></td></tr><tr><th>In wide use</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Astronomical_year_numbering">Astronomical</a></li> <li><a href="https://en.wikipedia.org/wiki/Bengali_calendar">Bengali</a></li> <li><a href="https://en.wikipedia.org/wiki/Buddhist_calendar">Buddhist</a></li> <li><a href="https://en.wikipedia.org/wiki/Chinese_calendar">Chinese</a></li> <li><a href="https://en.wikipedia.org/wiki/Ethiopian_calendar">Ethiopian</a></li> <li><a href="https://en.wikipedia.org/wiki/Gregorian_calendar">Gregorian</a></li> <li><a href="https://en.wikipedia.org/wiki/Hindu_calendar">Hindu</a></li> <li><a href="https://en.wikipedia.org/wiki/Islamic_calendar">Lunar Hijri</a></li> <li><a href="https://en.wikipedia.org/wiki/Indian_national_calendar">Saka</a></li> <li><a href="https://en.wikipedia.org/wiki/Solar_Hijri_calendar">Solar Hijri</a></li> <li><a href="https://en.wikipedia.org/wiki/ISO_week_date">ISO</a></li> <li>Unix time</li></ul> </div></td></tr><tr><th><div>In limited use</div></th><td><table><tbody><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Akan_calendar">Akan</a></li> <li><a href="https://en.wikipedia.org/wiki/Armenian_calendar">Armenian</a></li> <li><a href="https://en.wikipedia.org/wiki/Assamese_calendar">Assamese</a></li> <li><a href="https://en.wikipedia.org/wiki/Assyrian_calendar">Assyrian</a></li> <li><a href="https://en.wikipedia.org/wiki/Bah%C3%A1%CA%BC%C3%AD_calendar">Baháʼí</a></li> <li><a href="https://en.wikipedia.org/wiki/Balinese_calendar_(disambiguation)">Bali</a> <ul><li><a href="https://en.wikipedia.org/wiki/Pawukon_calendar">Pawukon</a></li> <li><a href="https://en.wikipedia.org/wiki/Balinese_saka_calendar">Saka</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Bangladeshi_national_calendar">Bangladeshi</a></li> <li><a href="https://en.wikipedia.org/wiki/Berber_calendar">Berber</a></li> <li><a href="https://en.wikipedia.org/wiki/Borana_calendar">Borana</a></li> <li><a href="https://en.wikipedia.org/wiki/Burmese_calendar">Burmese</a></li> <li><a href="https://en.wikipedia.org/wiki/Heathen_holidays">Germanic heathen</a></li> <li><a href="https://en.wikipedia.org/wiki/Georgian_calendar">Georgian</a></li> <li><a href="https://en.wikipedia.org/wiki/Hebrew_calendar">Hebrew</a></li> <li><a href="https://en.wikipedia.org/wiki/Hmong_calendar">Hmong</a></li> <li><a href="https://en.wikipedia.org/wiki/Igbo_calendar">Igbo</a></li> <li><a href="https://en.wikipedia.org/wiki/Iranian_calendars">Iranian</a> <ul><li><a href="https://en.wikipedia.org/wiki/Jalali_calendar">Jalali</a></li> <li><a href="https://en.wikipedia.org/wiki/Zoroastrian_calendar">Zoroastrian</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Irish_calendar">Irish</a></li> <li><a href="https://en.wikipedia.org/wiki/Islamic_calendar">Islamic</a> <ul><li><a href="https://en.wikipedia.org/wiki/Fasli_calendar">Fasli</a></li> <li><a href="https://en.wikipedia.org/wiki/Tabular_Islamic_calendar">Tabular</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Vira_Nirvana_Samvat">Jain</a></li> <li><a href="https://en.wikipedia.org/wiki/Japanese_calendar">Japanese</a></li> <li><a href="https://en.wikipedia.org/wiki/Javanese_calendar">Javanese</a></li> <li><a href="https://en.wikipedia.org/wiki/Korean_calendar">Korean</a></li> <li><a href="https://en.wikipedia.org/wiki/Kurdish_calendar">Kurdish</a></li> <li><a href="https://en.wikipedia.org/wiki/Lithuanian_calendar">Lithuanian</a></li> <li><a href="https://en.wikipedia.org/wiki/Tirhuta_Panchang">Maithili</a></li> <li><a href="https://en.wikipedia.org/wiki/Malayalam_calendar">Malayalam</a></li> <li><a href="https://en.wikipedia.org/wiki/Mandaean_calendar">Mandaean</a></li> <li><a href="https://en.wikipedia.org/wiki/Meitei_calendar">Manipuri (Meitei)</a></li> <li><a href="https://en.wikipedia.org/wiki/Melanau_calendar">Melanau</a></li> <li><a href="https://en.wikipedia.org/wiki/Republic_of_China_calendar">Minguo</a></li> <li><a href="https://en.wikipedia.org/wiki/Mizo_calendar">Mizo (Lushai)</a></li> <li><a href="https://en.wikipedia.org/wiki/Mongolian_calendar">Mongolian</a></li> <li><a href="https://en.wikipedia.org/wiki/Nepali_calendar_(disambiguation)">Nepali</a> <ul><li><a href="https://en.wikipedia.org/wiki/Nepal_Sambat">Nepal Sambat</a></li> <li><a href="https://en.wikipedia.org/wiki/Yele_Sambat">Yele Sambat</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Nanakshahi_calendar">Nanakshahi</a></li> <li><a href="https://en.wikipedia.org/wiki/Nisga%27a#Nisga’a_calendar/life">Nisg̱a&#39;a</a></li> <li><a href="https://en.wikipedia.org/wiki/Odia_calendar">Odia</a></li> <li><a href="https://en.wikipedia.org/wiki/Punjabi_calendar">Punjabi</a></li> <li><a href="https://en.wikipedia.org/wiki/Romanian_calendar">Romanian</a></li> <li><a href="https://en.wikipedia.org/wiki/Shona_calendar">Shona</a></li> <li><a href="https://en.wikipedia.org/wiki/Somali_calendar">Somali</a></li> <li><a href="https://en.wikipedia.org/wiki/Sotho_calendar">Sesotho</a></li> <li><a href="https://en.wikipedia.org/wiki/Slavic_calendar">Slavic</a> <ul><li><a href="https://en.wikipedia.org/wiki/Slavic_Native_Faith%27s_calendars_and_holidays">Slavic Native Faith</a></li> <li><a href="https://en.wikipedia.org/wiki/Macedonian_months">Macedonian</a></li></ul></li> <li><a href="https://en.wikipedia.org/w/index.php?title=Sundanese_calendar&amp;action=edit&amp;redlink=1">Sundanese</a></li> <li><a href="https://en.wikipedia.org/wiki/Tamil_calendar">Tamil</a></li> <li><a href="https://en.wikipedia.org/wiki/Thai_calendar">Thai</a> <ul><li><a href="https://en.wikipedia.org/wiki/Thai_lunar_calendar">lunar</a></li> <li><a href="https://en.wikipedia.org/wiki/Thai_solar_calendar">solar</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Tibetan_calendar">Tibetan</a></li> <li><a href="https://en.wikipedia.org/wiki/Tripuri_calendar">Tripuri</a></li> <li><a href="https://en.wikipedia.org/wiki/Tulu_calendar">Tulu</a></li> <li><a href="https://en.wikipedia.org/wiki/Vietnamese_calendar">Vietnamese</a></li> <li><a href="https://en.wikipedia.org/wiki/Vikram_Samvat">Vikram Samvat</a></li> <li><a href="https://en.wikipedia.org/wiki/Wheel_of_the_Year">Wicca</a></li> <li><a href="https://en.wikipedia.org/wiki/Xhosa_calendar">Xhosa</a></li> <li><a href="https://en.wikipedia.org/wiki/Yoruba_calendar">Yoruba</a></li> <li><a href="https://en.wikipedia.org/wiki/Zulu_calendar">Zulu</a></li></ul> </div></td></tr><tr><th>Types</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Runic_calendar">Runic</a></li> <li><a href="https://en.wikipedia.org/wiki/Mesoamerican_calendars">Mesoamerican</a> <ul><li><a href="https://en.wikipedia.org/wiki/Mesoamerican_Long_Count_calendar">Long Count</a></li> <li><a href="https://en.wikipedia.org/wiki/Calendar_round">Calendar round</a></li></ul></li></ul> </div></td></tr><tr><th>Christian variants</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Coptic_calendar">Coptic</a></li> <li><a href="https://en.wikipedia.org/wiki/Ethiopian_calendar">Ethiopian and Eritrean</a></li> <li><a href="https://en.wikipedia.org/wiki/Julian_calendar">Julian</a> <ul><li><a href="https://en.wikipedia.org/wiki/Revised_Julian_calendar">Revised</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Liturgical_year">Liturgical year</a> <ul><li><a href="https://en.wikipedia.org/wiki/Eastern_Orthodox_liturgical_calendar">Eastern Orthodox</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Calendar_of_saints">Saints</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Historical</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Calendars_in_pre-Islamic_Arabia">Arabian</a></li> <li><a href="https://en.wikipedia.org/wiki/Attic_calendar">Attic</a></li> <li><a href="https://en.wikipedia.org/wiki/Aztec_calendar">Aztec</a> <ul><li><a href="https://en.wikipedia.org/wiki/T%C5%8Dnalp%C5%8Dhualli">Tōnalpōhualli</a></li> <li><a href="https://en.wikipedia.org/wiki/Xiuhp%C5%8Dhualli">Xiuhpōhualli</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Babylonian_calendar">Babylonian</a></li> <li><a href="https://en.wikipedia.org/wiki/Bulgar_calendar">Bulgar</a></li> <li><a href="https://en.wikipedia.org/wiki/Byzantine_calendar">Byzantine</a></li> <li><a href="https://en.wikipedia.org/wiki/Cappadocian_calendar">Cappadocian</a></li> <li><a href="https://en.wikipedia.org/wiki/Celtic_calendar">Celtic</a></li> <li><a href="https://en.wikipedia.org/wiki/Cham_calendar">Cham</a></li> <li><a href="https://en.wikipedia.org/wiki/Chula_Sakarat">Culāsakaraj</a></li> <li><a href="https://en.wikipedia.org/wiki/Coligny_calendar">Coligny</a></li> <li><a href="https://en.wikipedia.org/wiki/Egyptian_calendar">Egyptian</a></li> <li><a href="https://en.wikipedia.org/wiki/Enoch_calendar">Enoch</a></li> <li><a href="https://en.wikipedia.org/wiki/Florentine_calendar">Florentine</a></li> <li><a href="https://en.wikipedia.org/wiki/French_Republican_calendar">French Republican</a></li> <li><a href="https://en.wikipedia.org/wiki/Germanic_calendar">Germanic</a></li> <li><a href="https://en.wikipedia.org/wiki/Ancient_Greek_calendars">Greek</a></li> <li><a href="https://en.wikipedia.org/wiki/Inca_calendar">Inca</a></li> <li><a href="https://en.wikipedia.org/wiki/Juche_calendar">Juche</a></li> <li><a href="https://en.wikipedia.org/wiki/Ancient_Macedonian_calendar">Macedonian</a></li> <li><a href="https://en.wikipedia.org/wiki/Maya_calendar">Maya</a> <ul><li><a href="https://en.wikipedia.org/wiki/Haab%CA%BC">Haabʼ</a></li> <li><a href="https://en.wikipedia.org/wiki/Tzolk%CA%BCin">Tzolkʼin</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Muisca_calendar">Muisca</a></li> <li><a href="https://en.wikipedia.org/wiki/Pentecontad_calendar">Pentecontad</a></li> <li><a href="https://en.wikipedia.org/wiki/Pisan_calendar">Pisan</a></li> <li><a href="https://en.wikipedia.org/wiki/Qumran_calendrical_texts">Qumran</a></li> <li><a href="https://en.wikipedia.org/wiki/Rapa_Nui_calendar">Rapa Nui</a></li> <li><a href="https://en.wikipedia.org/wiki/Roman_calendar">Roman</a></li> <li><a href="https://en.wikipedia.org/wiki/Rumi_calendar"><i>Rumi</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Sexagenary_cycle">Sexagenary</a></li> <li><a href="https://en.wikipedia.org/wiki/Soviet_calendar">Soviet</a></li> <li><a href="https://en.wikipedia.org/wiki/Swedish_calendar">Swedish</a></li> <li><a href="https://en.wikipedia.org/wiki/2002_renaming_of_Turkmen_months_and_days_of_week">Turkmen</a></li></ul> </div></td></tr><tr><th>By specialty</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Holocene_calendar">Holocene</a> <ul><li>anthropological</li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Proleptic_Gregorian_calendar">Proleptic Gregorian</a> / <a href="https://en.wikipedia.org/wiki/Proleptic_Julian_calendar">Proleptic Julian</a> <ul><li>historiographical</li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Darian_calendar">Darian</a> <ul><li>Martian</li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Dreamspell">Dreamspell</a> <ul><li>New Age</li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Discordian_calendar">Discordian</a></li> <li><a href="https://en.wikipedia.org/wiki/%27Pataphysics#Pataphysical_calendar">&#39;Pataphysical</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Calendar_reform">Reform proposals</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Hanke%E2%80%93Henry_Permanent_Calendar">Hanke–Henry Permanent</a></li> <li><a href="https://en.wikipedia.org/wiki/International_Fixed_Calendar">International Fixed</a></li> <li><a href="https://en.wikipedia.org/wiki/Pax_Calendar">Pax</a></li> <li><a href="https://en.wikipedia.org/wiki/Positivist_calendar">Positivist</a></li> <li><a href="https://en.wikipedia.org/wiki/Symmetry454">Symmetry454</a></li> <li><a href="https://en.wikipedia.org/wiki/World_Calendar">World</a></li></ul> </div></td></tr><tr><th><div>Displays and<br/>applications</div></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Digital_calendar">Electronic</a></li> <li><a href="https://en.wikipedia.org/wiki/Perpetual_calendar">Perpetual</a></li> <li><a href="https://en.wikipedia.org/wiki/Calendar_(stationery)">Wall</a></li></ul> </div></td></tr><tr><th><div>Year naming<br/>and numbering</div></th><td><table><tbody><tr><th>Terminology</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Calendar_era">Era</a></li> <li><a href="https://en.wikipedia.org/wiki/Epoch">Epoch</a></li> <li><a href="https://en.wikipedia.org/wiki/Leap_year">Leap year</a></li> <li><a href="https://en.wikipedia.org/wiki/New_Year">New Year</a></li> <li><a href="https://en.wikipedia.org/wiki/Regnal_name">Regnal name</a></li> <li><a href="https://en.wikipedia.org/wiki/Regnal_year">Regnal year</a></li> <li><a href="https://en.wikipedia.org/wiki/Year_zero">Year zero</a></li></ul> </div></td></tr><tr><th>Systems</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Ab_urbe_condita">Ab urbe condita</a></li> <li><a href="https://en.wikipedia.org/wiki/Anka_year">Anka year</a></li> <li><a href="https://en.wikipedia.org/wiki/Anno_Domini">Anno Domini</a>/<a href="https://en.wikipedia.org/wiki/Common_Era">Common Era</a></li> <li><a href="https://en.wikipedia.org/wiki/Anno_Lucis">Anno Lucis</a></li> <li><a href="https://en.wikipedia.org/wiki/Era_of_the_Martyrs">Anno Martyrum</a></li> <li><a href="https://en.wikipedia.org/wiki/Anno_Mundi">Anno Mundi</a></li> <li><a href="https://en.wikipedia.org/wiki/Eponym_dating_system">Assyrian</a></li> <li><a href="https://en.wikipedia.org/wiki/Before_Present">Before Present</a></li> <li><a href="https://en.wikipedia.org/wiki/Chinese_era_name">Chinese Imperial</a></li> <li><a href="https://en.wikipedia.org/wiki/Regnal_years_of_English_and_British_monarchs">English and British regnal year</a></li> <li><a href="https://en.wikipedia.org/wiki/Hijri_year">Hijri year</a></li> <li><a href="https://en.wikipedia.org/wiki/Japanese_era_name">Japanese</a></li> <li><a href="https://en.wikipedia.org/wiki/Korean_era_name">Korean</a></li> <li><a href="https://en.wikipedia.org/wiki/Nirayana_system">Nirayana system</a></li> <li><a href="https://en.wikipedia.org/wiki/Samvatsara">Samvatsara</a></li> <li><a href="https://en.wikipedia.org/wiki/Seleucid_era">Seleucid</a></li> <li><a href="https://en.wikipedia.org/wiki/Sexagenary_cycle">Sexagenary</a></li> <li><a href="https://en.wikipedia.org/wiki/Spanish_era">Spanish</a></li> <li><a href="https://en.wikipedia.org/wiki/Yuga">Yugas</a> <ul><li><a href="https://en.wikipedia.org/wiki/Satya_Yuga">Satya</a></li> <li><a href="https://en.wikipedia.org/wiki/Treta_Yuga">Treta</a></li> <li><a href="https://en.wikipedia.org/wiki/Dvapara_Yuga">Dvapara</a></li> <li><a href="https://en.wikipedia.org/wiki/Kali_Yuga">Kali</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Vietnamese_era_name">Vietnamese</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Fictional</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Discworld_(world)#Calendar">Discworld</a> (<i><a href="https://en.wikipedia.org/wiki/Discworld">Discworld</a></i>)</li> <li><a href="https://en.wikipedia.org/wiki/Flanaess#Calendar">Greyhawk</a> (<i><a href="https://en.wikipedia.org/wiki/Dungeons_%26_Dragons">Dungeons &amp; Dragons</a></i>)</li> <li><a href="https://en.wikipedia.org/wiki/Middle-earth_calendar">Middle-earth</a> (<i><a href="https://en.wikipedia.org/wiki/The_Lord_of_the_Rings">The Lord of the Rings</a></i>)</li> <li><a href="https://en.wikipedia.org/wiki/Stardate">Stardate</a> (<i><a href="https://en.wikipedia.org/wiki/Star_Trek">Star Trek</a></i>)</li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li> <a href="https://en.wikipedia.org/wiki/List_of_calendars">List of calendars</a></li> <li> <a href="https://en.wikipedia.org/wiki/Category:Calendars">Category</a></li></ul> </div></td></tr></tbody></table></div> Java package - Wikipedia https://en.wikipedia.org/wiki/Java_package j_33HPkBGUG9pBM8Ms_9hKxc93L657FrZjJLKg== Sat, 09 May 2026 12:00:02 +0000 Package of Java software <div>Package of Java software</div><p>A <b>Java package</b> organizes <a href="https://en.wikipedia.org/wiki/Java_(programming_language)">Java</a> <a href="https://en.wikipedia.org/wiki/Class_(computer_science)">classes</a> into <a href="https://en.wikipedia.org/wiki/Namespaces">namespaces</a>,<sup><span>[</span>1<span>]</span></sup> providing a unique namespace for each type it contains. Classes in the same package can access each other&#39;s package-private and protected members. </p><p>In general, a package can contain the following kinds of <a href="https://en.wikipedia.org/wiki/Datatypes">types</a>: classes, <a href="https://en.wikipedia.org/wiki/Interface_(Java)">interfaces</a>, enumerations, records and <a href="https://en.wikipedia.org/wiki/Java_annotation">annotation</a> types. A package allows a developer to group classes (and interfaces) together. These classes will all be related in some way – they might all have to do with a specific application or perform a specific set of tasks. Programmers also typically use packages to organize classes belonging to the same category or providing similar functionality. </p><div><h2>Using packages</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>In a Java source file, the package that this file&#39;s class or classes belong to is specified with the <code>package</code> <a href="https://en.wikipedia.org/wiki/Keyword_(computer_programming)">keyword</a>. This keyword is usually the first keyword in the source file. At most one package declaration can appear in a source file. </p><div><pre><span>package</span> <span>java.awt.event</span><span>;</span> </pre></div><p>To use a package&#39;s classes inside a Java source file, it is convenient to import the classes from the package with an <code>import</code> declaration, which dequalifies the <a href="https://en.wikipedia.org/wiki/Namespace">namespaces</a> of the class into scope. The following declaration </p><div><pre><span>import</span> <span>java.awt.event.*</span><span>;</span> </pre></div><p>imports all classes from the <code>java.awt.event</code> package, while the next declaration </p><div><pre><span>import</span> <span>java.awt.event.ActionEvent</span><span>;</span> </pre></div><p>imports only the <code>ActionEvent</code> class from the package. After either of these import declarations, the <code>ActionEvent</code> class can be referenced using its simple class name: </p><div><pre><span>ActionEvent</span> <span>myEvent</span> <span>=</span> <span>new</span> <span>ActionEvent</span><span>();</span> </pre></div><p>Classes can also be used directly without an import declaration by using the <a href="https://en.wikipedia.org/wiki/Fully_qualified_name">fully qualified name</a> of the class. For example, </p><p>does not require a preceding import declaration. </p><div><h3>Package-wide Javadoc &amp; annotations</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>Documentation explaining the package as a whole is written as <a href="https://en.wikipedia.org/wiki/Javadoc">Javadoc</a> in a file named exactly <span>package-info.java</span>. That file is also the place for annotations to be used across all classes of the package.<sup><span>[</span>2<span>]</span></sup> </p><div><h3>The unnamed package</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>If a package declaration is not used, classes are placed in an unnamed package. Classes in an unnamed package cannot be imported by classes in any other package.<sup><span>[</span>3<span>]</span></sup> The official Java Tutorial advises against this: </p><dl><dd>Generally speaking, an unnamed package is only for small or temporary applications or when you are just beginning the development process. Otherwise, classes and interfaces belong in named packages.<sup><span>[</span>4<span>]</span></sup></dd></dl><div><h2>Package access protection</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Public members and classes are visible everywhere and private members are visible only in the same class. Classes within a package can access classes and members declared with <i>default</i> (<i>package-private</i>) access as well as class members declared with the <i><code>protected</code></i> access modifier. Default (package-private) access is enforced when a class or member has not been declared as <code>public</code>, <code>protected</code> or <code>private</code>. By contrast, classes in other packages cannot access classes and members declared with default access. However, class members declared as <code>protected</code> can be accessed from the classes in the same package as well as classes in other packages that are subclasses of the declaring class.<sup><span>[</span>5<span>]</span></sup> </p><div><h2>Creation of JAR files</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>JAR files are created with the jar command-line utility. The command </p><pre>jar cf myPackage.jar *.class </pre><p>compresses all .class files into the JAR file <i>myPackage.jar</i>. The &#39;c&#39; option on the command line tells the jar command to &quot;create new archive.&quot; The &#39; f &#39; option tells it to create a file. The file&#39;s name comes next before the contents of the JAR file. </p><div><h2>Package naming conventions</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>Packages are usually defined using a <a href="https://en.wikipedia.org/wiki/Hierarchical">hierarchical</a> naming <a href="https://en.wikipedia.org/wiki/Pattern">pattern</a>, with some levels in the hierarchy separated by periods (<code>.</code>, pronounced &quot;dot&quot;). Although packages lower in the naming hierarchy are often referred to as &quot;subpackages&quot; of the corresponding packages higher in the hierarchy, there is almost no semantic relationship between packages. The Java Language Specification establishes package naming conventions to avoid the possibility of two published packages having the same name. The naming conventions describe how to create unique package names, so that packages that are widely distributed will have unique namespaces. This allows packages to be separately, easily and automatically installed and catalogued. </p><p>In general, a package name begins with the top level domain name of the organization and then the organization&#39;s domain and then any subdomains, listed in reverse order. The organization can then choose a specific name for its package. Subsequent components of the package name vary according to an organization&#39;s own internal naming conventions.<sup><span>[</span>6<span>]</span></sup> </p><p>For example, if an organization in Canada called MySoft creates a package to deal with fractions, naming the package <code>ca.mysoft.fractions</code> distinguishes the fractions package from another similar package created by another company. If a German company named MySoft also creates a fractions package, but names it <code>de.mysoft.fractions</code>, then the classes in these two packages are defined in a unique and separate namespace. There is no requirement that the TLD must be the name of the country of the company. For instance, many packages also use other TLDs such as <code>org</code>, <code>com</code>, etc. The Java standard library puts all symbols in the <code>java.*</code>, <code>javax.*</code>, or <code>jdk.*</code> namespace, though some classes associated with other technologies may <a href="https://en.wikipedia.org/wiki/Java_Class_Library#Packages_outside_of_the_main_namespace">reside in other namespaces</a>. Some projects, such as Project Lombok, may not use TLDs at all (all symbols are located in namespace <code>lombok</code>). </p><p>Using TLDs in package names is a convention primarily associated with Java, but seldom used in other languages. In other languages such as <a href="https://en.wikipedia.org/wiki/C%2B%2B">C++</a> and <a href="https://en.wikipedia.org/wiki/C_Sharp_(programming_language)">C#</a> it is sufficient to just prefix package/namespace names with the company name. </p><p>Complete conventions for disambiguating package names and rules for naming packages when the Internet domain name cannot be directly used as a package name are described in section 7.7 of the Java Language Specification.<sup><span>[</span>7<span>]</span></sup> </p><div><h2>Core packages in Java SE 8</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Java_Platform,_Standard_Edition">Java Platform, Standard Edition</a></div><table> <tbody><tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.lang</code> </th> <td>Basic language functionality and fundamental types. Implicitly imported by every program. </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.util</code> </th> <td>Collection <a href="https://en.wikipedia.org/wiki/Data_structure">data structure</a> classes </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.io</code> </th> <td>File operations </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.math</code> </th> <td>Multiprecision arithmetics </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.nio</code> </th> <td>The <a href="https://en.wikipedia.org/wiki/Non-blocking_I/O_(Java)">Non-blocking I/O</a> framework for Java </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.net</code> </th> <td>Networking operations, sockets, <a href="https://en.wikipedia.org/wiki/DNS_lookup">DNS lookups</a>, ... </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.security</code> </th> <td>Key generation, encryption and decryption </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.sql</code> </th> <td><a href="https://en.wikipedia.org/wiki/Java_Database_Connectivity">Java Database Connectivity</a> (JDBC) to access databases </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.awt</code> </th> <td>Basic hierarchy of packages for native GUI components </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.text</code> </th> <td>Provides classes and interfaces for handling text, dates, numbers, and messages in a manner independent of natural languages. </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.rmi</code> </th> <td>Provides the RMI package. </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.time</code> </th> <td>The main API for dates, times, instants, and durations. </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.beans</code> </th> <td>The java.beans package contains classes and interfaces related to JavaBeans components. </td></tr> <tr> <th><code class="mw-highlight mw-highlight-lang-text mw-content-ltr">java.applet</code> </th> <td>This package provides classes and methods to create and communicate with the applets. </td></tr></tbody></table><div><h2>Modules</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><div>Further information: <a href="https://en.wikipedia.org/wiki/Java_Platform_Module_System">Java Platform Module System</a></div><p>In <a href="https://en.wikipedia.org/wiki/Java_9">Java 9</a> (released on September 21, 2017) support for &quot;<a href="https://en.wikipedia.org/wiki/Modular_programming">modules</a>&quot;, a kind of collection of packages, was implemented as a result of the development effort of Project Jigsaw. The &quot;modules&quot; were earlier called &quot;superpackages&quot; and originally planned for Java 7. </p><p>Modules describe their dependencies in a declaration placed in a file named <i>module-info.java</i> at the root of the module&#39;s source-file hierarchy. Since <a href="https://en.wikipedia.org/wiki/Java_version_history#Java_SE_9">Java 9</a>, the JDK is able to check the module dependencies both at <a href="https://en.wikipedia.org/wiki/Compile_time">compile time</a> and runtime. The JDK itself is modularized for <a href="https://en.wikipedia.org/wiki/Java_version_history#Java_SE_9">Java 9</a>.<sup><span>[</span>8<span>]</span></sup><sup><span>[</span>9<span>]</span></sup> For example, the majority of the Java standard library is exported by the module <code>java.base</code>. </p><p>As an example, the following module declaration declares that the module <i>com.foo.bar</i> depends on another <i>com.foo.baz</i> module, and exports the following packages: <i>com.foo.bar.alpha</i> and <i>com.foo.bar.beta</i>: </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Translation_unit_(programming)">Translation unit (programming)</a></li> <li><a href="https://en.wikipedia.org/wiki/Modules_(C%2B%2B)">Modules (C++)</a></li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span>James Gosling, Bill Joy, Guy Steele, Gilad Bracha, <i>The Java Language Specification, Third Edition</i>, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-321-24678-0"><bdi>0-321-24678-0</bdi></a>, 2005. In the Introduction, it is stated &quot;Chapter 7 describes the structure of a program, which is organized into packages similar to the modules of Modula.&quot;</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://docs.oracle.com/javase/specs/jls/se11/html/jls-7.html#jls-7.4.1">&quot;Chapter 7. Packages and Modules&quot;</a>. <i>docs.oracle.com</i><span>. Retrieved <span>2021-12-10</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://docs.oracle.com/javase/specs/jls/se7/html/jls-7.html#jls-7.5">&quot;Chapter 7. Packages&quot;</a>. Docs.oracle.com<span>. Retrieved <span>2013-09-15</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://docs.oracle.com/javase/tutorial/java/package/packages.html">&quot;Creating and Using Packages (The Java™ Tutorials &gt; Learning the Java Language &gt; Packages)&quot;</a>. <i>docs.oracle.com</i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://docs.oracle.com/javase/tutorial/java/javaOO/accesscontrol.html">&quot;Controlling Access to Members of a Class (The Java™ Tutorials &gt; Learning the Java Language &gt; Classes and Objects)&quot;</a>. <i>docs.oracle.com</i>.</cite></span> </li> <li><span><b>^</b></span> <span><a href="http://www.oracle.com/technetwork/java/codeconventions-135099.html">Code Conventions for the Java Programming Language: 9. Naming Conventions</a></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://docs.oracle.com/javase/specs/jls/se6/html/packages.html">&quot;Packages&quot;</a>. <i>docs.oracle.com</i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://web.archive.org/web/20151208074800/http://cr.openjdk.java.net/~mr/jigsaw/ea/module-summary.html">&quot;JDK Module Summary&quot;</a>. <a href="https://en.wikipedia.org/wiki/Oracle_Corporation">Oracle Corporation</a>. 2015-10-23. Archived from <a href="http://cr.openjdk.java.net/~mr/jigsaw/ea/module-summary.html">the original</a> on 2015-12-08<span>. Retrieved <span>2015-11-29</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.oracle.com/corporate/features/understanding-java-9-modules.html">&quot;Understanding Java 9 Modules&quot;</a>. <a href="https://en.wikipedia.org/wiki/Oracle_Corporation">Oracle Corporation</a>. October 1, 2017<span>. Retrieved <span>2022-10-04</span></span>.</cite></span> </li> </ol></div></div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Java_package&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://docs.oracle.com/en/java/javase/24/docs/api/">Java SE 24 API Javadocs</a></li></ul> Variable shadowing - Wikipedia https://en.wikipedia.org/wiki/Variable_shadowing HTp6FDnqsO-N2okriRBCQyHyTUSAtaioh_B9LA== Sat, 09 May 2026 11:59:49 +0000 Variable masking one with the same name <div>Variable masking one with the same name</div><p>In <a href="https://en.wikipedia.org/wiki/Computer_programming">computer programming</a>, <b>variable shadowing</b> occurs when a variable declared within a certain <a href="https://en.wikipedia.org/wiki/Scope_(computer_science)">scope</a> (decision block, method, or <a href="https://en.wikipedia.org/wiki/Inner_class">inner class</a>) has the same name as a variable declared in an outer scope. At the level of <a href="https://en.wikipedia.org/wiki/Identifier_(computer_languages)">identifiers</a> (names, rather than variables), this is known as <a href="https://en.wikipedia.org/wiki/Name_masking">name masking</a>. This outer variable is said to be shadowed by the inner variable, while the inner identifier is said to <i>mask</i> the outer identifier. This can lead to confusion, as it may be unclear which variable subsequent uses of the shadowed variable name refer to, which depends on the <a href="https://en.wikipedia.org/wiki/Name_resolution_(programming_languages)">name resolution</a> rules of the language. </p><p>One of the first languages to introduce variable shadowing was <a href="https://en.wikipedia.org/wiki/ALGOL">ALGOL</a>, which first introduced blocks to establish scopes. It was also permitted by many of the derivative programming languages including <a href="https://en.wikipedia.org/wiki/C_(programming_language)">C</a>, <a href="https://en.wikipedia.org/wiki/C%2B%2B">C++</a> and <a href="https://en.wikipedia.org/wiki/Java_(programming_language)">Java</a>. </p><p>The <a href="https://en.wikipedia.org/wiki/C_Sharp_(programming_language)">C#</a> language breaks this tradition, allowing variable shadowing between an inner and an outer class, and between a method and its containing class, but not between an if-block and its containing method, or between case statements in a <a href="https://en.wikipedia.org/wiki/Switch_statement">switch</a> block. </p><p>Some languages allow variable shadowing in more cases than others. For example <a href="https://en.wikipedia.org/wiki/Kotlin_(programming_language)">Kotlin</a> allows an inner variable in a function to shadow a passed argument and a variable in an inner block to shadow another in an outer block, while <a href="https://en.wikipedia.org/wiki/Java_(programming_language)">Java</a> does not allow these (see the example below). Both languages allow a passed argument to a function/Method to shadow a Class Field.<sup><span>[</span>1<span>]</span></sup> </p><p>Some languages disallow variable shadowing completely such as <a href="https://en.wikipedia.org/wiki/CoffeeScript">CoffeeScript</a><sup><span>[</span>2<span>]</span></sup> and <a href="https://en.wikipedia.org/wiki/V_(programming_language)">V (Vlang)</a>.<sup><span>[</span>3<span>]</span></sup> </p><div><h2>Example</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Variable_shadowing&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><div><h3>Lua</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Variable_shadowing&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>The following <a href="https://en.wikipedia.org/wiki/Lua_(programming_language)">Lua</a> code provides an example of variable shadowing, in multiple blocks. </p><div><h3>Python</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Variable_shadowing&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>The following <a href="https://en.wikipedia.org/wiki/Python_(programming_language)">Python</a> code provides another example of variable shadowing: </p><p>As there is no variable declaration but only variable assignment in Python, the keyword <code>nonlocal</code> introduced in Python 3 is used to avoid variable shadowing and assign to non-local variables: </p><p>The keyword <code>global</code> is used to avoid variable shadowing and assign to global variables: </p><div><h3>Rust</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Variable_shadowing&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><div><h3>C++</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Variable_shadowing&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><div><h3>Java</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Variable_shadowing&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><div><pre><span>public</span> <span>class</span> <span>Shadow</span> <span>{</span> <span> </span><span>private</span> <span>int</span> <span>myIntVar</span> <span>=</span> <span>0</span><span>;</span> <span> </span><span>public</span> <span>void</span> <span>shadowTheVar</span><span>()</span> <span>{</span> <span> </span><span>// Since it has the same name as above object instance field, it shadows above </span> <span> </span><span>// field inside this method.</span> <span> </span><span>int</span> <span>myIntVar</span> <span>=</span> <span>5</span><span>;</span> <span> </span><span>// If we simply refer to &#39;myIntVar&#39; the one of this method is found </span> <span> </span><span>// (shadowing a second one with the same name)</span> <span> </span><span>System</span><span>.</span><span>out</span><span>.</span><span>println</span><span>(</span><span>myIntVar</span><span>);</span> <span>// prints 5</span> <span> </span><span>// If we want to refer to the shadowed myIntVar from this class we need to </span> <span> </span><span>// refer to it like this:</span> <span> </span><span>System</span><span>.</span><span>out</span><span>.</span><span>println</span><span>(</span><span>this</span><span>.</span><span>myIntVar</span><span>);</span> <span>// prints 0</span> <span> </span><span>}</span> <span> </span><span>public</span> <span>static</span> <span>void</span> <span>main</span><span>(</span><span>String</span><span>[]</span> <span>args</span><span>){</span> <span> </span><span>new</span> <span>Shadow</span><span>().</span><span>shadowTheVar</span><span>();</span> <span> </span><span>}</span> <span>}</span> </pre></div><p> However, the following code will <i>not</i> compile: </p><div><h3>JavaScript</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Variable_shadowing&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p><a href="https://en.wikipedia.org/wiki/ECMAScript_6">ECMAScript 6</a> introduction of <code>let</code> and <code>const</code> with block scoping allow variable shadowing. </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Variable_shadowing&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Function_overloading">Overloading</a></li> <li><a href="https://en.wikipedia.org/wiki/Type_polymorphism">Type polymorphism</a></li> <li><a href="https://en.wikipedia.org/wiki/Name_binding">Name binding</a></li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Variable_shadowing&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span><cite><a href="https://allegro.tech/2018/05/From-Java-to-Kotlin-and-Back-Again.html">&quot;From Java to Kotlin and Back Again&quot;</a>. <a href="https://web.archive.org/web/20201128024109/https://allegro.tech/2018/05/From-Java-to-Kotlin-and-Back-Again.html">Archived</a> from the original on 2020-11-28<span>. Retrieved <span>2021-10-04</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://github.com/jashkenas/coffeescript/issues/2697">&quot;Please introduce explicit shadowing · Issue #2697 · jashkenas/Coffeescript&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/GitHub">GitHub</a></i>. <a href="https://web.archive.org/web/20211004092726/https://github.com/jashkenas/coffeescript/issues/2697">Archived</a> from the original on 2021-10-04<span>. Retrieved <span>2021-10-04</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://github.com/vlang/v/blob/master/doc/docs.md#warnings-and-declaration-errors">&quot;Vlang documentation- &quot;Unlike most languages, variable shadowing is not allowed&quot;&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/GitHub">GitHub</a></i><span>. Retrieved <span>2024-06-27</span></span>.</cite></span> </li> </ol></div></div> Genoa Economic and Financial Conference (1922) - Wikipedia https://en.wikipedia.org/wiki/Genoa_Economic_and_Financial_Conference_(1922) dey_9qNufhlGzT9w6DubE4_tjvLuh9P_fpIWsA== Sat, 09 May 2026 11:58:00 +0000 International economic conference <div>International economic conference</div><figure><a href="https://en.wikipedia.org/wiki/File:Genoa_conference_1922.jpg"></a><figcaption>Participants at the 1922 Genoa Conference.</figcaption></figure><p>The <b>Economic and Financial Conference</b> was a formal conclave of representatives from 34 European countries held in the ancient <a href="https://en.wikipedia.org/wiki/Palazzo_San_Giorgio">Palazzo San Giorgio</a> of <a href="https://en.wikipedia.org/wiki/Genoa">Genoa</a>, <a href="https://en.wikipedia.org/wiki/Italy">Italy</a>, from 10 April to 19 May 1922. </p><p>Unlike the previous <a href="https://en.wikipedia.org/wiki/International_Monetary_and_Economic_Conferences">international economic conference</a> in <a href="https://en.wikipedia.org/wiki/Brussels_Conference_(1920)">Brussels (1920)</a>, the Genoa conference was attended by heads of government and not only experts,<sup><span>[</span>1<span>]</span></sup><sup><span>: 9 </span></sup> which enhanced its authority but also the risks of <a href="https://en.wikipedia.org/wiki/Politicization">politicization</a> and <a href="https://en.wikipedia.org/wiki/Grandstanding">grandstanding</a>, at a time of contention on the unresolved issue of German <a href="https://en.wikipedia.org/wiki/War_reparations">war reparations</a>. </p><p>The conference was intended by the British Prime Minister <a href="https://en.wikipedia.org/wiki/David_Lloyd_George">David Lloyd George</a> to resolve the major economic and political issues facing Europe and to address the <a href="https://en.wikipedia.org/wiki/Outcast_(person)">pariah</a> status of <a href="https://en.wikipedia.org/wiki/Weimar_Republic">Germany</a> and the <a href="https://en.wikipedia.org/wiki/Soviet_Union">Soviet Union</a>, both of which had been excluded from the <a href="https://en.wikipedia.org/wiki/Paris_Peace_Conference_of_1919">Paris Peace Conference of 1919</a>. The conference was particularly intended to develop a strategy to rebuild a defeated Germany, as well as the states of both <a href="https://en.wikipedia.org/wiki/Central_Europe">Central Europe</a> and <a href="https://en.wikipedia.org/wiki/Eastern_Europe">Eastern Europe</a>, and to negotiate a relationship between European <a href="https://en.wikipedia.org/wiki/Capitalist">capitalist</a> economies and the <a href="https://en.wikipedia.org/wiki/Bolshevik">Bolshevik</a> regime in <a href="https://en.wikipedia.org/wiki/Moscow">Moscow</a>. Germany and the Soviet Union predictably expressed loud dissent and stole the limelight by negotiating a separate bilateral agreement on the conference&#39;s sidelines, the <a href="https://en.wikipedia.org/wiki/Treaty_of_Rapallo_(1922)">Treaty of Rapallo</a>. </p><p>Even so, the conference further cemented the policy consensus on principles formed at the Brussels gathering two years before. The <a href="https://en.wikipedia.org/wiki/Economic_and_Financial_Organization_of_the_League_of_Nations">Economic and Financial Organization of the League of Nations</a> (EFO) presented a report to the conference, which provided the first official articulation of the <a href="https://en.wikipedia.org/wiki/Gold_exchange_standard">gold exchange standard</a>,<sup><span>[</span>2<span>]</span></sup> and also tackled novel fields for international financial cooperation such as <a href="https://en.wikipedia.org/wiki/Capital_flight">capital flight</a>, <a href="https://en.wikipedia.org/wiki/Tax_evasion">tax evasion</a>, and <a href="https://en.wikipedia.org/wiki/Double_taxation">double taxation</a>.<sup><span>[</span>1<span>]</span></sup><sup><span>: 11 </span></sup> The conference also found agreement on the principle that financial stability must come first before trade restrictions could be beneficially lifted, even though no convergence was achieved on trade liberalization measures as the EFO had recommended.<sup><span>[</span>1<span>]</span></sup><sup><span>: 12 </span></sup> </p><div><h2>Background</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:2211-lloyd-george.jpg"></a><figcaption>British Prime Minister David Lloyd George (1863–1945) designed the 1922 conference in Genoa, Italy.</figcaption></figure><p>The idea for a general economic and financial conference of European nations had roots in a January 1922 session of the <a href="https://en.wikipedia.org/wiki/Supreme_War_Council">Supreme War Council</a>, held in <a href="https://en.wikipedia.org/wiki/Cannes_Conference_(1922)">Cannes</a>.<sup><span>[</span>3<span>]</span></sup> With Europe facing an economic catastrophe brought about by the half-decade <a href="https://en.wikipedia.org/wiki/First_World_War">First World War</a>, marked by millions of deaths, shattered infrastructure and vast sums of squandered economic resources, British Prime Minister <a href="https://en.wikipedia.org/wiki/David_Lloyd_George">David Lloyd George</a> sought an authoritative international gathering to set Europe&#39;s political and financial house in order and to establish his leadership firmly at home.<sup><span>[</span>4<span>]</span></sup> </p><p>The formal proposal was made at Cannes on 6 January 1922 in the form of a draft resolution calling for such a conference that was presented by Lloyd George and was approved unanimously the same date.<sup><span>[</span>5<span>]</span></sup> </p><p>Lloyd George told the <a href="https://en.wikipedia.org/wiki/British_Parliament">British Parliament</a> that the primary intent of the conference was to provide for the &quot;reconstruction of economic Europe, devastated and broken into fragments by the desolating agency of war&quot;.<sup><span>[</span>6<span>]</span></sup> The economy of Europe was at the point of collapse, as Lloyd George noted: </p><blockquote><p> If European countries had gathered together their mobile wealth accumulated by centuries of industry and thrift on to one pyramid and then set fire to it, the result could hardly have been more complete. International trade has been disorganized through and through. The recognized medium of commerce, exchange based upon currency, has become almost worthless and unworkable; vast areas, upon which Europe has hitherto depended for a large proportion of its food supplies and its raw material, completely destroyed for all purposes of commerce; nations, instead of cooperating to restore, broken up by suspicions and creating difficulties and new artificial restrictions; great armies ready to march, and nations already overburdened with taxation having to bear the additional taxation which the maintenance of these huge armaments to avoid suspected dangers renders necessary.<sup><span>[</span>6<span>]</span></sup></p></blockquote><p>Lloyd George controversially sought the inclusion of <a href="https://en.wikipedia.org/wiki/Weimar_Republic">Germany</a> and <a href="https://en.wikipedia.org/wiki/Soviet_Russia">Soviet Russia</a> to the international conference as equal members, which was met by particular opposition of France, which sought to neutralise and to isolate the two pariah nations of Europe by including them only in an inferior capacity.<sup><span>[</span>7<span>]</span></sup> Any softening in the hardline stance towards Germany was perceived by France as a weakening of the <a href="https://en.wikipedia.org/wiki/Treaty_of_Versailles">Treaty of Versailles</a> of which France was a prime beneficiary and to which it was immutably committed.<sup><span>[</span>8<span>]</span></sup> </p><div><h2>Reparations and recognition</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Portrait_of_Aristide_Briand.jpg"></a><figcaption>French Prime Minister <a href="https://en.wikipedia.org/wiki/Aristide_Briand">Aristide Briand</a> (1862–1932), whose government fell shortly before the convocation of the Genoa Conference.</figcaption></figure><p>Two great issues lay as impediments to convocation of a multilateral convention to plan the <a href="https://en.wikipedia.org/wiki/Economic_reconstruction">economic reconstruction</a> of Europe. One was the issue of reparations, which was regarded as the primary matter of contention between the <a href="https://en.wikipedia.org/wiki/Triple_Entente">Triple Entente</a> powers of France and Britain in the postwar era.<sup><span>[</span>9<span>]</span></sup> At issue was whether the terms of economic <a href="https://en.wikipedia.org/wiki/War_reparations">reparations</a> in the <a href="https://en.wikipedia.org/wiki/Treaty_of_Versailles">Treaty of Versailles</a>, which ended the war, were to be enforced or amended. The British thought that massive reconstruction costs laid upon Germany would undermine European economic recovery and the market for British exports of manufactured goods. The French believed that if Germany was allowed to skirt the severe financial obligations detailed in the peace treaty, its economic rise would be massively accelerated, and its political and military hegemony on the continent would be rapidly restored.<sup><span>[</span>9<span>]</span></sup> </p><p>France, among the main battlegrounds of the European conflagration, was particularly hard-hit and in need of external funds for reconstruction. Germany was seen as having largely escaped the destruction of infrastructure and economic capacity during the war and currently engaged in the systematic underestimation of its ability to pay.<sup><span>[</span>10<span>]</span></sup> The political and economic weakness of Germany was emphasized by its new Weimar government, which effectively made the argument that it would be unable to maintain the specified payment schedule.<sup><span>[</span>11<span>]</span></sup> </p><p>Germany&#39;s position came to be regarded as reasonably correct by British, American and other policymakers despite quiet indications from even some German authorities that some substantial portion of the reparations bill could be safely managed. German politicians sought to minimise their country&#39;s tax burden by the acquisition of foreign loans and the reduction of the overall reparations bill.<sup><span>[</span>12<span>]</span></sup> British, American and Swiss bankers were adamant that necessary loans would not be available until a final achievable reparations bill and repayment schedule could be agreed upon by all of the main parties in the dispute.<sup><span>[</span>13<span>]</span></sup> </p><p>In the meantime, German authorities attempted to raise the foreign currency necessary for reparations by dumping paper currency unbacked by gold on the market. That triggered a <a href="https://en.wikipedia.org/wiki/Hyperinflation">hyperinflation</a> paralyzing the country&#39;s economy, which had a desired subsidiary effect of helping to make the case that the current schedule of reparations was untenable.<sup><span>[</span>13<span>]</span></sup> It was hoped by Germany, the United Kingdom and the United States and feared by France that the Genoa Conference would provide an opportunity for downward revision of the reparations schedule that had been set forth by the treaty.<sup><span>[</span>14<span>]</span></sup> </p><p>The apparent softening of the economic terms of the peace, which had taken place at <a href="https://en.wikipedia.org/wiki/Cannes_Conference_(1922)">Cannes</a>, had led to the toppling of the government of the <a href="https://en.wikipedia.org/wiki/French_Prime_Minister">French Prime Minister</a> <a href="https://en.wikipedia.org/wiki/Aristide_Briand">Aristide Briand</a> and threatened the conference by leaving his successor, <a href="https://en.wikipedia.org/wiki/Raymond_Poincar%C3%A9">Raymond Poincaré</a>, with little appetite for participation.<sup><span>[</span>15<span>]</span></sup> It was only through a dedicated diplomatic offensive by Lloyd George towards the French government in February 1922 that its participation at the April conference was won, under terms that had been agreed to by the Briand government.<sup><span>[</span>16<span>]</span></sup> Although antagonism between France and Britain had festered in the months immediately after the war, France found itself in the uncomfortable position of having to submit to British desires on the matter of an economic conference since without British support, France would have had little chance of collecting reparations from Germany or joining any potential strategic military alliance.<sup><span>[</span>17<span>]</span></sup> </p><p>The second potential hurdle to holding the Genoa Conference surrounded participation of the new Bolshevik <a href="https://en.wikipedia.org/wiki/Government_of_Russia">government of Russia</a>, as the United States and most of Europe did not maintain formal diplomatic relations with the regime and harboured economic claims against it. That inconvenient situation had been effectively set aside by the Supreme Council itself, which approved a formal resolution at its meeting of 10 January 1922 that invited Soviet participation and called upon the Bolsheviks to submit a list of delegates and support staff seeking to attend so that safe-conduct passes for travel and accommodation could be arranged.<sup><span>[</span>18<span>]</span></sup> </p><div><h2>Opening</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Palazzo_di_San_Giorgio-interior.jpg"></a><figcaption>Interior view of the main hall of the Palazzo di San Giorgio, location of plenary meetings of the Genoa Conference of 1922.</figcaption></figure><p>The opening ceremony of the Genoa Conference took place at 3 pm on 10 April 1922 at the <a href="https://en.wikipedia.org/wiki/Palazzo_di_San_Giorgio">Palazzo di San Giorgio</a>, one of the oldest palaces in the city.<sup><span>[</span>19<span>]</span></sup> Delegations entered at one end of the palace and ran a gauntlet of news photographers from around the world. At the opposite end, guests, journalists and members of the delegations&#39; support staffs disembarked from a column of automobiles to go inside the building.<sup><span>[</span>20<span>]</span></sup> Admission to journalists was through tickets distributed ahead of the event, which were strictly limited.<sup><span>[</span>20<span>]</span></sup> </p><p>The entrance of Lloyd George was met with a great ovation from those assembled in the hall as he took his seat to the left of the chairman&#39;s seat at the front of the room.<sup><span>[</span>20<span>]</span></sup> As the chief architect of the gathering, he effectively dominated the conference&#39;s public sessions.<sup><span>[</span>20<span>]</span></sup> </p><div><h2>Return to gold standard</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Among the propositions formulated at the conference was the proposal that central banks make a partial return to the <a href="https://en.wikipedia.org/wiki/Gold_standard">gold standard</a>, which had been dropped to print money to pay for the war. Central banks wanted a return to a gold-based economy to ease international trade and facilitating economic stability, but they wanted a gold standard that &quot;conserved&quot; gold stocks, with the gold remaining in the vaults and day-to-day transactions being conducted with representative paper notes.<sup><span>[</span>21<span>]</span></sup> </p><p>The partial return to the gold standard was accomplished by permitting central banks to keep part of their reserves in currencies, which were themselves directly exchangeable for gold coins. However, citizens would not receive gold coins of the realm in exchange for their notes, unlike the prewar gold standard. </p><p>Citizens of European countries had to redeem their banknotes in large gold bars, which were unsuitable for day-to-day transactions and largely achieved the goal of keeping the gold in the vaults. </p><div><h2>Treaty of Rapallo</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Treaty_of_Rapallo_(1922)">Treaty of Rapallo (1922)</a></div><p>On 16 April 1922 on the sidelines of the Genoa Conference, Russia and Germany signed the <a href="https://en.wikipedia.org/wiki/Treaty_of_Rapallo_(1922)">Treaty of Rapallo</a>. Ratifications were exchanged in Berlin on 31 January 1923. The treaty did not include secret military provisions, but secret military co-operation soon followed.<sup><span>[</span>22<span>]</span></sup> </p><div><h2>Conclusion and assessment</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>With the Treaty of Rapallo pulling Russia and Germany out of the main picture, the conference lapsed into a stalemate. The major powers at first agreed on a contingency package of financial aid to Russia, but the Allies could not agree on the final plan and so nothing was offered. The issue of German reparations went nowhere after Poincaré threatened to invade Germany unilaterally if Berlin defaulted on its next round of payments. Lloyd George was increasingly undercut by heavy attacks from the London newspapers but offered a final series of linked proposals, which would reduce Germany&#39;s liabilities for reparations, increase the French share of payments and float an international loan to finance German payments, with the money from the loan going directly to France. However, nothing was approved, Germany was expelled, France and Belgium withdrew and the final draft communiqué to Russia was signed only by Britain, Italy, Japan, Poland, Romania, Switzerland, and Sweden and left out the key world powers except Britain itself. Russia, in turn, rejected this final document. The last decision was to set up another conference at <a href="https://en.wikipedia.org/wiki/The_Hague">The Hague</a> to take up the same issues. </p><p>The British historian <a href="https://en.wikipedia.org/wiki/Kenneth_O._Morgan">Kenneth O. Morgan</a> concluded: </p><dl><dd>Genoa was a watershed in international diplomacy.... Never again would such a large, rambling assembly, on the lines of Paris in 1919, be convened, until <a href="https://en.wikipedia.org/wiki/United_Nations_Conference_on_International_Organization">San Francisco in 1945</a>.... There was too little detailed preparation, too much generalized optimism, too many disparate issues muddled up with one another. In many ways, it was a parody of summit diplomacy at its worst.<sup><span>[</span>23<span>]</span></sup></dd></dl><p>Despite its ending in failure, the Genoa Conference has been assessed as having a lasting intellectual impact. It cemented a consensus on the need for a stable value of money to support Europe&#39;s economic reconstruction, building on the prior debates at the <a href="https://en.wikipedia.org/wiki/Brussels_Conference_(1920)">Brussels conference of 1920</a>. Its resolutions represent the first official endorsement of the need for international cooperation among <a href="https://en.wikipedia.org/wiki/Central_bank">central banks</a>, paving the way for the creation several years later of the <a href="https://en.wikipedia.org/wiki/Bank_for_International_Settlements">Bank for International Settlements</a>.<sup><span>[</span>24<span>]</span></sup><sup><span>: 20 </span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/International_Monetary_and_Economic_Conferences">International Monetary and Economic Conferences</a></li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><div><ol> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>Louis W. Pauly (December 1996), <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173443">&quot;The League of Nations and the Foreshadowing of the International Monetary Fund&quot;</a>, <i>Essays in International Finance</i>, <b>201</b>, Princeton University, <a href="https://en.wikipedia.org/wiki/SSRN_(identifier)">SSRN</a> <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173443">2173443</a></cite></span> </li> <li><span><b>^</b></span> <span>Kenneth O. Morgan, <i>Consensus and Disunity: The Lloyd George Coalition Government 1918-1922</i> (1986) pp 310-16.</span> </li> <li><span><b>^</b></span> <span>John Saxon Mills, <a href="https://archive.org/details/genoaconference00milluoft"><i>The Genoa Conference.</i></a> London: Hutchinson &amp; Co., 1922; p. 9.</span> </li> <li><span><b>^</b></span> <span>Mills, <i>The Genoa Conference,</i> pp. 9-10.</span> </li> <li><span><b>^</b></span> <span>Mills, <i>The Genoa Conference,</i> p. 11.</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>David Lloyd George, Speech to Commons of 3 April 1922, quoted in Mills, <i>The Genoa Conference,</i> p. 10.</span> </li> <li><span><b>^</b></span> <span>Mills, <i>The Genoa Conference,</i> pp. 21-22.</span> </li> <li><span><b>^</b></span> <span>Mills, <i>The Genoa Conference,</i> p. 25.</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>Sally Marks, &quot;Reparations in 1922,&quot; in Carole Fink, Axel Frohn, and Jürgen Heideking (eds.), <i>Genoa, Rapallo, and European Reconstruction in 1922</i>. Cambridge, England: Cambridge University Press, 1991; p. 66.</span> </li> <li><span><b>^</b></span> <span>Marks, &quot;Reparations in 1922,&quot; pp. 66-67.</span> </li> <li><span><b>^</b></span> <span>Marks, &quot;Reparations in 1922,&quot; p. 67.</span> </li> <li><span><b>^</b></span> <span>Marks, &quot;Reparations in 1922,&quot; pp. 67-68.</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>Marks, &quot;Reparations in 1922,&quot; p. 68.</span> </li> <li><span><b>^</b></span> <span>Manfred Berg, &quot;Germany and the United States: The Concept of World Economic Interdependence,&quot; in Carole Fink, Axel Frohn, and Jürgen Heideking (eds.), <i>Genoa, Rapallo, and European Reconstruction in 1922.</i> Cambridge, England: Cambridge University Press, 1991; p. 82.</span> </li> <li><span><b>^</b></span> <span>Mills, <i>The Genoa Conference,</i> pp. 25-26.</span> </li> <li><span><b>^</b></span> <span>Mills, <i>The Genoa Conference,</i> p. 29.</span> </li> <li><span><b>^</b></span> <span>Carole Fink, <i>The Genoa Conference: European Diplomacy, 1921-1922.</i> Chapel Hill, NC: University of North Carolina Press, 1984; p. 32.</span> </li> <li><span><b>^</b></span> <span>&quot;Invitation to Russia,&quot; part of Appendix I, reprinted in Mills, <i>The Genoa Conference,</i> pg. 315.</span> </li> <li><span><b>^</b></span> <span>Mills, <i>The Genoa Conference,</i> pg. 45.</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup></span> <span>Mills, <i>The Genoa Conference,</i> p. 46.</span> </li> <li><span><b>^</b></span> <span><cite>Edwin Walter Kemmerer (1944). <a href="https://books.google.com/books?id=_aDIEAre3GMC&amp;pg=PA164"><i>Gold and the Gold Standard: The Story of Gold Money, Past, Present and Future</i></a>. Ludwig von Mises Institute. pp. <span>164–</span>55. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9781610164429"><bdi>9781610164429</bdi></a>.</cite> <span><code class="cs1-code">{{cite book}}</code>: </span><span>ISBN / Date incompatibility (<a href="https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_isbn_date">help</a>)</span></span> </li> <li><span><b>^</b></span> <span>Gordon H. Mueller, &quot;Rapallo Reexamined: A New Look at Germany&#39;s Secret Military Collaboration with Russia in 1922,&quot; <i>Military Affairs</i> (1976) 40#3 pp 109-117 <a href="https://www.jstor.org/stable/1986524">in JSTOR</a></span> </li> <li><span><b>^</b></span> <span>Morgan, <i>Consensus and Disunity: The Lloyd George Coalition Government 1918-1922</i> (1986) p, 314, quote on p. 315.</span> </li> <li><span><b>^</b></span> <span><cite>Gianni Toniolo (2005). <i>Central Bank Cooperation at the Bank for International Settlements, 1930-1973</i>. Cambridge University Press.</cite></span> </li> </ol></div><div><h2>Sources</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><ul><li>Jane Degras (ed.), <i>Soviet Documents on Foreign Policy.</i> London: Oxford University Press, 1951.</li> <li>David Lloyd George, &quot;The Genoa Conference and Britain&#39;s Part,&quot; <i>Advocate of Peace through Justice,</i> vol. 84, no. 4 (April 1922), pp. 131–137. <a href="https://www.jstor.org/stable/20659976">In JSTOR</a> <small>—Speech to Commons of 3 April 1922.</small></li></ul><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Genoa_Economic_and_Financial_Conference_(1922)&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Magda_%C3%81d%C3%A1m">Ádám, Magda</a>. &quot;The Genoa Conference and the Little Entente,&quot; in Carole Fink, Axel Frohn, and Jürgen Heideking (eds.), <i>Genoa, Rapallo, and European Reconstruction in 1922.</i> Cambridge, England: Cambridge University Press, 1991; pp. 187–200.</li> <li>Chossudovsky, Evgeny. &quot;Genoa Revisited: Russia and Coexistence,&quot; <i>Foreign Affairs,</i> vol. 50, no. 3 (April 1972), pp. 554–577. <a href="https://www.jstor.org/stable/20037929">In JSTOR</a></li> <li>Clarke, Stephen V.O. <a href="https://www.princeton.edu/~ies/IES_Studies/S33.pdf"><i>The Reconstruction of the International Monetary System: The Attempts of 1922 and 1933.</i></a> Princeton, NJ: International Finance Section, Department of Economics, Princeton University, 1973.</li> <li>Dennis, Alfred L.P. &quot;The Genoa Conference,&quot; <i>North American Review,</i> vol. 215, no. 796 (March 1922), pp. 289–299. <a href="https://www.jstor.org/stable/25120982">In JSTOR</a></li> <li>Fink, Carole. <i>The Genoa Conference: European Diplomacy, 1921-1922.</i> Chapel Hill, NC: University of North Carolina Press, 1984. <a href="https://www.questia.com/read/43111648/the-genoa-conference-european-diplomacy-1921-1922">online</a> <a href="https://web.archive.org/web/20181122131859/https://www.questia.com/read/43111648/the-genoa-conference-european-diplomacy-1921-1922">Archived</a> 2018-11-22 at the <a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a></li> <li>Fink, Carole. &quot;Italy and the Genoa Conference of 1922,&quot; <i>International History Review,</i> vol. 8, no. 1 (Feb. 1986), pp. 41–55. <a href="https://www.jstor.org/stable/40105562">In JSTOR</a></li> <li>Fischer, Louis. <i>Russia&#39;s Road from Peace to War: Soviet Foreign Relations, 1917-1941</i> (1969) pp 93. <a href="https://archive.org/details/russiasroadfromp00fisc">online</a></li> <li>Harris, Wilson. &quot;The Genoa Conference,&quot; <i>Journal of the British Institute of International Affairs,</i> vol. 1, no. 5 (Sept. 1922), pp. 150–158. <a href="https://www.jstor.org/stable/3014637">In JSTOR</a></li> <li>Himmer, Robert. &quot;Rathenau, Russia, and Rapallo.&quot; <i>Central European History</i> (1976) 9#2 pp 146–183.</li> <li><a href="https://en.wikipedia.org/wiki/George_F._Kennan">Kennan, George F.</a> <i>Russia and the West under Lenin and Stalin</i> (1961) pp 208–223. <a href="https://archive.org/search.php?query=title%3A%28russia%20west%29%20AND%20creator%3A%28kennan%29">online</a></li> <li>MArks, Sally. &quot;Reparations in 1922,&quot; in Carole Fink, Axel Frohn, and Jürgen Heideking (eds.), <i>Genoa, Rapallo, and European Reconstruction in 1922.</i> Cambridge, England: Cambridge University Press, 1991; pp. 65–76.</li> <li>Meyer, Richard. <i>Bankers&#39; Diplomacy: Monetary Stabilization in the 1920s.</i> New York: Columbia University Press, 1970.</li> <li>Mills, John Saxon. <a href="https://archive.org/details/genoaconference00milluoft"><i>The Genoa Conference.</i></a> London: Hutchinson &amp; Co., 1922.</li> <li>Pasvolsky, Leo, &quot;The Gold Standard before and after the War,&quot; <i>Annals of the American Academy of Political and Social Science,</i> (Jan. 1933), pp. 171–175. <a href="https://www.jstor.org/stable/1018177">In JSTOR</a></li> <li>Schuker, Stephen A. &quot;American Policy Toward Debts and Reconstruction at Genoa, 1922,&quot; in Carole Fink, Axel Frohn, and Jürgen Heideking (eds.), <i>Genoa, Rapallo, and European Reconstruction in 1922.</i> Cambridge, England: Cambridge University Press, 1991; pp. 95–130.</li> <li>Silverman, Dan P. <i>Reconstructing Europe After the Great War.</i> Cambridge, MA: Harvard University Press, 1982.</li> <li>White, Stephen. <i>The Origins of Detente: The Genoa Conference and Soviet-Western Relations, 1921-1922.</i> Cambridge, England: Cambridge University Press, 2002.</li> <li>Williams, Andrew. &quot;The Genoa Conference of 1922: Lloyd George and the Politics of Recognition,” in Carole Fink, Axel Frohn, and Jürgen Heideking (eds.), <i>Genoa, Rapallo, and European Reconstruction in 1922.</i> Cambridge, England: Cambridge University Press, 1991; pp. 29–48.</li></ul><div><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q697067#identifiers"></a></span></div></th></tr><tr><th>International</th><td><div><ul><li><span><a href="https://viaf.org/viaf/123799566">VIAF</a></span></li><li><span><a href="https://d-nb.info/gnd/4289516-9">GND</a></span></li><li><span><a href="https://id.worldcat.org/fast/1407657">FAST</a></span></li></ul></div></td></tr><tr><th>National</th><td><div><ul><li><span><a href="https://id.loc.gov/authorities/n90648322">United States</a></span></li><li><span><a href="https://catalogue.bnf.fr/ark:/12148/cb150009579">France</a></span></li><li><span><a href="https://data.bnf.fr/ark:/12148/cb150009579">BnF data</a></span></li><li><span><a href="https://kopkatalogs.lv/F?func=direct&amp;local_base=lnc10&amp;doc_number=000198904&amp;P_CON_LNG=ENG">Latvia</a></span></li></ul></div></td></tr><tr><th>Other</th><td><div><ul><li><span><a href="https://www.idref.fr/092370721">IdRef</a></span></li></ul></div></td></tr></tbody></table></div> Work-to-rule - Wikipedia https://en.wikipedia.org/wiki/Work-to-rule RAV8amWjr-35Kyp5ppfSnqVFjj7yCDYBS1KRPg== Sat, 09 May 2026 11:57:43 +0000 Industrial action in which employees do no more than the minimum required <div>Industrial action in which employees do no more than the minimum required</div><p> </p><table><tbody><tr><td>Part of <a href="https://en.wikipedia.org/wiki/Category:Labor"><span>a series</span></a> on</td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Portal:Organized_Labour"><span>Organized labour</span></a></th></tr><tr><td><span><a href="https://en.wikipedia.org/wiki/File:Co-op_activism5.svg"></a></span></td></tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Labour_movement">Movement</a></div><div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Conflict_theories">Conflict theories</a></li> <li><a href="https://en.wikipedia.org/wiki/Decent_work">Decent work</a></li> <li><a href="https://en.wikipedia.org/wiki/Exploitation_of_labor">Exploitation of labour</a></li> <li><a href="https://en.wikipedia.org/wiki/Timeline_of_labor_issues_and_events">Timeline</a></li> <li><a href="https://en.wikipedia.org/wiki/New_unionism">New unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Proletariat">Proletariat</a></li> <li><a href="https://en.wikipedia.org/wiki/Sectoral_collective_bargaining">Sectoral collective bargaining</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_movement_unionism">Social movement unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_democracy">Social democracy</a></li> <li><a href="https://en.wikipedia.org/wiki/Christian_democracy">Christian democracy</a></li> <li><a href="https://en.wikipedia.org/wiki/Socialism">Socialism</a> <ul><li><a href="https://en.wikipedia.org/wiki/Democratic_socialism">Democratic</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Communism">Communism</a></li> <li><a href="https://en.wikipedia.org/wiki/Syndicalism">Syndicalism</a> <ul><li><a href="https://en.wikipedia.org/wiki/Anarcho-syndicalism">Anarchist</a></li> <li><a href="https://en.wikipedia.org/wiki/National-syndicalism">Nationalist</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Union_busting">Union busting</a></li> <li><a href="https://en.wikipedia.org/wiki/Workplace_democracy">Workplace democracy</a></li></ul> </div></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Labor_rights">Rights</a></div><div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Annual_leave">Annual leave</a></li> <li><a href="https://en.wikipedia.org/wiki/Child_labour">Child labour</a></li> <li><a href="https://en.wikipedia.org/wiki/Collective_bargaining">Collective bargaining</a></li> <li><a href="https://en.wikipedia.org/wiki/Diversity,_equity,_and_inclusion">Diversity, equity, and inclusion</a></li> <li><a href="https://en.wikipedia.org/wiki/Economic_globalization">Economic globalization</a></li> <li><a href="https://en.wikipedia.org/wiki/Eight-hour_day">Eight-hour day</a></li> <li><a href="https://en.wikipedia.org/wiki/Employment_discrimination">Employment discrimination</a></li> <li><a href="https://en.wikipedia.org/wiki/Employment_protection_legislation">Employment protection</a></li> <li><a href="https://en.wikipedia.org/wiki/Equal_pay_for_equal_work">Equal pay</a></li> <li><a href="https://en.wikipedia.org/wiki/Four-day_week">Four-day week</a></li> <li><a href="https://en.wikipedia.org/wiki/Freedom_of_association">Freedom of association</a></li> <li><a href="https://en.wikipedia.org/wiki/Global_Rights_Index">Global Rights Index</a></li> <li><a href="https://en.wikipedia.org/wiki/Low-cost_country_sourcing">Low-cost country sourcing</a></li> <li><a href="https://en.wikipedia.org/wiki/Legal_working_age">Legal working age</a></li> <li><a href="https://en.wikipedia.org/wiki/Minimum_wage">Minimum wage</a></li> <li><a href="https://en.wikipedia.org/wiki/Neurodiversity_and_labor_rights">Neurodiversity and labour rights</a></li> <li><a href="https://en.wikipedia.org/wiki/Occupational_safety_and_health">Occupational safety and health</a></li> <li><a href="https://en.wikipedia.org/wiki/Overwork">Overwork</a></li> <li><a href="https://en.wikipedia.org/wiki/Paid_time_off">Paid time off</a></li> <li><a href="https://en.wikipedia.org/wiki/Professional_abuse">Professional abuse</a></li> <li><a href="https://en.wikipedia.org/wiki/Race_to_the_bottom">Race to the bottom</a> <ul><li><a href="https://en.wikipedia.org/wiki/Exploitation_of_labour">Exploitation of labour</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Right_to_rest_and_leisure">Right to rest and leisure</a></li> <li><a href="https://en.wikipedia.org/wiki/Right_to_sit">Right to sit</a></li> <li><a href="https://en.wikipedia.org/wiki/Sabbatical">Sabbatical</a></li> <li><a href="https://en.wikipedia.org/wiki/Sick_leave">Sick leave</a></li> <li><a href="https://en.wikipedia.org/wiki/Toxic_workplace">Toxic workplace</a></li> <li><a href="https://en.wikipedia.org/wiki/Unfree_labour">Unfree labour</a></li> <li><a href="https://en.wikipedia.org/wiki/Workers%27_right_to_access_the_toilet">Workers&#39; right to access the toilet</a></li></ul> </div></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Trade_union">Trade unions</a></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_trade_unions">Trade unions by country</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_federations_of_trade_unions">Trade union federations</a></li> <li><a href="https://en.wikipedia.org/wiki/International_comparisons_of_trade_unions">International comparisons</a></li> <li><div><ul><li><a href="https://en.wikipedia.org/wiki/International_Trade_Union_Confederation">ITUC</a></li><li><a href="https://en.wikipedia.org/wiki/World_Federation_of_Trade_Unions">WFTU</a></li></ul></div></li></ul></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Strike_action">Strike action</a></div><div><div> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_strikes">Chronological list</a></li> <li><a href="https://en.wikipedia.org/wiki/Hartal">Hartal</a></li> <li><a href="https://en.wikipedia.org/wiki/General_strike">General strike</a> <ul><li><a href="https://en.wikipedia.org/wiki/Bandh">Bandh</a></li> <li><a href="https://en.wikipedia.org/wiki/Strike_paper">newspapers</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Green_ban">Green bans</a></li> <li><a href="https://en.wikipedia.org/wiki/Lockout_(industry)">Lockouts</a></li> <li><a href="https://en.wikipedia.org/wiki/Overtime_ban">Overtime bans</a></li> <li><a href="https://en.wikipedia.org/wiki/Pen-down_strike">Pen-down strikes</a></li> <li><a href="https://en.wikipedia.org/wiki/Sitdown_strike">Sitdown strikes</a></li> <li><a href="https://en.wikipedia.org/wiki/Solidarity_action">Solidarity action</a></li> <li><a href="https://en.wikipedia.org/wiki/Walkout">Walkouts</a></li> <li><a href="https://en.wikipedia.org/wiki/Whipsaw_strike">Whipsaw strikes</a></li> <li><a href="https://en.wikipedia.org/wiki/Wildcat_strike">Wildcat strikes</a></li> <li><a href="https://en.wikipedia.org/wiki/Rolling_strike">Rolling strikes</a></li> <li>Work-to-rule</li></ul> </div></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/List_of_Labour_parties">Parties</a></div><div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Australian_Labor_Party">Australia</a></li> <li><a href="https://en.wikipedia.org/wiki/Barbados_Labour_Party">Barbados</a></li> <li><a href="https://en.wikipedia.org/wiki/Brazilian_Labour_Party_(current)">Brazil</a></li> <li><a href="https://en.wikipedia.org/wiki/Fiji_Labour_Party">Fiji</a></li> <li><a href="https://en.wikipedia.org/wiki/Georgian_Labour_Party">Georgia</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_Party_(Hong_Kong)">Hong Kong</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_Party_(Ireland)">Ireland</a></li> <li><a href="https://en.wikipedia.org/wiki/Israeli_Labor_Party">Israel</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_Party_(Malta)">Malta</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_Party_(New_Caledonia)">New Caledonia</a></li> <li><a href="https://en.wikipedia.org/wiki/New_Zealand_Labour_Party">New Zealand</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_Party_(Netherlands)">Netherlands</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_Party_(Norway)">Norway</a></li> <li><a href="https://en.wikipedia.org/wiki/Portuguese_Labour_Party">Portugal</a></li> <li><a href="https://en.wikipedia.org/wiki/Congolese_Party_of_Labour">Republic of the Congo</a></li> <li><a href="https://en.wikipedia.org/wiki/Workers%27_Party_(Singapore)">Singapore</a></li> <li><a href="https://en.wikipedia.org/wiki/Labor_Party_(South_Korea)">South Korea</a></li> <li><a href="https://en.wikipedia.org/wiki/Swedish_Social_Democratic_Party">Sweden</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_Party_(UK)">United Kingdom</a></li></ul> </div></div></div></td> </tr><tr><td> <div><div>Academic disciplines</div><div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Critique_of_work">Critique of work</a></li> <li><a href="https://en.wikipedia.org/wiki/Industrial_relations">Industrial relations</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_economics">Labour economics</a></li> <li><a href="https://en.wikipedia.org/wiki/Labor_history_(discipline)">Labour history</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_law">Labour law</a></li> <li><a href="https://en.wikipedia.org/wiki/Post-work_society">Post-work society</a></li> <li><a href="https://en.wikipedia.org/wiki/Refusal_of_work">Refusal of work</a></li></ul> </div></div></div></td> </tr><tr><td> <ul><li><span><span><a href="https://en.wikipedia.org/wiki/File:Syndicalism.svg"></a></span> </span><a href="https://en.wikipedia.org/wiki/Portal:Organized_Labour">Organized Labour portal</a></li></ul></td></tr><tr><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Labour"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Labour"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Labour"><abbr>e</abbr></a></li></ul></div></td></tr></tbody></table><p><b>Work-to-rule</b>, also known as an <b>Italian strike</b> or a <b>slowdown</b> in United States usage, and <span><i>sciopero bianco</i></span> (&#39;white strike&#39;) in Italy,<sup><span>[</span>1<span>]</span></sup> is a <a href="https://en.wikipedia.org/wiki/Job_action">job action</a> in which <a href="https://en.wikipedia.org/wiki/Employee">employees</a> do no more than the minimum required by the rules of their contract or job,<sup><span>[</span>2<span>]</span></sup><sup><span>[</span>3<span>]</span></sup> and <a href="https://en.wikipedia.org/wiki/Malicious_compliance">strictly follow</a> time-consuming rules normally not enforced.<sup><span>[</span>4<span>]</span></sup> It is a <a href="https://en.wikipedia.org/wiki/Passive-aggressive_behavior">passive-aggressive</a> form of labor opposition. This may cause a <a href="https://en.wikipedia.org/wiki/Slowdown">slowdown</a> or decrease in productivity if the employer does not hire enough employees or pay the appropriate salary and consequently does not have the requirements needed to run normally.<sup><span>[</span>5<span>]</span></sup><sup><span>[</span>6<span>]</span></sup> </p><p>It is a form of protest against low pay and poor working conditions,<sup><span>[</span>3<span>]</span></sup> and is considered less disruptive than a <a href="https://en.wikipedia.org/wiki/Strike_action">strike</a>; obeying the rules is not susceptible to disciplinary action or loss of pay. It can also highlight rules that are technically in place but impractical and thus hamper the organization, if they were to be followed as written. In practice, there may be ambiguous conditions – for example, a contract that requires working additional hours when necessary, or a requirement to work to operational requirements. In such cases, workers have been recommended to ask for a written direction to carry out the work, which can be used as evidence if necessary.<sup><span>[</span>7<span>]</span></sup> </p><div><h2>Applications</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Work-to-rule&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>Work-to-rule may be employed formally or informally by workers and organizers as an alternative to traditional strike action in contexts where strikes are prohibited, either by law or due to lack of workforce union participation or political will. Work-to-rule has been employed in sectors where striking is prohibited, including education,<sup><span>[</span>8<span>]</span></sup> policing,<sup><span>[</span>9<span>]</span></sup><sup><span>[</span>10<span>]</span></sup> and healthcare,<sup><span>[</span>11<span>]</span></sup> as well as in <a href="https://en.wikipedia.org/wiki/Authoritarian">authoritarian</a> societies like <a href="https://en.wikipedia.org/wiki/Russia">Russia</a>, which prohibit strikes generally.<sup><span>[</span>12<span>]</span></sup> In this respect, work-to-rule tactics can resemble other forms of industrial action such as an <a href="https://en.wikipedia.org/wiki/Overtime_ban">overtime ban</a> or <a href="https://en.wikipedia.org/wiki/Blue_flu">blue flu</a>. </p><div><h3>Quiet quitting</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Work-to-rule&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>Quiet quitting is a specific, often spontaneous or <a href="https://en.wikipedia.org/wiki/Grassroots">grassroots</a> application of work-to-rule tactics.<sup><span>[</span>13<span>]</span></sup><sup><span>[</span>14<span>]</span></sup> Despite the name, the philosophy of quiet quitting is not connected to <a href="https://en.wikipedia.org/wiki/Resignation">quitting a job</a> outright, but rather, employees avoid going above and beyond the call of duty by doing the bare minimum required and engage in work-related activities solely within defined <a href="https://en.wikipedia.org/wiki/Work_hours">work hours</a>.<sup><span>[</span>15<span>]</span></sup> Proponents of quiet quitting also refer to it as &quot;acting your wage&quot;,<sup><span>[</span>16<span>]</span></sup> or &quot;calibrated contributing&quot;,<sup><span>[</span>17<span>]</span></sup> and say that the goal of quiet quitting is not primarily to disrupt the workplace as part of an organized movement, but to avoid <a href="https://en.wikipedia.org/wiki/Occupational_burnout">occupational burnout</a> and to reassert <a href="https://en.wikipedia.org/wiki/Autonomy">autonomy</a> and <a href="https://en.wikipedia.org/wiki/Work%E2%80%93life_interface">work-life balance</a> on an individual level. </p><p>There are no verifiable sources as to who coined the phrase.<sup><span>[</span>18<span>]</span></sup> It was also thought to be inspired by the <span><i><a href="https://en.wikipedia.org/wiki/Tang_ping">tang ping</a></i></span> (&#39;lying flat&#39;) movement that began in April 2021 on Chinese <a href="https://en.wikipedia.org/wiki/Social_media">social media</a> and became a buzzword on <a href="https://en.wikipedia.org/wiki/Sina_Weibo">Sina Weibo</a>.<sup><span>[</span>19<span>]</span></sup><sup><span>[</span>20<span>]</span></sup><sup><span>[</span>21<span>]</span></sup> Later that year, Chinese Internet users combined <span><i>tang ping</i></span> with <a href="https://en.wikipedia.org/wiki/Involution_(sociology)">involution</a>, a process researched by American anthropologist <a href="https://en.wikipedia.org/wiki/Clifford_Geertz">Clifford Geertz</a> in his 1963 book <i><a href="https://en.wikipedia.org/wiki/Agricultural_Involution">Agricultural Involution</a></i>. The book gained attention in the late 1980s from social sciences research about China which led to the term &quot;involution&quot; gaining great attention in China.<sup><span>[</span>22<span>]</span></sup> In 2020, &quot;involution&quot; became one of the most commonly used words on Chinese-language media, where it is used to describe the feeling of exhaustion in an overly competitive society.<sup><span>[</span>23<span>]</span></sup><sup><span>[</span>24<span>]</span></sup> </p><p>After <span><i>tang ping</i></span> became a buzzword and inspired numerous <a href="https://en.wikipedia.org/wiki/Internet_meme">Internet memes</a>, business magazine <i>ABC Money</i> claimed it resonated with a growing <a href="https://en.wikipedia.org/wiki/Silent_majority">silent majority</a> of youth disillusioned by the officially endorsed &quot;<a href="https://en.wikipedia.org/wiki/Chinese_Dream">Chinese Dream</a>&quot; that encourages a life of hard work and sacrifice with no actual <a href="https://en.wikipedia.org/wiki/Life_satisfaction">life satisfaction</a> to show for it.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> An editorial published in the journal of the <a href="https://en.wikipedia.org/wiki/American_Institute_of_Chemical_Engineers">American Institute of Chemical Engineers</a> defined quiet quitting as a rejection of &quot;<a href="https://en.wikipedia.org/wiki/Hustle_culture">hustle culture</a>&quot; and the belief that value of work is intrinsically tied to number of hours.<sup><span>[</span>25<span>]</span></sup> </p><p>Though the term is recent, the ideas behind quiet quitting are not and go back decades.<sup><span>[</span>26<span>]</span></sup> The phrase &quot;quiet quitting&quot; became popular during 2022 in the United States, mostly through the social video platform <a href="https://en.wikipedia.org/wiki/TikTok">TikTok</a>.<sup><span>[</span>27<span>]</span></sup> In 2022, quiet quitting experienced a surge in popularity in numerous publications following a viral <a href="https://en.wikipedia.org/wiki/TikTok">TikTok</a> video,<sup><span>[</span>28<span>]</span></sup> which was inspired by a <i><a href="https://en.wikipedia.org/wiki/Business_Insider">Business Insider</a></i> article.<sup><span>[</span>29<span>]</span></sup> That same year, <a href="https://en.wikipedia.org/wiki/Gallup,_Inc.">Gallup</a> found that roughly half of the American workforce were quiet quitters.<sup><span>[</span>30<span>]</span></sup> </p><p>Industry observers argue the <a href="https://en.wikipedia.org/wiki/Coronavirus_pandemic">COVID-19 pandemic</a> accelerated the social movement of quiet quitting, with a resurgence in labor sentiments among <a href="https://en.wikipedia.org/wiki/Generation_Z">Generation Z</a> as a result of the economic fallout.<sup><span>[</span>31<span>]</span></sup> A 2021 survey conducted by the <a href="https://en.wikipedia.org/wiki/American_Psychological_Association">American Psychological Association</a> revealed that forty percent of American workers surveyed intend to change jobs, which the report attributed to lack of compensation for the amount of stress and burnout endured.<sup><span>[</span>32<span>]</span></sup> In 2023, a trend called <a href="https://en.wikipedia.org/wiki/Quiet_cutting">quiet cutting</a> was seen where employers would reassign rather than lay off employees, suggesting a possible shift in workplace power.<sup><span>[</span>33<span>]</span></sup> It is possible that <a href="https://en.wikipedia.org/wiki/Conscious_quitting">conscious quitting</a> might follow quiet quitting.<sup><span>[</span>34<span>]</span></sup><sup><span>[</span>35<span>]</span></sup> </p><div><h2>Response</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Work-to-rule&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>While individual contributors might think in terms of otherwise &quot;engaged workers setting reasonable boundaries&quot;, their employers might see them instead as &quot;slackers who are willfully <a href="https://en.wikipedia.org/wiki/Workplace_performance">underperforming</a>&quot;.<sup><span>[</span>36<span>]</span></sup> Depending on jurisdiction, work-to-rule may sometimes be considered by employers as <a href="https://en.wikipedia.org/wiki/Malicious_compliance">malicious compliance</a>, and they may attempt to pursue legal action against workers. While generally not grounds for legal retaliation on an individual basis, employers may attempt to enforce onerous contract terms such as: </p><ul><li>Mandatory overtime</li> <li>Breaks set by management</li> <li>Vague description including &quot;ad-hoc task&quot; or &quot;as assigned&quot;</li> <li><a href="https://en.wikipedia.org/wiki/At-will_employment">Termination for any reason</a></li></ul><p>They may also take standard forms of action especially where custom terms were not negotiated during the offer: </p><ul><li>Warning and noting employee file for <a href="https://en.wikipedia.org/wiki/Professional_misconduct">professional misconduct</a> or <a href="https://en.wikipedia.org/wiki/Insubordination">insubordination</a></li> <li>Reassigning employee to insignificant, <a href="https://en.wiktionary.org/wiki/scutwork">routine, or mundane tasks</a></li></ul><p>The employer counterpart of &#39;quiet quitting&#39; is &#39;quiet firing&#39;, in which an employer deliberately offers only a minimum wage and benefits and denies any advances in the hope that an unwanted employee will quit.<sup><span>[</span>37<span>]</span></sup><sup><span>[</span>38<span>]</span></sup> The term has also been used to refer to employers reducing the scope of a worker&#39;s responsibilities to encourage them to quit voluntarily.<sup><span>[</span>36<span>]</span></sup> &quot;Quiet hiring&quot; is another related term that has been used to describe a strategy by employers to give additional responsibilities and unpaid extra workload to hard-working employees.<sup><span>[</span>39<span>]</span></sup> </p><p>In countries or sectors where other forms of striking is regulated or illegal, work-to-rule tactics may be subject to scrutiny or punishment.<sup><span>[</span>12<span>]</span></sup> In the United States, work-to-rule tactics which are coordinated by a <a href="https://en.wikipedia.org/wiki/Trade_union">labor organization</a> or its <a href="https://en.wikipedia.org/wiki/Law_of_agency">agents</a> may be ruled and treated as a strike under the <a href="https://en.wikipedia.org/wiki/National_Labor_Relations_Act_of_1935">National Labor Relations Act</a>, and may be interpreted as failure to bargain in <a href="https://en.wikipedia.org/wiki/Good_faith_(law)">good faith</a>, a requirement of <a href="https://en.wikipedia.org/wiki/Collective_bargaining">collective bargaining</a>.<sup><span>[</span>40<span>]</span></sup><sup><span>[</span>41<span>]</span></sup> In the case of non-union workplaces, employees suspected of work-to-rule tactics, organizing, or quiet quitting, may be fired if their employment is considered <a href="https://en.wikipedia.org/wiki/At-will_employment">at-will</a>, though such termination may still be considered <a href="https://en.wikipedia.org/wiki/Wrongful_dismissal">wrongful</a> if there is overt evidence it is done to infringe on workers&#39; protected rights to organize.<sup><span>[</span>42<span>]</span></sup> </p><div><h2>Examples</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Work-to-rule&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Cases of work-to-rule tactics have included: </p><ul><li>British postal workers normally arrived an hour before their official start time, did unpaid overtime at the end of deliveries, used their own (uninsured) cars for deliveries, and carried mailbags too heavy by health and safety guidelines. During a dispute they arrived at start time, stopped deliveries at the end of their allotted shift, only used official vans, and weighed mailbags to keep within the limit.<sup><span>[</span>43<span>]</span></sup></li> <li>French railway workers, who are not allowed to strike, were required by law to be sure of the safety of all bridges the train had to pass over; if doubtful of safety they had to consult other train crew members. During a dispute they inspected every bridge, and consulted other crew members on the bridge&#39;s condition in every instance; as a consequence, the trains did not arrive on time.<sup><span>[</span>4<span>]</span></sup></li> <li>Austrian postal workers normally accept without weighing all items that are obviously not overweight. During a dispute they observed the rule that all mail must be weighed, taking it to the scales, weighing, and then taking it back. The office was crammed with unweighed mail by the second day.<sup><span>[</span>4<span>]</span></sup></li> <li>German doctors, who are not permitted to strike, have employed work to rule tactics in protest of announced caps on insurance reimbursement.<sup><span>[</span>11<span>]</span></sup></li> <li>Workers may have the right to a specified number of toilet breaks; they may insist on taking the maximum allowed during a dispute.<sup><span>[</span>4<span>]</span></sup></li> <li>During a work-to-rule strike, teachers may choose to instruct students during classroom hours only; and not participate in extra-curricular activities such as sports, tutoring or meetings before/after school.<sup><span>[</span>44<span>]</span></sup> Such tactics are associated with a significant reduction in standardized test scores by students at affected schools.<sup><span>[</span>8<span>]</span></sup></li> <li>Actions taken by police in the United States, including <a href="https://en.wikipedia.org/wiki/Blue_flu">coordinated use of sick days</a>, and declines in tickets issued and arrests made, may resemble work to rule tactics, however the exact terminology is disputed,<sup><span>[</span>10<span>]</span></sup> partly because police are prohibited from striking,<sup><span>[</span>9<span>]</span></sup> partly because of the contentious relationship between police, <a href="https://en.wikipedia.org/wiki/Police_unions_in_the_United_States">police unions</a>, and the labor movement as a whole.<sup><span>[</span>45<span>]</span></sup></li> <li>In Paris, taxi drivers historically employed grève de zèle (&quot;zeal strike&quot;) to protest municipal policies. By strictly adhering to the code routier (French traffic code), such as obeying all speed limits, refusing to use bus lanes, or stopping at every pedestrian crossing, drivers exploited the fact that Parisian traffic flow relies on routine, pragmatic violations of minor rules. Their collective over-compliance caused severe congestion, effectively paralyzing the city to pressure authorities.<sup><span>[</span>46<span>]</span></sup></li> <li>In 1984, French and Italian customs officers staged a work-to-rule tactic by meticulously inspecting every vehicle at border crossings, causing massive traffic jams. According to Belgian public broadcaster RTBF, these protests highlighted the inefficiency of systematic border checks and contributed to discussions that later led to the Schengen Agreement, which abolished many internal EU border controls.<sup><span>[</span>47<span>]</span></sup></li></ul><p>Although the term <i>quiet quitting</i> was popularised in 2022,<sup><span>[</span>48<span>]</span></sup> aspects of quiet quitting have existed in the workplace and popular culture for much longer. The film <i><a href="https://en.wikipedia.org/wiki/Office_Space">Office Space</a></i> (1999) depicts a character engaging in quiet quitting; in the film, <a href="https://en.wikipedia.org/wiki/Ron_Livingston">Ron Livingston</a>&#39;s character Peter Gibbons abandons the concept of work entirely and does the bare minimum required of him.<sup><span>[</span>49<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Work-to-rule&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Work-to-rule&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span><cite><a href="https://www.collinsdictionary.com/dictionary/italian-english/sciopero-bianco">&quot;English translation of &#39;sciopero bianco&#39;&quot;</a>. <i>collinsdictionary.com</i><span>. Retrieved <span>29 December</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.collinsdictionary.com/us/dictionary/english/work-to-rule">&quot;work to rule&quot;</a>. <i>Collins Dictionary</i>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://dictionary.cambridge.org/us/dictionary/english/work-to-rule">&quot;work-to-rule&quot;</a>. <i>Cambridge Dictionary</i>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup></span> <span><cite><a href="https://libcom.org/article/work-rule-guide">&quot;Work-to-rule: a guide&quot;</a>. <i>libcom.org</i>. 11 November 2006.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Morgan, Gareth (1998). <a href="https://books.google.com/books?id=a_W8jXt4_eMC&amp;dq=work-to-rule&amp;pg=PA165"><i>Images of Organization</i></a>. Thousand Oaks, California: Sage Publications. p. 165. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-7619-1752-7"><bdi>0-7619-1752-7</bdi></a><span>. Retrieved <span>12 January</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://news.google.com/newspapers?id=uJZlAAAAIBAJ&amp;pg=6026,3158040&amp;dq=work-to-rule&amp;hl=en">&quot;Air Canada Hit By Work-to-Rule&quot;</a>. <i>The Sun</i>. Vancouver, British Columbia, Canada. 9 December 1968. pp. <span>1–</span>2<span>. Retrieved <span>12 January</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://unitethefca.org/working-to-rule/">&quot;Working to Rule&quot;</a>. Unite. The union for staff at the FCA. 20 April 2022. <a href="https://web.archive.org/web/20220702211454/https://unitethefca.org/working-to-rule/">Archived</a> from the original on 2 July 2022.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Johnson, David R. (December 2011). <span><a href="https://utpjournals.press/doi/10.3138/cpp.37.4.479">&quot;Do Strikes and Work-to-Rule Campaigns Change Elementary School Assessment Results?&quot;</a></span>. <i>Canadian Public Policy</i>. <b>37</b> (4): <span>479–</span>494. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.3138%2Fcpp.37.4.479">10.3138/cpp.37.4.479</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0317-0861">0317-0861</a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://www.nytimes.com/1971/01/28/archives/injunction-ends-a-police-strike-milwaukee-blue-flu-over-after-4day.html">&quot;INJUNCTION ENDS A POLICE STRIKE&quot;</a>. <i>The New York Times</i>. 28 January 1971. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0362-4331">0362-4331</a><span>. Retrieved <span>6 April</span> 2023</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Sestanovich, Clare (6 January 2015). <a href="https://www.themarshallproject.org/2015/01/06/a-short-history-of-police-protest">&quot;A Short History of Police Protest&quot;</a>. <i>The Marshall Project</i><span>. Retrieved <span>6 April</span> 2023</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Tuffs, A. (8 February 2003). <span><a href="https://www.bmj.com/lookup/doi/10.1136/bmj.326.7384.303">&quot;German doctors &quot;work to rule&quot; in protest at government plans&quot;</a></span>. <i>BMJ</i>. <b>326</b> (7384): 303. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1136%2Fbmj.326.7384.303">10.1136/bmj.326.7384.303</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:71455189">71455189</a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Р, Ахмадуллин Ильдар (18 December 2020). <span><a href="https://ras.jes.su/socis/s013216250009284-5-1">&quot;Итальянские забастовки в России&quot;</a></span>. <i>Социологические исследования</i> (in Russian) (10): <span>95–</span>105. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.31857%2FS013216250009284-5">10.31857/S013216250009284-5</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0132-1625">0132-1625</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:234678765">234678765</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.latimes.com/business/story/2022-08-25/quiet-quitting-is-just-a-new-name-for-an-ancient-reality">&quot;Column: &#39;Quiet quitting&#39; is just a new name for an old reality&quot;</a>. <i>Los Angeles Times</i>. 25 August 2022.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Lord, Jonathan (9 September 2022). <a href="https://theconversation.com/quiet-quitting-is-a-new-name-for-an-old-method-of-industrial-action-189752">&quot;Quiet quitting is a new name for an old method of industrial action&quot;</a>. <i>The Conversation</i>.</cite></span> </li> <li><span><b>^</b></span> <span>Multiple sources: <ul><li><cite>Tapper, James (6 August 2022). <a href="https://www.theguardian.com/money/2022/aug/06/quiet-quitting-why-doing-the-bare-minimum-at-work-has-gone-global">&quot;Quiet quitting: why doing the bare minimum at work has gone global&quot;</a>. <i>the Guardian</i><span>. Retrieved <span>12 August</span> 2022</span>.</cite></li> <li><cite>Bakshi, Pema. <a href="https://www.refinery29.com/en-gb/quiet-quitting-job">&quot;In Defence Of &#39;Quiet Quitting&#39; Your Job&quot;</a>. <i>www.refinery29.com</i><span>. Retrieved <span>12 August</span> 2022</span>.</cite></li> <li><cite>Scott, Ellen (29 July 2022). <a href="https://metro.co.uk/2022/07/29/could-the-quiet-quitting-trend-be-the-answer-to-burnout-what-you-need-to-know-17085827/">&quot;Could &#39;quiet quitting&#39; your job be the answer to burnout? What you need to know&quot;</a>. <i>Metro</i><span>. Retrieved <span>12 August</span> 2022</span>.</cite></li> <li><cite>Yang, Lindsay Ellis and Angela (12 August 2022). <a href="https://www.wsj.com/articles/if-your-gen-z-co-workers-are-quiet-quitting-heres-what-that-means-11660260608">&quot;If Your Co-Workers Are &#39;Quiet Quitting,&#39; Here&#39;s What That Means&quot;</a>. <i>The Wall Street Journal</i>.</cite></li></ul> </span></li> <li><span><b>^</b></span> <span><cite><a href="https://www.economist.com/the-world-this-week/2022/09/01/business">&quot;Business&quot;</a>. <i>The Economist</i>. 1 September 2022.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Reddy, Venk (19 December 2022). <a href="https://www.gurufocus.com/news/1913128/quiet-quitting-quiet-firing-more-like-quiet-retiring">&quot;Quiet Quitting? Quiet Firing? More Like Quiet Retiring&quot;</a>. <i>GuruFocus</i>. Osterweis Capital Management. <a href="https://en.wikipedia.org/wiki/ProQuest">ProQuest</a> <a href="https://www.proquest.com/docview/2755632700">2755632700</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Hitt, Tarpley (10 October 2020). <a href="https://web.archive.org/web/20231004222408/https://www.gawker.com/news/the-libertarian-who-supposedly-coined-quiet-quitting">&quot;The Libertarian Who Supposedly Coined &#39;Quiet Quitting&#39;&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Gawker">Gawker</a></i>. Archived from <a href="https://www.gawker.com/news/the-libertarian-who-supposedly-coined-quiet-quitting">the original</a> on 4 October 2023<span>. Retrieved <span>3 October</span> 2024</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Perisha Kudhail (31 August 2022). <a href="https://www.bbc.com/news/business-62638908">&quot;Quiet quitting: The workplace trend taking over TikTok&quot;</a>. BBC.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Henry Bodkin (7 August 2022). <a href="https://www.telegraph.co.uk/news/2022/08/07/workers-embrace-bare-minimum-quiet-quitting-trend/">&quot;Workers embrace the bare minimum in &#39;quiet quitting&#39; trend&quot;</a>. <i>The Telegraph</i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.bbc.com/news/world-asia-china-57348406">&quot;China&#39;s new &#39;tang ping&#39; trend aims to highlight pressures of work culture&quot;</a>. <a href="https://en.wikipedia.org/wiki/BBC">BBC</a>. 3 June 2021.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Picoche, Ariane (17 January 2022). <a href="https://web.archive.org/web/20220928133445/https://www.welcometothejungle.com/en/articles/tang-ping-chinese-milennials-protest-overwork">&quot;Tang ping: the Chinese millennials lying flat to protest against overwork&quot;</a>. <i>Welcome to the Jungle</i>. Archived from <a href="https://www.welcometothejungle.com/en/articles/tang-ping-chinese-milennials-protest-overwork">the original</a> on 28 September 2022<span>. Retrieved <span>24 September</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Liu, Yi-Ling (14 May 2021). <a href="https://www.newyorker.com/culture/cultural-comment/chinas-involuted-generation">&quot;China&#39;s &quot;Involuted&quot; Generation&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/The_New_Yorker">The New Yorker</a></i><span>. Retrieved <span>28 March</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Wang, Qianni; Ge, Shifan (4 November 2020). <a href="https://www.sixthtone.com/news/1006391/how-one-obscure-word-captures-urban-chinas-unhappiness">&quot;How One Obscure Word Captures Urban China&#39;s Unhappiness&quot;</a>. <i>Sixth Tone</i><span>. Retrieved <span>28 March</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.aiche.org/resources/publications/cep/2022/october/editorial-reversing-quiet-quitting-trend">&quot;Editorial: Reversing the Quiet Quitting Trend&quot;</a>. <i>www.aiche.org</i>. 3 October 2022<span>. Retrieved <span>22 March</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Serenko, A. (2024). <a href="https://www.aserenko.com/papers/QuietQuittingSerenkoJKM.pdf">&quot;The human capital management perspective on quiet quitting: Recommendations for employees, managers, and national policymakers&quot;</a> <span>(PDF)</span>. <i>Journal of Knowledge Management</i>. <b>28</b> (1): <span>27–</span>43. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1108%2FJKM-10-2022-0792">10.1108/JKM-10-2022-0792</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:258026195">258026195</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.wsj.com/articles/if-your-gen-z-co-workers-are-quiet-quitting-heres-what-that-means-11660260608">&quot;If Your Co-Workers Are &#39;Quiet Quitting,&#39; Here&#39;s What That Means&quot;</a>. <i>Wall Street Journal</i>. 12 August 2022.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Teitell, Beth (16 September 2022). <a href="https://www.bostonglobe.com/2022/09/16/business/quiet-quitting-season-1-brutally-honest-recap/">&quot;As quiet quitting goes viral, it&#39;s turning into the pumpkin spice of 2022&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/The_Boston_Globe">The Boston Globe</a></i><span>. Retrieved <span>23 September</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Seward, Zachary M. (26 October 2022). <a href="https://qz.com/the-guy-who-inspired-the-quiet-quitting-movement-is-b-1849704130">&quot;The guy who inspired the &#39;quiet quitting&#39; movement is back to working 50 hours a week&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Quartz_(publication)">Quartz</a></i><span>. Retrieved <span>3 November</span> 2022</span>.</cite> <ul><li><cite>Ito, Aki (2 March 2022). <a href="https://www.businessinsider.com/overachievers-leaning-back-hustle-culture-coasting-employees-work">&quot;&#39;My company is not my family&#39;: Fed up with long hours, many employees have quietly decided to take it easy at work rather than quit their jobs&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Business_Insider">Business Insider</a></i><span>. Retrieved <span>3 November</span> 2022</span>.</cite></li></ul> </span></li> <li><span><b>^</b></span> <span><cite>Harter, Jim (6 September 2022). <a href="https://www.gallup.com/workplace/398306/quiet-quitting-real.aspx">&quot;Is Quiet Quitting Real?&quot;</a>. <i>Gallup.com</i><span>. Retrieved <span>6 September</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Formica, Sandro; Sfodera, Fabiola (17 November 2022). &quot;The Great Resignation and Quiet Quitting paradigm shifts: An overview of current situation and future research directions&quot;. <i>Journal of Hospitality Marketing &amp; Management</i>. <b>31</b> (8): <span>899–</span>907. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1080%2F19368623.2022.2136601">10.1080/19368623.2022.2136601</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:253077483">253077483</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.apa.org/pubs/reports/work-well-being/compounding-pressure-2021">&quot;The American workforce faces compounding pressure: APA&#39;s 2021 Work and Well-being Survey results&quot;</a>. <i>www.apa.org</i><span>. Retrieved <span>22 March</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Smith, Ray A. (28 August 2023). <a href="https://www.wsj.com/lifestyle/careers/youve-heard-of-quiet-quitting-now-companies-are-quiet-cutting-ba2c326d">&quot;You&#39;ve Heard of Quiet Quitting. Now Companies Are Quiet Cutting&quot;</a>. <i>WSJ</i><span>. Retrieved <span>14 October</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://finance.yahoo.com/news/conscious-quitting-newest-trend-sweeping-122118047.html">&quot;&#39;Conscious quitting&#39; is the newest trend sweeping the workplace. Here&#39;s what leaders can do to avoid it&quot;</a>. <i>Yahoo Finance</i><span>. Retrieved <span>2 February</span> 2025</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Song-Marshall, Judy (Haejoo). <a href="https://www.forbes.com/councils/forbesnonprofitcouncil/2023/07/07/how-to-find-a-job-you-dont-need-to-consciously-quit/">&quot;Council Post: How To Find A Job You Don&#39;t Need To &#39;Consciously Quit&#39;&quot;</a>. <i>Forbes</i><span>. Retrieved <span>2 February</span> 2025</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Miller, Karla L. (8 September 2022). <a href="https://www.washingtonpost.com/business/2022/09/08/quiet-quitting-quiet-firing-what-to-do/">&quot;Actually, we&#39;ve been &#39;quiet quitting&#39; and &#39;quiet firing&#39; for years&quot;</a>. <i>The Washington Post</i><span>. Retrieved <span>12 September</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Miller, Karla L. (1 September 2022). <a href="https://www.washingtonpost.com/business/2022/09/01/quiet-quitting-and-firing/">&quot;After &#39;quiet quitting,&#39; here comes &#39;quiet firing&#39;&quot;</a>. Business. <i>The Washington Post</i><span>. Retrieved <span>21 September</span> 2022</span>.</cite><span><code class="cs1-code">{{cite news}}</code>: CS1 maint: deprecated archival service (<a href="https://en.wikipedia.org/wiki/Category:CS1_maint:_deprecated_archival_service">link</a>)</span></span> </li> <li><span><b>^</b></span> <span><cite>Borchers, Callum (29 September 2022). &quot;Employers strike back at &#39;Quitters&#39;&quot;. <i><a href="https://en.wikipedia.org/wiki/The_Wall_Street_Journal">The Wall Street Journal</a></i>. pp. A12.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Breen, Amanda (9 September 2022). <a href="https://www.entrepreneur.com/business-news/googles-quiet-hiring-method-is-bad-news-for-quiet/435043">&quot;Google&#39;s &#39;Quiet Hiring&#39; Method Is Bad News for &#39;Quiet Quitters&#39;&quot;</a>. <i>Entrepreneur</i><span>. Retrieved <span>13 September</span> 2022</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.nlrb.gov/guidance/key-reference-materials/national-labor-relations-act">&quot;National Labor Relations Act&quot;</a>. <i>www.nlrb.gov</i><span>. Retrieved <span>28 March</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.nlrb.gov/about-nlrb/rights-we-protect/the-law/collective-bargaining-section-8d-8b3">&quot;Collective bargaining (Section 8(d) &amp; 8(b)(3)) | National Labor Relations Board&quot;</a>. <i>www.nlrb.gov</i><span>. Retrieved <span>6 March</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.law.cornell.edu/wex/employment-at-will_doctrine">&quot;employment-at-will doctrine&quot;</a>. <i>LII / Legal Information Institute</i><span>. Retrieved <span>6 March</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://libcom.org/article/royal-mail-strikes-suspended-talks-work-rule-continues">&quot;Royal Mail strikes suspended for talks as work to rule continues&quot;</a>. <i>libcom.org</i>. 10 August 2007.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.cbc.ca/news/canada/nova-scotia/teachers-work-to-rule-labour-contract-negotiations-education-1.3871527">&quot;&#39;No concerts, no meetings: what work-to-rule means for students and teachers&#39;&quot;</a>. 29 November 2016.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Nolan, Hamilton (13 June 2020). <a href="https://www.theguardian.com/commentisfree/2020/jun/13/police-unions-afl-cio-labor-movement">&quot;It&#39;s time to kick police unions out of the labor movement. They aren&#39;t allies&quot;</a>. <i>The Guardian</i>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0261-3077">0261-3077</a><span>. Retrieved <span>10 April</span> 2023</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.lemonde.fr/archives/article/1952/10/03/greve-du-zele-des-agents-du-metro-et-des-autobus-decident-plusieurs-syndicats_1996424_1819218.html">&quot;&quot;Grève du zèle&quot; des agents du métro et des autobus décident plusieurs syndicats&quot;</a> (in French). 3 October 1952<span>. Retrieved <span>30 March</span> 2025</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.rtbf.be/article/greve-du-zele-quand-la-minutie-devient-un-moyen-de-pression-qui-fait-ses-preuves-videos-10437929">&quot;Grève du zèle: quand la minutie devient un moyen de pression qui fait ses preuves (vidéos)&quot;</a>. <i>RTBF</i> (in French)<span>. Retrieved <span>30 March</span> 2025</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.bbc.com/news/business-62638908.amp">&quot;&#39;I was working 60 hours a week so I quiet quit&#39;&quot;</a>. 30 August 2022.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Albom, Mitch (28 August 2022). <a href="https://www.freep.com/story/sports/columnists/mitch-albom/2022/08/28/mitch-albom-the-only-thing-new-about-quiet-quitting-is-the-name/65460190007/">&quot;Mitch Albom: The only thing new about quiet quitting is the name&quot;</a>. <i>Detroit Free Press</i><span>. Retrieved <span>5 September</span> 2022</span>.</cite></span> </li> </ol></div></div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Work-to-rule&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Organized_labour"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Organized_labour"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Organized_labour"><abbr>e</abbr></a></li></ul></div><div>Organized labour</div></th></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Labor_history_(discipline)">Labour history</a></li> <li><a href="https://en.wikipedia.org/wiki/Labor_rights">Labour rights</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_movement">Labour movement</a></li> <li><a href="https://en.wikipedia.org/wiki/Trade_union">Trade union</a> (<a href="https://en.wikipedia.org/wiki/Public-sector_trade_union">public sector</a>)</li></ul> </div></td></tr><tr><th>Formation</th><td><table><tbody><tr><th>Structure</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Labour_council">Labour council</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_organizer">Union organizer</a></li> <li><a href="https://en.wikipedia.org/wiki/National_trade_union_center">National trade union centre</a></li> <li><a href="https://en.wikipedia.org/wiki/Global_union_federation">Global union federation</a></li> <li><a href="https://en.wikipedia.org/wiki/Unionization">Unionization</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_representative">Union representative</a></li> <li><a href="https://en.wikipedia.org/wiki/Local_union">Local union</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_dues">Union dues</a></li> <li><a href="https://en.wikipedia.org/wiki/Vigilance_committee_(trade_union)">Vigilance committee</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_label">Union label</a></li> <li><a href="https://en.wikipedia.org/wiki/Salt_(union_organizing)">Salt</a></li> <li><a href="https://en.wikipedia.org/wiki/Trades_hall">Trades hall</a></li> <li><a href="https://en.wikipedia.org/wiki/Duty_of_fair_representation">Duty of fair representation</a></li> <li><a href="https://en.wikipedia.org/wiki/Worker_center">Worker centre</a></li></ul> </div></td></tr><tr><th>Models</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Organizing_model">Organizing model</a></li> <li><a href="https://en.wikipedia.org/wiki/Service_model">Service model</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_movement_unionism">Social movement unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Community_unionism">Community unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Members-only_unionism">Members-only unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/One_Big_Union_(concept)">One Big Union</a></li> <li><a href="https://en.wikipedia.org/wiki/Open-source_unionism">Open-source unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Business_unionism">Business unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Dual_unionism">Dual unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Solidarity_unionism">Solidarity unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Syndicalism">Syndicalism</a></li></ul> </div></td></tr><tr><th>Types</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Company_union">Company union</a></li> <li><a href="https://en.wikipedia.org/wiki/Independent_union">Independent union</a></li> <li><a href="https://en.wikipedia.org/wiki/General_union">General union</a></li> <li><a href="https://en.wikipedia.org/wiki/Craft_unionism">Craft unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Industrial_unionism">Industrial unionism</a></li> <li><a href="https://en.wikipedia.org/wiki/Police_union">Police union</a></li> <li><a href="https://en.wikipedia.org/wiki/Public-sector_trade_union">Public-sector union</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Industrial<br/>relations</th><td><table><tbody><tr><th>Shops and hiring</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Closed_shop">Closed shop</a></li> <li><a href="https://en.wikipedia.org/wiki/Open_shop">Open shop</a></li> <li><a href="https://en.wikipedia.org/wiki/Agency_shop">Agency shop</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_shop">Union shop</a></li> <li><a href="https://en.wikipedia.org/wiki/Hiring_hall">Hiring hall</a></li> <li><a href="https://en.wikipedia.org/wiki/Bump_(union)">Bump</a></li> <li><a href="https://en.wikipedia.org/wiki/Scope_clause">Scope clause</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_co-op_model">Union co-op model</a></li></ul> </div></td></tr><tr><th>Actions</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Bossnapping">Bossnapping</a></li> <li><a href="https://en.wikipedia.org/wiki/Contingent_work">Contingent work</a></li> <li><a href="https://en.wikipedia.org/wiki/Diversity_training">Diversity training</a></li> <li><a href="https://en.wikipedia.org/wiki/Gherao">Gherao</a></li> <li><a href="https://en.wikipedia.org/wiki/Grievance_(labour)">Grievance</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_revolt">Labour revolt</a></li> <li><a href="https://en.wikipedia.org/wiki/Occupation_of_factories">Occupation of factories</a></li> <li><a href="https://en.wikipedia.org/wiki/Precarious_work">Precarious work</a></li> <li><a href="https://en.wikipedia.org/wiki/Precarity">Precarity</a></li> <li><a href="https://en.wikipedia.org/wiki/Picketing">Picketing</a></li> <li><a href="https://en.wikipedia.org/wiki/Salting_(union_organizing)">Salting</a></li> <li><a href="https://en.wikipedia.org/wiki/Slowdown">Slowdown</a></li> <li><a href="https://en.wikipedia.org/wiki/Stay-away">Stay-away</a></li> <li><a href="https://en.wikipedia.org/wiki/Strike_notice">Strike notice</a></li> <li><a href="https://en.wikipedia.org/wiki/Organizational_dissent">Organizational dissent</a></li> <li><a href="https://en.wikipedia.org/wiki/Industrial_action">Industrial action</a></li> <li><a href="https://en.wikipedia.org/wiki/Unfair_list">Unfair list</a></li> <li>Work-to-rule</li></ul> </div><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Strike_action">Strike actions</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Hartal">Hartal</a></li> <li><a href="https://en.wikipedia.org/wiki/General_strike">General strike</a> <ul><li><a href="https://en.wikipedia.org/wiki/Bandh">Bandh</a></li> <li><a href="https://en.wikipedia.org/wiki/Strike_paper">newspapers</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Green_ban">Green bans</a></li> <li><a href="https://en.wikipedia.org/wiki/Overtime_ban">Overtime bans</a></li> <li><a href="https://en.wikipedia.org/wiki/Pen-down_strike">Pen-down strikes</a></li> <li><a href="https://en.wikipedia.org/wiki/Recognition_strike">Recognition</a></li> <li><a href="https://en.wikipedia.org/wiki/Sitdown_strike">Sitdown strike</a></li> <li><a href="https://en.wikipedia.org/wiki/Solidarity_action">Solidarity actions</a></li> <li><a href="https://en.wikipedia.org/wiki/Walkout">Walkout</a></li> <li><a href="https://en.wikipedia.org/wiki/Whipsaw_strike">Whipsaw</a></li> <li><a href="https://en.wikipedia.org/wiki/Wildcat_strike">Wildcat strikes</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th>Bargaining</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Bargaining_unit">Bargaining unit</a></li> <li><a href="https://en.wikipedia.org/wiki/Collaborative_bargaining">Collaborative bargaining</a></li> <li><a href="https://en.wikipedia.org/wiki/Collective_bargaining">Collective bargaining</a> <ul><li><a href="https://en.wikipedia.org/wiki/Sectoral_collective_bargaining">Sectoral</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Enterprise_bargaining_agreement">Enterprise bargaining agreement</a></li> <li><a href="https://en.wikipedia.org/wiki/Global_Framework_Agreement">Global Framework Agreement</a></li> <li><a href="https://en.wikipedia.org/wiki/Master_contract_(labor)">Master contract</a></li> <li><a href="https://en.wikipedia.org/wiki/Pattern_bargaining">Pattern bargaining</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_security_agreement">Union security agreement</a></li></ul> </div></td></tr><tr><th>Compensation</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Strike_pay">Strike pay</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_wage_premium">Union wage premium</a></li> <li><a href="https://en.wikipedia.org/wiki/Workers%27_compensation">Workers&#39; compensation</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Reactions</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Labor_spying_in_the_United_States">Labour spies in the United States</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_busting">Union busting</a></li> <li><a href="https://en.wikipedia.org/wiki/Givebacks">Givebacks</a></li> <li><a href="https://en.wikipedia.org/wiki/Paper_local">Paper local</a></li> <li><a href="https://en.wikipedia.org/wiki/Anti-union_violence">Anti-union violence</a> <ul><li><a href="https://en.wikipedia.org/wiki/Anti-union_violence_in_the_United_States">United States</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Union_violence">Union violence</a></li> <li><a href="https://en.wikipedia.org/wiki/Demarcation_dispute">Demarcation dispute</a></li> <li><a href="https://en.wikipedia.org/wiki/Strikebreaker">Strikebreaking</a></li> <li><a href="https://en.wikipedia.org/wiki/Goon_squad">Goon squads</a></li> <li><a href="https://en.wikipedia.org/wiki/Featherbedding">Featherbedding</a></li> <li><a href="https://en.wikipedia.org/wiki/Union_raid">Union raids</a></li></ul> </div></td></tr><tr><th>Other topics</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/35-hour_workweek">35-hour workweek</a></li> <li><a href="https://en.wikipedia.org/wiki/Eight-hour_day">Eight-hour day</a></li> <li><a href="https://en.wikipedia.org/wiki/Six-hour_day">Six-hour day</a></li> <li><a href="https://en.wikipedia.org/wiki/Four-day_workweek">Four-day workweek</a></li> <li><a href="https://en.wikipedia.org/wiki/Conflict_theories">Conflict theories</a></li> <li><a href="https://en.wikipedia.org/wiki/Critique_of_work">Critique of work</a></li> <li><a href="https://en.wikipedia.org/wiki/Decent_work">Decent work</a></li> <li><a href="https://en.wikipedia.org/wiki/Diversity,_equity,_and_inclusion">Diversity, equity, and inclusion</a></li> <li><a href="https://en.wikipedia.org/wiki/Equal_pay_for_equal_work">Equal pay for equal work</a></li> <li><a href="https://en.wikipedia.org/wiki/Exploitation_of_labour">Exploitation of labour</a></li> <li><a href="https://en.wikipedia.org/wiki/Forced_labour">Forced labour</a></li> <li><a href="https://en.wikipedia.org/wiki/Hunger_strike">Hunger strikes</a></li> <li><a href="https://en.wikipedia.org/wiki/International_comparisons_of_labor_unions">International comparisons of labour unions</a></li> <li><a href="https://en.wikipedia.org/wiki/Job_strain">Job strain</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_code">Labour code</a></li> <li><a href="https://en.wikipedia.org/wiki/Labour_law">Labour law</a></li> <li><a href="https://en.wikipedia.org/wiki/Minimum_wage">Minimum wage</a></li> <li><a href="https://en.wikipedia.org/wiki/Maximum_wage">Maximum wage</a></li> <li><a href="https://en.wikipedia.org/wiki/Prison_strike">Prison strikes</a></li> <li><a href="https://en.wikipedia.org/wiki/Professional_abuse">Professional abuse</a></li> <li><a href="https://en.wikipedia.org/wiki/Protection">Protection</a></li> <li><a href="https://en.wikipedia.org/wiki/Occupational_safety_and_health">Occupational safety and health</a></li> <li><a href="https://en.wikipedia.org/wiki/Occupational_stress">Occupational stress</a></li> <li><a href="https://en.wikipedia.org/wiki/Overwork">Overwork</a></li> <li><a href="https://en.wikipedia.org/wiki/Social_support">Social support</a></li> <li><a href="https://en.wikipedia.org/wiki/Wage_slavery">Wage slavery</a></li> <li><a href="https://en.wikipedia.org/wiki/Workload">Workload</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q1078746#identifiers"></a></span></th><td><div><ul><li><span><a href="https://d-nb.info/gnd/4149732-6">GND</a></span></li></ul></div></td></tr></tbody></table></div> Modulor - Wikipedia https://en.wikipedia.org/wiki/Modulor BaKQ3QtMu-z6v8QGaQlR0Qx2Bojak09kMuNPMQ== Sat, 09 May 2026 11:57:43 +0000 Le Corbusier's anthropometric scale of proportions <div>Le Corbusier&#39;s anthropometric scale of proportions</div><figure><a href="https://en.wikipedia.org/wiki/File:Swiss-Commemorative-Coin-1987-CHF-5-obverse.png"></a><figcaption>Commemorative Swiss coin showing the <i>modulor</i>.</figcaption></figure><p>It was developed as a visual bridge between two incompatible scales, the <a href="https://en.wikipedia.org/wiki/Imperial_and_US_customary_measurement_systems">Imperial</a> and the <a href="https://en.wikipedia.org/wiki/Metric_system">metric</a> systems. It is based on the height of a man with his arm raised. The Modulor deemed the standard human height to be 1.83 m (6 ft 0 in), excluding feminine measures. The dimensions were refined with overall height of raised arm set at 2.26 m (7 ft 5 in). </p><p>It was used as a system to set out a number of Le Corbusier&#39;s buildings and was later codified into two books. </p><figure><a href="https://en.wikipedia.org/wiki/File:Le_Modulor.png"></a><figcaption>Modern recreation of the cover of Le Corbusier&#39;s book on the Modulor</figcaption></figure><div><h2>History</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>Le Corbusier developed the Modulor in the long tradition of <a href="https://en.wikipedia.org/wiki/Vitruvius">Vitruvius</a>, <a href="https://en.wikipedia.org/wiki/Leonardo_da_Vinci">Leonardo da Vinci&#39;s</a> <a href="https://en.wikipedia.org/wiki/Vitruvian_Man">Vitruvian Man</a>, the work of <a href="https://en.wikipedia.org/wiki/Leon_Battista_Alberti">Leon Battista Alberti</a>, and other attempts to discover mathematical proportions in the human body and then to use that knowledge to improve both the appearance and function of <a href="https://en.wikipedia.org/wiki/Architecture">architecture</a>.<sup><span>[</span>1<span>]</span></sup> The system is inspired by but does not exactly correspond to <a href="https://en.wikipedia.org/wiki/Anthropometry">human measurements</a>,<sup><span>[</span>2<span>]</span></sup> and it also draws inspiration from the <a href="https://en.wikipedia.org/wiki/Fibonacci_numbers">Fibonacci numbers</a> and the <a href="https://en.wikipedia.org/wiki/Golden_ratio">golden ratio</a>.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> Le Corbusier described it as a &quot;range of harmonious measurements to suit the human scale, universally applicable to architecture and to mechanical things&quot;.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>With the Modulor, Le Corbusier sought to introduce a scale of visual measures that would unite two virtually incompatible systems: the <a href="https://en.wikipedia.org/wiki/Anglo-Saxons">Anglo-Saxon</a> <a href="https://en.wikipedia.org/wiki/Foot_(length)">foot</a> and <a href="https://en.wikipedia.org/wiki/Inch">inch</a> and the international <a href="https://en.wikipedia.org/wiki/Metric_system">metric system</a>.<sup><span>[</span>3<span>]</span></sup> Whilst he was intrigued by ancient civilisations who used measuring systems linked to the human body: elbow (<a href="https://en.wikipedia.org/wiki/Cubit">cubit</a>), finger (<a href="https://en.wikipedia.org/wiki/Digit_(length)">digit</a>), thumb (inch) etc., he was troubled by the <a href="https://en.wikipedia.org/wiki/Metre">metre</a> as a measure that was a forty-millionth part of the meridian of the earth.<sup><span>[</span>4<span>]</span></sup> </p><p>In 1943, in response to the French National Organisation for Standardisation&#39;s (<a href="https://en.wikipedia.org/wiki/AFNOR">AFNOR</a>) requirement for standardising all the objects involved in the construction process, Le Corbusier asked an apprentice to consider a scale based upon a man with his arm raised to 2.20 m in height.<sup><span>[</span>5<span>]</span></sup> The result, in August 1943 was the first graphical representation of the derivation of the scale. This was refined after a visit to the Dean of the Faculty of Sciences in Sorbonne on 7 February 1945 which resulted in the inclusion of a golden section into the representation.<sup><span>[</span>6<span>]</span></sup> </p><p>Whilst initially the Modulor Man&#39;s height was based on an average French man&#39;s height of 1.75 metres (5 ft 9 in) it was changed to 1.83 m in 1946 because &quot;in English detective novels, the good-looking men, such as policemen, are always six feet tall!&quot;.<sup><span>[</span>7<span>]</span></sup> The dimensions were refined to give round numbers and the overall height of the raised arm was set at 2.26 m (7 ft 5 in).<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>Of the works leading to the creation of the Modulor, Robin Evans notes that the female body &quot;was only belatedly considered and rejected as a source of proportional harmony&quot;.<sup><span>[</span>1<span>]</span></sup> </p><figure><a href="https://en.wikipedia.org/wiki/File:Le_Corbusier%27s_Modulor.png"></a><figcaption>Le Corbusier&#39;s Modulor generated in Python. For full resolution see the file on Wikimedia Commons</figcaption></figure><div><h2>Promotion</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>On 10 January 1946 during a visit to New York, Le Corbusier met with <a href="https://en.wikipedia.org/wiki/Henry_J._Kaiser">Henry J. Kaiser</a>, an American industrialist whose <a href="https://en.wikipedia.org/wiki/Kaiser_Shipyard">Kaiser Shipyard</a> had built <a href="https://en.wikipedia.org/wiki/Liberty_ship">Liberty ships</a> during World War II. Kaiser&#39;s project was to build ten thousand new houses a day, but he had changed his mind and decided to build cars instead.<sup><span>[</span>8<span>]</span></sup> During the interview, Le Corbusier sympathised with Kaiser&#39;s problems of coordinating the adoption of equipment between the American and British armies because of the differences in units of length; and promoted his own <i>harmonious scale</i>.<sup><span>[</span>9<span>]</span></sup> </p><p>On the same trip he met with <a href="https://en.wikipedia.org/wiki/David_E._Lilienthal">David E. Lilienthal</a> of the <a href="https://en.wikipedia.org/wiki/Tennessee_Valley_Authority">Tennessee Valley Authority</a> to promote the use of his <i>harmonious scale</i> on further civil engineering projects.<sup><span>[</span>10<span>]</span></sup> </p><p>He also applied the principle of the Modulor to the efficient design of distribution crates in post war France.<sup><span>[</span>11<span>]</span></sup> </p><div><h2>Graphic representation</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Modulor_measurements.svg"></a><figcaption>Modulor measurements of humans in various positions</figcaption></figure><p>The graphic representation of the Modulor, a stylised human figure with one arm raised, stands next to two vertical measurements, a red series based on the figure&#39;s navel height (1.08 m (3 ft 7 in) in the original version, (1.13 m (3 ft 8 in) in the revised version) and segmented according to the <a href="https://en.wikipedia.org/wiki/Golden_ratio">Golden ratio</a> and a blue series based on the figure&#39;s entire height, double the navel height ((2.16 m (7 ft 1 in) in the original version, (2.26 m (7 ft 5 in) in the revised), segmented similarly. A <a href="https://en.wikipedia.org/wiki/Spiral">spiral</a>, graphically developed between the red and blue segments, seems to mimic the volume of the human figure.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p>The Modulor 2 was drawn by <a href="https://en.wikipedia.org/w/index.php?title=Andr%C3%A9_Maissonier&amp;action=edit&amp;redlink=1">André Maissonier</a> and <a href="https://en.wikipedia.org/w/index.php?title=Justino_Serralta&amp;action=edit&amp;redlink=1">Justino Serralta</a>.<sup><span>[</span>12<span>]</span></sup> </p><div><h2>Practical application</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Le Corbusier used his Modulor scale in the design of many <a href="https://en.wikipedia.org/wiki/Le_Corbusier#Key_buildings">buildings</a>, including: </p><div><h3>Unité d&#39;Habitation à Marseille</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>In his first book on the subject <i>The Modulor</i>, Le Corbusier has a chapter on the use of the modular in the <a href="https://en.wikipedia.org/wiki/Unit%C3%A9_d%27Habitation">Unité d&#39;Habitation</a>. The modular governs: the plan, section and elevations; the <a href="https://en.wikipedia.org/wiki/Brise_soleil">brise-soleil</a>; the roof; the supporting columns and the plan and section of the apartments. It was also used for the dimensions of the commemorative stone laid on 14 October 1947.<sup><span>[</span>13<span>]</span></sup> A version of the Modulor Man was <a href="https://en.wikipedia.org/wiki/Casting">cast</a> in <a href="https://en.wikipedia.org/wiki/Concrete">concrete</a> near the entrance. </p><div><h3>Church of Sainte Marie de La Tourette</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>In the Church of <a href="https://en.wikipedia.org/wiki/Sainte_Marie_de_La_Tourette">Sainte Marie de La Tourette</a> Le Corbusier floors the majority of the church in pale concrete panels set to Modulor dimensions.<sup><span>[</span>14<span>]</span></sup> Also, the engineer <a href="https://en.wikipedia.org/wiki/Iannis_Xenakis">Iannis Xenakis</a> applied the Modulor system to the design of the exterior vertical ventilators or &quot;ondulatoires&quot;.<sup><span>[</span>15<span>]</span></sup> </p><div><h3>Carpenter Center for the Visual Arts</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>In the <a href="https://en.wikipedia.org/wiki/Carpenter_Center_for_the_Visual_Arts">Carpenter Center</a> the Modulor system was used for the brise-soleil distances, the floor to floor heights, the bay distances and the column thicknesses.<sup><span>[</span>16<span>]</span></sup> Le Corbusier conceived that the dimensioning of the entrance ramp would be &quot;<i>visible essay on the mathematics of the human body</i>&quot;.<sup><span>[</span>17<span>]</span></sup> </p><div><h3>Unite d&#39;Habitation a Berlin.</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Modulor_image_in_Berlin.jpg"></a><figcaption>Modulor applied in Berlin</figcaption></figure><p>In this image of the Modulor in Berlin, there are several messages cast in the facade: </p><ol><li>The typical apartment is designed for four people. (Note 4 people in bed on the right).</li> <li>The patterns of paint on the side of the balconies is explained by diagonal line.</li> <li>Brie Soleil is sized by the height of the Modulor man.</li> <li>The room height is calculated by the Modulor.</li></ol><div><h2>Publication</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>Le Corbusier published <i>Le Modulor</i> in 1948, followed by <i>Modulor 2</i> in 1955. These works were first published in English as <i>The Modulor</i> in 1954 and <i>Modulor 2 (Let the User Speak Next)</i> in 1958. </p><p>The 2004 reprinted box set including both books was printed in a square format using the Modulor with the series twenty seven to one hundred and forty reduced in size to one tenth.<sup><span>[</span>18<span>]</span></sup> </p><div><h2>Commemorative usage</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:CHF10_8_back_horizontal.jpg"></a><figcaption>Reverse side of the Swiss 10 CHF banknote, showing the Modulor</figcaption></figure><ul><li>A picture of the Modulor appears on the eighth banknote series on the 10 CHF <a href="https://en.wikipedia.org/wiki/Banknotes_of_the_Swiss_franc">Swiss banknote</a> dedicated to Le Corbusier.</li></ul><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Body_proportions">Body proportions</a> – Proportions of the human body in art <ul><li><a href="https://en.wikipedia.org/wiki/Artistic_canons_of_body_proportion">Artistic canons of body proportion</a> – Criteria used in formal figurative art</li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Ergonomics">Ergonomics</a> – Designing systems to suit their users</li> <li><a href="https://en.wikipedia.org/wiki/List_of_unusual_units_of_measurement">List of unusual units of measurement</a> – Units that are not part of a coherent system<span>Pages displaying short descriptions of redirect targets</span></li> <li><a href="https://en.wikipedia.org/wiki/Preferred_number">Preferred number</a> – Selection constraint in industrial design, especially the section about Renard series, which covers a mathematical approach on evenly distributed numbers using <a href="https://en.wikipedia.org/wiki/Geometric_sequence">geometric sequences</a>, for use in constructing houses or devices.</li> <li><a href="https://en.wikipedia.org/wiki/Rudolf_Wittkower">Rudolf Wittkower</a> – British art historian (1901–1971)</li> <li><a href="https://en.wikipedia.org/wiki/Rule_of_thumb">Rule of thumb</a> – Approximate method for doing something</li></ul><div><h2>Citations</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><div><ol> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>Ostwald (2001), p. 146.</span> </li> <li><span><b>^</b></span> <span><cite>Burrows, Terry; Larter, Sarah; Anderson, Janice, eds. (1999). <i>ITV Visual History of the Twentieth Century</i>. London: <a href="https://en.wikipedia.org/wiki/Carlton_Books">Carlton Books</a>. p. 318. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/1-85868-688-1"><bdi>1-85868-688-1</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 17.</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 20.</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 36.</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 43.</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 56.</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 52.</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 115.</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 53.</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 122.</span> </li> <li><span><b>^</b></span> <span>Jorge Nudelman, <a href="http://www.farq.edu.uy/patio/institucion/en-recuerdo.html">&quot;En recuerdo: Justino Serralta, &#39;arquitecto de comunidades&#39;, 1919–2011&quot;</a>, <i>Boletín Facultad de Arquitectura UDELAR</i> (30 October 2011).</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. 131.</span> </li> <li><span><b>^</b></span> <span>Samuel (2007), p. 62.</span> </li> <li><span><b>^</b></span> <span>Samuel (2007), p. 83.</span> </li> <li><span><b>^</b></span> <span>Sekler &amp; Curtis (1978), p. 158.</span> </li> <li><span><b>^</b></span> <span>Sekler &amp; Curtis (1978), p. 182.</span> </li> <li><span><b>^</b></span> <span>Le Corbusier (2004), p. back cover.</span> </li> </ol></div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><div> <ul><li><cite>Sekler, Eduard F.; Curtis, William (1978). <i>Le Corbusier at Work: The Genesis of the Carpenter Center for Visual Arts</i>. Cambridge, MA: <a href="https://en.wikipedia.org/wiki/Harvard_University_Press">Harvard University Press</a>.</cite></li> <li><cite>Evans, Robin (1995). <i>The Projective Cast: Architecture and Its Three Geometries</i>. Cambridge, MA: <a href="https://en.wikipedia.org/wiki/MIT_Press">MIT Press</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0262050498"><bdi>0262050498</bdi></a>.</cite></li> <li><cite>Le Corbusier (2004) [First published in two volumes in 1954 and 1958.]. <i>The Modulor: A Harmonious Measure to the Human Scale, Universally Applicable to Architecture and Mechanics</i>. Basel &amp; Boston: Birkhäuser. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/3764361883"><bdi>3764361883</bdi></a>.</cite></li> <li><cite>Ostwald, Michael J. (2001). <a href="https://doi.org/10.1007%2Fs00004-000-0015-0">&quot;<i>The Modulor</i> and <i>Modulor 2</i> by Le Corbusier (Charles Edouard Jeanneret), 2 volumes. Basel: Birkhäuser, 2000&quot;</a>. <i>Nexus Network Journal</i>. <b>3</b> (1): <span>145–</span>48. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1007%2Fs00004-000-0015-0">10.1007/s00004-000-0015-0</a></span>.</cite></li> <li><cite>Samuel, Flora (2007). <i>Corbusier in Detail</i>. Architectural Press.</cite></li></ul> </div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Modulor&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Commons-logo.svg"></a></span></div> <div>Wikimedia Commons has media related to <span><a href="https://commons.wikimedia.org/wiki/Category:Modulor">Modulor</a></span>.</div></div> </div><div><table><tbody><tr><th colspan="3"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Le_Corbusier"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Le_Corbusier"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Le_Corbusier"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Le_Corbusier">Le Corbusier</a></div></th></tr><tr><th>Private houses</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Villa_Fallet">Villa Fallet</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_Jeanneret-Perret">Villa Jeanneret-Perret</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_Savoye">Villa Savoye</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_Schwob">Villa Schwob</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_Le_Lac">Villa Le Lac</a></li> <li><a href="https://en.wikipedia.org/wiki/Maison_Planeix">Planeix House</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_Cook">Villa Cook</a></li> <li><a href="https://en.wikipedia.org/wiki/Maison_Guiette">Maison Guiette/Les Peupliers</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_Stein">Villa Stein</a></li> <li><a href="https://en.wikipedia.org/wiki/Curutchet_House">Curutchet House</a></li> <li><a href="https://en.wikipedia.org/wiki/Maisons_Jaoul">Maisons Jaoul</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_Sarabhai">Villa Sarabhai</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_Shodhan">Villa Shodhan</a></li></ul> </div></td><td rowspan="10"><div><span><a href="https://en.wikipedia.org/wiki/File:Le_Corbusier_(1964).jpg"></a></span></div></td></tr><tr><th>Other buildings</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Tsentrosoyuz_building">Tsentrosoyuz building</a></li> <li><a href="https://en.wikipedia.org/wiki/Notre-Dame_du_Haut">Notre-Dame du Haut</a></li> <li><a href="https://en.wikipedia.org/wiki/National_Museum_of_Western_Art">National Museum of Western Art</a></li> <li><a href="https://en.wikipedia.org/wiki/Carpenter_Center_for_the_Visual_Arts">Carpenter Center for the Visual Arts</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Open_Hand_Monument">Open Hand Monument</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Pavillon_de_l%27Esprit_Nouveau">Pavillon de l&#39;Esprit Nouveau</a></li> <li><a href="https://en.wikipedia.org/wiki/Pavillon_Suisse">Pavillon Suisse</a></li> <li><a href="https://en.wikipedia.org/wiki/Immeuble_Clart%C3%A9">Immeuble Clarté</a></li> <li><a href="https://en.wikipedia.org/wiki/Immeuble_Molitor">Immeuble Molitor</a></li> <li><a href="https://en.wikipedia.org/wiki/Cabanon_de_vacances">Cabanon de vacances</a></li> <li><a href="https://en.wikipedia.org/wiki/Mill_Owners%27_Association_Building">Mill Owners&#39; Association Building</a></li> <li><a href="https://en.wikipedia.org/wiki/United_Nations_Secretariat_Building">United Nations Secretariat Building</a></li> <li><a href="https://en.wikipedia.org/wiki/Sanskar_Kendra">Sanskar Kendra Museum</a></li> <li><a href="https://en.wikipedia.org/wiki/Government_Museum_and_Art_Gallery,_Chandigarh">Museum and Art Gallery</a></li> <li><a href="https://en.wikipedia.org/wiki/Secretariat_Building,_Chandigarh">Secretariat Building</a></li> <li><a href="https://en.wikipedia.org/wiki/Palace_of_Assembly">Palace of Assembly</a></li> <li><a href="https://en.wikipedia.org/wiki/Baghdad_Gymnasium">Baghdad Gymnasium</a></li> <li><a href="https://en.wikipedia.org/wiki/Maison_du_Br%C3%A9sil">Maison du Brésil</a></li> <li><a href="https://en.wikipedia.org/wiki/Saint-Pierre,_Firminy">Church of Saint-Pierre, Firminy</a></li> <li><a href="https://en.wikipedia.org/wiki/Firminy-Vert_Stadium">Firminy-Vert Stadium</a></li> <li><a href="https://en.wikipedia.org/wiki/Chandigarh_Capitol_Complex">Complexe du Capitole</a></li> <li><a href="https://en.wikipedia.org/wiki/Sainte_Marie_de_La_Tourette">Couvent Sainte-Marie-de-la-Tourette</a></li> <li><a href="https://en.wikipedia.org/wiki/Maison_de_la_Culture_de_Firminy">Maison de la Culture de Firminy</a></li> <li><a href="https://en.wikipedia.org/wiki/Usine_Claude_et_Duval">Usine Claude et Duval</a></li></ul> </div></td></tr><tr><th>Unbuilt</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Governor%27s_Palace_(Chandigarh)">Governor&#39;s Palace</a></li> <li><a href="https://en.wikipedia.org/wiki/Palace_of_the_Soviets">Palace of the Soviets</a></li> <li><a href="https://en.wikipedia.org/wiki/Plan_Voisin">Plan Voisin</a></li> <li><a href="https://en.wikipedia.org/wiki/Ville_Contemporaine">Ville Contemporaine</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_Meyer">Villa Meyer</a></li> <li><a href="https://en.wikipedia.org/wiki/Ville_Radieuse">Ville Radieuse</a></li></ul> </div></td></tr><tr><th>Housing systems</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Weissenhof_Estate">Maisons de la Weissenhof-Siedlung</a></li> <li><a href="https://en.wikipedia.org/wiki/Butterfly_roof">Butterfly roof</a></li> <li><a href="https://en.wikipedia.org/wiki/Dom-Ino_House">Dom-Ino House</a></li> <li><a href="https://en.wikipedia.org/wiki/Le_Corbusier%27s_Five_Points_of_Architecture">Le Corbusier&#39;s Five Points of Architecture</a></li> <li><a href="https://en.wikipedia.org/wiki/Cit%C3%A9_Frug%C3%A8s_de_Pessac">Cité Frugès de Pessac</a></li> <li><a href="https://en.wikipedia.org/wiki/Cit%C3%A9_du_Refuge">Cité du Refuge</a></li> <li><a href="https://en.wikipedia.org/wiki/Unit%C3%A9_d%27habitation">Unité d&#39;habitation</a> <ul><li><a href="https://en.wikipedia.org/wiki/Unit%C3%A9_d%27Habitation_of_Nantes-Rez%C3%A9">Unité d&#39;Habitation of Nantes-Rezé</a></li> <li><a href="https://en.wikipedia.org/wiki/Unit%C3%A9_d%27Habitation_of_Berlin">Unité d&#39;Habitation of Berlin</a></li> <li><a href="https://en.wikipedia.org/wiki/Unit%C3%A9_d%27Habitation_of_Briey">Unité d&#39;Habitation of Briey</a></li> <li><a href="https://en.wikipedia.org/wiki/Unit%C3%A9_d%27Habitation_of_Firminy-Vert">Unité d&#39;Habitation of Firminy-Vert</a></li></ul></li></ul> </div></td></tr><tr><th>Furniture</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Chaise_Longue_(Le_Corbusier)">Chaise Longue LC4</a></li> <li><a href="https://en.wikipedia.org/wiki/Grand_Confort">Grand Confort</a></li> <li><a href="https://en.wikipedia.org/wiki/Le_Corbusier%27s_Furniture">Le Corbusier&#39;s Furniture</a></li></ul> </div></td></tr><tr><th>Paintings and poems</th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Poem_of_the_Right_Angle">Poem of the Right Angle</a></i> (1947–1953)</li></ul> </div></td></tr><tr><th>Books</th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Toward_an_Architecture">Toward an Architecture</a></i> (1923)</li></ul> </div></td></tr><tr><th>Museums</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Pavillon_Le_Corbusier">Pavillon Le Corbusier</a></li> <li><a href="https://en.wikipedia.org/wiki/Villa_La_Roche">Villa La Roche</a></li></ul> </div></td></tr><tr><th>Related</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Fondation_Le_Corbusier">Fondation Le Corbusier</a></li> <li><a href="https://en.wikipedia.org/wiki/Congr%C3%A8s_Internationaux_d%27Architecture_Moderne">Congrès Internationaux d&#39;Architecture Moderne</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_Le_Corbusier_buildings">List of Le Corbusier buildings</a></li> <li><a href="https://en.wikipedia.org/wiki/The_Architectural_Work_of_Le_Corbusier">The Architectural Work of Le Corbusier</a></li> <li>Modulor</li> <li><a href="https://en.wikipedia.org/wiki/Gustavo_Capanema_Palace">Palace of Ministry of National Education and Public Health</a></li> <li><a href="https://en.wikipedia.org/wiki/Philips_Pavilion">Philips Pavilion</a></li> <li><a href="https://en.wikipedia.org/wiki/Purism">Purism</a></li> <li><a href="https://en.wikipedia.org/wiki/United_Nations_headquarters">United Nations headquarters</a></li> <li><i><a href="https://en.wikipedia.org/wiki/The_Price_of_Desire">The Price of Desire</a></i> (2014 film)</li></ul> </div></td></tr><tr><th>People</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Eileen_Gray">Eileen Gray</a></li> <li><a href="https://en.wikipedia.org/wiki/Am%C3%A9d%C3%A9e_Ozenfant">Amédée Ozenfant</a></li> <li><a href="https://en.wikipedia.org/wiki/Pierre_Jeanneret">Pierre Jeanneret</a></li> <li><a href="https://en.wikipedia.org/wiki/Auguste_Perret">Auguste Perret</a></li> <li><a href="https://en.wikipedia.org/wiki/Adolf_Loos">Adolf Loos</a></li> <li><a href="https://en.wikipedia.org/wiki/Charlotte_Perriand">Charlotte Perriand</a></li></ul> </div></td></tr><tr><td colspan="3"><div> <ul><li><span><a href="https://en.wikipedia.org/wiki/File:Commons-logo.svg"></a></span> <a href="https://commons.wikimedia.org/wiki/Category:Le_Corbusier">Commons</a></li> <li><span><a href="https://en.wikipedia.org/wiki/File:Wikinews-logo.svg"></a></span> <a href="https://en.wikinews.org/wiki/Special:Search/Le_Corbusier">Wikinews</a></li> <li> <a href="https://en.wikiquote.org/wiki/Special:Search/Le_Corbusier">Wikiquote</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Systems_of_measurement"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Systems_of_measurement"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Systems_of_measurement"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/System_of_measurement">Systems of measurement</a></div></th></tr><tr><th>Current</th><td><table><tbody><tr><th>General</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/International_System_of_Units">International System of Units (SI)</a></li> <li><a href="https://en.wikipedia.org/wiki/Imperial_units">UK imperial system</a></li> <li><a href="https://en.wikipedia.org/wiki/United_States_customary_units">US customary units (USCS/USC)</a></li></ul> </div></td></tr><tr><th>Specific</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Apothecaries%27_system">Apothecaries&#39;</a></li> <li><a href="https://en.wikipedia.org/wiki/Avoirdupois">Avoirdupois</a></li> <li><a href="https://en.wikipedia.org/wiki/Troy_weight">Troy</a></li> <li><a href="https://en.wikipedia.org/wiki/Astronomical_system_of_units">Astronomical</a></li> <li><a href="https://en.wikipedia.org/wiki/Conventional_electrical_unit">Electrical</a></li> <li><a href="https://en.wikipedia.org/wiki/English_Engineering_Units">English Engineering Units</a> (US)</li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Natural_units">Natural</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Atomic_units">Atomic</a></li> <li><a href="https://en.wikipedia.org/wiki/Geometrized_unit_system">Geometrised</a></li> <li><a href="https://en.wikipedia.org/wiki/Heaviside%E2%80%93Lorentz_units">Heaviside–Lorentz</a></li> <li><a href="https://en.wikipedia.org/wiki/Planck_units">Planck</a></li> <li><a href="https://en.wikipedia.org/wiki/Natural_units#Quantum_chromodynamics_units">Quantum chromodynamical</a></li> <li><a href="https://en.wikipedia.org/wiki/Stoney_units">Stoney</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Background</th><td><table><tbody><tr><th>Metric</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Metric_system">Overview</a></li> <li><a href="https://en.wikipedia.org/wiki/Outline_of_the_metric_system">Outline</a></li> <li><a href="https://en.wikipedia.org/wiki/History_of_the_metric_system">History</a></li> <li><a href="https://en.wikipedia.org/wiki/Metrication">Metrication</a></li></ul> </div></td></tr><tr><th>UK/US</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Imperial_and_US_customary_measurement_systems">Overview</a></li> <li><a href="https://en.wikipedia.org/wiki/Comparison_of_the_imperial_and_US_customary_measurement_systems">Comparison</a></li> <li><a href="https://en.wikipedia.org/wiki/Foot%E2%80%93pound%E2%80%93second_system">Foot–pound–second</a> (FPS)</li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Historic</th><td><table><tbody><tr><th>Metric</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/MKS_system_of_units">metre–kilogram–second</a> (MKS)</li> <li><a href="https://en.wikipedia.org/wiki/Metre%E2%80%93tonne%E2%80%93second_system_of_units">metre–tonne–second</a> (MTS)</li> <li><a href="https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units">centimetre–gram–second</a> (CGS)</li> <li><a href="https://en.wikipedia.org/wiki/Gravitational_metric_system">gravitational</a></li></ul> </div></td></tr><tr><th>Europe</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Old_Cornish_units_of_measurement">Cornish</a></li> <li><a href="https://en.wikipedia.org/wiki/Czech_units_of_measurement">Czech</a></li> <li><a href="https://en.wikipedia.org/wiki/Danish_units_of_measurement">Danish</a></li> <li><a href="https://en.wikipedia.org/wiki/Dutch_units_of_measurement">Dutch</a></li> <li><a href="https://en.wikipedia.org/wiki/English_units_of_measurement">English</a> <ul><li><a href="https://en.wikipedia.org/wiki/Winchester_measure">Winchester</a></li> <li><a href="https://en.wikipedia.org/wiki/Exchequer_Standards">Exchequer</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Estonian_units_of_measurement">Estonian</a></li> <li><a href="https://en.wikipedia.org/wiki/Obsolete_Finnish_units_of_measurement">Finnish</a></li> <li><a href="https://en.wikipedia.org/wiki/French_units_of_measurement">French</a> <ul><li><a href="https://en.wikipedia.org/wiki/Traditional_French_units_of_measurement">Traditional</a></li> <li><a href="https://en.wikipedia.org/wiki/Mesures_usuelles">Mesures usuelles</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Obsolete_German_units_of_measurement">German</a></li> <li><a href="https://en.wikipedia.org/wiki/Greek_units_of_measurement">Greek</a> <ul><li><a href="https://en.wikipedia.org/wiki/Byzantine_units_of_measurement">Byzantine</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Hungarian_units_of_measurement">Hungarian</a></li> <li><a href="https://en.wikipedia.org/wiki/Icelandic_units_of_measurement">Icelandic</a></li> <li><a href="https://en.wikipedia.org/wiki/Old_Irish_units_of_measurement">Irish</a></li> <li><a href="https://en.wikipedia.org/wiki/Italian_units_of_measurement">Italian</a></li> <li><a href="https://en.wikipedia.org/wiki/Latvian_units_of_measurement">Latvian</a></li> <li><a href="https://en.wikipedia.org/wiki/Luxembourgian_units_of_measurement">Luxembourgian</a></li> <li><a href="https://en.wikipedia.org/wiki/Maltese_units_of_measurement">Maltese</a></li> <li><a href="https://en.wikipedia.org/wiki/Norwegian_units_of_measurement">Norwegian</a></li> <li><a href="https://en.wikipedia.org/wiki/Polish_units_of_measurement">Polish</a></li> <li><a href="https://en.wikipedia.org/wiki/Portuguese_units_of_measurement">Portuguese</a></li> <li><a href="https://en.wikipedia.org/wiki/Romanian_units_of_measurement">Romanian</a></li> <li><a href="https://en.wikipedia.org/wiki/Historical_Russian_units_of_measurement">Russian</a></li> <li><a href="https://en.wikipedia.org/wiki/Scottish_units_of_measurement">Scottish</a></li> <li><a href="https://en.wikipedia.org/wiki/Obsolete_Serbian_units_of_measurement">Serbian</a></li> <li><a href="https://en.wikipedia.org/wiki/Slovak_units_of_measurement">Slovak</a></li> <li><a href="https://en.wikipedia.org/wiki/Spanish_units_of_measurement">Spanish</a></li> <li><a href="https://en.wikipedia.org/wiki/Swedish_units_of_measurement">Swedish</a></li> <li><a href="https://en.wikipedia.org/wiki/Swiss_units_of_measurement">Swiss</a></li> <li><a href="https://en.wikipedia.org/wiki/Obsolete_Tatar_units_of_measurement">Tatar</a></li> <li><a href="https://en.wikipedia.org/wiki/Welsh_units">Welsh</a></li></ul> </div></td></tr><tr><th>Asia</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Afghan_units_of_measurement">Afghan</a></li> <li><a href="https://en.wikipedia.org/wiki/Cambodian_units_of_measurement">Cambodian</a></li> <li><a href="https://en.wikipedia.org/wiki/Chinese_units_of_measurement">Chinese</a> <ul><li><a href="https://en.wikipedia.org/wiki/Hong_Kong_units_of_measurement">Hong Kong</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Cypriot_units_of_measurement">Cypriot</a></li> <li><a href="https://en.wikipedia.org/wiki/Indian_units_of_measurement">Indian</a></li> <li><a href="https://en.wikipedia.org/wiki/Indonesian_units_of_measurement">Indonesian</a></li> <li><a href="https://en.wikipedia.org/wiki/Japanese_units_of_measurement">Japanese</a></li> <li><a href="https://en.wikipedia.org/wiki/Korean_units_of_measurement">Korean</a></li> <li><a href="https://en.wikipedia.org/wiki/Mongolian_units">Mongolian</a></li> <li><a href="https://en.wikipedia.org/wiki/Myanmar_units_of_measurement">Myanmar</a></li> <li><a href="https://en.wikipedia.org/wiki/Nepalese_customary_units_of_measurement">Nepalese</a></li> <li><a href="https://en.wikipedia.org/wiki/Omani_units_of_measurement">Omani</a></li> <li><a href="https://en.wikipedia.org/wiki/Ottoman_units_of_measurement">Ottoman</a></li> <li><a href="https://en.wikipedia.org/wiki/History_of_measurement_systems_in_Pakistan">Pakistani</a></li> <li><a href="https://en.wikipedia.org/wiki/Philippine_units_of_measurement">Philippine</a></li> <li><a href="https://en.wikipedia.org/wiki/Abucco">Pegu</a></li> <li><a href="https://en.wikipedia.org/wiki/Singaporean_units_of_measurement">Singaporean</a></li> <li><a href="https://en.wikipedia.org/wiki/Sri_Lankan_units_of_measurement">Sri Lankan</a></li> <li><a href="https://en.wikipedia.org/wiki/Syrian_units_of_measurement">Syrian</a></li> <li><a href="https://en.wikipedia.org/wiki/Taiwanese_units_of_measurement">Taiwanese</a></li> <li><a href="https://en.wikipedia.org/wiki/Thai_units_of_measurement">Thai</a></li> <li><a href="https://en.wikipedia.org/wiki/Vietnamese_units_of_measurement">Vietnamese</a></li></ul> </div></td></tr><tr><th>Africa</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Algerian_units_of_measurement">Algerian</a></li> <li><a href="https://en.wikipedia.org/wiki/Ethiopian_units_of_measurement">Ethiopian</a></li> <li><a href="https://en.wikipedia.org/wiki/Egyptian_units_of_measurement">Egyptian</a></li> <li><a href="https://en.wikipedia.org/wiki/Eritrean_units_of_measurement">Eritrean</a></li> <li><a href="https://en.wikipedia.org/wiki/Guinean_units_of_measurement">Guinean</a></li> <li><a href="https://en.wikipedia.org/wiki/Libyan_units_of_measurement">Libyan</a></li> <li><a href="https://en.wikipedia.org/wiki/Malagasy_units_of_measurement">Malagasy</a></li> <li><a href="https://en.wikipedia.org/wiki/Mauritian_units_of_measurement">Mauritian</a></li> <li><a href="https://en.wikipedia.org/wiki/Moroccan_units_of_measurement">Moroccan</a></li> <li><a href="https://en.wikipedia.org/wiki/Seychellois_units_of_measurement">Seychellois</a></li> <li><a href="https://en.wikipedia.org/wiki/Somali_units_of_measurement">Somali</a></li> <li><a href="https://en.wikipedia.org/wiki/South_African_units_of_measurement">South African</a></li> <li><a href="https://en.wikipedia.org/wiki/Tunisian_units_of_measurement">Tunisian</a></li> <li><a href="https://en.wikipedia.org/wiki/Tanzanian_units_of_measurement">Tanzanian</a></li></ul> </div></td></tr><tr><th>North and Central<br/>America</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Costa_Rican_units_of_measurement">Costa Rican</a></li> <li><a href="https://en.wikipedia.org/wiki/Cuban_units_of_measurement">Cuban</a></li> <li><a href="https://en.wikipedia.org/wiki/Haitian_units_of_measurement">Haitian</a></li> <li><a href="https://en.wikipedia.org/wiki/Honduran_units_of_measurement">Honduran</a></li> <li><a href="https://en.wikipedia.org/wiki/Mexican_units_of_measurement">Mexican</a></li> <li><a href="https://en.wikipedia.org/wiki/Nicaraguan_units_of_measurement">Nicaraguan</a></li> <li><a href="https://en.wikipedia.org/wiki/Puerto_Rican_units_of_measurement">Puerto Rican</a></li></ul> </div></td></tr><tr><th>South America</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Argentine_units_of_measurement">Argentine</a></li> <li><a href="https://en.wikipedia.org/wiki/Bolivian_units_of_measurement">Bolivian</a></li> <li><a href="https://en.wikipedia.org/wiki/Brazilian_units_of_measurement">Brazilian</a></li> <li><a href="https://en.wikipedia.org/wiki/Chilean_units_of_measurement">Chilean</a></li> <li><a href="https://en.wikipedia.org/wiki/Colombian_units_of_measurement">Colombian</a></li> <li><a href="https://en.wikipedia.org/wiki/Paraguayan_units_of_measurement">Paraguayan</a></li> <li><a href="https://en.wikipedia.org/wiki/Peruvian_units_of_measurement">Peruvian</a></li> <li><a href="https://en.wikipedia.org/wiki/Uruguayan_units_of_measurement">Uruguayan</a></li> <li><a href="https://en.wikipedia.org/wiki/Venezuelan_units_of_measurement">Venezuelan</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Ancient</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Ancient_Arabic_units_of_measurement">Arabic</a></li> <li><a href="https://en.wikipedia.org/wiki/Biblical_and_Talmudic_units_of_measurement">Biblical and Talmudic</a></li> <li><a href="https://en.wikipedia.org/wiki/Ancient_Egyptian_units_of_measurement">Egyptian</a></li> <li><a href="https://en.wikipedia.org/wiki/Ancient_Greek_units_of_measurement">Greek</a></li> <li><a href="https://en.wikipedia.org/wiki/Hindu_units_of_time">Hindu</a></li> <li><a href="https://en.wikipedia.org/wiki/History_of_measurement_systems_in_India">Indian</a></li> <li><a href="https://en.wikipedia.org/wiki/Ancient_Mesopotamian_units_of_measurement">Mesopotamian</a></li> <li><a href="https://en.wikipedia.org/wiki/Persian_units_of_measurement">Persian</a></li> <li><a href="https://en.wikipedia.org/wiki/Ancient_Roman_units_of_measurement">Roman</a></li></ul> </div></td></tr><tr><th>List articles</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_humorous_units_of_measurement">Humorous</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_non-coherent_units_of_measurement">Non-coherent</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_obsolete_units_of_measurement">Obsolete</a></li></ul> </div></td></tr><tr><th>Other</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Absolute_scale">Absolute scale</a></li> <li><a href="https://en.wikipedia.org/wiki/N-body_units"><i>N</i>-body</a></li> <li>Modulor</li></ul> </div></td></tr></tbody></table></div><p> </p> Interval tree - Wikipedia https://en.wikipedia.org/wiki/Interval_tree pYP3Wq9mCu5VrFHdIKOzGGAdhU1v0HUet1i-GQ== Sat, 09 May 2026 11:51:12 +0000 Not to be confused with segment tree. <div>Not to be confused with <a href="https://en.wikipedia.org/wiki/Segment_tree">segment tree</a>.</div><div>Tree data structure to hold intervals</div><p>In <a href="https://en.wikipedia.org/wiki/Computer_science">computer science</a>, an <b>interval tree</b> is a <a href="https://en.wikipedia.org/wiki/Tree_(data_structure)">tree data structure</a> to hold <a href="https://en.wikipedia.org/wiki/Interval_(mathematics)">intervals</a>. Specifically, it allows one to efficiently find all intervals that overlap with any given interval or point. It is often used for windowing queries,<sup><span>[</span>1<span>]</span></sup> for instance, to find all roads on a computerized map inside a rectangular viewport, or to find all visible elements inside a three-dimensional scene. A similar data structure is the <a href="https://en.wikipedia.org/wiki/Segment_tree">segment tree</a>. </p><p>The trivial solution is to visit each interval and test whether it intersects the given point or interval, which requires <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34109fe397fdcff370079185bfdb65826cb5565a" alt="{\displaystyle O(n)}" title=""/></span> time, where <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span> is the number of intervals in the collection. Since a query may return all intervals, for example if the query is a large interval intersecting all intervals in the collection, this is <a href="https://en.wikipedia.org/wiki/Asymptotically_optimal">asymptotically optimal</a>; however, <a href="https://en.wikipedia.org/wiki/Output-sensitive_algorithm">output-sensitive algorithms</a>, where the runtime is expressed in terms of <span><span><math> <semantics> <mrow> <mstyle> <mi>m</mi> </mstyle> </mrow> <annotation>{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" alt="{\displaystyle m}" title=""/></span> (the number of intervals produced by the query) may also be considered. Interval trees have a query time of <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>+</mo> <mi>m</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(\log n+m)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8f08f139c8022b2da3554deebfcd48995028db6" alt="{\displaystyle O(\log n+m)}" title=""/></span> and an initial creation time of <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(n\log n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d2320768fb54880ca4356e61f60eb02a3f9d9f1" alt="{\displaystyle O(n\log n)}" title=""/></span>, while limiting memory consumption to <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34109fe397fdcff370079185bfdb65826cb5565a" alt="{\displaystyle O(n)}" title=""/></span>. After creation, interval trees may be dynamic, allowing efficient insertion and deletion of an interval in <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(\log n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aae0f22048ba6b7c05dbae17b056bfa16e21807d" alt="{\displaystyle O(\log n)}" title=""/></span> time. If the endpoints of intervals are within a small integer range (<i>e.g.</i>, in the range <span><span><math> <semantics> <mrow> <mstyle> <mo>[</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> <mo>]</mo> </mstyle> </mrow> <annotation>{\displaystyle [1,\ldots ,O(n)]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/292672ded6aef6ae4a14183608844cb053711060" alt="{\displaystyle [1,\ldots ,O(n)]}" title=""/></span>), faster and in fact optimal data structures exist<sup><span>[</span>2<span>]</span></sup><sup><span>[</span>3<span>]</span></sup> with preprocessing time <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34109fe397fdcff370079185bfdb65826cb5565a" alt="{\displaystyle O(n)}" title=""/></span> and query time <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>m</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(1+m)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0347e8f69f1f556f5493edc2c8da90c3113babfb" alt="{\displaystyle O(1+m)}" title=""/></span> for reporting <span><span><math> <semantics> <mrow> <mstyle> <mi>m</mi> </mstyle> </mrow> <annotation>{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" alt="{\displaystyle m}" title=""/></span> intervals containing a given query point (see<sup><span>[</span>2<span>]</span></sup> for a very simple one). </p><div><h2>Naïve approach</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>In a simple case, the intervals do not overlap and they can be inserted into a simple <a href="https://en.wikipedia.org/wiki/Binary_search_tree">binary search tree</a> and queried in <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(\log n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aae0f22048ba6b7c05dbae17b056bfa16e21807d" alt="{\displaystyle O(\log n)}" title=""/></span> time. However, with arbitrarily overlapping intervals, there is no way to compare two intervals for insertion into the tree since orderings sorted by the beginning points or the ending points may be different. A naïve approach might be to build two parallel trees, one ordered by the beginning point, and one ordered by the ending point of each interval. This allows discarding half of each tree in <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(\log n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aae0f22048ba6b7c05dbae17b056bfa16e21807d" alt="{\displaystyle O(\log n)}" title=""/></span> time, but the results must be merged, requiring <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34109fe397fdcff370079185bfdb65826cb5565a" alt="{\displaystyle O(n)}" title=""/></span> time. This returns queries in <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> <mo>=</mo> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(n+\log n)=O(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c7504fd00f2630fdf659d4b931d6d98658ea67f" alt="{\displaystyle O(n+\log n)=O(n)}" title=""/></span>, which is no better than brute-force. </p><p>Interval trees solve this problem. This article describes two alternative designs for an interval tree, dubbed the <i>centered interval tree</i> and the <i>augmented tree</i>. </p><div><h2>Centered interval tree</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>Queries require <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>+</mo> <mi>m</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(\log n+m)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8f08f139c8022b2da3554deebfcd48995028db6" alt="{\displaystyle O(\log n+m)}" title=""/></span> time, with <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span> being the total number of intervals and <span><span><math> <semantics> <mrow> <mstyle> <mi>m</mi> </mstyle> </mrow> <annotation>{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" alt="{\displaystyle m}" title=""/></span> being the number of reported results. Construction requires <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(n\log n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d2320768fb54880ca4356e61f60eb02a3f9d9f1" alt="{\displaystyle O(n\log n)}" title=""/></span> time, and storage requires <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34109fe397fdcff370079185bfdb65826cb5565a" alt="{\displaystyle O(n)}" title=""/></span> space. </p><div><h3>Construction</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Given a set of <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span> intervals on the number line, a data structure needs to be constructed so that all intervals overlapping another interval or point can be efficiently retrieved. </p><p>First, the entire range of all the intervals is taken and divided in half at <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span> (in practice, <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span> should be picked to keep the tree relatively balanced). This gives three sets of intervals, those completely to the left of <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>, called <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>left</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {left}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59bcdd25a9823a27ed9194e0d8bcd1fee4f47c5d" alt="{\displaystyle S_{\textrm {left}}}" title=""/></span>, those completely to the right of <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>, called <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>right</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {right}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/646282c786c1d477f58970e41ea7020357c58548" alt="{\displaystyle S_{\textrm {right}}}" title=""/></span>, and those overlapping <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>, called <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span>. </p><p>The intervals in <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span> that overlap the center point are stored in a separate data structure linked to the node in the interval tree. This data structure consists of two lists, one containing all the intervals sorted by their beginning points, and another containing all the intervals sorted by their ending points. </p><p>The result is a <a href="https://en.wikipedia.org/wiki/Binary_tree">binary tree</a> with each node storing: </p><ul><li>A center point</li> <li>A pointer to another node containing all intervals completely to the left of the center point</li> <li>A pointer to another node containing all intervals completely to the right of the center point</li> <li>All intervals overlapping the center point sorted by their beginning point</li> <li>All intervals overlapping the center point sorted by their ending point</li></ul><div><h3>Intersecting</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Interval trees allow for quickly computing all the ranges overlapping any input. </p><div><h4>With a point</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>The task is to find all intervals in the tree that overlap a given point <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>. The tree is walked with a similar recursive algorithm as would be used to traverse a traditional binary tree, but with extra logic to support searching the intervals overlapping the &quot;center&quot; point at each node. </p><p>For each tree node, <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is compared to <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>, the midpoint used in node construction above. If <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is less than <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>, the leftmost set of intervals, <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>left</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {left}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59bcdd25a9823a27ed9194e0d8bcd1fee4f47c5d" alt="{\displaystyle S_{\textrm {left}}}" title=""/></span>, is considered. If <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is greater than <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>, the rightmost set of intervals, <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>right</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {right}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/646282c786c1d477f58970e41ea7020357c58548" alt="{\displaystyle S_{\textrm {right}}}" title=""/></span>, is considered. </p><figure><a href="https://en.wikipedia.org/wiki/File:Check_if_a_point_overlaps_the_intervals_in_S_center_of_a_centered_interval_tree.svg"></a><figcaption>All intervals in <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span> that begin before <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> must overlap <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> if <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is less than <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>.<br/>Similarly, the same technique also applies in checking a given interval. If a given interval ends at <i>y</i> and <i>y</i> is less than <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>, all intervals in <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span> that begin before <i>y</i> must also overlap the given interval.</figcaption></figure><p>As each node is processed as the tree is traversed from the root to a leaf, the ranges in its <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span> are processed. If <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is less than <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>, all intervals in <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span> must end after <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>, or they could not also overlap <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>. Therefore, it is only necessary find those intervals in <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span> that begin before <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>. The lists of <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span>, which have already been constructed, can be consulted. Since only the interval beginnings are relevant in this scenario, the list can be sorted by beginnings. If the closest number no greater than <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is found in this list, all ranges from the beginning of the list to that found point overlap <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> because they begin before <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> and end after <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> (because they overlap <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span> which is larger than <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>). Thus, the intervals in the list can be enumerated until the startpoint value exceeds <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>. </p><p>Likewise, if <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is greater than <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>x</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle x_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610d04c729413d931e262ba95dd82557bb72f339" alt="{\displaystyle x_{\textrm {center}}}" title=""/></span>, all intervals in <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span> must begin before <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>, so the intervals that end after <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> can be found using the list sorted by interval endings. </p><div><h4>With an interval</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>We first find all intervals with start and/or end points inside <span><span><math> <semantics> <mrow> <mstyle> <mi>q</mi> </mstyle> </mrow> <annotation>{\displaystyle q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" alt="{\displaystyle q}" title=""/></span> using a separately-constructed tree. In the one-dimensional case, we can use a search tree containing all the start and end points in the interval set, each with a pointer to its corresponding interval. A binary search in <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(\log n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aae0f22048ba6b7c05dbae17b056bfa16e21807d" alt="{\displaystyle O(\log n)}" title=""/></span> time for the start and end of <span><span><math> <semantics> <mrow> <mstyle> <mi>q</mi> </mstyle> </mrow> <annotation>{\displaystyle q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" alt="{\displaystyle q}" title=""/></span> reveals the minimum and maximum points to consider. Each point within this range references an interval that overlaps <span><span><math> <semantics> <mrow> <mstyle> <mi>q</mi> </mstyle> </mrow> <annotation>{\displaystyle q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" alt="{\displaystyle q}" title=""/></span> and is added to the result list. Care must be taken to avoid duplicates, since an interval might both begin and end within <span><span><math> <semantics> <mrow> <mstyle> <mi>q</mi> </mstyle> </mrow> <annotation>{\displaystyle q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" alt="{\displaystyle q}" title=""/></span>. This can be done using a binary flag on each interval to mark whether or not it has been added to the result set. </p><div><h3>Higher dimensions</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>First, a <a href="https://en.wikipedia.org/wiki/Range_tree">range tree</a> in <span><span><math> <semantics> <mrow> <mstyle> <mi>N</mi> </mstyle> </mrow> <annotation>{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" alt="{\displaystyle N}" title=""/></span> dimensions is constructed that allows efficient retrieval of all intervals with beginning and end points inside the query region <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> </mstyle> </mrow> <annotation>{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" alt="{\displaystyle R}" title=""/></span>. Once the corresponding ranges are found, the only thing that is left are those ranges that enclose the region in some dimension. To find these overlaps, <span><span><math> <semantics> <mrow> <mstyle> <mi>N</mi> </mstyle> </mrow> <annotation>{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" alt="{\displaystyle N}" title=""/></span> interval trees are created, and one axis intersecting <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> </mstyle> </mrow> <annotation>{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" alt="{\displaystyle R}" title=""/></span> is queried for each. For example, in two dimensions, the bottom of the square <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> </mstyle> </mrow> <annotation>{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" alt="{\displaystyle R}" title=""/></span> (or any other horizontal line intersecting <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> </mstyle> </mrow> <annotation>{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" alt="{\displaystyle R}" title=""/></span>) would be queried against the interval tree constructed for the horizontal axis. Likewise, the left (or any other vertical line intersecting <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> </mstyle> </mrow> <annotation>{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" alt="{\displaystyle R}" title=""/></span>) would be queried against the interval tree constructed on the vertical axis. </p><p>Each interval tree also needs an addition for higher dimensions. At each node we traverse in the tree, <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is compared with <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span> to find overlaps. Instead of two sorted lists of points as was used in the one-dimensional case, a range tree is constructed. This allows efficient retrieval of all points in <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>S</mi> <mrow> <mrow> <mtext>center</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle S_{\textrm {center}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec18349b29033c28e5d6c99ddb8c8c22872e7ff1" alt="{\displaystyle S_{\textrm {center}}}" title=""/></span> that overlap region <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> </mstyle> </mrow> <annotation>{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" alt="{\displaystyle R}" title=""/></span>. </p><div><h3>Deletion</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>If after deleting an interval from the tree, the node containing that interval contains no more intervals, that node may be deleted from the tree. This is more complex than a normal binary tree deletion operation. </p><p>An interval may overlap the center point of several nodes in the tree. Since each node stores the intervals that overlap it, with all intervals completely to the left of its center point in the left subtree, similarly for the right subtree, it follows that each interval is stored in the node closest to the root from the set of nodes whose center point it overlaps. </p><p>Normal deletion operations in a binary tree (for the case where the node being deleted has two children) involve promoting a node further from the leaf to the position of the node being deleted (usually the leftmost child of the right subtree, or the rightmost child of the left subtree). </p><figure><a href="https://en.wikipedia.org/wiki/File:Binary_search_tree_delete.svg"></a><figcaption>Deleting a node with two children from a binary search tree using the in-order predecessor (rightmost node in the left subtree, labelled <b>6</b>).</figcaption></figure><p>As a result of this promotion, some nodes that were above the promoted node will become its descendants; it is necessary to search these nodes for intervals that also overlap the promoted node, and move those intervals into the promoted node. As a consequence, this may result in new empty nodes, which must be deleted, following the same algorithm again. </p><div><h3>Balancing</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>The same issues that affect deletion also affect rotation operations; rotation must preserve the invariant that nodes are stored as close to the root as possible. </p><div><h2>Augmented tree</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Example_of_augmented_tree_with_low_value_as_the_key_and_maximum_high_as_extra_annotation.png"></a><figcaption>An augmented tree with low value as the key and maximum high as the extra annotation.For example, when testing if the given interval <i>[40 ,60)</i> overlaps the intervals in the tree shown above, we see that it does not overlap the interval <i>[20, 36)</i> in the root, but since the root&#39;s low value (20) is less than the sought high value (60), we must search the right subtree. The left subtree&#39;s maximum high of 41 exceeds the sought low value (40), so we must search the left subtree as well. However, both descendants of the <i>[3, 41)</i> node have maximum highs less than 40, so the left subtree search ends there and it is not necessary to search them.</figcaption></figure><p>Another way to represent intervals is described in Cormen et al. (2009, Section 14.3: Interval trees, pp. 348–354). </p><p>An augmented tree can be built from a simple ordered tree, for example a <a href="https://en.wikipedia.org/wiki/Binary_search_tree">binary search tree</a> or <a href="https://en.wikipedia.org/wiki/Self-balancing_binary_search_tree">self-balancing binary search tree</a>, ordered by the &#39;low&#39; values of the intervals. An extra annotation is then added to every node, recording the maximum upper value among all the intervals from this node down. Maintaining this attribute involves updating all ancestors of the node from the bottom up whenever a node is added or deleted. This takes only O(<i>h</i>) steps per node addition or removal, where <i>h</i> is the height of the node added or removed in the tree. If there are any <a href="https://en.wikipedia.org/wiki/Tree_rotation">tree rotations</a> during insertion and deletion, the affected nodes may need updating as well. </p><p>Now, it is known that two intervals <span><span><math> <semantics> <mrow> <mstyle> <mi>A</mi> </mstyle> </mrow> <annotation>{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" alt="{\displaystyle A}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>B</mi> </mstyle> </mrow> <annotation>{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" alt="{\displaystyle B}" title=""/></span> overlap only when both <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>A</mi> <mrow> <mrow> <mtext>low</mtext> </mrow> </mrow> </msub> <mo>≤</mo> <msub> <mi>B</mi> <mrow> <mrow> <mtext>high</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle A_{\textrm {low}}\leq B_{\textrm {high}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c206f7ae59ba8ff11b5a2d9a09710fc46702cde4" alt="{\displaystyle A_{\textrm {low}}\leq B_{\textrm {high}}}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>A</mi> <mrow> <mrow> <mtext>high</mtext> </mrow> </mrow> </msub> <mo>≥</mo> <msub> <mi>B</mi> <mrow> <mrow> <mtext>low</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle A_{\textrm {high}}\geq B_{\textrm {low}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/193391cf66ca03f97e1224d16c0161c6baab6eae" alt="{\displaystyle A_{\textrm {high}}\geq B_{\textrm {low}}}" title=""/></span>. When searching the trees for nodes overlapping with a given interval, you can immediately skip: </p><ul><li>all nodes to the right of nodes whose low value is past the end of the given interval.</li> <li>all nodes that have their maximum high value below the start of the given interval.</li></ul><div><h3>Membership queries</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><p>Some performance may be gained if the tree avoids unnecessary traversals. These can occur when adding intervals that already exist or removing intervals that don&#39;t exist. </p><p>A total order can be defined on the intervals by ordering them first by their lower bounds and then by their upper bounds. Then, a membership check can be performed in <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(\log n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aae0f22048ba6b7c05dbae17b056bfa16e21807d" alt="{\displaystyle O(\log n)}" title=""/></span> time, versus the <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(k+\log n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52ea4d30b861cebb6d7deaf008c82812da9579a5" alt="{\displaystyle O(k+\log n)}" title=""/></span> time required to find duplicates if <span><span><math> <semantics> <mrow> <mstyle> <mi>k</mi> </mstyle> </mrow> <annotation>{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" alt="{\displaystyle k}" title=""/></span> intervals overlap the interval to be inserted or removed. This solution has the advantage of not requiring any additional structures. The change is strictly algorithmic. The disadvantage is that membership queries take <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>log</mi> <mo>⁡</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(\log n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aae0f22048ba6b7c05dbae17b056bfa16e21807d" alt="{\displaystyle O(\log n)}" title=""/></span> time. </p><p>Alternately, at the rate of <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle O(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34109fe397fdcff370079185bfdb65826cb5565a" alt="{\displaystyle O(n)}" title=""/></span> memory, membership queries in expected constant time can be implemented with a hash table, updated in lockstep with the interval tree. This may not necessarily double the total memory requirement, if the intervals are stored by reference rather than by value. </p><div><h3>Java example: Adding a new interval to the tree</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><p>The key of each node is the interval itself, hence nodes are ordered first by low value and finally by high value, and the value of each node is the end point of the interval: </p><div><h3>Java example: Searching a point or an interval in the tree</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><p>To search for an interval, one walks the tree, using the key (<code>n.getKey()</code>) and high value (<code>n.getValue()</code>) to omit any branches that cannot overlap the query. The simplest case is a point query: </p><div><pre><span>// Search for all intervals containing &quot;p&quot;, starting with the</span> <span>// node &quot;n&quot; and adding matching intervals to the list &quot;result&quot;</span> <span>public</span> <span>void</span> <span>search</span><span>(</span><span>IntervalNode</span> <span>n</span><span>,</span> <span>Point</span> <span>p</span><span>,</span> <span>List</span><span>&lt;</span><span>Interval</span><span>&gt;</span> <span>result</span><span>)</span> <span>{</span> <span> </span><span>// Don&#39;t search nodes that don&#39;t exist</span> <span> </span><span>if</span> <span>(</span><span>n</span> <span>==</span> <span>null</span><span>)</span> <span> </span><span>return</span><span>;</span> <span> </span><span>// If p is to the right of the rightmost point of any interval</span> <span> </span><span>// in this node and all children, there won&#39;t be any matches.</span> <span> </span><span>if</span> <span>(</span><span>p</span><span>.</span><span>compareTo</span><span>(</span><span>n</span><span>.</span><span>getValue</span><span>())</span> <span>&gt;</span> <span>0</span><span>)</span> <span> </span><span>return</span><span>;</span> <span> </span><span>// Search left children</span> <span> </span><span>search</span><span>(</span><span>n</span><span>.</span><span>getLeft</span><span>(),</span> <span>p</span><span>,</span> <span>result</span><span>);</span> <span> </span><span>// Check this node</span> <span> </span><span>if</span> <span>(</span><span>n</span><span>.</span><span>getKey</span><span>().</span><span>contains</span><span>(</span><span>p</span><span>))</span> <span> </span><span>result</span><span>.</span><span>add</span><span>(</span><span>n</span><span>.</span><span>getKey</span><span>());</span> <span> </span><span>// If p is to the left of the start of this interval,</span> <span> </span><span>// then it can&#39;t be in any child to the right.</span> <span> </span><span>if</span> <span>(</span><span>p</span><span>.</span><span>compareTo</span><span>(</span><span>n</span><span>.</span><span>getKey</span><span>().</span><span>getStart</span><span>())</span> <span>&lt;</span> <span>0</span><span>)</span> <span> </span><span>return</span><span>;</span> <span> </span><span>// Otherwise, search right children</span> <span> </span><span>search</span><span>(</span><span>n</span><span>.</span><span>getRight</span><span>(),</span> <span>p</span><span>,</span> <span>result</span><span>);</span> <span>}</span> </pre></div><p>where </p><p>The code to search for an interval is similar, except for the check in the middle: </p><p><code>overlapsWith()</code> is defined as: </p><div><h3>Higher dimensions</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><p>Augmented trees can be extended to higher dimensions by cycling through the dimensions at each level of the tree. For example, for two dimensions, the odd levels of the tree might contain ranges for the <i>x</i>-coordinate, while the even levels contain ranges for the <i>y</i>-coordinate. This approach effectively converts the data structure from an augmented binary tree to an augmented <a href="https://en.wikipedia.org/wiki/Kd-tree">kd-tree</a>, thus significantly complicating the balancing algorithms for insertions and deletions. </p><p>A simpler solution is to use nested interval trees. First, create a tree using the ranges for the <i>y</i>-coordinate. Now, for each node in the tree, add another interval tree on the <i>x</i>-ranges, for all elements whose <i>y</i>-range is the same as that node&#39;s <i>y</i>-range. </p><p>The advantage of this solution is that it can be extended to an arbitrary number of dimensions using the same code base. </p><p>At first, the additional cost of the nested trees might seem prohibitive, but this is usually not so. As with the non-nested solution earlier, one node is needed per <i>x</i>-coordinate, yielding the same number of nodes for both solutions. The only additional overhead is that of the nested tree structures, one per vertical interval. This structure is usually of negligible size, consisting only of a pointer to the root node, and possibly the number of nodes and the depth of the tree. </p><div><h2>Medial- or length-oriented tree</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div><p>A medial- or length-oriented tree is similar to an augmented tree, but symmetrical, with the binary search tree ordered by the medial points of the intervals. There is a maximum-oriented <a href="https://en.wikipedia.org/wiki/Binary_heap">binary heap</a> in every node, ordered by the length of the interval (or half of the length). Also we store the minimum and maximum possible value of the subtree in each node (thus the symmetry). </p><div><h3>Overlap test</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div><p>This can be simplified using the sum and difference: </p><p>Which reduces the overlap test to: </p><div><h3>Adding interval</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=17"><span>edit</span></a><span>]</span></span></div><p>Adding new intervals to the tree is the same as for a binary search tree using the medial value as the key. We push <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>d</mi> <mrow> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle d_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abe3154db7d4f92fb42dd1f80f52f528c6312e4a" alt="{\displaystyle d_{i}}" title=""/></span> onto the binary heap associated with the node, and update the minimum and maximum possible values associated with all higher nodes. </p><div><h3>Searching for all overlapping intervals</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=18"><span>edit</span></a><span>]</span></span></div><p>Starting with root node, in each node, first we check if it is possible that our query interval overlaps with the node subtree using minimum and maximum values of node (if it is not, we don&#39;t continue for this node). </p><p>Then we pass through both left and right children of the node, doing the same thing. </p><p>In the worst-case, we have to scan all nodes of the binary search tree, but since binary heap query is optimum, this is acceptable (a 2- dimensional problem can not be optimum in both dimensions) </p><p>This algorithm is expected to be faster than a traditional interval tree (augmented tree) for search operations. Adding elements is a little slower in practice, though the order of growth is the same. </p><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=19"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Mark_de_Berg">Mark de Berg</a>, <a href="https://en.wikipedia.org/wiki/Marc_van_Kreveld">Marc van Kreveld</a>, <a href="https://en.wikipedia.org/wiki/Mark_Overmars">Mark Overmars</a>, and <a href="https://en.wikipedia.org/wiki/Otfried_Schwarzkopf">Otfried Schwarzkopf</a>. <i>Computational Geometry</i>, Second Revised Edition. Springer-Verlag 2000. Section 10.1: Interval Trees, pp. 212–217.</li> <li><cite><a href="https://en.wikipedia.org/wiki/Thomas_H._Cormen">Cormen, Thomas H.</a>; <a href="https://en.wikipedia.org/wiki/Charles_E._Leiserson">Leiserson, Charles E.</a>; <a href="https://en.wikipedia.org/wiki/Ronald_L._Rivest">Rivest, Ronald L.</a>; <a href="https://en.wikipedia.org/wiki/Clifford_Stein">Stein, Clifford</a> (2009), <a href="https://en.wikipedia.org/wiki/Introduction_to_Algorithms"><i>Introduction to Algorithms</i></a> (3rd ed.), MIT Press and McGraw-Hill, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-262-03384-8"><bdi>978-0-262-03384-8</bdi></a></cite></li> <li><a href="https://en.wikipedia.org/wiki/Franco_P._Preparata">Franco P. Preparata</a> and <a href="https://en.wikipedia.org/wiki/Michael_Ian_Shamos">Michael Ian Shamos</a>. <i>Computational Geometry: An Introduction</i>. Springer-Verlag, 1985</li></ul><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Interval_tree&amp;action=edit&amp;section=20"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://www.cgal.org/">CGAL : Computational Geometry Algorithms Library in C++</a> contains a robust implementation of Range Trees</li> <li><a href="https://www.boost.org/doc/libs/1_64_0/libs/icl/doc/html/index.html">Boost.Icl</a> offers C++ implementations of interval sets and maps.</li> <li><a href="https://github.com/chaimleib/intervaltree">IntervalTree (Python)</a> - a centered interval tree with AVL balancing, compatible with tagged intervals</li> <li><a href="https://code.google.com/p/intervaltree/">Interval Tree (C#)</a> - an augmented interval tree, with AVL balancing</li> <li><a href="https://github.com/misshie/interval-tree/">Interval Tree (Ruby)</a> - a centered interval tree, immutable, compatible with tagged intervals</li> <li><a href="https://github.com/Breinify/brein-time-utilities/#intervaltree">IntervalTree (Java)</a> - an augmented interval tree, with AVL balancing, supporting overlap, find, Collection interface, id-associated intervals</li> <li><a href="https://metacpan.org/dist/Tree-Interval-Fast">Tree::Interval::Fast (Perl/C)</a> - Efficient creation and manipulation of interval trees.</li></ul><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:CS_trees"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:CS_trees"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:CS_trees"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Tree_(abstract_data_type)">Tree data structures</a></div></th></tr><tr><th><a href="https://en.wikipedia.org/wiki/Search_tree">Search trees</a><br/>(<a href="https://en.wikipedia.org/wiki/Set_(abstract_data_type)">dynamic sets</a>,<br/><a href="https://en.wikipedia.org/wiki/Associative_array">associative arrays</a>)</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/2%E2%80%933_tree">2–3</a></li> <li><a href="https://en.wikipedia.org/wiki/2%E2%80%933%E2%80%934_tree">2–3–4</a></li> <li><a href="https://en.wikipedia.org/wiki/AA_tree">AA</a></li> <li><a href="https://en.wikipedia.org/wiki/(a,b)-tree">(a,b)</a></li> <li><a href="https://en.wikipedia.org/wiki/AVL_tree">AVL</a></li> <li><a href="https://en.wikipedia.org/wiki/B-tree">B</a></li> <li><a href="https://en.wikipedia.org/wiki/B%2B_tree">B+</a> <ul><li><a href="https://en.wikipedia.org/wiki/K-D-B-tree">K-Dimensional</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/B*-tree">B*</a></li> <li><a href="https://en.wikipedia.org/wiki/Bx-tree">B<sup>x</sup></a></li> <li><a href="https://en.wikipedia.org/wiki/Binary_search_tree">Binary search</a> <ul><li><a href="https://en.wikipedia.org/wiki/Optimal_binary_search_tree">Optimal</a></li> <li><a href="https://en.wikipedia.org/wiki/Self-balancing_binary_search_tree">Self-balancing</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Dancing_tree">Dancing</a></li> <li><a href="https://en.wikipedia.org/wiki/HTree">HTree</a></li> <li>Interval</li> <li><a href="https://en.wikipedia.org/wiki/Order_statistic_tree">Order statistic</a></li> <li><a href="https://en.wikipedia.org/wiki/Palindrome_tree">Palindrome</a></li> <li>(<a href="https://en.wikipedia.org/wiki/Left-leaning_red%E2%80%93black_tree">Left-leaning</a>) <a href="https://en.wikipedia.org/wiki/Red%E2%80%93black_tree">Red–black</a></li> <li><a href="https://en.wikipedia.org/wiki/Scapegoat_tree">Scapegoat</a></li> <li><a href="https://en.wikipedia.org/wiki/Splay_tree">Splay</a></li> <li><a href="https://en.wikipedia.org/wiki/T-tree">T</a></li> <li><a href="https://en.wikipedia.org/wiki/Treap">Treap</a></li> <li><a href="https://en.wikipedia.org/wiki/UB-tree">UB</a></li> <li><a href="https://en.wikipedia.org/wiki/Weight-balanced_tree">Weight-balanced</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Heap_(data_structure)">Heaps</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Binary_heap">Binary</a></li> <li><a href="https://en.wikipedia.org/wiki/Binomial_heap">Binomial</a></li> <li><a href="https://en.wikipedia.org/wiki/Brodal_queue">Brodal</a></li> <li><a href="https://en.wikipedia.org/wiki/D-ary_heap"><i>d</i>-ary</a></li> <li><a href="https://en.wikipedia.org/wiki/Fibonacci_heap">Fibonacci</a></li> <li><a href="https://en.wikipedia.org/wiki/Leftist_tree">Leftist</a></li> <li><a href="https://en.wikipedia.org/wiki/Pairing_heap">Pairing</a></li> <li><a href="https://en.wikipedia.org/wiki/Skew_binomial_heap">Skew binomial</a></li> <li><a href="https://en.wikipedia.org/wiki/Skew_heap">Skew</a></li> <li><a href="https://en.wikipedia.org/wiki/Van_Emde_Boas_tree">van Emde Boas</a></li> <li><a href="https://en.wikipedia.org/wiki/Weak_heap">Weak</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Trie">Tries</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Ctrie">Ctrie</a></li> <li><a href="https://en.wikipedia.org/wiki/C-trie">C-trie</a> (compressed ADT)</li> <li><a href="https://en.wikipedia.org/wiki/Hash_tree_(persistent_data_structure)">Hash</a></li> <li><a href="https://en.wikipedia.org/wiki/Radix_tree">Radix</a></li> <li><a href="https://en.wikipedia.org/wiki/Suffix_tree">Suffix</a></li> <li><a href="https://en.wikipedia.org/wiki/Ternary_search_tree">Ternary search</a></li> <li><a href="https://en.wikipedia.org/wiki/X-fast_trie">X-fast</a></li> <li><a href="https://en.wikipedia.org/wiki/Y-fast_trie">Y-fast</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Spatial_index">Spatial</a> data<br/>partitioning trees</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Ball_tree">Ball</a></li> <li><a href="https://en.wikipedia.org/wiki/BK-tree">BK</a></li> <li><a href="https://en.wikipedia.org/wiki/BSP_tree">BSP</a></li> <li><a href="https://en.wikipedia.org/wiki/Cartesian_tree">Cartesian</a></li> <li><a href="https://en.wikipedia.org/wiki/Hilbert_R-tree">Hilbert R</a></li> <li><a href="https://en.wikipedia.org/wiki/K-d_tree"><i>k</i>-d</a> (<a href="https://en.wikipedia.org/wiki/Implicit_k-d_tree">implicit <i>k</i>-d</a>)</li> <li><a href="https://en.wikipedia.org/wiki/M-tree">M</a></li> <li><a href="https://en.wikipedia.org/wiki/Metric_tree">Metric</a></li> <li><a href="https://en.wikipedia.org/wiki/MVP_tree">MVP</a></li> <li><a href="https://en.wikipedia.org/wiki/Octree">Octree</a></li> <li><a href="https://en.wikipedia.org/wiki/PH-tree">PH</a></li> <li><a href="https://en.wikipedia.org/wiki/Priority_R-tree">Priority R</a></li> <li><a href="https://en.wikipedia.org/wiki/Quadtree">Quad</a></li> <li><a href="https://en.wikipedia.org/wiki/R-tree">R</a></li> <li><a href="https://en.wikipedia.org/wiki/R%2B_tree">R+</a></li> <li><a href="https://en.wikipedia.org/wiki/R*_tree">R*</a></li> <li><a href="https://en.wikipedia.org/wiki/Segment_tree">Segment</a></li> <li><a href="https://en.wikipedia.org/wiki/Vantage-point_tree">VP</a></li> <li><a href="https://en.wikipedia.org/wiki/X-tree">X</a></li></ul> </div></td></tr><tr><th>Other trees</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Cover_tree">Cover</a></li> <li><a href="https://en.wikipedia.org/wiki/Exponential_tree">Exponential</a></li> <li><a href="https://en.wikipedia.org/wiki/Fenwick_tree">Fenwick</a></li> <li><a href="https://en.wikipedia.org/wiki/Finger_tree">Finger</a></li> <li><a href="https://en.wikipedia.org/wiki/Fractal_tree_index">Fractal index</a></li> <li><a href="https://en.wikipedia.org/wiki/Fusion_tree">Fusion</a></li> <li><a href="https://en.wikipedia.org/wiki/Hash_calendar">Hash calendar</a></li> <li><a href="https://en.wikipedia.org/wiki/IDistance">iDistance</a></li> <li><a href="https://en.wikipedia.org/wiki/K-ary_tree">K-ary</a></li> <li><a href="https://en.wikipedia.org/wiki/Left-child_right-sibling_binary_tree">Left-child right-sibling</a></li> <li><a href="https://en.wikipedia.org/wiki/Link/cut_tree">Link/cut</a></li> <li><a href="https://en.wikipedia.org/wiki/Log-structured_merge-tree">Log-structured merge</a></li> <li><a href="https://en.wikipedia.org/wiki/Merkle_tree">Merkle</a></li> <li><a href="https://en.wikipedia.org/wiki/PQ_tree">PQ</a></li> <li><a href="https://en.wikipedia.org/wiki/Range_tree">Range</a></li> <li><a href="https://en.wikipedia.org/wiki/SPQR_tree">SPQR</a></li> <li><a href="https://en.wikipedia.org/wiki/Top_tree">Top</a></li></ul> </div></td></tr></tbody></table></div> Harry Markopolos - Wikipedia https://en.wikipedia.org/wiki/Harry_Markopolos OlFPOTwr7ZnnnBqDI1TdJ1-Pqpm4bXanxEdv4g== Sat, 09 May 2026 11:08:54 +0000 American accountant who exposed the Madoff investment scandal <div>American accountant who exposed the Madoff investment scandal</div><p> </p><table><tbody><tr><th colspan="2"><div>Harry Markopolos</div></th></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Harry_M._Markopolos.jpg"></a></span><div>College yearbook portrait, 1981</div></td></tr><tr><th>Born</th><td><span> (<span>1956-10-22</span>) </span>October 22, 1956<span> (age 69)</span><br/><div><a href="https://en.wikipedia.org/wiki/Erie,_Pennsylvania">Erie, Pennsylvania</a>, U.S</div></td></tr><tr><th>Alma mater</th><td><span><a href="https://en.wikipedia.org/wiki/Loyola_University_Maryland">Loyola College in Maryland</a> (<a href="https://en.wikipedia.org/wiki/Bachelor_of_Arts">BA</a>)</span><br/><a href="https://en.wikipedia.org/wiki/Boston_College">Boston College</a> (<a href="https://en.wikipedia.org/wiki/Master_of_Science">MS</a>)</td></tr><tr><th>Occupations</th><td><a href="https://en.wikipedia.org/wiki/Securities_fraud">Financial fraud</a> investigator, Retired securities executive, <a href="https://en.wikipedia.org/wiki/Chartered_Financial_Analyst">CFA</a>, <a href="https://en.wikipedia.org/wiki/Certified_Fraud_Examiner">CFE</a></td></tr><tr><th>Known for</th><td><a href="https://en.wikipedia.org/wiki/Whistleblower">Whistleblower</a> in <a href="https://en.wikipedia.org/wiki/Bernie_Madoff">Bernie Madoff</a> <a href="https://en.wikipedia.org/wiki/Madoff_investment_scandal">securities fraud scandal</a></td></tr><tr><th>Spouse</th><td>Faith Markopolos</td></tr><tr><th>Children</th><td>3</td></tr></tbody></table><p><b>Harry M. Markopolos</b> (born October 22, 1956) is an American <a href="https://en.wikipedia.org/wiki/Forensic_accounting">forensic accounting</a> and <a href="https://en.wikipedia.org/wiki/Securities_fraud">financial fraud</a> investigator and former <a href="https://en.wikipedia.org/wiki/Security_(finance)">securities</a> industry executive best known for initially discovering <a href="https://en.wikipedia.org/wiki/Bernie_Madoff">Bernie Madoff</a>&#39;s <a href="https://en.wikipedia.org/wiki/Ponzi_scheme">Ponzi scheme</a> in the late 1990s. </p><p>From 1999 to 2008, Markopolos uncovered evidence that suggested that Madoff&#39;s wealth management business was a fraudulent Ponzi scheme. In 2000, 2001, and 2005, Markopolos alerted the <a href="https://en.wikipedia.org/wiki/U.S._Securities_and_Exchange_Commission">U.S. Securities and Exchange Commission</a> (SEC) of his views, supplying supporting documents, but each time the SEC ignored him or gave his evidence only a cursory investigation.<sup><span>[</span>1<span>]</span></sup> Madoff was finally revealed to be a fraud in December 2008, when his sons contacted the <a href="https://en.wikipedia.org/wiki/Federal_Bureau_of_Investigation">Federal Bureau of Investigation</a>. After admitting to operating the <a href="https://en.wikipedia.org/wiki/Madoff_investment_scandal">largest private Ponzi scheme in history</a>, Madoff was sentenced in 2009 to 150 years in prison.<sup><span>[</span>2<span>]</span></sup><sup><span>[</span>3<span>]</span></sup> </p><p>In 2010, Markopolos&#39;s book on uncovering the Madoff fraud, <i><a href="https://en.wikipedia.org/wiki/No_One_Would_Listen">No One Would Listen: A True Financial Thriller</a></i>, was published.<sup><span>[</span>4<span>]</span></sup><sup><span>[</span>5<span>]</span></sup> Markopolos has criticized the SEC for failing to discover the Madoff fraud despite repeated tips, and for failing to investigate properly the larger companies it supervised.<sup><span>[</span>6<span>]</span></sup> </p><div><h2>Education and career</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>Markopolos attended <a href="https://en.wikipedia.org/wiki/Catholic_Church">Roman Catholic</a> schools, graduating from <a href="https://en.wikipedia.org/wiki/Cathedral_Preparatory_School">Cathedral Preparatory School</a> in <a href="https://en.wikipedia.org/wiki/Erie,_Pennsylvania">Erie, Pennsylvania</a>, in 1974.<sup><span>[</span>7<span>]</span></sup> He received an undergraduate degree in Business Administration from <a href="https://en.wikipedia.org/wiki/Loyola_University_Maryland">Loyola College in Maryland</a> in 1981, and a <a href="https://en.wikipedia.org/wiki/Master_of_Finance">Master of Science in Finance</a> from <a href="https://en.wikipedia.org/wiki/Boston_College">Boston College</a> in 1997.<sup><span>[</span>8<span>]</span></sup> He is a <a href="https://en.wikipedia.org/wiki/Chartered_Financial_Analyst">CFA charterholder</a>, and a <a href="https://en.wikipedia.org/wiki/Certified_Fraud_Examiner">Certified Fraud Examiner</a> (CFE).<sup><span>[</span>9<span>]</span></sup> </p><p>He began his career on <a href="https://en.wikipedia.org/wiki/Wall_Street">Wall Street</a> in 1987 as a broker with Makefield Securities, a small Erie-based brokerage owned by Barry C. Hixon.<sup><span>[</span>10<span>]</span></sup> In 1988, he obtained a job with Darien Capital Management in <a href="https://en.wikipedia.org/wiki/Darien,_Connecticut">Darien, Connecticut</a>, as an assistant <a href="https://en.wikipedia.org/wiki/Portfolio_manager">portfolio manager</a>. </p><p>From 1991 to 2004, he served as a portfolio manager at <a href="https://en.wikipedia.org/wiki/Boston">Boston</a>-based <a href="https://en.wikipedia.org/wiki/Option_(finance)">options</a> trading company Rampart Investment Management, ultimately becoming its <a href="https://en.wikipedia.org/wiki/Chief_investment_officer">chief investment officer</a>.<sup><span>[</span>11<span>]</span></sup> </p><p>He now works as a <a href="https://en.wikipedia.org/wiki/Forensic_accounting">forensic accounting</a> analyst for attorneys who sue companies under the <a href="https://en.wikipedia.org/wiki/False_Claims_Act">False Claims Act</a> and other laws, emphasizing tips that result in continuing investigations into medical billing, <a href="https://en.wikipedia.org/wiki/Internal_Revenue_Service">Internal Revenue Service</a>, and <a href="https://en.wikipedia.org/wiki/United_States_Department_of_Defense">United States Department of Defense</a> frauds, in which a &quot;whistleblower&quot; would be compensated.<sup><span>[</span>12<span>]</span></sup><sup><span>[</span>13<span>]</span></sup> </p><div><h2>Madoff investigation</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:BernardMadoff.jpg"></a><figcaption><a href="https://en.wikipedia.org/wiki/Bernie_Madoff">Bernard &quot;Bernie&quot; Madoff</a></figcaption></figure><p>During 1999, Markopolos learned that one of Rampart&#39;s frequent trading partners, <a href="https://en.wikipedia.org/wiki/Access_International_Advisors">Access International Advisors</a>, was dealing with a <a href="https://en.wikipedia.org/wiki/Hedge_fund">hedge fund</a> manager who consistently delivered net returns of 1% to 2% a month. </p><p>Frank Casey, one of Rampart&#39;s principals, met with Access CEO <a href="https://en.wikipedia.org/wiki/Thierry_Magon_de_La_Villehuchet">René-Thierry Magon de La Villehuchet</a>, and learned the manager was Bernie Madoff, who was operating a <a href="https://en.wikipedia.org/wiki/Wealth_management">wealth management</a> business in which his clients essentially gave him <i>carte blanche</i> to invest the money as he saw fit, in a set of securities.<sup><span>[</span>14<span>]</span></sup> Casey and Rampart&#39;s managing partner, Dave Fraley, asked Markopolos to try to design a product similar to Madoff&#39;s <a href="https://en.wikipedia.org/wiki/Collar_(finance)">split-strike conversion</a>, in hopes of luring away Access from investing in Madoff.<sup><span>[</span>4<span>]</span></sup> </p><p>When Markopolos obtained a copy of Madoff&#39;s <a href="https://en.wikipedia.org/wiki/Revenue_stream">revenue stream</a>, he spotted problems. The biggest red flag, he believed, was that the return stream rose steadily with only a few downticks – represented graphically by a nearly perfect 45-degree angle. According to Markopolos, anyone who understood the underlying math of the markets would have known that such a return stream &quot;simply doesn&#39;t exist in finance&quot;, since the markets were too volatile even in the most favorable conditions for this to be possible. Based on this and other factors, Markopolos eventually concluded that Madoff could not mathematically deliver his purported returns using the strategies he claimed to use. As he saw it, there were only two ways to explain the figures: Madoff was either running a Ponzi scheme (by paying established clients with newer clients&#39; money) or <a href="https://en.wikipedia.org/wiki/Front_running">front running</a> (buying stock for his own and the hedge fund&#39;s accounts, based on <a href="https://en.wikipedia.org/wiki/Insider_trading">insider knowledge</a> about market impacts from about-to-be-executed client orders at his company&#39;s unrelated <a href="https://en.wikipedia.org/wiki/Broker-dealer">broker-dealer</a> business).<sup><span>[</span>4<span>]</span></sup> </p><p>Markopolos later said that he knew within five minutes that Madoff&#39;s numbers didn&#39;t add up. He claimed it took him another four hours to uncover enough evidence that he could mathematically prove that they could have been obtained only by fraud.<sup><span>[</span>15<span>]</span></sup><sup><span>[</span>16<span>]</span></sup><sup><span>[</span>17<span>]</span></sup> </p><p>Despite this, Markopolos&#39;s bosses at Rampart asked Markopolos to deconstruct Madoff&#39;s strategy to see if he could replicate it. He could not simulate Madoff&#39;s returns, using information he had gathered about Madoff&#39;s trades in stocks and options. For instance, he discovered that for Madoff&#39;s strategy to work, he would have had to buy more options on the <a href="https://en.wikipedia.org/wiki/Chicago_Board_Options_Exchange">Chicago Board Options Exchange</a> than actually existed.<sup><span>[</span>15<span>]</span></sup> </p><p>His calculations of Madoff&#39;s trades revealed that there was almost no correlation between Madoff&#39;s stocks and the <a href="https://en.wikipedia.org/wiki/S%26P_100">S&amp;P 100</a>, as Madoff claimed. Markopolos also could find no evidence that the market was responding to any Madoff trades, even though by his estimate Madoff was managing as much as $6 billion, three times more than any known hedge fund at the time. Given that Madoff&#39;s supposed trades should have had a substantial ripple effect on broader markets, Markopolos suspected that Madoff was not even trading.<sup><span>[</span>4<span>]</span></sup> </p><p>With the help of two of his colleagues at Rampart, Casey and fellow <a href="https://en.wikipedia.org/wiki/Quantitative_analyst">quant</a> Neil Chelo, Markopolos continued to probe the Madoff operation. What they found concerned him enough that he filed a formal complaint with the Boston office of the SEC during the spring of 2000. However, the SEC took no action. Nonetheless, others in the investing world took Markopolos&#39;s findings seriously. In 2000, Joel Tillinghast of <a href="https://en.wikipedia.org/wiki/Fidelity_Investments">Fidelity Investments</a> dropped his plans to study Madoff&#39;s strategies after a meeting with Markopolos. Tillinghast wrote years later that his discussion with Markopolos convinced him that Madoff was almost certainly engaging in fraud; as he put it, &quot;nothing in Madoff&#39;s ostensible strategy made sense.&quot;<sup><span>[</span>18<span>]</span></sup> </p><p>Michael Ocrant, editor-in-chief of <i><a href="https://en.wikipedia.org/wiki/MARHedge">MARHedge</a></i>, joined the effort to publicize Madoff&#39;s questionable actions. Casey surprised Ocrant with information that Madoff, whom Ocrant only knew to be one of the largest <a href="https://en.wikipedia.org/wiki/Market_maker">market makers</a> on <a href="https://en.wikipedia.org/wiki/Nasdaq">NASDAQ</a> and one of the largest <a href="https://en.wikipedia.org/wiki/Broker">brokers</a> on the <a href="https://en.wikipedia.org/wiki/New_York_Stock_Exchange">New York Stock Exchange</a>, actually ran a secretive multi-billion dollar hedge fund, directly managing investors&#39; money.<sup><span>[</span>19<span>]</span></sup> Ocrant investigated and wrote an article, &quot;Madoff tops charts; skeptics ask how&quot;, published May 1, 2001, questioning Madoff&#39;s returns.<sup><span>[</span>19<span>]</span></sup> Within a week, <a href="https://en.wikipedia.org/wiki/Erin_Arvedlund">Erin Arvedlund</a> followed with an investigative article in <i><a href="https://en.wikipedia.org/wiki/Barron%27s_(newspaper)">Barron&#39;s</a></i>, further questioning Madoff&#39;s secrecy and results; despite the details in these scathing articles, they generated no action from the SEC, and did not scare off Madoff&#39;s existing investors.<sup><span>[</span>19<span>]</span></sup><sup><span>[</span>20<span>]</span></sup> </p><p>Markopolos sent a more detailed submission to the SEC a year later. He also offered to let the SEC send him to Madoff&#39;s headquarters undercover, obtain the trading tickets, and compare them with the <a href="https://en.wikipedia.org/wiki/Options_Price_Reporting_Authority">Options Price Reporting Authority</a> tape. By then, Markopolos was convinced that Madoff was not really trading. He believed that his trading tickets would not match the OPRA tape, which would have been hard proof that Madoff was a fraud. This submission also passed without action from the SEC.<sup><span>[</span>4<span>]</span></sup> </p><p>From the beginning, Markopolos believed that Madoff was most likely running a Ponzi scheme, given his voracious appetite for cash; a Ponzi scheme can last only as long as new money is flowing in to pay existing investors. His colleagues, Casey and Chelo, were more inclined to think that Madoff was front running. Casey and Chelo believed Madoff was already a very wealthy man, and on paper it made no sense for him essentially to steal billions of dollars that he didn&#39;t need. They suspected that it was more feasible for him to increase his returns on actual trades via front running. Markopolos was willing to accept that possibility, but thought it was unlikely since front-runners don&#39;t need the massive amount of new investor money that Madoff kept bringing in. Additionally, Markopolos believed that if Madoff was front running, he would have to siphon off money from his broker-dealer arm to pay the investors in his hedge fund. This would have resulted in the customers of his broker-dealer operation getting shortchanged — something that would not have gone unnoticed by Madoff&#39;s more sophisticated broker-dealer customers.<sup><span>[</span>4<span>]</span></sup> </p><p>Soon after his second submission, Markopolos traveled to Europe with Magon de La Villehuchet to help get investors for an alternative product to Madoff that he&#39;d developed for Rampart. While in Europe, Markopolos found that 14 different funds, at various firms, were invested with Madoff. Each manager believed that his fund was the only one from which Madoff was taking new money, a classic &quot;<a href="https://en.wikipedia.org/wiki/To_rob_Peter_to_pay_Paul">robbing Peter to pay Paul</a>&quot; scenario. When Markopolos heard this, he was convinced that Madoff&#39;s wealth-management business was a Ponzi scheme. He warned Magon de la Villehuchet, but Magon de la Villehuchet refused to disengage from Madoff. Magon de La Villehuchet committed suicide soon after Madoff&#39;s scheme collapsed, having lost $1.5 billion of his own and clients&#39; money.<sup><span>[</span>4<span>]</span></sup><sup><span>[</span>21<span>]</span></sup><sup><span>[</span>22<span>]</span></sup> </p><p>Markopolos persevered, even though he felt that it created a considerable risk to his own safety. He learned during his European tour that a large number of funds invested with Madoff operated <a href="https://en.wikipedia.org/wiki/Offshore_fund">offshore</a>. To his mind, this was evidence that the <a href="https://en.wikipedia.org/wiki/Russian_mafia">Russian mafia</a> and Latin-American drug cartels were invested with Madoff, and might want to silence anyone who threatened the viability of the hedge funds.<sup><span>[</span>4<span>]</span></sup><sup><span>[</span>23<span>]</span></sup><sup><span>[</span>24<span>]</span></sup> </p><p>On December 17, 2002, Markopolos came up with a plan to deliver an investigative file anonymously to an aide of then <a href="https://en.wikipedia.org/wiki/Attorney_General_of_New_York">Attorney General of New York</a> <a href="https://en.wikipedia.org/wiki/Eliot_Spitzer">Eliot Spitzer</a> as Spitzer delivered a speech at the <a href="https://en.wikipedia.org/wiki/John_F._Kennedy_Presidential_Library_and_Museum">John F. Kennedy Library</a> in Boston. He put on a pair of white gloves to prevent leaving fingerprints, and wore an oversize coat.<sup><span>[</span>23<span>]</span></sup><sup><span>[</span>25<span>]</span></sup><sup><span>[</span>26<span>]</span></sup><sup><span>[</span>27<span>]</span></sup><sup><span>[</span>28<span>]</span></sup> </p><p>Even after leaving Rampart in 2004, frustrated that he was in a business that had to compete with cheats and lawbreakers,<sup><span>[</span>19<span>]</span></sup> Markopolos continued to be driven by the intellectual challenge of solving the problem, and the ongoing encouragement from Boston SEC staffer Ed Manion. The culmination of Markopolos&#39;s analysis was a 21-page memo sent during November 2005 to SEC regulators, entitled &quot;The World&#39;s Largest Hedge Fund is a Fraud&quot;. It outlined his suspicions in more detail and invited officials to check his theories. He outlined 30 red flags that he believed proved Madoff&#39;s returns could not be legitimate. His analysis was based on more than 14 years of Madoff return numbers, during which time Madoff reported only four losing months, an implausible scenario that Markopolos said could be achieved only by fraud.<sup><span>[</span>12<span>]</span></sup><sup><span>[</span>29<span>]</span></sup><sup><span>[</span>30<span>]</span></sup> In the document Markopolos states: </p><blockquote><p> Bernie Madoff is running the world&#39;s largest unregistered hedge fund. He&#39;s organized this business as [a] hedge fund of funds privately labeling their own hedge funds, which Bernie Madoff secretly runs for them using a split-strike conversion strategy, getting paid only trading commissions, which are not disclosed.</p></blockquote><p>Although Madoff&#39;s scheme did not collapse until 2008, Markopolos believed that Madoff was on the brink of insolvency as early as the summer of 2005, when Casey found out that at least two banks were no longer lending money to their clients to invest with Madoff. This prompted Madoff to seek loans from banks. In June 2008 – six months before Madoff&#39;s scheme imploded – Markopolos&#39;s team uncovered evidence that Madoff was accepting <a href="https://en.wikipedia.org/wiki/Leverage_(finance)">leveraged money</a>. In his book, Markopolos wrote that this was a sign Madoff was running out of cash and needed to increase his intake of new funds to keep the scheme going.<sup><span>[</span>4<span>]</span></sup> </p><figure><a href="https://en.wikipedia.org/wiki/File:Thierry_de_la_villehuchet.png"></a><figcaption><a href="https://en.wikipedia.org/wiki/Thierry_Magon_de_La_Villehuchet">Thierry Magon de La Villehuchet</a> committed suicide three days before Christmas in 2008, shortly after Madoff was arrested by the <a href="https://en.wikipedia.org/wiki/Federal_Bureau_of_Investigation">FBI</a></figcaption></figure><p>On June 3, 2009, Markopolos told a conference at <a href="https://en.wikipedia.org/wiki/Boston_College">Boston College</a>, his alma mater, that he believed Madoff personally kept less than 1 percent of the $65 billion reported stolen, and would probably lose what remained of his portion to <a href="https://en.wikipedia.org/wiki/Money_laundering">money launderers</a>. Markopolos estimated that $35 billion to $55 billion of the money Madoff claimed to have stolen never really existed, but were simply fictional profits he reported to his clients. Markopolos believed that Madoff&#39;s customers lost $10 billion to $35 billion, most of which went to early investors. &quot;Madoff will wind up in a special prison designed as much to keep the crook&#39;s victims out as Madoff in. He&#39;s a guy who can&#39;t afford not to be in prison,&quot; he said.<sup><span>[</span>31<span>]</span></sup> </p><div><h3>Congressional testimony</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Markopolos harshly criticized the SEC for ignoring his warnings about Madoff. &quot;Nothing was done. There was an abject failure by the regulatory agencies we entrust as our watchdog,&quot; he said in 65 pages of prepared testimony. He said that his original 2000 complaint gave the SEC enough evidence to stop Madoff when he was supposedly managing as little as $3 billion.<sup><span>[</span>16<span>]</span></sup><sup><span>[</span>32<span>]</span></sup><sup><span>[</span>34<span>]</span></sup> </p><p>Describing Madoff as &quot;one of the most powerful men on Wall Street&quot;, Markopolos stated that there was &quot;great danger&quot; in investigating him: &quot;My team and I surmised that if Mr. Madoff gained knowledge of our activities, he may feel threatened enough to seek to stifle us.&quot; He testified that he feared for his, as well as his family&#39;s safety, until after Madoff&#39;s arrest, when the SEC finally acknowledged that it had received &quot;credible evidence&quot; of Madoff&#39;s Ponzi scheme years before.<sup><span>[</span>32<span>]</span></sup> He said that Madoff&#39;s &quot;math never made sense&quot;, that his &quot;return stream never resembled any known <a href="https://en.wikipedia.org/wiki/Financial_instrument">financial instrument</a> or strategy&quot;, and that Madoff wasn&#39;t making the volumes of trades he claimed. According to Markopolos, the best warning about Madoff came during his initial analysis of 87 months (a little more than seven years) of Madoff trades. During that time, Madoff reported only three losing months. By comparison, the <a href="https://en.wikipedia.org/wiki/S%26P_500_Index">S&amp;P 500 Index</a> reported 28 losing months during the same period. He likened Madoff&#39;s purported returns to a baseball player batting .966 for the season and &quot;no one suspecting a cheat&quot;.<sup><span>[</span>34<span>]</span></sup> </p><p>Markopolos had originally concealed his identity from SEC regulators during May 1999,<sup><span>[</span>35<span>]</span></sup> although he did meet face-to-face with SEC officials in Boston during 2000 and 2001.<sup><span>[</span>16<span>]</span></sup><sup><span>[</span>36<span>]</span></sup> After the SEC did not respond, Markopolos was fearful of taking his complaints to the industry&#39;s self-regulatory authority, the National Association of Securities Dealers (since succeeded by the <a href="https://en.wikipedia.org/wiki/Financial_Industry_Regulatory_Authority">Financial Industry Regulatory Authority</a> (FINRA)). </p><p>He not only feared the power of Madoff&#39;s brother, Peter, had in that organization (he is a former Vice Chairman), but also feared that Madoff might have had associations with Russian and South American organized crime.<sup><span>[</span>34<span>]</span></sup><sup><span>[</span>35<span>]</span></sup> Markopolos believed the <a href="https://en.wikipedia.org/wiki/Federal_Bureau_of_Investigation">FBI</a> would reject his allegations without the SEC staff&#39;s endorsement.<sup><span>[</span>35<span>]</span></sup> He believed that only a few SEC officials, including Manion and SEC Boston branch chief Mike Garrity, understood Madoff&#39;s operation well enough to detect the fraud. Markopolos met with Garrity during 2005, and said that while Garrity realized almost immediately that Madoff was violating the law, he could not take any action because Madoff was not based in New England.<sup><span>[</span>34<span>]</span></sup> </p><p>Markopolos later wrote that a few days after that meeting, Garrity called him and said his preliminary investigation revealed serious irregularities in the Madoff operation, and that he would have had inspection teams &quot;tearing the place apart&quot; if Madoff had been based in New England. However, since the Boston office&#39;s jurisdiction extended only as far as <a href="https://en.wikipedia.org/wiki/Greenwich,_Connecticut">Greenwich, Connecticut</a>; Garrity had no choice but to pass it down to the New York office.<sup><span>[</span>4<span>]</span></sup> &quot;My experiences with other SEC officials proved to be a systemic disappointment and led me to conclude that the SEC securities lawyers, if only through their investigative ineptitude and financial illiteracy, colluded to maintain large frauds such as the one to which Madoff later confessed.&quot;<sup><span>[</span>37<span>]</span></sup> </p><p>He also added that during 2005 it was Meaghan Cheung, the branch chief of the SEC&#39;s New York office, to whom he gave his 21-page report alleging that Madoff was paying old investors with money from fresh recruits. &quot;Ms. Cheung never expressed even the slightest interest in asking me questions&quot;, Markopolos said, claiming she was too concerned with Markopolos mentioning the possibility of a reward and the fact that he was a competitor of Madoff. Cheung approved an internal memo during November 2007 to close an SEC investigation of Madoff without bringing any claim. Subsequently, she left the agency.<sup><span>[</span>37<span>]</span></sup> He testified he gave details about the case during 2005 to <a href="https://en.wikipedia.org/wiki/John_Wilke">John Wilke</a>, an investigative reporter for <i><a href="https://en.wikipedia.org/wiki/The_Wall_Street_Journal">The Wall Street Journal</a></i>, but that it was never pursued.<sup><span>[</span>38<span>]</span></sup><sup><span>[</span>39<span>]</span></sup> Markopolos testified he (anonymously) sent a package of documents concerning Madoff to former New York Attorney General <a href="https://en.wikipedia.org/wiki/Eliot_Spitzer">Eliot Spitzer</a>, who had successfully prosecuted a number of securities fraud cases, but that Spitzer apparently did not act, either. Spitzer&#39;s family firm had invested in Madoff&#39;s business.<sup><span>[</span>40<span>]</span></sup> </p><p>&quot;Government has coddled, accepted, and ignored <a href="https://en.wikipedia.org/wiki/White-collar_crime">white-collar crime</a> for too long,&quot; he testified. &quot;It is time the nation woke up and realized that it&#39;s not the armed robbers or drug dealers who cause the most economic harm, it&#39;s the white collar criminals living in the most expensive homes who have the most impressive resumes who harm us the most. They steal our pensions, bankrupt our companies, and destroy thousands of jobs, ruining countless lives.&quot; He testified to Rep. <a href="https://en.wikipedia.org/wiki/Gary_Ackerman">Gary Ackerman</a> (D-NY) that he had never been compensated for his efforts. &quot;I did it for our flag, for patriotism.&quot;<sup><span>[</span>38<span>]</span></sup> Markopolos presented recommendations to improve the SEC&#39;s operations, which included mandatory department standards: good ethics, full transparency, full disclosure, and fair dealing for all. The SEC must establish a unit to accept &quot;whistleblower&quot; tips, and move its activity closer to financial centers away from <a href="https://en.wikipedia.org/wiki/Washington,_D.C.">Washington, D.C.</a><sup><span>[</span>13<span>]</span></sup> </p><p>His testimony included a reference to another $1 billion Ponzi scheme, which he shared the next day with SEC Inspector General <a href="https://en.wikipedia.org/wiki/H._David_Kotz">H. David Kotz</a>, who gave the tips to SEC Chairman <a href="https://en.wikipedia.org/wiki/Mary_Schapiro">Mary Schapiro</a>.<sup><span>[</span>41<span>]</span></sup><sup><span>[</span>42<span>]</span></sup> He disclosed information regarding a dozen as-yet-unknown foreign Madoff <a href="https://en.wikipedia.org/wiki/Feeder_fund">feeder funds</a>, &quot;hiding in the weeds&quot; in Europe, the victims of which likely included <a href="https://en.wikipedia.org/wiki/Russian_mafia">Russian mafia</a> and <a href="https://en.wikipedia.org/wiki/Drug_cartel">drug cartels</a>, &quot;dirty money&quot; investors.<sup><span>[</span>42<span>]</span></sup> Markopolos remarked that European royal families had also lost assets.<sup><span>[</span>37<span>]</span></sup> </p><p>Because of concerns of improper conduct by Inspector General Kotz in the Madoff investigation, Inspector General <a href="https://en.wikipedia.org/wiki/David_C._Williams_(inspector_general)">David C. Williams</a> of the <a href="https://en.wikipedia.org/wiki/United_States_Postal_Service">United States Postal Service</a> was brought in to conduct an independent outside review.<sup><span>[</span>43<span>]</span></sup> The Williams Report questioned Kotz&#39;s work on the Madoff investigation, because Kotz was a &quot;very good friend&quot; with Markopolos.<sup><span>[</span>44<span>]</span></sup><sup><span>[</span>45<span>]</span></sup> Investigators were not able to determine when Kotz and Markopolos became friends. A violation of the ethics rule would have taken place if the friendship had been concurrent with Kotz&#39;s investigation of Madoff.<sup><span>[</span>44<span>]</span></sup><sup><span>[</span>46<span>]</span></sup> </p><div><h3>Other statements</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>In his interview with <a href="https://en.wikipedia.org/wiki/Steve_Kroft">Steve Kroft</a> of <i>60 Minutes</i>, Markopolos said the biggest warning he noticed during his initial 1999 analysis of Madoff was that he reported losing months only four percent of the time. To Markopolos&#39;s mind, no one could possibly be that good, given the volatility of the markets. &quot;As we know, markets go up and down, and his only went up,&quot; he said. Markopolos noted that during his tenure at Rampart, he traded with some of the biggest derivatives companies in the world, and none of them dealt with Madoff, because they didn&#39;t think his numbers were real. He admitted that he had some financial incentive to eliminate Madoff, as the two competed against each other from 2000 to 2004. However, he said, he felt compelled to pursue it, because &quot;when someone&#39;s competing on your playing field, who&#39;s a dirty player, you want him tossed off the field.&quot; He assailed the SEC once again for ignoring his warnings, saying that the only reason Madoff was caught was that he ultimately collapsed under the weight of his own lies.<sup><span>[</span>15<span>]</span></sup> </p><p>Markopolos expanded on his criticism of the SEC in <i>No One Would Listen</i>. He claimed that SEC regulators don&#39;t have nearly enough expertise to understand the various products offered in the modern market; as he put it, the SEC was still &quot;panning by hand&quot;. He also believed that the SEC&#39;s enforcement staff didn&#39;t take his complaints seriously, because they were expecting legal proof Madoff was a fraud, not the mathematical evidence he provided. To his mind, the investigators didn&#39;t understand that mathematical proof was stronger evidence than legal proof, because &quot;with a math problem, there is only one correct answer.&quot;<sup><span>[</span>4<span>]</span></sup> </p><p>As a result of the Madoff scandal, the SEC&#39;s chairman <a href="https://en.wikipedia.org/wiki/Christopher_Cox">Christopher Cox</a> stated that an investigation will delve into &quot;all staff contact and relationships with the Madoff family and firm, and their impact, if any, on decisions by staff regarding the firm&quot;.<sup><span>[</span>47<span>]</span></sup> </p><div><h2>General Electric fraud allegation</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>In 2019, Markopolos published a report alleging fraudulent accounting within <a href="https://en.wikipedia.org/wiki/General_Electric">General Electric</a>. The report caused the company&#39;s stock to drop 10.3% on August 15, 2019.<sup><span>[</span>48<span>]</span></sup><sup><span>[</span>49<span>]</span></sup> The stock closed at $9.03 prior to the report, and then closed at $8.01 the following day when the report was published. Markopolos claimed GE was a fraud &quot;bigger than Enron&quot;.<sup><span>[</span>50<span>]</span></sup> Subsequently, GE called the report &quot;meritless&quot; and an attempt at &quot;<a href="https://en.wikipedia.org/wiki/Market_manipulation">market manipulation</a>&quot; by Markopolos; Wall Street analysts shrugged off the report; and the regulators called the report &quot;fairly simplistic&quot;.<sup><span>[</span>51<span>]</span></sup> A Financial Times article labeled the report &quot;some ill-thought out twaddle disguised as deep financial analysis&quot;.<sup><span>[</span>52<span>]</span></sup> The Markopolos website (www.gefraud.com) alleging this giant fraud disappeared after criticism about the quality of his analyses.<sup><span>[</span>53<span>]</span></sup><sup><span>[</span>54<span>]</span></sup> The full report is still available, however, in internet archives.<sup><span>[</span>55<span>]</span></sup> Three months after the 175 page Markopolos report, GE stock had risen almost 44% to close at $11.52 on November 15, outperforming the general stock market.<sup><span>[</span>56<span>]</span></sup> </p><p>According to Bloomberg in November 2021, &quot;For GE, the never-ending storm may pass, but at the moment, its future looks cloudy.&quot;<sup><span>[</span>57<span>]</span></sup> However, according to Bloomberg in April 2024, &quot;GE&#39;s insurance liability [the focus of the Markopolos report] &#39;doesn&#39;t really matter.<span>&#39;</span>&quot;<sup><span>[</span>58<span>]</span></sup> </p><div><h2>Bridgewater Associates</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>Markopolos investigated the <a href="https://en.wikipedia.org/wiki/Hedge_fund">hedge fund</a>, <a href="https://en.wikipedia.org/wiki/Bridgewater_Associates">Bridgewater Associates, LP</a>.<sup><span>[</span>59<span>]</span></sup><sup><span>[</span>60<span>]</span></sup> </p><div><h2>Personal life</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>Markopolos is an <a href="https://en.wikipedia.org/wiki/Greek-Americans">American of Greek descent</a> and is the eldest of three children of Georgia and Louis Markopolos, Greek-American<sup><span>[</span>61<span>]</span></sup> restaurateurs. </p><p>His father and two uncles once owned 12 <a href="https://en.wikipedia.org/wiki/Arthur_Treacher%27s">Arthur Treacher&#39;s Fish and Chips restaurants</a> in Maryland and Delaware. His younger brother, Louie, once managed the trading office for a New Jersey brokerage company. He has a sister, Melissa.<sup><span>[</span>4<span>]</span></sup> </p><p>He and his wife Faith, who works in the financial industry for an investment company conducting due diligence of portfolio managers,<sup><span>[</span>4<span>]</span></sup> have three sons,<sup><span>[</span>62<span>]</span></sup> two of whom ⁠ – Harry &quot;Hare Bear&quot; Markopolos and Louis &quot;Big Lou&quot; Markopolos ⁠ – are twins. Louis is following in his father&#39;s footsteps to become a forensic accountant. He is currently attending Bentley University as an accounting major.<sup><span>[</span>4<span>]</span></sup> Harry served in the United States Army Reserve and obtained the rank of Major and held the branch of Civil Affairs.<sup><span>[</span>63<span>]</span></sup> </p><div><h2>Bibliography</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>Markopolos&#39;s account of the Madoff scandal was published in a book titled <i><a href="https://en.wikipedia.org/wiki/No_One_Would_Listen">No One Would Listen: A True Financial Thriller</a>.</i> The book was released in 2010.<sup><span>[</span>64<span>]</span></sup> </p><div><h2>Filmography</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p><i><a href="https://en.wikipedia.org/wiki/Chasing_Madoff">Chasing Madoff</a></i>, a documentary film based on the book, was released in 2011.<sup><span>[</span>65<span>]</span></sup> </p><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span><cite>Tofel, Richard J. (March 8, 2010). <a href="https://www.wsj.com/articles/SB10001424052748703936804575108180543849168">&quot;Shadowing a Swindler; Early on, he figured out what Bernard Madoff was up to&quot;</a>. <i>Wall Street Journal Online</i><span>. Retrieved <span>January 4,</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Douglas, Craig M. (December 16, 2008). <a href="http://www.bizjournals.com/boston/stories/2008/12/15/daily23.html">&quot;Madoff had early skeptic in Boston gumshoe&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Boston_Business_Journal">Boston Business Journal</a></i><span>. Retrieved <span>December 22,</span> 2008</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Wagner, Daniel; Pete Yost (December 21, 2008). <a href="https://www.google.com/hostednews/ap/article/ALeqM5jdzRd-nOH0G-5xuw1FsC078lIhCQD9579EB80">&quot;SEC has been slow to react to fraud claims&quot;</a>. Associated Press<span>. Retrieved <span>December 22,</span> 2008</span>.</cite><sup><span>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Link_rot"><span>dead link</span></a></i>]</span></sup></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup> <sup><i><b>e</b></i></sup> <sup><i><b>f</b></i></sup> <sup><i><b>g</b></i></sup> <sup><i><b>h</b></i></sup> <sup><i><b>i</b></i></sup> <sup><i><b>j</b></i></sup> <sup><i><b>k</b></i></sup> <sup><i><b>l</b></i></sup> <sup><i><b>m</b></i></sup> <sup><i><b>n</b></i></sup></span> <span><cite>Markopolos, Harry (2010). <i><a href="https://en.wikipedia.org/wiki/No_One_Would_Listen">No One Would Listen: A True Financial Thriller</a></i>. <a href="https://en.wikipedia.org/wiki/Hoboken,_New_Jersey">Hoboken, New Jersey</a>: <a href="https://en.wikipedia.org/wiki/Wiley_(publisher)">John Wiley &amp; Sons</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-55373-2"><bdi>978-0-470-55373-2</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Bandler, James (February 25, 2010). <a href="https://money.cnn.com/2010/02/25/news/companies/harry_markopolos_full_interview.fortune/index.htm">&quot;Harry Markopolos: The man who hunted Madoff&quot;</a>. <i>Archive.fortune.com</i><span>. Retrieved <span>March 15,</span> 2016</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Levin, Bess (April 13, 2010). <a href="https://observer.com/2010/04/the-madoff-hunter">&quot;The Madoff Hunter&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/The_New_York_Observer">The New York Observer</a></i><span>. Retrieved <span>April 30,</span> 2010</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Erwin, Erica (December 20, 2008). <a href="http://www.goerie.com/apps/pbcs.dll/article?AID=2008312209970">&quot;Erie man blew whistle on Madoff&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Erie_Times-News">Erie Times-News</a></i><span>. Retrieved <span>December 22,</span> 2008</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Lindsay, Jay (December 20, 2008). <a href="https://web.archive.org/web/20090722060500/http://www.deseretnews.com/article/1,5143,705271831,00.html">&quot;Investor saw inside Madoff scam&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Deseret_News">Deseret News</a></i>. <a href="https://en.wikipedia.org/wiki/Associated_Press">Associated Press</a>. Archived from <a href="http://www.deseretnews.com/article/1,5143,705271831,00.html">the original</a> on July 22, 2009<span>. Retrieved <span>December 22,</span> 2008</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.businesswire.com/news/home/20081218006062/en">&quot;Certified Fraud Examiner Markopolos is Madoff Whistleblower&quot;</a> (Press release). <a href="https://en.wikipedia.org/wiki/Association_of_Certified_Fraud_Examiners">Association of Certified Fraud Examiners</a>. December 18, 2008<span>. Retrieved <span>December 22,</span> 2008</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://pennsylvaniadb.com/company/809330/makefield-securities-corporation">&quot;Makefield Securities Corporation – Washington Crossing – Company Information&quot;</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://krannert.purdue.edu/events/ethics/speakers/markopolos.php">&quot;Harry Markopolos – Purdue Krannert&quot;</a>. <i>krannert.purdue.edu</i><span>. Retrieved <span>January 23,</span> 2021</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Kerber, Ross (January 8, 2009). <a href="http://www.boston.com/business/articles/2009/01/08/the_whistleblower/?page=3">&quot;The whistleblower&quot;</a>. <i>The Boston Globe</i>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Zuckerman, Gregory; Gauthier-Villars, David (February 3, 2009). <a href="https://www.wsj.com/articles/SB123361899636241467?mod=googlenews_wsj">&quot;A Lonely Lament From a Whistle-Blower&quot;</a>. <i>Wall Street Journal</i><span>. Retrieved <span>February 3,</span> 2009</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://fortune.com/2011/05/10/how-they-failed-to-catch-madoff">&quot;How they failed to catch Madoff&quot;</a>. <i>Fortune.com</i>. May 10, 2011<span>. Retrieved <span>March 15,</span> 2016</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup></span> <span><cite><a href="https://www.cbsnews.com/news/the-man-who-figured-out-madoffs-scheme-27-02-2009/">&quot;The Man Who Figured Out Madoff&#39;s Scheme&quot;</a>. <i>CBS News</i>. February 27, 2009.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>Markopolos, Harry (February 4, 2009). <a href="https://www.wsj.com/public/resources/documents/MarkopolosTestimony20090203.pdf">&quot;Markopolos Written Testimony (February 4, 2009)&quot;</a> <span>(PDF)</span>. <i>The Wall Street Journal</i><span>. Retrieved <span>February 4,</span> 2009</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.nbcnews.com/id/wbna28310980">&quot;Madoff whistleblower went unheeded for years&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/NBC_News">NBC News</a></i>. December 19, 2008<span>. Retrieved <span>March 15,</span> 2016</span>.</cite></span> </li> <li><span><b>^</b></span> <span>Joel Tillinghast (2017). Big Money Thinks Small: Biases, Blind Spots and Smarter Investing. Columbia Business School Publishing, pp. 123–124</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup></span> <span><cite>Prosserman, Jeff (Director, Producer); Markopolos, Harry (Book) (August 26, 2011). <i><a href="https://en.wikipedia.org/wiki/Chasing_Madoff">Chasing Madoff</a></i> (Documentary). United States.</cite><span><code class="cs1-code">{{cite AV media}}</code>: CS1 maint: multiple names: authors list (<a href="https://en.wikipedia.org/wiki/Category:CS1_maint:_multiple_names:_authors_list">link</a>)</span></span> </li> <li><span><b>^</b></span> <span><cite>Arvedlund, Erin E. (May 7, 2001). <a href="http://online.barrons.com/article/SB989019667829349012.html">&quot;Don&#39;t Ask, Don&#39;t Tell: Bernie Madoff Attracts Skeptics in 2001&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Barron%27s_(newspaper)">Barron&#39;s</a></i><span>. Retrieved <span>August 30,</span> 2018</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Berenson, Alex; Saltmarsh, Matthew (January 2, 2009). <a href="https://www.nytimes.com/2009/01/02/business/02madoff.html">&quot;Madoff Investor&#39;s Suicide Leaves Questions&quot;</a>. <i>The New York Times</i><span>. Retrieved <span>June 22,</span> 2021</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Gendar, Alison; Feiden, Douglas (December 26, 2008). <a href="https://web.archive.org/web/20081226034135/https://www.nydailynews.com/news/2008/12/23/2008-12-23_hedge_fund_founder_thierry_de_la_villehu.html">&quot;Hedge fund founder Thierry de la Villehuchet kills self after losing $1B in Madoff scandal&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/New_York_Daily_News">New York Daily News</a></i>. Archived from <a href="https://www.nydailynews.com/news/2008/12/23/2008-12-23_hedge_fund_founder_thierry_de_la_villehu.html">the original</a> on December 26, 2008<span>. 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Retrieved <span>May 29,</span> 2013</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Markopolos, Harry (November 7, 2005). <a href="https://math.nyu.edu/faculty/avellane/madoffmarkopoulos.pdf">&quot;The World&#39;s Largest Hedge Fund is a Fraud&quot;</a> <span>(PDF)</span><span>. Retrieved <span>December 27,</span> 2020</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Fox, Justin (December 18, 2008). <a href="https://business.time.com/2008/12/18/harry-markopolos-really-did-have-the-goods-on-bernie-madoff/?xid=rss-topstories">&quot;Harry Markopolos really did have the goods on Bernie Madoff&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Time_(magazine)">Time</a></i><span>. Retrieved <span>December 22,</span> 2008</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.bostonherald.com/business/general/view.bg?articleid=1176905&amp;srvc=business&amp;position=4">&quot;Business &amp; Markets&quot;</a>. <i>Boston Herald</i><span>. Retrieved <span>February 9,</span> 2013</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite><a href="https://dealbook.blogs.nytimes.com/2009/02/03/madoff-whistleblower-assails-sec-for-ignoring-him">&quot;Madoff Whistleblower Assails SEC for Ignoring Him&quot;</a>. <i>The New York Times</i>. February 3, 2009<span>. Retrieved <span>February 3,</span> 2009</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.bostonherald.com/business/general/view/2009_02_03_Man_who_warned_about_Bernard_Madoff_to_testify/srvc=business&amp;position=also">&quot;Man who warned about Bernard Madoff to testify&quot;</a>. <i>Boston Herald</i>. February 3, 2009<span>. Retrieved <span>February 3,</span> 2009</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup></span> <span><cite>Chew, Robert (February 4, 2009). <a href="https://web.archive.org/web/20090207034751/http://www.time.com/time/business/article/0,8599,1877181,00.html">&quot;A Madoff Whistleblower Tells His Story&quot;</a>. <i>Time</i>. Archived from <a href="http://www.time.com/time/business/article/0,8599,1877181,00.html">the original</a> on February 7, 2009<span>. Retrieved <span>February 4,</span> 2009</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>Henriques, Diana (February 3, 2009). <a href="https://www.nytimes.com/2009/02/04/business/04madoff.html">&quot;Madoff Witness Tells of Fear for Safety&quot;</a>. <i>New York Times</i><span>. Retrieved <span>February 3,</span> 2009</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Scannell, Kara (January 5, 2009). <a href="https://www.wsj.com/articles/SB123111743915052731?mod=googlenews_wsj">&quot;Madoff Chasers Dug for Years, to No Avail&quot;</a>. <i>The Wall Street Journal</i><span>. Retrieved <span>February 3,</span> 2009</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite><a href="https://web.archive.org/web/20090122224028/http://www.bloomberg.com/apps/news?pid=20601103">&quot;Madoff Tipster Markopolos Cites SEC&#39;s &#39;Ineptitude&#39; (Update 3) by Jesse Westbrook, David Scheer and Mark Pittman&quot;</a>. <i>Bloomberg</i>. February 4, 2009. Archived from <a href="https://www.bloomberg.com/apps/news?pid=20601103&amp;sid=axvJfch6PDjs&amp;">the original</a> on January 22, 2009<span>. Retrieved <span>February 4,</span> 2009</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite> <a href="http://www.c-spanarchives.org/library/includes/templates/library/flash_popup.php?pID=283836-1&amp;clipStart=&amp;clipStop=">http://www.c-spanarchives.org/library/includes/templates/library/flash_popup.php?pID=283836-1&amp;clipStart=&amp;clipStop=</a><span>. Retrieved <span>February 4,</span> 2009</span>.</cite> <span><code class="cs1-code">{{cite web}}</code>: </span><span>Missing or empty <code class="cs1-code">|title=</code> (<a href="https://en.wikipedia.org/wiki/Help:CS1_errors#citation_missing_title">help</a>)</span><sup><span>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Link_rot"><span>dead link</span></a></i>]</span></sup></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.jewishjournal.com/swindlerslist/item/wall_street_journal_missed_madoff_fraud_three_years_ago_20090204">&quot;Wall Street Journal missed Madoff fraud three years ago&quot;</a>. <i>Jewish Journal (Swindler&#39;s List blog)</i>. February 4, 2009<span>. Retrieved <span>February 4,</span> 2009</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Conaway, Laura (December 16, 2008). <a href="https://www.npr.org/sections/money/2008/12/eliot_spitzer_lost_too.html">&quot;Eliot Spitzer Lost, Too&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/NPR">NPR</a></i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Younglai, Rachelle (February 5, 2009). <a href="https://www.reuters.com/article/privateEquity/idUSN0540255820090205">&quot;Madoff whistleblower gives fraud tips to SEC&quot;</a>. <i>Reuters</i>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Henriques, Diana (February 4, 2009). <a href="https://www.nytimes.com/2009/02/05/business/05madoff.html">&quot;Madoff Witness Talks of Other Possible Ponzi Cases&quot;</a>. <i>New York Times</i><span>. Retrieved <span>February 4,</span> 2009</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Schmidt, Robert; Gallu, Joshua (January 25, 2013). <a href="https://www.bloomberg.com/news/articles/2013-01-25/sec-said-to-back-hire-of-u-s-capitol-police-inspector-general">&quot;SEC Said to Back Hire of U.S. Capitol Police Inspector General&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Bloomberg_L.P.">Bloomberg L.P.</a></i><span> Retrieved <span>October 15,</span> 2015</span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Schmidt, Robert; Joshua Gallu (October 26, 2012). <a href="https://www.bloomberg.com/news/2012-10-06/former-sec-watchdog-kotz-violated-ethics-rules-review-finds-1-.html">&quot;Former SEC Watchdog Kotz Violated Ethics Rules, Review Finds&quot;</a>. Bloomberg<span>. Retrieved <span>February 10,</span> 2013</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="http://www.huffingtonpost.com/2012/10/05/david-kotz-conflict-of-interest_n_1944205.html">&quot;David Kotz, Ex-SEC Inspector General, May Have Had Conflicts Of Interest&quot;</a>. Huffington Post. October 5, 2012<span>. Retrieved <span>February 10,</span> 2013</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Sarah N. Lynch (November 15, 2012). <a href="http://www.huffingtonpost.com/2012/11/15/davir-weber-lawsuit_n_2140452.html">&quot;David Weber Lawsuit: Ex-SEC Investigator Accused Of Wanting To Carry A Gun At Work, Suing For $20 Million&quot;</a>. Huffingtonpost.com<span>. Retrieved <span>February 10,</span> 2013</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Serchuk, David (December 20, 2008). <a href="https://www.forbes.com/intelligentinvesting/2008/12/20/intelligent-investing-madoff-sec-fraud-panelDec22.html?partner=contextstory">&quot;Love, Madoff And The SEC&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Forbes">Forbes</a></i><span>. Retrieved <span>December 24,</span> 2008</span>.</cite><span><code class="cs1-code">{{cite news}}</code>: CS1 maint: deprecated archival service (<a href="https://en.wikipedia.org/wiki/Category:CS1_maint:_deprecated_archival_service">link</a>)</span></span> </li> <li><span><b>^</b></span> <span><cite>Thomas Gryta; Mark Maremont (August 15, 2019). <a href="https://www.wsj.com/articles/ge-is-new-target-of-madoff-whistleblower-11565866617">&quot;GE Is New Target of Madoff Whistleblower&quot;</a>. <i>Wall Street Journal</i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Rushe, Dominic (August 15, 2019). <a href="https://www.theguardian.com/business/2019/aug/15/general-electric-stock-harry-markopolos-fraud-claims">&quot;General Electric shares tank following accusation of &#39;bigger fraud than Enron&#39;&quot;</a>. Business. <i><a href="https://en.wikipedia.org/wiki/The_Guardian">The Guardian</a></i>. New York<span>. Retrieved <span>August 15,</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Marte, Jonnelle. <a href="https://www.washingtonpost.com/business/2019/08/15/general-electric-shares-fall-after-new-report-alleges-bigger-fraud-than-enron/">&quot;General Electric shares plunge after report alleges it&#39;s a &#39;bigger fraud than Enron&#39;&quot;</a>. <i>Washington Post</i><span>. Retrieved <span>November 16,</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Root, Al. <a href="https://www.barrons.com/articles/wall-street-comfortable-with-ges-accounting-shrugs-off-markopolos-report-51567525632">&quot;Wall Street Is Shrugging Off Allegations of GE Accounting Fraud&quot;</a>. <i>www.barrons.com</i><span>. Retrieved <span>November 16,</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://ftalphaville.ft.com/2019/10/30/1572466417000/Missing--the-GE-short-report/">&quot;Missing: The GE short report&quot;</a>. <i>Financial Times</i>. October 30, 2019<span>. Retrieved <span>November 16,</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Root, Al. <a href="https://www.barrons.com/articles/website-alleging-ge-accounting-fraud-disappears-51569540660">&quot;The Website Alleging GE Accounting Fraud Just Disappeared&quot;</a>. <i>www.barrons.com</i><span>. Retrieved <span>November 16,</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Tully, Shawn (October 3, 2019). <a href="https://fortune.com/2019/10/03/ge-accounting-markopolos-madoff/">&quot;How the Man Who Nailed Madoff Got GE Wrong&quot;</a>. <i>Fortune</i><span>. Retrieved <span>November 16,</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Markopolos, Harry (September 15, 2019). <a href="https://fm.cnbc.com/applications/cnbc.com/resources/editorialfiles/2019/8/15/2019_08_15_GE_Whistleblower_Report.pdf">&quot;General Electric, A Bigger Fraud Than Enron&quot;</a> <span>(PDF)</span>. <i><a href="https://en.wikipedia.org/wiki/CNBC">CNBC</a></i><span>. Retrieved <span>July 20,</span> 2020</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://finance.yahoo.com/quote/GE/">&quot;General Electric Company (GE) Stock Price, Quote, History &amp; News&quot;</a>. <i>finance.yahoo.com</i><span>. Retrieved <span>November 16,</span> 2019</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.bloomberg.com/graphics/2019-general-electric-rise-and-downfall/">&quot;General Electric: The Rise and Fall of a Great American Company&quot;</a>. <i>Bloomberg.com</i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.bloomberg.com/news/newsletters/2024-04-05/why-ge-aerospace-insurance-still-remain-together-after-breakup/">&quot;New-Look GE Still Has an Insurance Sideshow. It Also Has Options[work=Bloomberg.com&quot;</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Copeland, Rob (November 2023). <a href="https://www.nytimes.com/2023/11/01/business/how-does-the-worlds-largest-hedge-fund-really-make-its-money.html">&quot;How Does the World&#39;s Largest Hedge Fund Really Make Its Money?&quot;</a>. <i>The New York Times</i>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://airmail.news/books/2023/11/burning-bridgewater/">&quot;Burning Bridgewater&quot;</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://web.archive.org/web/20120304192117/http://www.archons.org/news/detail.asp?id=322">&quot;Archon News&quot;</a>. Archons.org. Archived from <a href="http://www.archons.org/news/detail.asp?id=322">the original</a> on March 4, 2012<span>. Retrieved <span>February 9,</span> 2013</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Solomon, Deborah (February 28, 2010). <a href="https://www.nytimes.com/2010/02/28/magazine/28fob-q4-t.html">&quot;Questions for Harry Markopolos Math is Hard&quot;</a>. <i>New York Times Magazine</i><span>. Retrieved <span>August 30,</span> 2011</span>.</cite></span> </li> <li><span><b>^</b></span> <span><a href="https://krannert.purdue.edu/events/ethics/speakers/markopolos.php">https://krannert.purdue.edu/events/ethics/speakers/markopolos.php</a></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://web.archive.org/web/20100323005615/http://www.newsweek.com/id/235052">&quot;We Read It So You Don&#39;t Have To: &#39;No One Would Listen: A True Financial Thriller&#39; by Harry Markopolos&quot;</a>. March 17, 2010. Archived from <a href="http://www.newsweek.com/id/235052">the original</a> on March 23, 2010<span>. Retrieved <span>March 15,</span> 2016</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Gold, Daniel M. (August 25, 2011). <a href="https://www.nytimes.com/2011/08/26/movies/chasing-madoff-a-documentary-of-a-fraud-review.html">&quot;The High Human Cost of Following the Money in the Madoff Fraud Case&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/The_New_York_Times">The New York Times</a></i><span>. Retrieved <span>June 15,</span> 2018</span>.</cite></span> </li> </ol></div></div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Harry_Markopolos&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://www.c-span.org/person/?1031388">Appearances</a> on <a href="https://en.wikipedia.org/wiki/C-SPAN">C-SPAN</a></li> <li><cite><a href="https://web.archive.org/web/20090627070213/http://financialserv.edgeboss.net/wmedia/financialserv/hearing020409.wvx"><i>Assessing the Madoff Ponzi Scheme and Regulatory Failures (Archive of: Subcommittee on Capital Markets, Insurance, and Government Sponsored Enterprises Hearing)</i></a>. U.S. House Financial Services Committee. February 4, 2009. Archived from <a href="http://financialserv.edgeboss.net/wmedia/financialserv/hearing020409.wvx">the original</a> <span>(Windows Media)</span> on June 27, 2009<span>. Retrieved <span>June 29,</span> 2009</span>.</cite></li></ul><dl><dd><ul><li><cite><a href="https://web.archive.org/web/20090207135708/http://video.nytimes.com/video/2009/02/04/business/1231547065762/madoff-witness-testifies-part-1.html"><i>Madoff Witness Testifies: Part 1</i></a>. CNBC via The New York Times. February 4, 2009. Archived from <a href="https://video.nytimes.com/video/2009/02/04/business/1231547065762/madoff-witness-testifies-part-1.html">the original</a> <span>(Adobe Flash)</span> on February 7, 2009<span>. Retrieved <span>June 29,</span> 2009</span>.</cite></li> <li><cite><a href="https://web.archive.org/web/20090208180413/http://video.nytimes.com/video/2009/02/04/business/1231547064371/madoff-witness-testifies-part-2.html"><i>Madoff Witness Testifies: Part 2</i></a>. CNBC via The New York Times. February 4, 2009. Archived from <a href="https://video.nytimes.com/video/2009/02/04/business/1231547064371/madoff-witness-testifies-part-2.html">the original</a> <span>(Adobe Flash)</span> on February 8, 2009<span>. Retrieved <span>June 29,</span> 2009</span>.</cite></li></ul></dd></dl><ul><li><a href="https://web.archive.org/web/20120111062840/http://www.kingworldnews.com/kingworldnews/Broadcast/Entries/2010/1/10_Eric_King_files/Eric%20King%201%3A10%3A2010.mp3">Markopolos interview</a> (mp3) <a href="https://en.wikipedia.org/w/index.php?title=King_World_News&amp;action=edit&amp;redlink=1">King World News</a> (May 29, 2009). Retrieved May 10, 2011.</li> <li><a href="http://www.madofftrustee.com/">The Madoff Recovery Institute website</a></li></ul><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Madoff_investment_scandal"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Madoff_investment_scandal"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Madoff_investment_scandal"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Madoff_investment_scandal">Madoff investment scandal</a></div></th></tr><tr><th><a href="https://en.wikipedia.org/wiki/Participants_in_the_Madoff_investment_scandal">Participants</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Bernie_Madoff">Bernie Madoff</a></li> <li><a href="https://en.wikipedia.org/wiki/Stanley_Chais">Stanley Chais</a></li> <li><a href="https://en.wikipedia.org/wiki/Frank_DiPascali">Frank DiPascali</a></li> <li><a href="https://en.wikipedia.org/wiki/David_G._Friehling">David G. Friehling</a></li> <li><a href="https://en.wikipedia.org/wiki/Jeffry_Picower">Jeffry Picower</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_investors_in_Bernard_L._Madoff_Investment_Securities">Investors</a></li></ul> </div></td></tr><tr><th>Madoff family</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Ruth_Madoff">Ruth Madoff</a></li> <li><a href="https://en.wikipedia.org/wiki/Andrew_Madoff">Andrew Madoff</a></li> <li><a href="https://en.wikipedia.org/wiki/Mark_Madoff">Mark Madoff</a></li> <li><a href="https://en.wikipedia.org/wiki/Eric_Swanson">Eric Swanson</a></li></ul> </div></td></tr><tr><th>Response</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Recovery_of_funds_from_the_Madoff_investment_scandal">Recovery of funds</a> (<a href="https://en.wikipedia.org/wiki/Irving_Picard">Irving Picard</a>)</li> <li><i><a href="https://en.wikipedia.org/wiki/United_States_v._O%27Hara">United States v. Jerome O&#39;Hara and George Perez</a></i></li></ul> </div></td></tr><tr><th>Media</th><td><div> <ul><li><i><a href="https://en.wikipedia.org/wiki/Chasing_Madoff">Chasing Madoff</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/Imagining_Madoff">Imagining Madoff</a></i></li> <li><a href="https://en.wikipedia.org/wiki/In_God_We_Trust_(2013_film)"><i>In God We Trust</i> (film)</a></li> <li><a href="https://en.wikipedia.org/wiki/Madoff_(miniseries)"><i>Madoff</i> (miniseries)</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Madoff:_The_Monster_of_Wall_Street">Madoff: The Monster of Wall Street</a></i></li> <li><i><a href="https://en.wikipedia.org/wiki/No_One_Would_Listen">No One Would Listen</a></i> (Harry Markopolos)</li> <li><a href="https://en.wikipedia.org/wiki/The_Wizard_of_Lies"><i>The Wizard of Lies</i> (film)</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Great_Recession"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Great_Recession"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Great_Recession"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Great_Recession">Great Recession</a></div></th></tr><tr><th>By region</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Great_Recession_in_Africa">Africa</a></li> <li><a href="https://en.wikipedia.org/wiki/Great_Recession_in_the_Americas">Americas</a> <ul><li><a href="https://en.wikipedia.org/wiki/Great_Recession_in_the_United_States">United States</a></li> <li><a href="https://en.wikipedia.org/wiki/Great_Recession_in_South_America">South America</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Great_Recession_in_Asia">Asia</a></li> <li><a href="https://en.wikipedia.org/wiki/Great_Recession_in_Europe">Europe</a> <ul><li><a href="https://en.wikipedia.org/wiki/2008%E2%80%932011_Icelandic_financial_crisis">Iceland</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Great_Recession_in_Oceania">Oceania</a></li></ul> </div></td></tr><tr><th>United States-specific</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Automotive_industry_crisis_of_2008%E2%80%932010">Automotive industry crisis</a></li> <li><a href="https://en.wikipedia.org/wiki/2008%E2%80%932012_California_budget_crisis">California budget crisis</a></li> <li><a href="https://en.wikipedia.org/wiki/United_States_housing_bubble">Housing bubble</a></li> <li><a href="https://en.wikipedia.org/wiki/United_States_housing_market_correction">Housing market correction</a></li> <li><a href="https://en.wikipedia.org/wiki/Subprime_mortgage_crisis">Subprime mortgage crisis</a></li></ul> </div></td></tr><tr><th>Banking losses and fraud</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Libor_scandal">Libor scandal</a> <ul><li><a href="https://en.wikipedia.org/wiki/Tom_Hayes_(trader)">Tom Hayes</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/2008_Soci%C3%A9t%C3%A9_G%C3%A9n%C3%A9rale_trading_loss">Société Générale trading loss</a></li> <li><a href="https://en.wikipedia.org/wiki/Icesave_dispute">Icesave dispute</a></li> <li><a href="https://en.wikipedia.org/wiki/Forex_scandal">Forex scandal</a></li> <li><a href="https://en.wikipedia.org/wiki/Bernie_Madoff">Bernie Madoff</a></li> <li><a href="https://en.wikipedia.org/wiki/Tom_Petters">Tom Petters</a></li> <li><a href="https://en.wikipedia.org/wiki/Scott_W._Rothstein">Scott W. Rothstein</a></li> <li><a href="https://en.wikipedia.org/wiki/Allen_Stanford">Allen Stanford</a></li></ul> </div></td></tr><tr><th>Government entities</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Consumer_Financial_Protection_Bureau">Consumer Financial Protection Bureau</a></li> <li><a href="https://en.wikipedia.org/wiki/Federal_Deposit_Insurance_Corporation">Federal Deposit Insurance Corporation</a></li> <li><a href="https://en.wikipedia.org/wiki/Federal_Home_Loan_Banks">Federal Home Loan Banks</a></li> <li><a href="https://en.wikipedia.org/wiki/Federal_Housing_Administration">Federal Housing Administration</a></li> <li><a href="https://en.wikipedia.org/wiki/Federal_Housing_Finance_Agency">Federal Housing Finance Agency</a></li> <li><a href="https://en.wikipedia.org/wiki/Federal_Housing_Finance_Board">Federal Housing Finance Board</a></li> <li><a href="https://en.wikipedia.org/wiki/Federal_Reserve_System">Federal Reserve System</a></li> <li><a href="https://en.wikipedia.org/wiki/Government_National_Mortgage_Association">Government National Mortgage Association</a></li> <li><a href="https://en.wikipedia.org/wiki/National_Asset_Management_Agency">National Asset Management Agency</a></li> <li><a href="https://en.wikipedia.org/wiki/Office_of_Federal_Housing_Enterprise_Oversight">Office of Federal Housing Enterprise Oversight</a></li> <li><a href="https://en.wikipedia.org/wiki/Assistant_Secretary_of_the_Treasury_for_Financial_Stability">Office of Financial Stability</a></li> <li><a href="https://en.wikipedia.org/wiki/UK_Financial_Investments">UK Financial Investments</a></li></ul> </div></td></tr><tr><td colspan="2"><table><tbody><tr><th colspan="2"><div>Government policy and spending responses</div></th></tr><tr><th>Banking and finance<br/> stability and reform</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Banking_(Special_Provisions)_Act_2008">Banking (Special Provisions) Act 2008</a></li> <li><a href="https://en.wikipedia.org/wiki/China%E2%80%93Japan%E2%80%93South_Korea_trilateral_summit">China–Japan–South Korea trilateral summit</a></li> <li><a href="https://en.wikipedia.org/wiki/Commercial_Paper_Funding_Facility">Commercial Paper Funding Facility</a></li> <li><a href="https://en.wikipedia.org/wiki/Dodd%E2%80%93Frank_Wall_Street_Reform_and_Consumer_Protection_Act">Dodd–Frank Wall Street Reform and Consumer Protection Act</a></li> <li><a href="https://en.wikipedia.org/wiki/Emergency_Economic_Stabilization_Act_of_2008">Emergency Economic Stabilization Act of 2008</a></li> <li><a href="https://en.wikipedia.org/wiki/Irish_emergency_budget,_2009">Irish emergency budget, 2009</a></li> <li><a href="https://en.wikipedia.org/wiki/Temporary_Liquidity_Guarantee_Program">Temporary Liquidity Guarantee Program</a></li> <li><a href="https://en.wikipedia.org/wiki/Term_Asset-Backed_Securities_Loan_Facility">Term Asset-Backed Securities Loan Facility</a></li> <li><a href="https://en.wikipedia.org/wiki/Troubled_Asset_Relief_Program">Troubled Asset Relief Program</a></li> <li><a href="https://en.wikipedia.org/wiki/2008_United_Kingdom_bank_rescue_package">2008 United Kingdom bank rescue package</a></li></ul> </div><table><tbody><tr><th>Bank stress tests</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/2010_European_Union_bank_stress_test">EU</a></li> <li><a href="https://en.wikipedia.org/wiki/2009_Supervisory_Capital_Assessment_Program">U.S.</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th>Stimulus and recovery</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/2008_European_Union_stimulus_plan">2008 European Union stimulus plan</a></li> <li><a href="https://en.wikipedia.org/wiki/2008%E2%80%932009_Keynesian_resurgence">2008–2009 Keynesian resurgence</a></li> <li><a href="https://en.wikipedia.org/wiki/American_Recovery_and_Reinvestment_Act_of_2009">American Recovery and Reinvestment Act of 2009</a></li> <li><a href="https://en.wikipedia.org/wiki/Chinese_economic_stimulus_program">Chinese economic stimulus program</a></li> <li><a href="https://en.wikipedia.org/wiki/Economic_Stimulus_Act_of_2008">Economic Stimulus Act of 2008</a></li> <li><a href="https://en.wikipedia.org/wiki/Fraud_Enforcement_and_Recovery_Act_of_2009">Fraud Enforcement and Recovery Act of 2009</a></li> <li><a href="https://en.wikipedia.org/wiki/Green_New_Deal">Green New Deal</a></li> <li><a href="https://en.wikipedia.org/wiki/Housing_and_Economic_Recovery_Act_of_2008">Housing and Economic Recovery Act of 2008</a></li> <li><a href="https://en.wikipedia.org/wiki/National_fiscal_policy_response_to_the_Great_Recession">National fiscal policy response to the Great Recession</a></li> <li><a href="https://en.wikipedia.org/wiki/Zero_interest-rate_policy">Zero interest-rate policy</a></li></ul> </div></td></tr><tr><th>Government interventions,<br/> rescues, and acquisitions</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_banks_acquired_or_bankrupted_during_the_Great_Recession">List of banks acquired or bankrupted during the Great Recession</a></li></ul> </div><table><tbody><tr><th>Non-banking</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Chrysler">Chrysler</a></li> <li><a href="https://en.wikipedia.org/wiki/General_Motors">General Motors</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr></tbody></table></td></tr><tr><th>Securities involved <br/> and financial markets</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Auction_rate_security">Auction rate securities</a></li> <li><a href="https://en.wikipedia.org/wiki/Collateralized_debt_obligation">Collateralized debt obligations</a></li> <li><a href="https://en.wikipedia.org/wiki/Collateralized_mortgage_obligation">Collateralized mortgage obligations</a></li> <li><a href="https://en.wikipedia.org/wiki/Credit_default_swap">Credit default swaps</a></li> <li><a href="https://en.wikipedia.org/wiki/Mortgage-backed_security">Mortgage-backed securities</a></li> <li><a href="https://en.wikipedia.org/wiki/Secondary_mortgage_market">Secondary mortgage market</a></li></ul> </div></td></tr><tr><th>Social responses</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Tea_Party_protests">Tea Party protests</a> (United States; c. 2009)</li> <li><a href="https://en.wikipedia.org/wiki/2009_May_Day_protests">2009 May Day protests</a> (Europe, Middle East and North Africa, Asia; 2009)</li> <li><a href="https://en.wikipedia.org/wiki/Arab_Spring">Arab Spring</a> (MENA; 2010–2012)</li> <li><a href="https://en.wikipedia.org/wiki/Occupy_movement">Occupy movement</a> (worldwide; 2011–2012) <ul><li><a href="https://en.wikipedia.org/wiki/Occupy_Wall_Street">Occupy Wall Street</a></li></ul></li></ul> </div></td></tr><tr><th>Related topics</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/2000s_energy_crisis">2000s energy crisis</a> <ul><li><a href="https://en.wikipedia.org/wiki/2008_Central_Asia_energy_crisis">2008 Central Asia energy crisis</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Effects_of_the_Great_Recession_on_museums">Effects of the Great Recession on museums</a></li> <li><a href="https://en.wikipedia.org/wiki/Decline_of_newspapers">Decline of newspapers</a></li> <li><a href="https://en.wikipedia.org/wiki/2007%E2%80%932008_world_food_price_crisis">2007–2008 world food price crisis</a></li> <li><a href="https://en.wikipedia.org/wiki/Retail_apocalypse">Retail apocalypse</a></li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Euro_area_crisis">Euro area crisis</a></li> <li><a href="https://en.wikipedia.org/wiki/2008_financial_crisis">2008 financial crisis</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_public_debt">List of countries by public debt</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q2019135#identifiers"></a></span></div></th></tr><tr><th>International</th><td><div><ul><li><span><a href="https://isni.org/isni/0000000117204032">ISNI</a></span></li><li><span><a href="https://viaf.org/viaf/165133671">VIAF</a></span></li><li><span><a href="https://id.oclc.org/worldcat/entity/E39PBJkXB8vrmy4qDBftyQv8md">WorldCat</a></span></li></ul></div></td></tr><tr><th>National</th><td><div><ul><li><span><a href="https://id.loc.gov/authorities/n2009080470">United States</a></span></li><li><span><a href="https://aleph.nkp.cz/F/?func=find-c&amp;local_base=aut&amp;ccl_term=ica=jo2013746446&amp;CON_LNG=ENG">Czech Republic</a></span></li><li><span><a href="https://www.nli.org.il/en/authorities/987007342702805171">Israel</a></span></li></ul></div></td></tr><tr><th>Other</th><td><div><ul><li><span><a href="https://lux.collections.yale.edu/view/person/f5708119-3e6e-4cb1-878a-5ff4a1bc5557">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div> The Market for Lemons - Wikipedia https://en.wikipedia.org/wiki/The_Market_for_Lemons 5jJBgvbJ_eMqLJRuDkpNJ1vU6xw8fE016QgXkA== Fri, 08 May 2026 09:31:06 +0000 1970 economics paper by George Akerlof <div>1970 economics paper by George Akerlof</div><p> &quot;<b>The Market for &#39;Lemons&#39;: Quality Uncertainty and the Market Mechanism</b>&quot;<sup><span>[</span>1<span>]</span></sup> is a widely cited seminal paper in the field of economics which explores the concept of asymmetric information in markets. The paper was written in 1970 by <a href="https://en.wikipedia.org/wiki/George_Akerlof">George Akerlof</a> and published in the <a href="https://en.wikipedia.org/wiki/The_Quarterly_Journal_of_Economics"><i>Quarterly Journal of Economics</i></a>. The paper&#39;s theory has since been applied to many types of markets. </p><figure><a href="https://en.wikipedia.org/wiki/File:Used_car_dealers_on_the_Industrial_Estate_-_geograph.org.uk_-_766208.jpg"></a><figcaption>Akerlof&#39;s paper uses the <a href="https://en.wikipedia.org/wiki/Market_(economics)">market</a> for <a href="https://en.wikipedia.org/wiki/Used_car">used cars</a> as an example of the problem of quality uncertainty. It concludes that owners of high-quality used cars will not place their cars on the used car market. A car buyer should only be able to buy low-quality used cars, and will pay accordingly as the market for good used cars does not exist.</figcaption></figure><p>Akerlof examines how the quality of goods traded in a market can degrade in the presence of <a href="https://en.wikipedia.org/wiki/Information_asymmetry">information asymmetry</a> between buyers and sellers, which ultimately leaves goods that are found to be defective after purchase in the market, noted by the term &#39;lemon&#39; in the title of the paper. In American slang, a <a href="https://en.wikipedia.org/wiki/Lemon_(automobile)">lemon</a> is a car that is found to be defective after it has been bought. </p><p>Akerlof&#39;s theory of the &quot;Market for Lemons&quot; paper applies to markets with information asymmetry, focusing on the used car market. Information asymmetry within the market relates to the seller having more information about the quality of the car as opposed to the buyer, creating adverse selection.<sup><span>[</span>1<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Adverse_selection">Adverse selection</a> is a phenomenon where sellers are not willing to sell high quality goods at the lower prices buyers are willing to pay, with the result that buyers get lower quality goods. This can lead to a market collapse due to the lower equilibrium price and quantity of goods traded in the market than a market with <a href="https://en.wikipedia.org/wiki/Perfect_information">perfect information</a>. </p><p>Suppose buyers cannot distinguish between a high-quality car (a &quot;peach&quot;) and a low-quality car (a &quot;lemon&quot;). Then they are only willing to pay a fixed price for a car that averages the value of a &quot;peach&quot; and &quot;lemon&quot; together (<i>p</i><sub>avg</sub>). But sellers know whether they hold a peach or a lemon. Given the fixed price at which buyers will buy, sellers will sell only when they hold &quot;lemons&quot; (since <i>p</i><sub>lemon</sub> &lt; <i>p</i><sub>avg</sub>) and they will leave the market when they hold &quot;peaches&quot; (since <i>p</i><sub>peach</sub> &gt; <i>p</i><sub>avg</sub>). Eventually, as enough sellers of &quot;peaches&quot; leave the market, the average willingness-to-pay of buyers will decrease (since the average quality of cars on the market decreased), leading to even more sellers of high-quality cars to leave the market through a positive <a href="https://en.wikipedia.org/wiki/Feedback_loop">feedback loop</a>. Thus the uninformed buyer&#39;s price creates an <a href="https://en.wikipedia.org/wiki/Adverse_selection">adverse selection</a> problem that drives the high-quality cars from the market. Adverse selection is a market mechanism that can lead to a market collapse. </p><p>Akerlof&#39;s paper shows how prices can determine the quality of goods traded on the market. Low prices drive away sellers of high-quality goods, leaving only lemons behind. In 2001, Akerlof, along with <a href="https://en.wikipedia.org/wiki/Michael_Spence">Michael Spence</a>, and <a href="https://en.wikipedia.org/wiki/Joseph_Stiglitz">Joseph Stiglitz</a>, jointly received the <a href="https://en.wikipedia.org/wiki/Nobel_Memorial_Prize_in_Economic_Sciences">Nobel Memorial Prize in Economic Sciences</a>, for their research on issues related to asymmetric information. </p><div><h2>The paper</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><div><h3>Thesis</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Kovacs_special_1968.JPG"></a><figcaption>Actor <a href="https://en.wikipedia.org/wiki/Ernie_Kovacs">Ernie Kovacs</a> portraying a used-car salesman</figcaption></figure><p>Akerlof&#39;s paper uses the <a href="https://en.wikipedia.org/wiki/Market_(economics)">market</a> for <a href="https://en.wikipedia.org/wiki/Used_car">used cars</a> as an example of the problem of quality uncertainty. A used car is one in which ownership is transferred from one person to another, after a period of use by its first owner and its inevitable wear and tear. There are good used cars (&quot;peaches&quot;) and defective used cars (&quot;lemons&quot;), normally as a consequence of several not-always-traceable variables, such as the owner&#39;s driving style, quality and frequency of maintenance, and accident history. Because many important mechanical parts and other elements are hidden from view and not easily accessible for inspection, the buyer of a car does not know beforehand whether it is a peach or a lemon. So the buyer&#39;s best guess for a given car is that the car is of average quality; accordingly, the buyer will be willing to pay the price of a car of known average quality. This means that the owner of a carefully maintained, never-abused, good used car will not be able to get a high enough price to make selling that car worthwhile. </p><p>Therefore, owners of &#39;peaches&#39; will not place their cars on the used market as they believe their car is worth more than the market price. The withdrawal of good cars reduces the average quality of cars on the market, causing buyers to revise downward their expectations for any given car. This, in turn, motivates the owners of moderately good cars not to sell, and so on. The result is that a market in which there is <a href="https://en.wikipedia.org/wiki/Information_asymmetry">asymmetric information</a> with respect to quality shows characteristics similar to those described by <a href="https://en.wikipedia.org/wiki/Gresham%27s_law">Gresham&#39;s law</a>: the bad drives out the good. (Although Gresham&#39;s principle applies more specifically to exchange rates, modified analogies can be drawn.) <sup><span>[</span>2<span>]</span></sup> </p><div><h3>Statistical abstract of the problem</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>where <i>M</i> is the consumption of goods other than automobiles, <i>x</i> the car&#39;s quality and <i>n</i> the number of automobiles. Let <i>Y</i><sub><i>i</i></sub>, <i>D</i><sub><i>i</i></sub> and <i>S</i><sub><i>i</i></sub> be income, demand and supply for group <i>i</i>. Assuming that utilities are linear, that the traders are <a href="https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem">Von Neumann–Morgenstern utility</a> maximizers and that the price of other <i>M</i> goods is unitary, the demand <i>D</i><sub>1</sub> for cars is <i>Y</i><sub>1</sub>/<i>p</i> if <i>μ</i>/<i>p</i> &gt; 1, otherwise null. The demand <i>D</i><sub>2</sub> is <i>Y</i><sub>2</sub>/<i>p</i> if 3<i>μ</i>/<i>2</i> &gt; <i>p</i>, otherwise null. Market demand is given by: </p><div><h3>Asymmetric information</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>The paper by Akerlof describes how the interaction between quality heterogeneity and <a href="https://en.wikipedia.org/wiki/Information_asymmetry">asymmetric information</a> can lead to the disappearance of a market where guarantees are indefinite. In this model, as quality is indistinguishable beforehand by the buyer (due to the asymmetry of information), incentives exist for the seller to pass off low-quality goods as higher-quality ones. The buyer, however, takes this incentive into consideration, and takes the quality of the goods to be uncertain. Only the average quality of the goods will be considered, which in turn will have the side effect that goods that are above average in terms of quality will be driven out of the market. This mechanism is repeated until a <a href="https://en.wikipedia.org/wiki/No-trade_theorem">no-trade equilibrium</a> is reached. </p><p>As a consequence of the mechanism described in this paper, markets may fail to exist altogether in certain situations involving quality uncertainty. Examples given in Akerlof&#39;s paper include the market for used cars, the dearth of formal credit markets in developing countries, and the difficulties that the elderly encounter in buying health insurance. However, not all players in a given market will follow the same rules or have the same aptitude of assessing quality. So there will always be a distinct advantage for some vendors to offer low-quality goods to the less-informed segment of a market that, on the whole, appears to be of reasonable quality and have reasonable guarantees of certainty. This is part of the basis for the idiom <a href="https://en.wikipedia.org/wiki/Buyer_beware">buyer beware</a>. </p><div><h2>Critical reception</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>George E. Hoffer and Michael D. Pratt state that the &quot;economic literature is divided on whether a lemons market actually exists in used vehicles&quot;. The authors&#39; research supports the hypothesis that &quot;known defects provisions&quot;, used by US states (e.g., Wisconsin) to regulate used car sales, have been ineffectual, because the quality of used vehicles sold in these states is not significantly better than the vehicles in neighboring states without such <a href="https://en.wikipedia.org/wiki/Consumer_protection">consumer protection</a> legislation.<sup><span>[</span>3<span>]</span></sup> </p><p>Both the <i><a href="https://en.wikipedia.org/wiki/American_Economic_Review">American Economic Review</a></i> and the <i><a href="https://en.wikipedia.org/wiki/Review_of_Economic_Studies">Review of Economic Studies</a></i> rejected the paper for &quot;triviality&quot;, while the reviewers for <i><a href="https://en.wikipedia.org/wiki/Journal_of_Political_Economy">Journal of Political Economy</a></i> rejected it as incorrect, arguing that, if this paper were correct, then no goods could be traded.<sup><span>[</span>4<span>]</span></sup> Only on the fourth attempt did the paper get published in <i><a href="https://en.wikipedia.org/wiki/Quarterly_Journal_of_Economics">Quarterly Journal of Economics</a></i>.<sup><span>[</span>5<span>]</span></sup> Today, the paper is one of the most-cited papers in modern economic theory and most downloaded economic journal paper of all time in RePEC (more than 39,275 citations in academic papers as of February 2022).<sup><span>[</span>6<span>]</span></sup> It has profoundly influenced virtually every field of economics, from industrial organisation and <a href="https://en.wikipedia.org/wiki/Public_finance">public finance</a> to <a href="https://en.wikipedia.org/wiki/Macroeconomics">macroeconomics</a> and <a href="https://en.wikipedia.org/wiki/Contract_theory">contract theory</a>. </p><div><h2>Conditions for a lemon market</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>A lemon market will be produced by the following: </p><ol><li>Asymmetry of information, in which no buyers can accurately assess the value of a product through examination before sale is made and all sellers can more accurately assess the value of a product prior to sale</li> <li>An incentive exists for the seller to pass off a low-quality product as a higher-quality one</li> <li>Sellers have no credible disclosure technology (sellers with a great car have no way to disclose this credibly to buyers)</li> <li>Either a continuum of seller qualities exists or the average seller type is sufficiently low (buyers are sufficiently pessimistic about the seller&#39;s quality)</li> <li>Deficiency of <i>effective</i> public quality assurances (by reputation or regulation and/or of <i>effective</i> guarantees/warranties)</li></ol><div><h3>A more general mathematical model of market collapse</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>It is possible to generalize the reasoning in Akerlof&#39;s paper.<sup><span>[</span>7<span>]</span></sup> Suppose that there are two populations of cars: the peaches <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\mathcal {P}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10d6ec962de5797ba4f161c40e66dca74ae95cc6" alt="{\displaystyle {\mathcal {P}}}" title=""/></span> and the lemons <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\mathcal {L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9027196ecb178d598958555ea01c43157d83597c" alt="{\displaystyle {\mathcal {L}}}" title=""/></span>, where we assume that the quality <span><span><math> <semantics> <mrow> <mstyle> <mi>μ</mi> <mo>(</mo> <mo>⋅</mo> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle \mu (\cdot )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47b9e37847874ad1c3f29bc33de2a9def6d401f9" alt="{\displaystyle \mu (\cdot )}" title=""/></span> of peaches is always greater than the quality of lemons:<span><span><math> <semantics> <mrow> <mstyle> <mi>μ</mi> <mo>(</mo> <mi>ρ</mi> <mo>)</mo> <mo>&gt;</mo> <mi>μ</mi> <mo>(</mo> <mi>ℓ</mi> <mo>)</mo> <mo>,</mo> <mi>∀</mi> <mi>ρ</mi> <mo>∈</mo> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> <mo>,</mo> <mi>ℓ</mi> <mo>∈</mo> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> </mstyle> </mrow> <annotation>{\displaystyle \mu (\rho )&gt;\mu (\ell ),\quad \forall \rho \in {\mathcal {P}},\;\ell \in {\mathcal {L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b4e88ec85c3814f366803aef67c742921c101eb" alt="{\displaystyle \mu (\rho )&gt;\mu (\ell ),\quad \forall \rho \in {\mathcal {P}},\;\ell \in {\mathcal {L}}}" title=""/></span>Accordingly, the utility <span><span><math> <semantics> <mrow> <mstyle> <mi>U</mi> <mo>(</mo> <mo>⋅</mo> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle U(\cdot )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/036c155172c98d78b92cd49641aa1e3227ea3e08" alt="{\displaystyle U(\cdot )}" title=""/></span> and the price <span><span><math> <semantics> <mrow> <mstyle> <mi>p</mi> </mstyle> </mrow> <annotation>{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" alt="{\displaystyle p}" title=""/></span> of the peaches will also always be greater than that of the lemons. Let <span><span><math> <semantics> <mrow> <mstyle> <mi>η</mi> </mstyle> </mrow> <annotation>{\displaystyle \eta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4d701857cf5fbec133eebaf94deadf722537f64" alt="{\displaystyle \eta }" title=""/></span> be the probability of a buyer encountering a peach in the used car market. Then the <a href="https://en.wikipedia.org/wiki/Expected_utility_hypothesis">expected utility</a> for the buyer <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>U</mi> <mrow> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle U_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e82b758ddad8d8d1ff96696823b51ab14f7d1e05" alt="{\displaystyle U_{e}}" title=""/></span> from purchasing a used car is:<span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>U</mi> <mrow> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mi>η</mi> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ρ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mo>(</mo> <mn>1</mn> <mo>−</mo> <mi>η</mi> <mo>)</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ℓ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <msup> <mi>U</mi> <mo>′</mo> </msup> <mo>(</mo> <mo>⋅</mo> <mo>)</mo> <mo>&gt;</mo> <mn>0</mn> <mo>,</mo> <msup> <mi>U</mi> <mo>″</mo> </msup> <mo>(</mo> <mo>⋅</mo> <mo>)</mo> <mo>&lt;</mo> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle U_{e}=\eta U\left({\overline {\rho }}\right)+(1-\eta )U\left({\overline {\ell }}\right),\quad U&#39;(\cdot )&gt;0,\;U&#39;&#39;(\cdot )&lt;0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a99183f6b598b921bdabe9d2bbb2e5d944005209" alt="{\displaystyle U_{e}=\eta U\left({\overline {\rho }}\right)+(1-\eta )U\left({\overline {\ell }}\right),\quad U&#39;(\cdot )&gt;0,\;U&#39;&#39;(\cdot )&lt;0}" title=""/></span>where <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mover> <mi>ρ</mi> <mo>¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\overline {\rho }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8349786e9fac05950275329117d4aea37645e18e" alt="{\displaystyle {\overline {\rho }}}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mover> <mi>ℓ</mi> <mo>¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\overline {\ell }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11fca991a48f6cfd38e8f7065ecf1c09ca09d37f" alt="{\displaystyle {\overline {\ell }}}" title=""/></span> represent the mean peach and lemon respectively. The expected utility for the buyer will always increase - for a <a href="https://en.wikipedia.org/wiki/Monotonic_function">monotonic</a>, positive utility function - as the probability of encountering a peach increases.<span><span><math> <semantics> <mrow> <mstyle> <mrow> <mfrac> <mrow> <mi>∂</mi> <msub> <mi>U</mi> <mrow> <mi>e</mi> </mrow> </msub> </mrow> <mrow> <mi>∂</mi> <mi>η</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ρ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ℓ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>&gt;</mo> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle {\partial U_{e} \over {\partial \eta }}=U\left({\overline {\rho }}\right)-U\left({\overline {\ell }}\right)&gt;0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43bbe5e440f460ed150779e81b20ede5372f190f" alt="{\displaystyle {\partial U_{e} \over {\partial \eta }}=U\left({\overline {\rho }}\right)-U\left({\overline {\ell }}\right)&gt;0}" title=""/></span>Furthermore, the equation for a buyer&#39;s expected utility implies that the equilibrium price in an informationally symmetric market is:<span><span><math> <semantics> <mrow> <mstyle> <msubsup> <mi>p</mi> <mrow> <mtext>sym</mtext> </mrow> <mrow> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mi>η</mi> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ρ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mo>(</mo> <mn>1</mn> <mo>−</mo> <mi>η</mi> <mo>)</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ℓ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle p_{\text{sym}}^{*}=\eta U\left({\overline {\rho }}\right)+(1-\eta )U\left({\overline {\ell }}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d5131b08eaf1d77709d4f0a0171cafbdb543d8d" alt="{\displaystyle p_{\text{sym}}^{*}=\eta U\left({\overline {\rho }}\right)+(1-\eta )U\left({\overline {\ell }}\right)}" title=""/></span>However, the used car market is not a symmetric market: the sellers know which cars are peaches and lemons, while the buyers cannot distinguish between the two. Depending on the type of car he owns, the seller has a differing <a href="https://en.wikipedia.org/wiki/Decision_rule">decision rule</a> based on the offer price <span><span><math> <semantics> <mrow> <mstyle> <mi>O</mi> </mstyle> </mrow> <annotation>{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" alt="{\displaystyle O}" title=""/></span>:<span><span><math> <semantics> <mrow> <mstyle> <mrow> <mtext>Sell</mtext> </mrow> <mo>⟹</mo> <mrow> <mrow> <mo>{</mo> <mtable> <mtr> <mtd> <mi>O</mi> <mo>≥</mo> <msub> <mi>p</mi> <mrow> <mi>ρ</mi> </mrow> </msub> <mo>,</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mtext>Peach</mtext> </mrow> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>O</mi> <mo>≥</mo> <msub> <mi>p</mi> <mrow> <mi>ℓ</mi> </mrow> </msub> <mo>,</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mtext>Lemon</mtext> </mrow> <mo>)</mo> </mtd> </mtr> </mtable> </mrow> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\text{Sell}}\implies {\begin{cases}O\geq p_{\rho },\quad &amp;({\text{Peach}})\\O\geq p_{\ell },\quad &amp;({\text{Lemon}})\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ee9b25200154cc013b560f08a05812cc12fea37" alt="{\displaystyle {\text{Sell}}\implies {\begin{cases}O\geq p_{\rho },\quad &amp;({\text{Peach}})\\O\geq p_{\ell },\quad &amp;({\text{Lemon}})\end{cases}}}" title=""/></span>with <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>p</mi> <mrow> <mi>ρ</mi> </mrow> </msub> <mo>&gt;</mo> <msub> <mi>p</mi> <mrow> <mi>ℓ</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle p_{\rho }&gt;p_{\ell }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c09c01424bb52ab177b4705c854e04580147648" alt="{\displaystyle p_{\rho }&gt;p_{\ell }}" title=""/></span> by definition. It is also assumed that, for both peaches and lemons, sellers are willing to accept a price lower than the full value of the car:<span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>p</mi> <mrow> <mi>ℓ</mi> </mrow> </msub> <mo>&lt;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ℓ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi>p</mi> <mrow> <mi>ρ</mi> </mrow> </msub> <mo>&lt;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ρ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle p_{\ell }&lt;U\left({\overline {\ell }}\right)&lt;p_{\rho }&lt;U\left({\overline {\rho }}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d1a757eddac9f6c6fa285bed42f33cec8b257e2" alt="{\displaystyle p_{\ell }&lt;U\left({\overline {\ell }}\right)&lt;p_{\rho }&lt;U\left({\overline {\rho }}\right)}" title=""/></span>However, if <span><span><math> <semantics> <mrow> <mstyle> <msubsup> <mi>p</mi> <mrow> <mtext>sym</mtext> </mrow> <mrow> <mo>∗</mo> </mrow> </msubsup> <mo>&lt;</mo> <msub> <mi>p</mi> <mrow> <mi>ρ</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle p_{\text{sym}}^{*}&lt;p_{\rho }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29b8b9acedfb05367adb311168232eece6f8644c" alt="{\displaystyle p_{\text{sym}}^{*}&lt;p_{\rho }}" title=""/></span>, then the sellers possessing peaches will not put them on the market and the equilibrium price will drop. This occurs when:<span><span><math> <semantics> <mrow> <mstyle> <mi>η</mi> <mo>&lt;</mo> <mrow> <mfrac> <mrow> <msub> <mi>p</mi> <mrow> <mi>ρ</mi> </mrow> </msub> <mo>−</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ℓ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ρ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ℓ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation>{\displaystyle \eta &lt;{p_{\rho }-U\left({\overline {\ell }}\right) \over {U\left({\overline {\rho }}\right)-U\left({\overline {\ell }}\right)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47c52e40b281118a3b2d7fa590cfa0e50d4fb920" alt="{\displaystyle \eta &lt;{p_{\rho }-U\left({\overline {\ell }}\right) \over {U\left({\overline {\rho }}\right)-U\left({\overline {\ell }}\right)}}}" title=""/></span>with the associated asymmetric information price equilibrium:<span><span><math> <semantics> <mrow> <mstyle> <msubsup> <mi>p</mi> <mrow> <mtext>asym</mtext> </mrow> <mrow> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mi>η</mi> <mrow> <mo>[</mo> <mrow> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ρ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ℓ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mrow> <mi>I</mi> </mrow> <mo>(</mo> <msubsup> <mi>p</mi> <mrow> <mtext>sym</mtext> </mrow> <mrow> <mo>∗</mo> </mrow> </msubsup> <mo>≥</mo> <msub> <mi>p</mi> <mrow> <mi>ρ</mi> </mrow> </msub> <mo>)</mo> <mo>+</mo> <mi>U</mi> <mrow> <mo>(</mo> <mrow> <mover> <mi>ℓ</mi> <mo>¯</mo> </mover> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle p_{\text{asym}}^{*}=\eta \left[U\left({\overline {\rho }}\right)-U\left({\overline {\ell }}\right)\right]\mathbb {I} (p_{\text{sym}}^{*}\geq p_{\rho })+U\left({\overline {\ell }}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97a7d5859ad2bdc6985b556246fea8097ecb1f41" alt="{\displaystyle p_{\text{asym}}^{*}=\eta \left[U\left({\overline {\rho }}\right)-U\left({\overline {\ell }}\right)\right]\mathbb {I} (p_{\text{sym}}^{*}\geq p_{\rho })+U\left({\overline {\ell }}\right)}" title=""/></span>where <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mi>I</mi> </mrow> <mo>(</mo> <mo>⋅</mo> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle \mathbb {I} (\cdot )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90bd807d757bb8538061d370cc18173720980f4d" alt="{\displaystyle \mathbb {I} (\cdot )}" title=""/></span> is the <a href="https://en.wikipedia.org/wiki/Indicator_function">indicator function</a>. Once lemons saturate the market, the peaches are driven out of the market because their sellers cannot be matched with buyers to meet their selling price in equilibrium. The beauty of this example is that it illustrates how product quality can collapse in a market with asymmetric information. </p><div><h2>Laws in the United States</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>Five years after Akerlof&#39;s paper was published, the United States enacted a federal &quot;<a href="https://en.wikipedia.org/wiki/Lemon_law">lemon law</a>&quot; (the <a href="https://en.wikipedia.org/wiki/Magnuson%E2%80%93Moss_Warranty_Act">Magnuson–Moss Warranty Act</a>) that protects citizens of all states. There are also state laws regarding &quot;lemons&quot; which vary by state and may not necessarily cover used or leased vehicles. The rights afforded to consumers by &quot;lemon laws&quot; may exceed the warranties expressed in purchase contracts. These state laws provide remedies to consumers for automobiles that repeatedly fail to meet certain standards of quality and performance. &quot;Lemon law&quot; is the common nickname for these laws, but each state has different names for the laws and acts, which may also cover more than just automobiles. In California and federal law, &quot;Lemon Laws&quot; cover anything mechanical. </p><p>The federal &quot;lemon law&quot; also provides that the warrantor may be obligated to pay the attorney fees of the party prevailing in a lemon law suit, as do most state lemon laws. If a car has to be repaired for the same defect four or more times and the problem is still occurring, the car may be deemed to be a &quot;lemon&quot;. The defect must substantially hinder the vehicle&#39;s use, value, or safety. Dealers and manufacturers are required by branding the title as &quot;Lemon Law Buyback&quot; of such vehicles after their reacquiring them due to any defect, malfunctioning or failure under the federal statute or typically nonconformities under state &quot;lemon laws&quot;; dealers may not withhold the lemon branding of such vehicles and an &quot;as is&quot; or &quot;with all defects&quot; labeling does not protect a dealer from <a href="https://en.wikipedia.org/wiki/Legal_recourse">legal recourse</a> should they not disclose the &quot;lemon law buyback&quot; status of such vehicles. </p><div><h2>Developments of the model</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>Akerlof&#39;s original model has been developed by adjusting certain parameters to better represent the real world markets. Akerlof limited the market to fixed buyers and sellers, disregarding the possibility that agents are able to interchange their position, with low transaction costs. This would be valid for other markets with asymmetric information; however, the used car market is unique in that a buyer can purchase a car and become a seller. Kim incorporates a variability of agents in the market. Moreover, in this model, sellers are differentiated unlike the Akerlof model where sellers are heterogeneous apart from the cars they sell and therefore their behaviors are dependent on the car they own. By changing the parameters of the model this study&#39;s findings conclude that the lemon principle does not hold.<sup><span>[</span>8<span>]</span></sup> </p><p>Daley and Green elaborate the model by segmenting the market equilibrium into intervals of no trade periods and trade periods. Whereby, trade periods are facilitated by the arrival of &quot;news&quot;, categorized as stochastic information. The onset of bad news instigates trade as buyers are more pessimistic, whereas good news establishes confidence in the market. At the equilibrium the following states occur: </p><ul><li>A positive perspective of the seller results in an efficient market, whereby the price is the <a href="https://en.wikipedia.org/wiki/Expected_value">expected value</a> of the asset</li> <li>A negative perspective of the seller results in a partially selling off of the asset</li> <li>An indifferent perspective of the seller results in a no trade period, whereby consumers wait for more information.</li></ul><p>Both sellers with a positive and negative perspective eventually trade in equilibrium, thus mitigating the trade breakdown inefficiency prevalent in Akerlof&#39;s model. However, by integrating news into the model, a new inefficiency arises. This is where delays occur when more news is introduced in the market. Theoretically, more news would reduce market inefficiencies caused by information asymmetry. The dynamic market model constructed shows that this is only partially true.<sup><span>[</span>9<span>]</span></sup> </p><p>Zavolokina, Schlegel and Schwabe incorporate the benefits of modern technology into the model as <a href="https://en.wikipedia.org/wiki/Blockchain">blockchain</a> is able to solve issues relating to the asymmetry of information. The reliability of the information would improve accuracy of the valuation of cars, however, the advantages of the information stored is limited to the interpretation of the buyer. The information would have to be understandable to consumers with no car expertise to be an effective mechanism for decision making.<sup><span>[</span>10<span>]</span></sup> </p><div><h2>Empirical applications</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><p>Although Akerlof&#39;s &quot;Market for Lemons&quot; paper was written solely focusing on the used car market, there are many other applications of this theory in other types of markets beyond the used car market. Examples of applications include health insurance, vehicle related insurance and also within the labour market which, similarly to Akerlof&#39;s theory these examples can all lead to <a href="https://en.wikipedia.org/wiki/Market_failure">market failures</a> through adverse selection. </p><p>Beyond the used car market, insurance companies charge excessive premiums to those who are distinguished as high-risk individuals as people under this term are likely to file more claims to the insurance company. As a result, high risk individuals are likely to cost insurance companies more as they are likely to pay the individual out more money due to the increased claims. Akerlof&#39;s theory has been used to explain this scenario where insurance companies charge higher premiums to individuals who they believe carry out more risk in attempt to compensate for the greater chance that claims are filed under the individual&#39;s policy. </p><p>Another example of an empirical application is within the labour market where, wage discrimination could be a factor as the employer is likely to have more information of the skills and experience of the employee than the employee themself.<sup><span>[</span>11<span>]</span></sup> This is also applicable when employees apply for jobs as employers may be hesitant or decide not to hire workers without previous work experience in the specific field, resulting in those who do not have prior experience or are new to the workforce to be denied by employers. </p><p>Health insurance also falls into the consideration of adverse selection where healthy individuals with no family history of medical concerns may choose not to purchase health insurance as they don&#39;t feel the need to pay the premium, where other individuals with pre-existing conditions or a family history of medical issues are likely to purchase health insurance. As result, healthy individuals are pushed out of the market, creating a smaller group of policy holders, which drives up the price/premium of health insurance for other individuals who decide to purchase the insurance.<sup><span>[</span>12<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Adverse_selection">Adverse selection</a></li> <li><a href="https://en.wikipedia.org/wiki/Confusopoly">Confusopoly</a></li> <li><a href="https://en.wikipedia.org/wiki/Death_spiral_(insurance)">Death spiral (insurance)</a></li> <li><a href="https://en.wikipedia.org/wiki/Gresham%27s_law">Gresham&#39;s law</a></li> <li><a href="https://en.wikipedia.org/wiki/Tragedy_of_the_commons">Tragedy of the commons</a></li> <li><a href="https://en.wikipedia.org/wiki/Transaction_cost">Transaction cost</a></li> <li><a href="https://en.wikipedia.org/wiki/Transparency_(market)">Transparency (market)</a></li> <li><a href="https://en.wikipedia.org/wiki/Open_data">Open data</a></li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=The_Market_for_Lemons&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>Akerlof, George A. (1970). <span><a href="https://scholar.google.com/scholar?cluster=13357329716610593187&amp;hl=en&amp;as_sdt=0,24">&quot;The Market for &#39;Lemons&#39;: Quality Uncertainty and the Market Mechanism&quot;</a></span>. <i>Quarterly Journal of Economics</i>. <b>84</b> (3). The MIT Press: <span>488–</span>500. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F1879431">10.2307/1879431</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/1879431">1879431</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Phlips, Louis (June 30, 1983). <span><a href="https://archive.org/details/economicsofprice0000phli"><i>The Economics of Price Discrimination</i></a></span>. Cambridge University Press. p. <a href="https://archive.org/details/economicsofprice0000phli/page/239">239</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-521-28394-9"><bdi>0-521-28394-9</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Hoffer, George E.; Pratt, Michael D. (1987). &quot;Used vehicles, lemons markets, and Used Car Rules: Some empirical evidence&quot;. <i>Journal of Consumer Policy</i>. <b>10</b> (4): <span>409–</span>414. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2FBF00411482">10.1007/BF00411482</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:150724648">150724648</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Gans, Joshua S.; Shepherd, George B. (1994). <a href="https://doi.org/10.1257%2Fjep.8.1.165">&quot;How Are the Mighty Fallen: Rejected Classic Articles by Leading Economists&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Journal_of_Economic_Perspectives">Journal of Economic Perspectives</a></i>. <b>8</b> (1): <span>165–</span>179. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1257%2Fjep.8.1.165">10.1257/jep.8.1.165</a></span>.</cite></span> </li> <li><span><b>^</b></span> <span><a href="http://nobelprize.org/nobel_prizes/economics/laureates/2001/akerlof-article.html">Writing the &quot;The Market for &#39;Lemons&#39;&quot;: A Personal and Interpretive Essay</a> by George A. Akerlof</span> </li> <li><span><b>^</b></span> <span><cite>Akerlof, George A. (1970). <span><a href="https://www.jstor.org/stable/1879431">&quot;The Market for &quot;Lemons&quot;: Quality Uncertainty and the Market Mechanism&quot;</a></span>. <i><a href="https://en.wikipedia.org/wiki/Google_Scholar">Google Scholar</a></i>. <b>84</b> (3): <span>488–</span>500. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2307%2F1879431">10.2307/1879431</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/1879431">1879431</a><span>. Retrieved <span>2011-05-27</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>David H. Autor (2003-11-17). <a href="https://web.archive.org/web/20120926040801/http://economics.mit.edu:80/files/552">&quot;Lecture Note: Market Signaling — Theory and Evidence&quot;</a>. Archived from <a href="http://economics.mit.edu/files/552">the original</a> on 2012-09-26.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Kim, Jae-Cheol (1985). &quot;The Market for &quot;Lemons&quot; Reconsidered: A Model of the Used Car Market with Asymmetric Information&quot;. <i>The American Economic Review</i>. <b>75</b> (4): <span>836–</span>843. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/1821360">1821360</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Daley, Brendan; Green, Brett (2012). <a href="https://escholarship.org/content/qt1060044f/qt1060044f.pdf?t=o59vau">&quot;Waiting for News in the Market for Lemons&quot;</a> <span>(PDF)</span>. <i>Econometrica</i>. <b>80</b> (4): <span>1433–</span>1504. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.3982%2FECTA9278">10.3982/ECTA9278</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Zavolokina, Liudmila; Schlegel, Manuel; Schwabe, Gerhard (18 February 2020). <a href="https://www.zora.uzh.ch/id/eprint/185517/1/ISEB-Reputation_Paper_final.pdf">&quot;How can we reduce information asymmetries and enhance trust in &#39;The Market for Lemons&#39;?&quot;</a> <span>(PDF)</span>. <i>Information Systems and E-Business Management</i>. <b>19</b> (3): <span>883–</span>908. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2Fs10257-020-00466-4">10.1007/s10257-020-00466-4</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/1617-9854">1617-9854</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:213260199">213260199</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Stiglitz, Joseph E (1975). <a href="https://www.jstor.org/stable/1804834">&quot;The Theory of &quot;Screening,&quot; Education, and the Distribution of Income&quot;</a>. <i>American Economic Association</i>. <b>65</b> (3): <span>283–</span>300. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a> <a href="https://www.jstor.org/stable/1804834">1804834</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Abbring, Jaap H.; Chiappori, Pierre-Andre; Heckman, James J.; Pinquet, Jean (2003). <i>Adverse Selection and Moral Hazard in Insurance: Can Dynamic Data Help to Distinguish?</i>. Oxford University Press. pp. <span>512–</span>521.</cite></span> </li> </ol></div></div> Comparative advantage - Wikipedia https://en.wikipedia.org/wiki/Comparative_advantage xA6UVyp7_CSD-uz8LmzOPBrnkPIv1kK1TX2WGQ== Fri, 08 May 2026 09:29:32 +0000 Lower relative opportunity cost in producing a good <div>Lower relative opportunity cost in producing a good</div><div>Not to be confused with <a href="https://en.wikipedia.org/wiki/Absolute_advantage">Absolute advantage</a> or <a href="https://en.wikipedia.org/wiki/Competitive_advantage">Competitive advantage</a>.</div><p><b>Comparative advantage</b> is the condition of welfare maximization or means of welfare improvement afforded by allocating one&#39;s labor and other resources amongst one&#39;s own available opportunities. The allocation is generally performed in the context of trade opportunities and realizable prices. When re-allocation occurs prices usually change. The optimal allocation is not necessarily extreme specialization that excludes all but one productive activity. Comparative advantage is distinct from <a href="https://en.wikipedia.org/wiki/Competitive_advantage">competitive advantage</a> and <a href="https://en.wikipedia.org/wiki/Absolute_advantage">absolute advantage</a>. </p><p><a href="https://en.wikipedia.org/wiki/David_Ricardo">David Ricardo</a> developed the classical theory of comparative advantage in 1817 to explain why countries engage in <a href="https://en.wikipedia.org/wiki/International_trade">international trade</a> even when one country&#39;s workers are more efficient at producing <i>every</i> single good than workers in other countries. He demonstrated that if two countries capable of producing two commodities engage in the <a href="https://en.wikipedia.org/wiki/Free_market">free market</a> (albeit with the assumption that the capital and labour do not move internationally<sup><span>[</span>1<span>]</span></sup>), then each country will increase its overall consumption by exporting the good for which it has a comparative advantage while importing the other good, provided that there exist differences in <a href="https://en.wikipedia.org/wiki/Labor_productivity">labor productivity</a> between both countries.<sup><span>[</span>2<span>]</span></sup><sup><span>[</span>3<span>]</span></sup> Widely regarded as one of the most powerful<sup><span>[</span>4<span>]</span></sup> yet counter-intuitive<sup><span>[</span>5<span>]</span></sup> insights in economics, Ricardo&#39;s theory implies that comparative advantage rather than <a href="https://en.wikipedia.org/wiki/Absolute_advantage">absolute advantage</a> is responsible for much of international trade. </p><div><h2>Classical theory and David Ricardo&#39;s formulation</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p><a href="https://en.wikipedia.org/wiki/Adam_Smith">Adam Smith</a> first alluded to the concept of <i>absolute advantage</i> as the basis for international trade in 1776, in <i><a href="https://en.wikipedia.org/wiki/The_Wealth_of_Nations">The Wealth of Nations</a></i>: </p><blockquote><p>If a foreign country can supply us with a commodity cheaper than we ourselves can make it, better buy it off them with some part of the produce of our own industry employed in a way in which we have some advantage. The general industry of the country, being always in proportion to the capital which employs it, will not thereby be diminished [...] but only left to find out the way in which it can be employed with the greatest advantage.<sup><span>[</span>6<span>]</span></sup></p></blockquote><p>Writing two decades after Smith in 1808, <a href="https://en.wikipedia.org/wiki/Robert_Torrens_(economist)">Robert Torrens</a> articulated a preliminary definition of comparative advantage as the loss from the closing of trade: </p><blockquote><p>[I]f I wish to know the extent of the advantage, which arises to England, from her giving France a hundred pounds of <a href="https://en.wikipedia.org/wiki/Broadcloth">broadcloth</a>, in exchange for a hundred pounds of lace, I take the quantity of lace which she has acquired by this transaction, and compare it with the quantity which she might, at the same expense of labour and capital, have acquired by manufacturing it at home. The lace that remains, beyond what the labour and capital employed on the cloth, might have fabricated at home, is the amount of the advantage which England derives from the exchange.<sup><span>[</span>7<span>]</span></sup></p></blockquote><p> In 1814 the anonymously published pamphlet <i>Considerations on the Importation of Foreign Corn</i> featured the earliest recorded formulation of the concept of comparative advantage.<sup><span>[</span>8<span>]</span></sup><sup><span>[</span>9<span>]</span></sup> Torrens would later publish his work <i>External Corn Trade</i> in 1815 acknowledging this pamphlet author&#39;s priority.<sup><span>[</span>8<span>]</span></sup> </p><figure><a href="https://en.wikipedia.org/wiki/File:David_Ricardo_(grey).jpg"></a><figcaption>David Ricardo</figcaption></figure><p>In 1817, <a href="https://en.wikipedia.org/wiki/David_Ricardo">David Ricardo</a> published what has since become known as the theory of comparative advantage in his book <i><a href="https://en.wikipedia.org/wiki/On_the_Principles_of_Political_Economy_and_Taxation">On the Principles of Political Economy and Taxation</a></i>.<sup><span>[</span>10<span>]</span></sup> </p><div><h3>Ricardo&#39;s example</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Ricardo_example_of_comparative_advantage.svg"></a><figcaption>Graph illustrating Ricardo&#39;s example:<br/>In case I (diamonds), each country spends 3600 hours to produce a mixture of cloth and wine.<br/>In case II (squares), each country specializes in its comparative advantage, resulting in greater total output.</figcaption></figure><p>In a famous example, Ricardo considers a <a href="https://en.wikipedia.org/wiki/World_economy">world economy</a> consisting of two countries, <a href="https://en.wikipedia.org/wiki/Portugal">Portugal</a> and <a href="https://en.wikipedia.org/wiki/England">England</a>, each producing two goods of identical quality. In Portugal, the <i><a href="https://en.wikipedia.org/wiki/A_priori_and_a_posteriori">a priori</a></i> more efficient country, it is possible to produce <a href="https://en.wikipedia.org/wiki/Wine">wine</a> and <a href="https://en.wikipedia.org/wiki/Cloth">cloth</a> with less labor than it would take to produce the same quantities in England. However, the relative costs or ranking of cost of producing those two goods differ between the countries. </p><p>In this illustration, England could commit 100 hours of labor to produce one unit of cloth, or produce <span>⁠<span><span>5</span><span>/</span><span>6</span></span>⁠</span> units of wine. Meanwhile, in comparison, Portugal could commit 100 hours of labor to produce <span>⁠<span><span>10</span><span>/</span><span>9</span></span>⁠</span> units of cloth, or produce <span>⁠<span><span>10</span><span>/</span><span>8</span></span>⁠</span> units of wine. Portugal possesses an <i>absolute advantage</i> in producing both cloth and wine due to more produced per hour (since <span>⁠<span><span>10</span><span>/</span><span>9</span></span>⁠</span> &gt; 1). If the capital and labour were mobile, both wine and cloth should be made in Portugal, with the capital and labour of England removed there.<sup><span>[</span>11<span>]</span></sup> If they were not mobile, as Ricardo believed them to be generally, then England&#39;s <i>comparative advantage</i> (due to lower opportunity cost) in producing cloth means that it has an incentive to produce more of that good which is relatively cheaper for them to produce than the other—assuming they have an advantageous opportunity to trade in the marketplace for the other more difficult to produce good. </p><p>In the absence of trade, England requires 220 hours of work to both produce and consume one unit each of cloth and wine while Portugal requires 170 hours of work to produce and consume the same quantities. England is more efficient at producing cloth than wine, and Portugal is more efficient at producing wine than cloth. So, if each country specializes in the good for which it has a comparative advantage, then the global production of both goods increases, for England can spend 220 labor hours to produce 2.2 units of cloth while Portugal can spend 170 hours to produce 2.125 units of wine. Moreover, if both countries specialize in the above manner and England trades a unit of its cloth for <span>⁠<span><span>5</span><span>/</span><span>6</span></span>⁠</span> to <span>⁠<span><span>9</span><span>/</span><span>8</span></span>⁠</span> units of Portugal&#39;s wine, then both countries can consume at least a unit each of cloth and wine, with 0 to 0.2 units of cloth and 0 to 0.125 units of wine remaining in each respective country to be consumed or exported. Consequently, both England and Portugal can consume more wine and cloth under free trade than in <a href="https://en.wikipedia.org/wiki/Autarky">autarky</a>. </p><div><h3>Ricardian model</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>The Ricardian model is a <a href="https://en.wikipedia.org/wiki/General_equilibrium">general equilibrium</a> mathematical model of <a href="https://en.wikipedia.org/wiki/International_trade">international trade</a>. Although the idea of the Ricardian model was first presented in the <i>Essay on Profits</i> (a single-commodity version) and then in the <i>Principles</i> (a multi-commodity version) by <a href="https://en.wikipedia.org/wiki/David_Ricardo">David Ricardo</a>, the first mathematical Ricardian model was published by <a href="https://en.wikipedia.org/wiki/William_Whewell">William Whewell</a> in 1833.<sup><span>[</span>12<span>]</span></sup> The earliest test of the Ricardian model was performed by <a href="https://en.wikipedia.org/wiki/Donald_MacDougall">G. D. A. MacDougall</a>, which was published in <i><a href="https://en.wikipedia.org/wiki/The_Economic_Journal">The Economic Journal</a></i> of 1951 and 1952.<sup><span>[</span>13<span>]</span></sup> In the Ricardian model, trade patterns depend on productivity differences. </p><p>The following is a typical modern interpretation of the classical Ricardian model.<sup><span>[</span>14<span>]</span></sup> In the interest of simplicity, it uses notation and definitions, such as opportunity cost, unavailable to Ricardo. </p><p>The world economy consists of two countries, Home and Foreign, which produce wine and cloth. Labor, the only factor of production, is <a href="https://en.wikipedia.org/wiki/Labor_mobility">mobile</a> domestically but not internationally; there may be migration between sectors but not between countries. We denote the labor force in Home by <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <mi>L</mi> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cda6bb9fb712344826da560f9cee7f13da48cfb" alt="{\displaystyle \textstyle L}" title=""/></span>, the amount of labor required to produce one unit of wine in Home by <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle a_{LW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b8c0bbb1f935bfa00dbc0d1214a42cf510c487d" alt="{\displaystyle \textstyle a_{LW}}" title=""/></span>, and the amount of labor required to produce one unit of cloth in Home by <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle a_{LC}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4271ae1c64f3ea2c7f2938f0de00833127d8609f" alt="{\displaystyle \textstyle a_{LC}}" title=""/></span>. The total amount of wine and cloth produced in Home are <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>Q</mi> <mrow> <mi>W</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle Q_{W}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a58624e70a472b4a30bdeedbbfdce84bd765b705" alt="{\displaystyle Q_{W}}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>Q</mi> <mrow> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle Q_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa34fa85ab44838da15ab2a5b944c303c5a1e33a" alt="{\displaystyle Q_{C}}" title=""/></span> respectively. We denote the same variables for Foreign by appending a <a href="https://en.wikipedia.org/wiki/Prime_(symbol)">prime</a>. For instance, <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle a&#39;_{LW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0831e7b84b86cc256103b610b38017592213784a" alt="{\displaystyle \textstyle a&#39;_{LW}}" title=""/></span> is the amount of labor needed to produce a unit of wine in Foreign. </p><p>We do not know if Home can produce cloth using fewer hours of work than Foreign. That is, we do not know if <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mo>&lt;</mo> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mrow> <annotation>{\displaystyle a_{LC}&lt;a&#39;_{LC}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e58106595326da84efb9759821843b5704ad359" alt="{\displaystyle a_{LC}&lt;a&#39;_{LC}}" title=""/></span>. Similarly, we do not know if Home can produce wine using fewer hours of work. However, we assume Home is <i>relatively</i> more productive than Foreign in making in cloth vs. wine: </p><p>Equivalently, we may assume that Home has a comparative advantage in cloth in the sense that it has a lower opportunity cost for cloth in terms of wine than Foreign: </p><p>In the absence of trade, the relative price of cloth and wine in each country is determined solely by the relative labor cost of the goods. Hence the relative autarky price of cloth is <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle a_{LC}/a_{LW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbb0b6f1e09bfc3904e66528c60e66d772cb787e" alt="{\displaystyle a_{LC}/a_{LW}}" title=""/></span> in Home and <span><span><math> <semantics> <mrow> <mstyle> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> <mo>′</mo> </msubsup> <mrow> <mo>/</mo> </mrow> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mrow> <annotation>{\displaystyle a&#39;_{LC}/a&#39;_{LW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/668bae68ca0d1fba314f9291df6db833e064da72" alt="{\displaystyle a&#39;_{LC}/a&#39;_{LW}}" title=""/></span> in Foreign. With free trade, the price of cloth or wine in either country is the world price <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>P</mi> <mrow> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle P_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b258feadbba067fab08cbac9d1f817bc1748fe73" alt="{\displaystyle P_{C}}" title=""/></span> or<span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>P</mi> <mrow> <mi>W</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle P_{W}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c7671b5bff76a0a9896a2b1c2ccbf894f71b4ad" alt="{\displaystyle P_{W}}" title=""/></span>. </p><p>Instead of considering the world demand (or supply) for cloth and wine, we are interested in the world <i>relative demand</i> (or <i>relative supply</i>) for cloth and wine, which we define as the ratio of the world demand (or supply) for cloth to the world demand (or supply) for wine. In general equilibrium, the world relative price <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <msub> <mi>P</mi> <mrow> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>P</mi> <mrow> <mi>W</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle P_{C}/P_{W}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42ada6ab24d288e82425901501becf297baae532" alt="{\displaystyle \textstyle P_{C}/P_{W}}" title=""/></span> will be determined uniquely by the intersection of world relative demand <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <mi>R</mi> <mi>D</mi> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle RD}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15324f8ba296dc284ab3bf39426f22606e0052a5" alt="{\displaystyle \textstyle RD}" title=""/></span> and world relative supply <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <mi>R</mi> <mi>S</mi> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle RS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73741f6bfaeaaf617f7d3b5aaf014908f28d52bc" alt="{\displaystyle \textstyle RS}" title=""/></span> curves. </p><figure><a href="https://en.wikipedia.org/wiki/File:World_relative_supply_and_demand_in_the_classical_Ricardo_model_of_one-factor_international_trade_between_two_countries.svg"></a><figcaption>The demand for cloth relative to wine decreases with the relative price of cloth in terms of wine; the supply <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> <mi>S</mi> </mstyle> </mrow> <annotation>{\displaystyle RS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ecbca11e04b2fc4087dc23553a52f6c3d7c6ee8" alt="{\displaystyle RS}" title=""/></span> of cloth relative to wine increases with relative price. Two relative demand curves <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> <msub> <mi>D</mi> <mrow> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle RD_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f98e762ba13dca58aa273b15efd96ff2dacc589f" alt="{\displaystyle RD_{1}}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> <msub> <mi>D</mi> <mrow> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle RD_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/028ff8ce676a80a6defc7a8fde7d9034f760227a" alt="{\displaystyle RD_{2}}" title=""/></span> are drawn for illustrative purposes.</figcaption></figure><p>We assume that the relative demand curve reflects substitution effects and is decreasing with respect to relative price. The behavior of the relative supply curve, however, warrants closer study. Recalling our original assumption that Home has a comparative advantage in cloth, we consider five possibilities for the relative quantity of cloth supplied at a given price. </p><ul><li>If <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <msub> <mi>P</mi> <mrow> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>P</mi> <mrow> <mi>W</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> </msub> <mo>&lt;</mo> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> <mo>′</mo> </msubsup> <mrow> <mo>/</mo> </mrow> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle P_{C}/P_{W}=a_{LC}/a_{LW}&lt;a&#39;_{LC}/a&#39;_{LW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/694244d6b7d68b1f181bdfb29de5b6ff1486172b" alt="{\displaystyle \textstyle P_{C}/P_{W}=a_{LC}/a_{LW}&lt;a&#39;_{LC}/a&#39;_{LW}}" title=""/></span>, then Foreign specializes in wine, for the wage <span><span><math> <semantics> <mrow> <mstyle> <msubsup> <mi>P</mi> <mrow> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> <mrow> <mo>/</mo> </mrow> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mrow> <annotation>{\displaystyle P&#39;_{W}/a&#39;_{LW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f02820475d448a6caadbf2a16c1710b17e1a9475" alt="{\displaystyle P&#39;_{W}/a&#39;_{LW}}" title=""/></span> in the wine sector is greater than the wage <span><span><math> <semantics> <mrow> <mstyle> <msubsup> <mi>P</mi> <mrow> <mi>C</mi> </mrow> <mo>′</mo> </msubsup> <mrow> <mo>/</mo> </mrow> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mrow> <annotation>{\displaystyle P&#39;_{C}/a&#39;_{LC}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/224765aec76195bd4efbe3d14402b8b27c8a0068" alt="{\displaystyle P&#39;_{C}/a&#39;_{LC}}" title=""/></span> in the cloth sector. However, Home workers are indifferent between working in either sector. As a result, the quantity of cloth supplied can take any value.</li> <li>If <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <msub> <mi>P</mi> <mrow> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>P</mi> <mrow> <mi>W</mi> </mrow> </msub> <mo>&lt;</mo> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> </msub> <mo>&lt;</mo> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> <mo>′</mo> </msubsup> <mrow> <mo>/</mo> </mrow> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle P_{C}/P_{W}&lt;a_{LC}/a_{LW}&lt;a&#39;_{LC}/a&#39;_{LW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1437ee5cade43bfe7a94a25370b193f7135f6275" alt="{\displaystyle \textstyle P_{C}/P_{W}&lt;a_{LC}/a_{LW}&lt;a&#39;_{LC}/a&#39;_{LW}}" title=""/></span>, then both Home and Foreign specialize in wine, for similar reasons as above, and so the quantity of cloth supplied is zero.</li> <li>If <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> </msub> <mo>&lt;</mo> <msub> <mi>P</mi> <mrow> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>P</mi> <mrow> <mi>W</mi> </mrow> </msub> <mo>&lt;</mo> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> <mo>′</mo> </msubsup> <mrow> <mo>/</mo> </mrow> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle a_{LC}/a_{LW}&lt;P_{C}/P_{W}&lt;a&#39;_{LC}/a&#39;_{LW}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2398f316bae4d42c35e46acd705d7d79e1de7e96" alt="{\displaystyle \textstyle a_{LC}/a_{LW}&lt;P_{C}/P_{W}&lt;a&#39;_{LC}/a&#39;_{LW}}" title=""/></span>, then Home specializes in cloth whereas Foreign specializes in wine. The quantity of cloth supplied is given by the ratio <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <mrow> <mfrac> <mrow> <mi>L</mi> <mrow> <mo>/</mo> </mrow> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> </mrow> <mrow> <msup> <mi>L</mi> <mo>′</mo> </msup> <mrow> <mo>/</mo> </mrow> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> </mrow> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle {\frac {L/a_{LC}}{L&#39;/a&#39;_{LW}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c474541fbb0b841112611cd150b1814f95aee084" alt="{\displaystyle \textstyle {\frac {L/a_{LC}}{L&#39;/a&#39;_{LW}}}}" title=""/></span> of the world production of cloth to the world production of wine.</li> <li>If <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> </msub> <mo>&lt;</mo> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> <mo>′</mo> </msubsup> <mrow> <mo>/</mo> </mrow> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> <mo>&lt;</mo> <msub> <mi>P</mi> <mrow> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>P</mi> <mrow> <mi>W</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle a_{LC}/a_{LW}&lt;a&#39;_{LC}/a&#39;_{LW}&lt;P_{C}/P_{W}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef9e9282d4e68f4187a4ba80e3cb16bd79e244d0" alt="{\displaystyle \textstyle a_{LC}/a_{LW}&lt;a&#39;_{LC}/a&#39;_{LW}&lt;P_{C}/P_{W}}" title=""/></span>, then both Home and Foreign specialize in cloth. The quantity of cloth supplied tends to infinity as the quantity of wine supplied approaches zero.</li> <li>If <span><span><math> <semantics> <mrow> <mstyle> <mstyle> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> </msub> <mo>&lt;</mo> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> <mo>′</mo> </msubsup> <mrow> <mo>/</mo> </mrow> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mi>W</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>C</mi> </mrow> </msub> <mrow> <mo>/</mo> </mrow> <msub> <mi>P</mi> <mrow> <mi>W</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation>{\displaystyle \textstyle a_{LC}/a_{LW}&lt;a&#39;_{LC}/a&#39;_{LW}=P_{C}/P_{W}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f76d5eb6b12ba2aba6d8814a94a4827befdd0a8" alt="{\displaystyle \textstyle a_{LC}/a_{LW}&lt;a&#39;_{LC}/a&#39;_{LW}=P_{C}/P_{W}}" title=""/></span>, then Home specializes in cloth while Foreign workers are indifferent between sectors. Again, the relative quantity of cloth supplied can take any value.</li></ul><figure><a href="https://en.wikipedia.org/wiki/File:Consumption_possibilities_in_the_classical_Ricardo_model_of_one-factor_international_trade_between_two_countries.svg"></a><figcaption>The blue triangle depicts Home&#39;s original production (and consumption) possibilities. By trading, Home can also consume bundles in the pink triangle despite facing the same productions possibility frontier.</figcaption></figure><p>As long as the relative demand is finite, the relative price is always bounded by the inequality </p><p>In autarky, Home faces a <a href="https://en.wikipedia.org/wiki/Production%E2%80%93possibility_frontier">production constraint</a> of the form </p><p>from which it follows that Home&#39;s cloth consumption at the production possibilities frontier is </p><p>With free trade, Home produces cloth exclusively, an amount of which it exports in exchange for wine at the prevailing rate. Thus Home&#39;s overall consumption is now subject to the constraint </p><p>while its cloth consumption at the <i>consumption possibilities</i> frontier is given by </p><p>A symmetric argument holds for Foreign. Therefore, by trading and specializing in a good for which it has a comparative advantage, each country can expand its consumption possibilities. Consumers can choose from bundles of wine and cloth that they could not have produced themselves in closed economies. </p><p>There is another way to prove the theory of comparative advantage, which requires less assumption than the above-detailed proof, and in particular does not require for the hourly wages to be equal in both industries, nor requires any equilibrium between offer and demand on the market.<sup><span>[</span>15<span>]</span></sup> Such a proof can be extended to situations with many goods and many countries, non constant returns and more than one factor of production. </p><div><h3>Terms of trade</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Terms of trade is the rate at which one good could be traded for another. If both countries specialize in the good for which they have a comparative advantage then trade, the terms of trade for a good (that benefit both entities) will fall between each entities opportunity costs. In the example above one unit of cloth would trade for between <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\frac {5}{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c49fbcd8bd12062e0998418e4589521da0ba0a6" alt="{\displaystyle {\frac {5}{6}}}" title=""/></span> units of wine and <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mfrac> <mn>9</mn> <mn>8</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\frac {9}{8}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c7ee38d65cd9c5dba0a6b21a58b6b8ed3fdd7f1" alt="{\displaystyle {\frac {9}{8}}}" title=""/></span> units of wine.<sup><span>[</span>16<span>]</span></sup> </p><div><h3>Socio-political context of discovery</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>While the mathematical formalization of comparative advantage is attributed to David Ricardo&#39;s Principles (1817)<sup><span>[</span>17<span>]</span></sup> the doctrine emerged primarily as a response to the socio-political turmoil of the British Corn Laws. Following the Napoleonic Wars, the 1815 Corn Laws imposed high tariffs on imported grain to protect domestic landowners, sparking a fierce debate between the landed gentry and emerging industrial capitalists. </p><p>Economists such as Robert Torrens and David Ricardo sought to prove that protectionism hindered national growth by forcing capital into less efficient agricultural production. In his 1815 Essay on the External Corn Trade,<sup><span>[</span>18<span>]</span></sup> Torrens provided an early formulation of the principle, arguing that it was beneficial to import grain even if it could be grown cheaper at home, provided labor was better utilized in manufacturing. This context illustrates that the theory was not merely an abstract discovery but a targeted tool designed to advocate for the repeal of protectionist legislation and the transition toward a specialized global economy. </p><div><h2>Haberler&#39;s opportunity costs formulation</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>In 1930 Austrian-American economist <a href="https://en.wikipedia.org/wiki/Gottfried_Haberler">Gottfried Haberler</a> detached the doctrine of comparative advantage from Ricardo&#39;s labor theory of value and provided a modern opportunity cost formulation. Haberler&#39;s reformulation of comparative advantage revolutionized the theory of international trade and laid the conceptual groundwork of modern trade theories. </p><p>Haberler&#39;s innovation was to reformulate the theory of comparative advantage such that the value of good X is measured in terms of the forgone units of production of good Y rather than the labor units necessary to produce good X, as in the Ricardian formulation. Haberler implemented this opportunity-cost formulation of comparative advantage by introducing the concept of a production possibility curve into international trade theory.<sup><span>[</span>19<span>]</span></sup> </p><div><h2>Modern theories</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>Since 1817, economists have attempted to generalize the Ricardian model and derive the principle of comparative advantage in broader settings, most notably in the <a href="https://en.wikipedia.org/wiki/Neoclassical_economics">neoclassical</a> <em>specific factors</em> <a href="https://en.wikipedia.org/wiki/Richardo%E2%80%93Viner_model">Ricardo–Viner</a> (which allows for the model to include more factors than just labour)<sup><span>[</span>20<span>]</span></sup> and <em>factor proportions</em> <a href="https://en.wikipedia.org/wiki/Heckscher%E2%80%93Ohlin_model">Heckscher–Ohlin models</a>. Subsequent developments in the <a href="https://en.wikipedia.org/wiki/New_trade_theory">new trade theory</a>, motivated in part by the empirical shortcomings of the H–O model and its inability to explain <a href="https://en.wikipedia.org/wiki/Intra-industry_trade">intra-industry trade</a>, have provided an explanation for aspects of trade that are not accounted for by comparative advantage.<sup><span>[</span>21<span>]</span></sup> Nonetheless, economists like <a href="https://en.wikipedia.org/wiki/Alan_Deardorff">Alan Deardorff</a>,<sup><span>[</span>22<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/Avinash_Dixit">Avinash Dixit</a>, <a href="https://en.wikipedia.org/wiki/Victor_D._Norman">Victor D. Norman</a>,<sup><span>[</span>23<span>]</span></sup> and <a href="https://en.wikipedia.org/wiki/Gottfried_Haberler">Gottfried Haberler</a> have responded with weaker generalizations of the principle of comparative advantage, in which countries will only <i>tend</i> to export goods for which they have a comparative advantage. </p><div><h3>Dornbusch et al.&#39;s continuum of goods formulation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>In both the Ricardian and H–O models, the comparative advantage theory is formulated for a 2 countries/2 commodities case. It can be extended to a 2 countries/many commodities case, or a many countries/2 commodities case. Adding commodities in order to have a smooth continuum of goods is the major insight of the seminal paper by <a href="https://en.wikipedia.org/wiki/Rudi_Dornbusch">Dornbusch</a>, <a href="https://en.wikipedia.org/wiki/Stanley_Fischer">Fisher</a>, and <a href="https://en.wikipedia.org/wiki/Paul_Samuelson">Samuelson</a>. In fact, inserting an increasing number of goods into the chain of comparative advantage makes the gaps between the ratios of the labor requirements negligible, in which case the three types of equilibria around any good in the original model collapse to the same outcome. It notably allows for transportation costs to be incorporated, although the framework remains restricted to two countries.<sup><span>[</span>24<span>]</span></sup><sup><span>[</span>25<span>]</span></sup> But in the case with many countries (more than 3 countries) and many commodities (more than 3 commodities), the notion of comparative advantage requires a substantially more complex formulation.<sup><span>[</span>26<span>]</span></sup> </p><div><h3>Deardorff&#39;s general law of comparative advantage</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>Skeptics of comparative advantage have underlined that its theoretical implications hardly hold when applied to individual commodities or pairs of commodities in a world of multiple commodities. Deardorff argues that the insights of comparative advantage remain valid if the theory is restated in terms of averages across all commodities. His models provide multiple insights on the correlations between vectors of trade and vectors with relative-autarky-price measures of comparative advantage. &quot;Deardorff&#39;s general law of comparative advantage&quot; is a model incorporating multiple goods which takes into account tariffs, transportation costs, and other obstacles to trade. </p><div><h3>Alternative approaches</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><p>Recently, Y. Shiozawa succeeded in constructing a theory of international value in the tradition of Ricardo&#39;s <a href="https://en.wikipedia.org/wiki/Cost-of-production_theory_of_value">cost-of-production theory of value</a>.<sup><span>[</span>27<span>]</span></sup><sup><span>[</span>28<span>]</span></sup> This was based on a wide range of assumptions: Many countries; Many commodities; Several production techniques for a product in a country; Input trade (<a href="https://en.wikipedia.org/wiki/International_trade#Traded_intermediate_goods">intermediate goods</a> are freely traded); Durable capital goods with constant efficiency during a predetermined lifetime; No transportation cost (extendable to positive cost cases). </p><p>In a famous comment, McKenzie pointed that &quot;A moment&#39;s consideration will convince one that Lancashire would be unlikely to produce cotton cloth if the cotton had to be grown in England.&quot;<sup><span>[</span>29<span>]</span></sup> However, McKenzie and later researchers could not produce a general theory which includes traded input goods because of the mathematical difficulty.<sup><span>[</span>30<span>]</span></sup> As John Chipman points it, McKenzie found that &quot;introduction of trade in intermediate product necessitates a fundamental alteration in classical analysis.&quot;<sup><span>[</span>31<span>]</span></sup> Durable capital goods such as machines and installations are inputs to the productions in the same title as part and ingredients. </p><p>In view of the new theory, no physical criterion exists. Deardorff examines 10 versions of definitions in two groups but could not give a general formula for the case with intermediate goods.<sup><span>[</span>30<span>]</span></sup> The competitive patterns are determined by the traders trials to find cheapest products in a world. The search of cheapest product is achieved by world optimal procurement. Thus the new theory explains how the global supply chains are formed.<sup><span>[</span>32<span>]</span></sup><sup><span>[</span>33<span>]</span></sup> </p><div><h2>Empirical approach to comparative advantage</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><p>Comparative advantage is a theory about the benefits that specialization and trade would bring, rather than a strict prediction about actual behavior. (In practice, governments restrict international trade for a variety of reasons; under <a href="https://en.wikipedia.org/wiki/Ulysses_S._Grant">Ulysses S. Grant</a>, the US postponed opening up to free trade until its industries were up to strength, following the example set earlier by Britain.<sup><span>[</span>34<span>]</span></sup>) Nonetheless there is a large amount of <a href="https://en.wikipedia.org/wiki/Empirical_evidence">empirical</a> work testing the predictions of comparative advantage. The empirical works usually involve testing predictions of a particular model. For example, the Ricardian model predicts that technological differences in countries result in differences in labor productivity. The differences in labor productivity in turn determine the comparative advantages across different countries. Testing the Ricardian model for instance involves looking at the relationship between relative labor productivity and international trade patterns. A country that is relatively efficient in producing shoes tends to export shoes. </p><div><h3>Direct test: natural experiment of Japan</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><p>Assessing the validity of comparative advantage on a global scale with the examples of contemporary economies is analytically challenging because of the multiple factors driving globalization: indeed, investment, migration, and technological change play a role in addition to trade. Even if we could isolate the workings of open trade from other processes, establishing its causal impact also remains complicated: it would require a comparison with a counterfactual world without open trade. Considering the durability of different aspects of globalization, it is hard to assess the sole impact of open trade on a particular economy.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><p><a href="https://en.wikipedia.org/wiki/Daniel_Bernhofen">Daniel Bernhofen</a> and John Brown have attempted to address this issue, by using a natural experiment of a sudden transition to open trade in a market economy. They focus on the case of Japan.<sup><span>[</span>35<span>]</span></sup><sup><span>[</span>36<span>]</span></sup> The Japanese economy indeed developed over several centuries under autarky and a quasi-isolation from international trade but was, by the mid-19th century, a sophisticated market economy with a population of 30 million. Under Western military pressure, Japan opened its economy to foreign trade through a series of <a href="https://en.wikipedia.org/wiki/Unequal_treaties">unequal treaties</a>.<sup><span>[</span>37<span>]</span></sup> </p><p>In 1859, the treaties limited tariffs to 5% and opened trade to Westerners. Considering that the transition from autarky, or self-sufficiency, to open trade was brutal, few changes to the fundamentals of the economy occurred in the first 20 years of trade. The general law of comparative advantage theorizes that an economy should, on average, export goods with low self-sufficiency prices and import goods with high self-sufficiency prices. Bernhofen and Brown found that by 1869, the price of Japan&#39;s main export, silk and derivatives, saw a 100% increase in real terms, while the prices of numerous imported goods declined of 30-75%. In the next decade, the ratio of imports to gross domestic product reached 4%.<sup><span>[</span>38<span>]</span></sup> </p><div><h3>Structural estimation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><p>Another important way of demonstrating the validity of comparative advantage has consisted in &#39;structural estimation&#39; approaches. These approaches have built on the Ricardian formulation of two goods for two countries and subsequent models with many goods or many countries. The aim has been to reach a formulation accounting for both multiple goods and multiple countries, in order to reflect real-world conditions more accurately. <a href="https://en.wikipedia.org/wiki/Jonathan_Eaton">Jonathan Eaton</a> and <a href="https://en.wikipedia.org/wiki/Samuel_Kortum">Samuel Kortum</a> underlined that a convincing model needed to incorporate the idea of a &#39;continuum of goods&#39; developed by Dornbusch et al. for both goods and countries. They were able to do so by allowing for an arbitrary (integer) number <var>i</var> of countries, and dealing exclusively with unit labor requirements for each good (one for each point on the unit interval) in each country (of which there are <var>i</var>).<sup><span>[</span>39<span>]</span></sup> </p><div><h3>Earlier empirical work</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><p>Two of the first tests of comparative advantage were by MacDougall (1951, 1952).<sup><span>[</span>40<span>]</span></sup> A prediction of a two-country Ricardian comparative advantage model is that countries will export goods where output per worker (i.e. productivity) is higher. That is, we expect a positive relationship between output per worker and the number of exports. MacDougall tested this relationship with data from the US and UK, and did indeed find a positive relationship. The statistical test of this positive relationship was replicated with new data by Stern (1962)<sup><span>[</span>41<span>]</span></sup> and <a href="https://en.wikipedia.org/wiki/B%C3%A9la_Balassa">Balassa</a> (1963).<sup><span>[</span>42<span>]</span></sup> </p><p>Dosi et al. (1988)<sup><span>[</span>43<span>]</span></sup> conducted a book-length empirical examination that suggests that international trade in manufactured goods is largely driven by differences in national technological competencies. </p><p>One critique of the textbook model of comparative advantage is that there are only two goods. The results of the model are robust to this assumption.<sup><span>[</span>24<span>]</span></sup> generalized the theory to allow for such a large number of goods as to form a smooth continuum. Based in part on these generalizations of the model,<sup><span>[</span>44<span>]</span></sup> provides a more recent view of the Ricardian approach to explain trade between countries with similar resources. </p><p>More recently, Golub and Hsieh (2000)<sup><span>[</span>45<span>]</span></sup> presents modern statistical analysis of the relationship between relative productivity and trade patterns, which finds reasonably strong correlations, and Nunn (2007)<sup><span>[</span>46<span>]</span></sup> finds that countries that have greater enforcement of contracts specialize in goods that require relationship-specific investments. </p><p>Taking a broader perspective, there has been work about the benefits of international trade. Zimring &amp; Etkes (2014)<sup><span>[</span>47<span>]</span></sup> find that the <a href="https://en.wikipedia.org/wiki/Blockade_of_the_Gaza_Strip">blockade of the Gaza Strip</a>, which substantially restricted the availability of imports to Gaza, saw labor productivity fall by 20% in three years. <a href="https://en.wikipedia.org/wiki/James_Markusen">Markusen</a> et al. (1994)<sup><span>[</span>48<span>]</span></sup> reports the effects of moving away from <a href="https://en.wikipedia.org/wiki/Autarky">autarky</a> to <a href="https://en.wikipedia.org/wiki/Free_trade">free trade</a> during the <a href="https://en.wikipedia.org/wiki/Meiji_Restoration">Meiji Restoration</a>, with the result that national income increased by up to 65% in 15 years. </p><div><h3>Criticism</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div><p>Several arguments have been advanced against using comparative advantage as a justification for advocating free trade, and they have gained an audience among economists. <a href="https://en.wikipedia.org/wiki/James_Brander">James Brander</a> and <a href="https://en.wikipedia.org/wiki/Barbara_J._Spencer">Barbara J. Spencer</a> demonstrated how, in a strategic setting where a few firms compete for the world market, export subsidies and import restrictions can keep foreign firms from competing with national firms, increasing welfare in the country implementing these so-called strategic trade policies.<sup><span>[</span>49<span>]</span></sup> </p><p>There are some economists who dispute the claims of the benefit of comparative advantage. <a href="https://en.wikipedia.org/wiki/James_K._Galbraith">James K. Galbraith</a> has stated that &quot;free trade has attained the status of a god&quot; and that &quot;<span> </span>... none of the world&#39;s most successful trading regions, including Japan, Korea, Taiwan, and now mainland China, reached their current status by adopting <a href="https://en.wikipedia.org/wiki/Neoliberal">neoliberal</a> trading rules.&quot; He argues that comparative advantage relies on the assumption of <a href="https://en.wikipedia.org/wiki/Constant_returns">constant returns</a>, which he states is not generally the case.<sup><span>[</span>50<span>]</span></sup> According to Galbraith, nations trapped into specializing in agriculture are condemned to perpetual poverty, as agriculture is dependent on land, a finite non-increasing natural resource.<sup><span>[</span>51<span>]</span></sup> </p><div><h4>21st century</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div><p>In the 21st century, Ricardo&#39;s comparative advantage theory has faced new challenges due to the development of <a href="https://en.wikipedia.org/wiki/Global_value_chain">global value chains</a>. Unlike Ricardo&#39;s model of trade between anonymous parties with equal bargaining power, modern global value chains operate between connected firms with unequal power, with nations specializing in particular production stages rather than complete goods.<sup><span>[</span>52<span>]</span></sup> </p><p>The COVID-19 pandemic further challenged the theory when disruptions to globally distributed supply chains prompted nations to reconsider their reliance on foreign production, particularly for critical goods like medical equipment and pharmaceuticals.<sup><span>[</span>53<span>]</span></sup> In response, some countries have begun reinforcing supplier relationships or diversifying trade networks to mitigate future disruptions.<sup><span>[</span>54<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=17"><span>edit</span></a><span>]</span></span></div><ul> <li><span><span><a href="https://en.wikipedia.org/wiki/File:Emblem-money.svg"></a></span></span><span><a href="https://en.wikipedia.org/wiki/Portal:Business">Business portal</a></span></li></ul><ul><li><a href="https://en.wikipedia.org/wiki/Bureau_of_Labor_Statistics">Bureau of Labor Statistics</a></li> <li><a href="https://en.wikipedia.org/wiki/Resource_curse">Resource curse</a></li> <li><a href="https://en.wikipedia.org/wiki/Revealed_comparative_advantage">Revealed comparative advantage</a></li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=18"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span><cite>Schumacher, Reinhard (2012). <i>Free Trade and Absolute and Comparative Advantage: A Critical Comparison of Two Major Theories of International Trade</i>. Universitätsverlag Potsdam. pp. <span>51–</span>52. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9783869561950"><bdi>9783869561950</bdi></a>. <q>Neoclassical and modern theories maintain the difference between domestic and international trade. They retain the assumption that both labour and capital do not move internationally.</q></cite></span> </li> <li><span><b>^</b></span> <span><a href="https://en.wikipedia.org/wiki/William_Baumol">Baumol, William J.</a> and <a href="https://en.wikipedia.org/wiki/Alan_Blinder">Alan S. Blinder</a>, <i>Economics: Principles and Policy</i>, p. 50<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citing_sources#What_information_to_include"><span>full citation needed</span></a></i>]</sup></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Arthur_O%27Sullivan_(economist)">O&#39;Sullivan, Arthur</a>; <a href="https://en.wikipedia.org/wiki/Steven_M._Sheffrin">Sheffrin, Steven M.</a> (2003) [January 2002]. <i>Economics: Principles in Action</i>. The Wall Street Journal: Classroom Edition (2nd ed.). Upper Saddle River, New Jersey: Pearson Prentice Hall. p. 444. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9780130630858"><bdi>9780130630858</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Steven M. Suranovic (2010). <a href="http://internationalecon.com/Trade/Tch40/T40-0.php">&quot;International Trade Theory and Policy&quot;</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Paul_Krugman">Krugman, Paul</a> (1996). <a href="http://web.mit.edu/krugman/www/ricardo.htm">&quot;Ricardo&#39;s Difficult Idea&quot;</a><span>. Retrieved <span>2014-08-09</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Adam_Smith">Smith, Adam</a> (1776). <a href="https://en.wikipedia.org/wiki/The_Wealth_of_Nations"><i>An Inquiry into the Nature and Causes of the Wealth of Nations</i></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Robert_Torrens_(economist)">Torrens, Robert</a> (1808). <i>The Economists Refuted and Other Early Economic Writings</i> (1984 ed.). New York: Kelley. p. 37.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Noel W. Thompson; Nigel F. B. Allington, eds. (13 December 2010). <a href="https://books.google.com/books?id=6YPu0n04GfIC&amp;pg=PA101"><i>English, Irish and Subversives Among the Dismal Scientists</i></a>. Emerald Group Publishing. p. 101. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-85724-062-0"><bdi>978-0-85724-062-0</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Maneschi, Andrea (18 May 2017). <a href="https://books.google.com/books?id=jTslDwAAQBAJ&amp;pg=PA33">&quot;Chapter 3: David Ricardo&#39;s Trade Theory Anticipations and later developments&quot;</a>. In Shigeyoshi Senga; Masatomi Fujimoto; Taichi Tabuchi (eds.). <i>Ricardo and International Trade</i>. Taylor &amp; Francis. p. 33. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-351-68616-7"><bdi>978-1-351-68616-7</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Kalim Siddiqui. <a href="https://pure.hud.ac.uk/ws/portalfiles/portal/14132571/David_Ricardo_s_Comparative_Trade_Theory.pdf">&quot;David Ricardo&#39;s Comparative Advantage and Developing Countries: Myth and Reality&quot;</a> <span>(PDF)</span>. <i>International Critical Thought</i>. <b>8</b> (3) – via <a href="https://en.wikipedia.org/wiki/University_of_Huddersfield">University of Huddersfield</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/David_Ricardo">Ricardo, David</a> (1817). <i>On the Principles of Political Economy and Taxation</i>. J. Murray. pp. <span>160–</span>162. <q>It would undoubtedly be advantageous to the capitalists of England, and to the consumers in both countries, that under such circumstances, the wine and the cloth should both be made in Portugal, and therefore that the capital and labour of England employed in making cloth, should be removed to Portugal for that purpose</q></cite></span> </li> <li><span><b>^</b></span> <span><cite>Wood, John Cunningham (1991). <a href="https://books.google.com/books?id=h5GzUUfTL4sC&amp;q=Ricardian+model&amp;pg=PA312"><i>David Ricardo: Critical Assessments</i></a>. Taylor &amp; Francis. p. 312. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9780415063807"><bdi>9780415063807</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Ingham, Barbara (2004). <a href="https://books.google.com/books?id=zIaS9R7HUGIC&amp;q=international+economics"><i>International Economics: A European Focus</i></a>. Pearson Education. p. 22. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9780273655077"><bdi>9780273655077</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Paul_Krugman">Krugman, Paul</a>; <a href="https://en.wikipedia.org/wiki/Maurice_Obstfeld">Obstfeld, Maurice</a> (1988). <i>International Economics: Theory and Policy</i> (2008 ed.). 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(2016). &quot;Testing the General Validity of the Heckscher-Ohlin Theorem&quot;. <i><a href="https://en.wikipedia.org/wiki/American_Economic_Journal:_Microeconomics">American Economic Journal: Microeconomics</a></i>. <b>8</b> (4): <span>54–</span>90. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1257%2Fmic.20130126">10.1257/mic.20130126</a>.</cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/James_K._Galbraith">Galbraith, James K.</a> (2008). <i>The Predator State: How conservatives abandoned the free market and why liberals should too</i>. New York: free Press. p. <a href="https://archive.org/details/predatorstatehow00galb/page/70">70</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9781416566830"><bdi>9781416566830</bdi></a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a> <a href="https://search.worldcat.org/oclc/192109752">192109752</a>.</cite></li> <li><cite>Maneschi, Andrea (1998). <i>Comparative Advantage in International Trade: A Historical Perspective</i>. Cheltenham: Elgar. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9781781956243"><bdi>9781781956243</bdi></a>.</cite></li></ul> </div><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=20"><span>edit</span></a><span>]</span></span></div><ul><li><cite>Findlay, Ronald (1987). &quot;Comparative Advantage&quot;. <i><a href="https://en.wikipedia.org/wiki/The_New_Palgrave_Dictionary_of_Economics">The New Palgrave Dictionary of Economics</a></i>. <b>1</b>: <span>514–</span>517.</cite></li></ul><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Comparative_advantage&amp;action=edit&amp;section=21"><span>edit</span></a><span>]</span></span></div><div> <div> <div>Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Comparative_advantage">Comparative advantage</a></b></i>.</div></div> </div><ul><li><a href="http://voxeu.org/content/cloth-wine-relevance-ricardo-s-comparative-advantage-21st-century">&quot;Cloth for Wine? The Relevance of Ricardo&#39;s Comparative Advantage in the 21st Century&quot;</a>, VoxEU Ebook. <a href="https://web.archive.org/web/20220702132700/https://voxeu.org/content/cloth-wine-relevance-ricardo-s-comparative-advantage-21st-century">Archived</a> 2022-07-02 at the <a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a></li> <li><a href="https://web.archive.org/web/20020806175422/http://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/ricardo/prin/index.html"><i>The Principles of Trade and Taxation</i></a> by <a href="https://en.wikipedia.org/wiki/David_Ricardo">David Ricardo</a>, 3rd ed, (1821) (original source text)</li> <li><a href="http://internationalecon.com/v1.0/ch40/ch40.html">&quot;The Ricardian Model of Comparative Advantage&quot;</a>, internationalecon.com</li> <li><a href="http://icalc.co.il/calculators/index.php/economics-calculators/134-comparative-advantage-calculator.html">Comparative Advantage Calculator</a></li></ul><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:International_trade"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:International_trade"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:International_trade"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/International_trade">International trade</a></div></th></tr><tr><th>Terminology</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Absolute_advantage">Absolute advantage</a></li> <li><a href="https://en.wikipedia.org/wiki/Balance_of_payments">Balance of payments</a></li> <li><a href="https://en.wikipedia.org/wiki/Balance_of_trade">Balance of trade</a></li> <li><a href="https://en.wikipedia.org/wiki/Capital_account">Capital account</a></li> <li>Comparative advantage</li> <li><a href="https://en.wikipedia.org/wiki/Current_account_(balance_of_payments)">Current account</a></li> <li><a href="https://en.wikipedia.org/wiki/Export-oriented_industrialization">Export-oriented industrialization</a></li> <li><a href="https://en.wikipedia.org/wiki/Fair_trade">Fair trade</a></li> <li><a href="https://en.wikipedia.org/wiki/Foreign_exchange_reserves">Foreign exchange reserves</a></li> <li><a href="https://en.wikipedia.org/wiki/Globalization">Globalization</a></li> <li><a href="https://en.wikipedia.org/wiki/Global_labor_arbitrage">Global labor arbitrage</a></li> <li><a href="https://en.wikipedia.org/wiki/Import_substitution_industrialization">Import substitution industrialization</a></li> <li><a href="https://en.wikipedia.org/wiki/Multinational_corporation">Multinational corporation</a></li> <li><a href="https://en.wikipedia.org/wiki/Net_capital_outflow">Net capital outflow</a></li> <li><a href="https://en.wikipedia.org/wiki/Outsourcing">Outsourcing</a></li> <li><a href="https://en.wikipedia.org/wiki/Tariff">Tariff</a></li> <li><a href="https://en.wikipedia.org/wiki/Trade_justice">Trade justice</a></li> <li><a href="https://en.wikipedia.org/wiki/Trade_war">Trade war</a></li> <li><a href="https://en.wikipedia.org/wiki/Trading_nation">Trading nation</a></li></ul> </div></td></tr><tr><th><div>Organizations<br/>and policies</div></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/International_Monetary_Fund">International Monetary Fund</a></li> <li><a href="https://en.wikipedia.org/wiki/UN_Trade_and_Development">UN Trade and Development</a></li> <li><a href="https://en.wikipedia.org/wiki/World_Bank_Group">World Bank Group</a></li> <li><a href="https://en.wikipedia.org/wiki/World_Trade_Organization">World Trade Organization</a> <ul><li><a href="https://en.wikipedia.org/wiki/International_Trade_Centre">International Trade Centre</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/International_Chamber_of_Commerce">International Chamber of Commerce</a></li> <li><a href="https://en.wikipedia.org/wiki/Bilateral_investment_treaty">Bilateral investment treaty</a></li> <li><a href="https://en.wikipedia.org/wiki/Economic_integration">Economic integration</a></li> <li><a href="https://en.wikipedia.org/wiki/Incoterms">Incoterms</a></li> <li><a href="https://en.wikipedia.org/wiki/ATA_Carnet">ATA Carnet</a></li> <li><a href="https://en.wikipedia.org/wiki/Free-trade_zone">Free-trade zone</a></li> <li><a href="https://en.wikipedia.org/wiki/Special_economic_zone">Special economic zone</a></li> <li><a href="https://en.wikipedia.org/wiki/Trade_agreement">Trade agreement</a></li> <li><a href="https://en.wikipedia.org/wiki/Trade_barrier">Trade barrier</a></li> <li><a href="https://en.wikipedia.org/wiki/Trade_bloc">Trade bloc</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Political_economy">Political economy</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Free_trade">Free trade</a> <ul><li><a href="https://en.wikipedia.org/wiki/Adam_Smith">Adam Smith</a></li> <li><i><a href="https://en.wikipedia.org/wiki/The_Wealth_of_Nations">The Wealth of Nations</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Corn_Laws">Corn Laws</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Mercantilism">Mercantilism</a></li> <li><a href="https://en.wikipedia.org/wiki/Protectionism">Protectionism</a> <ul><li><a href="https://en.wikipedia.org/wiki/Economic_nationalism">Economic nationalism</a></li> <li><a href="https://en.wikipedia.org/wiki/Autarky">Autarky</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Dedollarisation">Dedollarisation</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Regional_organization">Regional organizations</a></th><td><table><tbody><tr><th>Americas</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Andean_Community">Andean Community</a></li> <li><a href="https://en.wikipedia.org/wiki/Caribbean_Community">Caribbean Community</a></li> <li><a href="https://en.wikipedia.org/wiki/Central_American_Integration_System">Central American Integration System</a></li> <li><a href="https://en.wikipedia.org/wiki/Mercosur">Mercosur</a></li></ul> </div></td></tr><tr><th>Asia-Pacific</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/ASEAN">Association of Southeast Asian Nations</a></li> <li><a href="https://en.wikipedia.org/wiki/Regional_Comprehensive_Economic_Partnership">Regional Comprehensive Economic Partnership</a></li> <li><a href="https://en.wikipedia.org/wiki/South_Asian_Association_for_Regional_Cooperation">South Asian Association for Regional Cooperation</a></li></ul> </div></td></tr><tr><th>Europe, Central Asia, and North Asia</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Customs_Union_of_the_Eurasian_Economic_Union">Customs Union of the Eurasian Economic Union</a></li> <li><a href="https://en.wikipedia.org/wiki/Eurasian_Economic_Union">Eurasian Economic Union</a></li> <li><a href="https://en.wikipedia.org/wiki/European_Union_Customs_Union">European Union Customs Union</a></li></ul> </div></td></tr><tr><th>Middle East and North Africa</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Arab_Customs_Union">Arab Customs Union</a></li> <li><a href="https://en.wikipedia.org/wiki/Gulf_Cooperation_Council">Gulf Cooperation Council</a></li></ul> </div></td></tr><tr><th>Subsaharan Africa</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/East_African_Community">East African Community</a></li> <li><a href="https://en.wikipedia.org/wiki/CEMAC">Economic and Monetary Community of Central Africa</a></li> <li><a href="https://en.wikipedia.org/wiki/Southern_African_Customs_Union">Southern African Customs Union</a></li> <li><a href="https://en.wikipedia.org/wiki/West_African_Economic_and_Monetary_Union">West African Economic and Monetary Union</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/List_of_top_exporting_countries_by_product_category">Exports by product</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_aircraft_and_spacecraft_exports">Aircraft &amp; Spacecraft</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_aircraft_component_exports">Aircraft parts</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_aluminium_exports">Aluminium</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_automotive_component_exports">Car parts</a></li> <li><a href="https://en.wikipedia.org/wiki/Coal#Major_exporters">Coal</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_coffee_exports">Coffee</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_computer_exports">Computers</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_copper_exports">Copper</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_maize_exports">Corn</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_raw_cotton_exports">Cotton</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_diamond_exports">Diamonds</a></li> <li><a href="https://en.wikipedia.org/wiki/Electricity_by_country">Electricity</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_electronics_exports">Electronics</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_engine_exports">Engines</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_gas_turbine_exports">Gas turbines</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_gold_exports">Gold</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_integrated_circuit_exports">Integrated circuits</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_iron-ore_exports">Iron ore</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_live_animal_exports">Live animals</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_natural_gas_exports">Natural gas</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_oil_exports">Oil</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_refined_petroleum_exports">Petrol</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_pharmaceutical_exports">Pharmaceuticals</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_photovoltaics_exports">Photovoltaics</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_ship_exports">Ships</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_steel_production#Exports">Steel</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_telecommunications_equipment_exports">Telecommunications equipment</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_telephone_exports">Telephones</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_textile_exports">Textiles</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_truck_exports">Trucks</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_vehicle_exports">Vehicles</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_countries_by_wheat_exports">Wheat</a></li> <li><a href="https://en.wikipedia.org/wiki/Wine#Exporting_countries">Wine</a></li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li> <a href="https://en.wikipedia.org/wiki/Category:International_trade">Category</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q215551#identifiers"></a></span></div></th></tr><tr><th>International</th><td><div><ul><li><span><a href="https://d-nb.info/gnd/4213502-3">GND</a></span></li></ul></div></td></tr><tr><th>National</th><td><div><ul><li><span><a href="https://id.loc.gov/authorities/sh85029294">United States</a></span></li><li><span><span><a href="https://aleph.nkp.cz/F/?func=find-c&amp;local_base=aut&amp;ccl_term=ica=ph333368&amp;CON_LNG=ENG">Czech Republic</a></span></span></li><li><span><a href="https://www.nli.org.il/en/authorities/987007545495505171">Israel</a></span></li></ul></div></td></tr><tr><th>Other</th><td><div><ul><li><span><a href="https://lux.collections.yale.edu/view/concept/2841a5ae-f3af-4f2e-aace-b3f63ef4645a">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div> Snapshot isolation - Wikipedia https://en.wikipedia.org/wiki/Snapshot_isolation qecrLEWEVmCFH8SvfvbgbWu55ajfEJVER4na5w== Fri, 08 May 2026 09:28:40 +0000 Database management technique <div>Database management technique</div><p>In <a href="https://en.wikipedia.org/wiki/Database">databases</a>, and <a href="https://en.wikipedia.org/wiki/Transaction_processing">transaction processing</a> (transaction management), <b>snapshot isolation</b> is a guarantee that all reads made in a <a href="https://en.wikipedia.org/wiki/Database_transaction">transaction</a> will see a consistent snapshot of the database (in practice it reads the last committed values that existed at the time it started), and the transaction itself will successfully commit only if no updates it has made conflict with any concurrent updates made since that snapshot. </p><p>Snapshot isolation has been adopted by several major <a href="https://en.wikipedia.org/wiki/Database_management_system">database management systems</a>, such as <a href="https://en.wikipedia.org/wiki/InterBase">InterBase</a>, <a href="https://en.wikipedia.org/wiki/Firebird_(database_server)">Firebird</a>, <a href="https://en.wikipedia.org/wiki/Oracle_database">Oracle</a>, <a href="https://en.wikipedia.org/wiki/MySQL">MySQL</a>,<sup><span>[</span>1<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/PostgreSQL">PostgreSQL</a>, <a href="https://en.wikipedia.org/wiki/Sql_anywhere">SQL Anywhere</a>, <a href="https://en.wikipedia.org/wiki/MongoDB">MongoDB</a><sup><span>[</span>2<span>]</span></sup> and <a href="https://en.wikipedia.org/wiki/Microsoft_SQL_Server">Microsoft SQL Server</a> (2005 and later). The main reason for its adoption is that it allows better performance than <a href="https://en.wikipedia.org/wiki/Serializability">serializability</a>, yet still avoids most of the concurrency anomalies that serializability avoids (but not all). In practice snapshot isolation is implemented within <a href="https://en.wikipedia.org/wiki/Multiversion_concurrency_control">multiversion concurrency control</a> (MVCC), where generational values of each data item (versions) are maintained: MVCC is a common way to increase concurrency and performance by generating a new version of a <a href="https://en.wikipedia.org/wiki/Database_object">database object</a> each time the object is written, and allowing transactions&#39; read operations of several last relevant versions (of each object). Snapshot isolation has been used<sup><span>[</span>3<span>]</span></sup> to criticize the <a href="https://en.wikipedia.org/wiki/ANSI">ANSI</a> <a href="https://en.wikipedia.org/wiki/SQL">SQL</a>-92 standard&#39;s definition of <a href="https://en.wikipedia.org/wiki/Isolation_(database_systems)">isolation</a> levels, as it exhibits none of the &quot;anomalies&quot; that the SQL standard prohibited, yet is not serializable (the anomaly-free isolation level defined by ANSI). </p><p>In spite of its distinction from serializability, snapshot isolation is sometimes referred to as <i>serializable</i> by Oracle. </p><div><h2>Definition</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Snapshot_isolation&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>A transaction executing under snapshot isolation appears to operate on a personal <i>snapshot</i> of the database, taken at the start of the transaction. When the transaction concludes, it will successfully commit only if the values updated by the transaction have not been changed externally since the snapshot was taken. Such a <a href="https://en.wikipedia.org/wiki/Write%E2%80%93write_conflict">write–write conflict</a> will cause the transaction to abort. </p><p>In a <i>write skew</i> anomaly, two transactions (T1 and T2) concurrently read an overlapping data set (e.g. values V1 and V2), concurrently make disjoint updates (e.g. T1 updates V1, T2 updates V2), and finally concurrently commit, neither having seen the update performed by the other. Were the system serializable, such an anomaly would be impossible, as either T1 or T2 would have to occur &quot;first&quot;, and be visible to the other. In contrast, snapshot isolation permits write skew anomalies. </p><p>As a concrete example, imagine V1 and V2 are two balances held by a single person, Phil. The bank will allow either V1 or V2 to run a deficit, provided the total held in both is never negative (i.e. V1 + V2 ≥ 0). Both balances are currently $100. Phil initiates two transactions concurrently, T1 withdrawing $200 from V1, and T2 withdrawing $200 from V2. </p><p>If the database guaranteed serializable transactions, the simplest way of coding T1 is to deduct $200 from V1, and then verify that V1 + V2 ≥ 0 still holds, aborting if not. T2 similarly deducts $200 from V2 and then verifies V1 + V2 ≥ 0. Since the transactions must serialize, either T1 happens first, leaving V1 = −$100, V2 = $100, and preventing T2 from succeeding (since V1 + (V2 − $200) is now −$200), or T2 happens first and similarly prevents T1 from committing. </p><p>If the database is under snapshot isolation(MVCC), however, T1 and T2 operate on private snapshots of the database: each deducts $200 from an account, and then verifies that the new total is zero, using the other account value that held when the snapshot was taken. Since neither <i>update</i> conflicts, both commit successfully, leaving V1 = V2 = −$100, and V1 + V2 = −$200. </p><p>Some systems built using <a href="https://en.wikipedia.org/wiki/Multiversion_concurrency_control">multiversion concurrency control</a> (MVCC) may support (only) snapshot isolation to allow transactions to proceed without worrying about concurrent operations, and more importantly without needing to re-verify all read operations when the transaction finally commits. This is convenient because MVCC maintains a series of recent history consistent states. The only information that must be stored during the transaction is a list of updates made, which can be scanned for conflicts fairly easily before being committed. However, MVCC systems (such as MarkLogic) will use locks to serialize writes together with MVCC to obtain some of the performance gains and still support the stronger &quot;serializability&quot; level of isolation. </p><div><h2>Workarounds</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Snapshot_isolation&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>Potential inconsistency problems arising from write skew anomalies can be fixed by adding (otherwise unnecessary) updates to the transactions in order to enforce the <a href="https://en.wikipedia.org/wiki/Serializability">serializability</a> property.<sup><span>[</span>4<span>]</span></sup><sup><span>[</span>5<span>]</span></sup><sup><span>[</span>6<span>]</span></sup><sup><span>[</span>7<span>]</span></sup> </p><dl><dt>Materialize the conflict</dt> <dd>Add a special conflict table, which both transactions update in order to create a direct write–write conflict.</dd> <dt>Promotion</dt> <dd>Have one transaction &quot;update&quot; a read-only location (replacing a value with the same value) in order to create a direct write–write conflict (or use an equivalent promotion, e.g. Oracle&#39;s SELECT FOR UPDATE).</dd></dl><p>In the example above, we can materialize the conflict by adding a new table which makes the hidden constraint explicit, mapping each person to their <i>total balance</i>. Phil would start off with a total balance of $200, and each transaction would attempt to subtract $200 from this, creating a write–write conflict that would prevent the two from succeeding concurrently. However, this approach violates the <a href="https://en.wikipedia.org/wiki/Database_normalization">normal form</a>. </p><p>Alternatively, we can promote one of the transaction&#39;s reads to a write. For instance, T2 could set V1 = V1, creating an artificial write–write conflict with T1 and, again, preventing the two from succeeding concurrently. This solution may not always be possible. </p><p>In general, therefore, snapshot isolation puts some of the problem of maintaining non-trivial constraints onto the user, who may not appreciate either the potential pitfalls or the possible solutions. The upside to this transfer is better performance. </p><div><h2>Terminology</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Snapshot_isolation&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Snapshot isolation is called &quot;serializable&quot; mode in <a href="https://en.wikipedia.org/wiki/Oracle_database">Oracle</a><sup><span>[</span>8<span>]</span></sup><sup><span>[</span>9<span>]</span></sup><sup><span>[</span>10<span>]</span></sup> and <a href="https://en.wikipedia.org/wiki/PostgreSQL">PostgreSQL</a> versions prior to 9.1,<sup><span>[</span>11<span>]</span></sup><sup><span>[</span>12<span>]</span></sup><sup><span>[</span>13<span>]</span></sup> which may cause confusion with the &quot;real <a href="https://en.wikipedia.org/wiki/Serializability">serializability</a>&quot; mode. There are arguments both for and against this decision; what is clear is that users must be aware of the distinction to avoid possible undesired anomalous behavior in their database system logic. </p><div><h2>History</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Snapshot_isolation&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Snapshot isolation arose from work on <a href="https://en.wikipedia.org/wiki/Multiversion_concurrency_control">multiversion concurrency control</a> databases, where multiple versions of the database are maintained concurrently to allow readers to execute without colliding with writers. Such a system allows a natural definition and implementation of such an isolation level.<sup><span>[</span>3<span>]</span></sup> <a href="https://en.wikipedia.org/wiki/InterBase">InterBase</a>, later owned by <a href="https://en.wikipedia.org/wiki/Borland">Borland</a>, was acknowledged to provide SI rather than full serializability in version 4,<sup><span>[</span>3<span>]</span></sup> and likely permitted write-skew anomalies since its first release in 1985.<sup><span>[</span>14<span>]</span></sup> </p><p>Unfortunately, the ANSI <a href="https://en.wikipedia.org/wiki/SQL-92">SQL-92</a> standard was written with a <a href="https://en.wikipedia.org/wiki/Database_lock">lock</a>-based database in mind, and hence is rather vague when applied to MVCC systems. Berenson <i>et al.</i> wrote a paper in 1995<sup><span>[</span>3<span>]</span></sup> critiquing the SQL standard, and cited snapshot isolation as an example of an isolation level that did not exhibit the standard anomalies described in the ANSI SQL-92 standard, yet still had anomalous behaviour when compared with <a href="https://en.wikipedia.org/wiki/Serializability">serializable</a> transactions. </p><p>In 2008, Cahill <i>et al.</i> showed that write-skew anomalies could be prevented by detecting and aborting &quot;dangerous&quot; triplets of concurrent transactions.<sup><span>[</span>15<span>]</span></sup> This implementation of serializability is well-suited to <a href="https://en.wikipedia.org/wiki/Multiversion_concurrency_control">multiversion concurrency control</a> databases, and has been adopted in PostgreSQL 9.1,<sup><span>[</span>12<span>]</span></sup><sup><span>[</span>13<span>]</span></sup><sup><span>[</span>16<span>]</span></sup> where it is known as Serializable Snapshot Isolation (SSI). When used consistently, this eliminates the need for the above workarounds. The downside over snapshot isolation is an increase in aborted transactions. This can perform better or worse than snapshot isolation with the above workarounds, depending on workload. </p><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Snapshot_isolation&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><div><ol> <li><span><b>^</b></span> <span><cite><a href="https://dev.mysql.com/doc/refman/8.0/en/innodb-consistent-read.html">&quot;MySQL :: MySQL 8.0 Reference Manual :: 15.5.2.3 Consistent Nonlocking Reads&quot;</a>. <i>dev.mysql.com</i><span>. Retrieved <span>2018-08-27</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span>Multiversion concurrency control in MongoDB, <a href="https://www.zdnet.com/article/mongodb-cto-how-our-new-wiredtiger-storage-engine-will-earn-its-stripes/">MongoDB CTO: How our new WiredTiger storage engine will earn its stripes</a></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup> <sup><i><b>d</b></i></sup></span> <span> <cite>Berenson, Hal; Bernstein, Phil; Gray, Jim; Melton, Jim; <a href="https://en.wikipedia.org/wiki/Elizabeth_O%27Neil">O&#39;Neil, Elizabeth</a>; <a href="https://en.wikipedia.org/wiki/Patrick_O%27Neil">O&#39;Neil, Patrick</a> (1995), &quot;A Critique of ANSI SQL Isolation Levels&quot;, <i>Proceedings of the 1995 ACM SIGMOD international Conference on Management of Data</i>, pp. <span>1–</span>10, <a href="https://en.wikipedia.org/wiki/ArXiv_(identifier)">arXiv</a>:<span><a href="https://arxiv.org/abs/cs/0701157">cs/0701157</a></span>, <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1145%2F223784.223785">10.1145/223784.223785</a>, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0897917315"><bdi>978-0897917315</bdi></a>, <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:2316540">2316540</a></cite></span> </li> <li><span><b>^</b></span> <span> <cite>Fekete, Alan; Liarokapis, Dimitrios; <a href="https://en.wikipedia.org/wiki/Elizabeth_O%27Neil">O&#39;Neil, Elizabeth</a>; <a href="https://en.wikipedia.org/wiki/Patrick_O%27Neil">O&#39;Neil, Patrick</a>; <a href="https://en.wikipedia.org/wiki/Dennis_Shasha">Shasha, Dennis</a> (2005), &quot;Making Snapshot Isolation Serializable&quot;, <i>ACM Transactions on Database Systems</i>, <b>30</b> (2): <span>492–</span>528, <a href="https://en.wikipedia.org/wiki/CiteSeerX_(identifier)">CiteSeerX</a> <span><a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.503.3169">10.1.1.503.3169</a></span>, <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1145%2F1071610.1071615">10.1145/1071610.1071615</a>, <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a> <a href="https://search.worldcat.org/issn/0362-5915">0362-5915</a>, <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:1815415">1815415</a></cite></span> </li> <li><span><b>^</b></span> <span>Michael J. Cahill, Uwe Röhm, Alan D. Fekete (2008): <a href="http://portal.acm.org/citation.cfm?id=1376690">&quot;Serializable isolation for snapshot databases&quot;</a>, <i>Proceedings of the 2008 ACM SIGMOD international conference on Management of data</i>, pp. 729-738, Vancouver, Canada, June 2008, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-60558-102-6"><bdi>978-1-60558-102-6</bdi></a> (SIGMOD 2008 best paper award)</span> </li> <li><span><b>^</b></span> <span>Michael J. Cahill, Uwe Röhm, Alan D. Fekete (2008): <a href="http://portal.acm.org/citation.cfm?id=1376690">&quot;Serializable isolation for snapshot databases&quot;</a>, <i>Proceedings of the 2008 ACM SIGMOD international conference on Management of data</i>, pp. 729-738, Vancouver, Canada, June 2008, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-60558-102-6"><bdi>978-1-60558-102-6</bdi></a> (SIGMOD 2008 best paper award)</span> </li> <li><span><b>^</b></span> <span>Alan Fekete (2009), <a href="http://www.it.usyd.edu.au/~fekete/teaching/serializableSI-Fekete.pdf">&quot;Snapshot Isolation and Serializable Execution&quot;</a>, Presentation, Page 4, 2009, The university of Sydney (Australia). Retrieved 16 September 2009</span> </li> <li><span><b>^</b></span> <span> <a href="http://docs.oracle.com/cd/B12037_01/server.101/b10743/consist.htm#i17856">Oracle Database Concepts 10g Release 1 (10.1) Chapter 13 : Data Concurrency and Consistency — Oracle Isolation Levels</a></span> </li> <li><span><b>^</b></span> <span> <a href="http://asktom.oracle.com/pls/asktom/f?p=100:11:::::P11_QUESTION_ID:7636765105002">Ask Tom : On Transaction Isolation Levels</a></span> </li> <li><span><b>^</b></span> <span><a href="http://asktom.oracle.com/pls/asktom/f?p=100:11:0::::P11_QUESTION_ID:3233191441609">Ask Tom : &quot;Serializable Transaction&quot;</a></span> </li> <li><span><b>^</b></span> <span><a href="http://www.postgresql.org/docs/9.0/static/transaction-iso.html#MVCC-SERIALIZABILITY">PostgreSQL 9.0 Documentation: 13.2.2.1. Serializable Isolation versus True Serializability</a></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><a href="http://www.postgresql.org/about/news/1349">PostgreSQL 9.1 press release</a></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><a href="http://www.postgresql.org/docs/9.1/static/transaction-iso.html#XACT-SERIALIZABLE">PostgreSQL 9.1.14 Documentation: 13.2.3. Serializable Isolation Level</a></span> </li> <li><span><b>^</b></span> <span><cite>Stuntz, Craig. <a href="https://web.archive.org/web/20071023164250/http://blogs.teamb.com/craigstuntz/2005/02/18/2699">&quot;Multiversion Concurrency Control Before InterBase&quot;</a>. Archived from <a href="http://blogs.teamb.com/craigstuntz/2005/02/18/2699/">the original</a> on October 23, 2007<span>. Retrieved <span>October 30,</span> 2014</span>.</cite></span> </li> <li><span><b>^</b></span> <span>Michael J. Cahill, Uwe Röhm, Alan D. Fekete (2008) <a href="http://portal.acm.org/citation.cfm?id=1376690">&quot;Serializable isolation for snapshot databases&quot;</a>, <i>Proceedings of the 2008 ACM SIGMOD international conference on Management of data</i>, pp. 729–738, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-60558-102-6"><bdi>978-1-60558-102-6</bdi></a> (SIGMOD 2008 best paper award)</span> </li> <li><span><b>^</b></span> <span> <cite>Ports, Dan R. K.; Grittner, Kevin (2012). <a href="http://drkp.net/drkp/papers/ssi-vldb12.pdf">&quot;Serializable Snapshot Isolation in PostgreSQL&quot;</a> <span>(PDF)</span>. <i>Proceedings of the VLDB Endowment</i>. <b>5</b> (12): <span>1850–</span>1861. <a href="https://en.wikipedia.org/wiki/ArXiv_(identifier)">arXiv</a>:<span><a href="https://arxiv.org/abs/1208.4179">1208.4179</a></span>. <a href="https://en.wikipedia.org/wiki/CiteSeerX_(identifier)">CiteSeerX</a> <span><a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.294.3803">10.1.1.294.3803</a></span>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.14778%2F2367502.2367523">10.14778/2367502.2367523</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:16006111">16006111</a>.</cite></span> </li> </ol></div><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Snapshot_isolation&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><ul><li>Bettina Kemme, Gustavo Alonso, <a href="http://doi.acm.org/10.1145/363951.363955">A new approach to developing and implementing eager database replication protocols</a>, ACM Transactions on Database Systems (TODS), v.25 n.3, p. 333-379, Sept. 2000.</li> <li>Gerhard Weikum, Gottfried Vossen, <i>Transactional information systems: theory, algorithms, and the practice of concurrency control and recovery</i>, Morgan Kaufmann, 2002, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/1-55860-508-8"><bdi>1-55860-508-8</bdi></a></li> <li>Yi Lin, Bettina Kemme, Marta Patiño-Martínez, Ricardo Jiménez-Peris. <a href="https://doi.org/10.1145/1066157.1066205">Middleware based data replication providing snapshot isolation</a>. Proceedings of the 2005 ACM SIGMOD international Conf., 2005.</li> <li>Marta Patiño-Martinez, Ricardo Jiménez-Peris, Bettina Kemme, Gustavo Alonso. <a href="https://doi.org/10.1145/1113574.1113576">MIDDLE-R: Consistent database replication at the middleware level</a>. ACM Transactions on Computer Systems (TOCS). Volume 23 Issue 4. Pages 375-423.</li> <li>Khuzaima Daudjee, Kenneth Salem, <i>Lazy Database Replication with Snapshot Isolation</i>, VLDB 2006: pages 715-726</li></ul> Database transaction schedule - Wikipedia https://en.wikipedia.org/wiki/Database_transaction_schedule Lw2nHEWLDXr6Nsf8vnuDYAFHZ6zmxN2AKuymSg== Fri, 08 May 2026 09:28:39 +0000 Order of execution of transactions in transaction processing <div>Order of execution of transactions in transaction processing</div><div>This article is about databases and transaction processing. For other uses, see <a href="https://en.wikipedia.org/wiki/Scheduling_(computing)">Scheduling (computing)</a>.</div><table><tbody><tr><td><div><span><a href="https://en.wikipedia.org/wiki/File:Question_book-new.svg"></a></span></div></td><td><div>This article <b>needs additional citations for <a href="https://en.wikipedia.org/wiki/Wikipedia:Verifiability">verification</a></b>.<span> Please help <a href="https://en.wikipedia.org/wiki/Special:EditPage/Database_transaction_schedule">improve this article</a> by <a href="https://en.wikipedia.org/wiki/Help:Referencing_for_beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br/><small><span><i>Find sources:</i> <a href="https://www.google.com/search?as_eq=wikipedia&amp;q=%22Database+transaction+schedule%22">&quot;Database transaction schedule&quot;</a> – <a href="https://www.google.com/search?tbm=nws&amp;q=%22Database+transaction+schedule%22+-wikipedia&amp;tbs=ar:1">news</a> <b>·</b> <a href="https://www.google.com/search?&amp;q=%22Database+transaction+schedule%22&amp;tbs=bkt:s&amp;tbm=bks">newspapers</a> <b>·</b> <a href="https://www.google.com/search?tbs=bks:1&amp;q=%22Database+transaction+schedule%22+-wikipedia">books</a> <b>·</b> <a href="https://scholar.google.com/scholar?q=%22Database+transaction+schedule%22">scholar</a> <b>·</b> <a href="https://www.jstor.org/action/doBasicSearch?Query=%22Database+transaction+schedule%22&amp;acc=on&amp;wc=on">JSTOR</a></span></small></span> <span><i>(<span>November 2012</span>)</i></span><span><i> (<small><a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table><p>In the fields of <a href="https://en.wikipedia.org/wiki/Database">databases</a> and <a href="https://en.wikipedia.org/wiki/Transaction_processing">transaction processing</a> (transaction management), a <b>schedule</b> (or <b>history</b>) of a system is an abstract model to describe the order of <a href="https://en.wikipedia.org/wiki/Execution_(computing)">executions</a> in a set of transactions running in the system. Often it is a <i>list</i> of operations (actions) ordered by time, performed by a set of <a href="https://en.wikipedia.org/wiki/Database_transaction">transactions</a> that are executed together in the system. If the order in time between certain operations is not determined by the system, then a <i><a href="https://en.wikipedia.org/wiki/Partial_order">partial order</a></i> is used. Examples of such operations are requesting a read operation, reading, writing, aborting, <a href="https://en.wikipedia.org/wiki/Commit_(data_management)">committing</a>, requesting a <a href="https://en.wikipedia.org/wiki/Lock_(computer_science)">lock</a>, locking, etc. Often, only a subset of the transaction operation types are included in a schedule. </p><p>Schedules are fundamental concepts in database <a href="https://en.wikipedia.org/wiki/Concurrency_control">concurrency control</a> theory. In practice, most general purpose database systems employ conflict-serializable and strict recoverable schedules. </p><div><h2>Notation</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>Grid notation: </p><ul><li><b>Columns:</b> The different transactions in the schedule.</li> <li><b>Rows:</b> The time <a href="https://en.wikipedia.org/wiki/Order_of_operations">order of operations</a> (a.k.a., actions).</li></ul><p>Operations (a.k.a., actions): </p><ul><li><b>R(X):</b> The corresponding transaction &quot;reads&quot; object X (i.e., it retrieves the data stored at X). This is done so that it can modify the data (e.g., X=X+4) during a &quot;write&quot; operation rather than merely overwrite it. When the schedule is represented as a list rather than a grid, the action is represented as <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> <mi>i</mi> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle Ri(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e17d26b9c6746d7e84f2da1b0244f20cebb00033" alt="{\displaystyle Ri(X)}" title=""/></span> where <span><span><math> <semantics> <mrow> <mstyle> <mi>i</mi> </mstyle> </mrow> <annotation>{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" alt="{\displaystyle i}" title=""/></span> is a number corresponding to a specific transaction.</li> <li><b>W(X):</b> The corresponding transaction &quot;writes&quot; to object X (i.e., it modifies the data stored at X). When the schedule is represented as a list rather than a grid, the action is represented as <span><span><math> <semantics> <mrow> <mstyle> <mi>W</mi> <mi>i</mi> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle Wi(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f8ce0cfa1fd54127a0967af1b2bee035571aadf" alt="{\displaystyle Wi(X)}" title=""/></span> where <span><span><math> <semantics> <mrow> <mstyle> <mi>i</mi> </mstyle> </mrow> <annotation>{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" alt="{\displaystyle i}" title=""/></span> is a number corresponding to a specific transaction.</li> <li><b>Com.:</b> This represents a &quot;commit&quot; operation in which the corresponding transaction has successfully completed its preceding actions, and has made all its changes permanent in the database.</li></ul><p>Alternatively, a schedule can be represented with a <i><a href="https://en.wikipedia.org/wiki/Acyclic_directed_graph">directed acyclic graph</a></i> (or DAG) in which there is an arc (i.e., <a href="https://en.wikipedia.org/wiki/Directed_edge">directed edge</a>) between each <i><a href="https://en.wikipedia.org/wiki/Ordered_pair">ordered pair</a></i> of operations. </p><div><h3>Example</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>The following is an example of a schedule: </p><p>In this example, the columns represent the different transactions in the schedule D. Schedule D consists of three transactions T1, T2, T3. First T1 Reads and Writes to object X, and then Commits. Then T2 Reads and Writes to object Y and Commits, and finally, T3 Reads and Writes to object Z and Commits. </p><p>The schedule D above can be represented as list in the following way: </p><p>D = R1(X) W1(X) Com1 R2(Y) W2(Y) Com2 R3(Z) W3(Z) Com3 </p><div><h2>Duration and order of actions</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>Usually, for the purpose of reasoning about concurrency control in databases, an operation is modelled as <i><a href="https://en.wikipedia.org/wiki/Atomicity_(database_systems)">atomic</a></i>, occurring at a point in time, without duration. Real executed operations always have some duration. </p><p>Operations of transactions in a schedule can interleave (i.e., transactions can be executed <a href="https://en.wikipedia.org/wiki/Concurrency_(computer_science)">concurrently</a>), but time orders between operations in each transaction must remain unchanged. The schedule is in <i><a href="https://en.wikipedia.org/wiki/Partial_order">partial order</a></i> when the operations of transactions in a schedule interleave (i.e., when the schedule is conflict-serializable but not serial). The schedule is in <i><a href="https://en.wikipedia.org/wiki/Partial_order">total order</a></i> when the operations of transactions in a schedule do not interleave (i.e., when the schedule is serial). </p><div><h2>Types of schedule</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>A <b>complete schedule</b> is one that contains either an abort (a.k.a. <b><a href="https://en.wikipedia.org/wiki/Rollback_(data_management)">rollback</a>)</b> or commit action for each of its transactions. A transaction&#39;s last action is either to commit or abort. To maintain <a href="https://en.wikipedia.org/wiki/Atomicity_(database_systems)">atomicity</a>, a transaction must undo all its actions if it is aborted. </p><div><h3>Serial</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>A schedule is <b>serial</b> if the executed transactions are non-interleaved (i.e., a serial schedule is one in which no transaction starts until a running transaction has ended). </p><p>Schedule D is an example of a serial schedule: </p><div><h3>Serializable</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>A schedule is <b>serializable</b> if it is equivalent (in its outcome) to a serial schedule. </p><p>In schedule E, the order in which the actions of the transactions are executed is not the same as in D, but in the end, E gives the same result as D. </p><p>Serializability is used to keep the data in the data item in a consistent state. It is the major criterion for the correctness of concurrent transactions&#39; schedule, and thus supported in all general purpose database systems. Schedules that are not serializable are likely to generate erroneous outcomes; which can be extremely harmful (e.g., when dealing with money within banks).<sup><span>[</span>1<span>]</span></sup><sup><span>[</span>2<span>]</span></sup><sup><span>[</span>3<span>]</span></sup> </p><p>If any specific order between some transactions is requested by an application, then it is enforced independently of the underlying serializability mechanisms. These mechanisms are typically indifferent to any specific order, and generate some unpredictable <a href="https://en.wikipedia.org/wiki/Partial_order">partial order</a> that is typically compatible with multiple serial orders of these transactions. </p><div><h4>Conflicting actions</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>Two actions are said to be in conflict (conflicting pair) <a href="https://en.wikipedia.org/wiki/If_and_only_if">if and only if</a> all of the 3 following conditions are satisfied: </p><ol><li>The actions belong to different transactions.</li> <li>At least one of the actions is a write operation.</li> <li>The actions access the same object (read or write).<sup><span>[</span>4<span>]</span></sup><sup><span>[</span>5<span>]</span></sup></li></ol><p>Equivalently, two actions are considered conflicting if and only if they are <a href="https://en.wikipedia.org/wiki/Commutative_property">noncommutative</a>. Equivalently, two actions are considered conflicting if and only if they are a <a href="https://en.wikipedia.org/wiki/Read%E2%80%93write_conflict">read-write</a>, <a href="https://en.wikipedia.org/wiki/Write%E2%80%93read_conflict">write-read</a>, or <a href="https://en.wikipedia.org/wiki/Write%E2%80%93write_conflict">write-write</a> conflict. </p><p>The following set of actions is conflicting: </p><ul><li>R1(X), W2(X), W3(X) (3 conflicting pairs)</li></ul><p>While the following sets of actions are not conflicting: </p><ul><li>R1(X), R2(X), R3(X)</li> <li>R1(X), W2(Y), R3(X)</li></ul><p>Reducing conflicts, such as through commutativity, enhances performance because conflicts are the fundamental cause of delays and aborts. </p><p>The conflict is <b>materialized</b> if the requested conflicting operation is actually executed: in many cases a requested/issued conflicting operation by a transaction is delayed and even never executed, typically by a <a href="https://en.wikipedia.org/wiki/Lock_(computer_science)">lock</a> on the operation&#39;s object, held by another transaction, or when writing to a transaction&#39;s temporary private workspace and materializing, copying to the database itself, upon commit; as long as a requested/issued conflicting operation is not executed upon the database itself, the conflict is <b>non-materialized</b>; non-materialized conflicts are not represented by an edge in the precedence graph. </p><div><h4>Conflict equivalence</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>The schedules S1 and S2 are said to be conflict-equivalent if and only if both of the following two conditions are satisfied: </p><ol><li>Both schedules S1 and S2 involve the same set of transactions such that each transaction has the same actions in the same order.</li> <li>Both schedules have the same set of conflicting pairs (such that the actions in each conflicting pair are in the same order).<sup><span>[</span>6<span>]</span></sup> This is equivalent to requiring that all conflicting operations (i.e., operations in any conflicting pair) are in the same order in both schedules.</li></ol><p>Equivalently, two schedules are said to be conflict equivalent if and only if one can be transformed to another by swapping pairs of non-conflicting operations (whether adjacent or not) while maintaining the order of actions for each transaction.<sup><span>[</span>4<span>]</span></sup> </p><p>Equivalently, two schedules are said to be conflict equivalent if and only if one can be transformed to another by swapping pairs of non-conflicting adjacent operations with different transactions.<sup><span>[</span>7<span>]</span></sup> </p><div><h4>Conflict-serializable</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>A schedule is said to be <b>conflict-serializable</b> when the schedule is conflict-equivalent to one or more serial schedules. </p><p>Equivalently, a schedule is conflict-serializable if and only if its <a href="https://en.wikipedia.org/wiki/Precedence_graph">precedence graph</a> is acyclic when only committed transactions are considered. Note that if the graph is defined to also include uncommitted transactions, then cycles involving uncommitted transactions may occur without conflict serializability violation. </p><p>The schedule K is conflict-equivalent to the serial schedule &lt;T1,T2&gt;, but not &lt;T2,T1&gt;. </p><p>Conflict serializability can be enforced by restarting any transaction within the cycle in the precedence graph, or by implementing <a href="https://en.wikipedia.org/wiki/Two-phase_locking">two-phase locking</a>, <a href="https://en.wikipedia.org/wiki/Timestamp-based_concurrency_control">timestamp ordering</a>, or <a href="https://en.wikipedia.org/wiki/Snapshot_isolation#Workarounds">serializable snapshot isolation</a>.<sup><span>[</span>8<span>]</span></sup> </p><div><h4>View equivalence</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><p>Two schedules S1 and S2 are said to be view-equivalent when the following conditions are satisfied: </p><ol><li>If the transaction <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8dd1c50cb9436474f83624c3f679ccf3eebbfef" alt="{\displaystyle T_{i}}" title=""/></span> in S1 reads an initial value for object X, so does the same transaction <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8dd1c50cb9436474f83624c3f679ccf3eebbfef" alt="{\displaystyle T_{i}}" title=""/></span> in S2.</li> <li>If the transaction <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8dd1c50cb9436474f83624c3f679ccf3eebbfef" alt="{\displaystyle T_{i}}" title=""/></span> reads a value (for an object X) written by the transaction <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27cdb9041c8aa769beb9153a48f41002297faacc" alt="{\displaystyle T_{j}}" title=""/></span> in S1, it must do so in S2.</li> <li>If the transaction <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8dd1c50cb9436474f83624c3f679ccf3eebbfef" alt="{\displaystyle T_{i}}" title=""/></span> in S1 does the final write for object X, so does the same transaction <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8dd1c50cb9436474f83624c3f679ccf3eebbfef" alt="{\displaystyle T_{i}}" title=""/></span> in S2.</li></ol><p>Additionally, two view-equivalent schedules must involve the same set of transactions such that each transaction has the same actions in the same order. </p><p>In the example below, the schedules S1 and S2 are view-equivalent, but neither S1 nor S2 are view-equivalent to the schedule S3. </p><p>The conditions for S3 to be view-equivalent to S1 and S2 were not satisfied at the corresponding superscripts for the following reasons: </p><ol><li>Failed the first condition of view equivalence because T1 read the initial value for B in S1 and S2, but T2 read the initial value for B in S3.</li> <li>Failed the second condition of view equivalence because T2 read the value written by T1 for B in S1 and S2, but T1 read the value written by T2 for B in S3.</li> <li>Failed the third condition of view equivalence because T2 did the final write for B in S1 and S2, but T1 did the final write for B in S3.</li></ol><p>To quickly analyze whether two schedules are view-equivalent, write both schedules as a list with each action&#39;s subscript representing which view-equivalence condition they match. The schedules are view equivalent if and only if all the actions have the same subscript (or lack thereof) in both schedules: </p><ul><li>S1: R1(A)<sub>initial read</sub>, W1(A), R1(B)<sub>initial read</sub>, W1(B), Com1, R2(A)<sub>written by T1</sub>, W2(A)<sub>final write</sub>, R2(B)<sub>written by T1</sub>, W2(B)<sub>final write</sub>, Com2</li> <li>S2: R1(A)<sub>initial read</sub>, W1(A), R2(A)<sub>written by T1</sub>, W2(A)<sub>final write</sub>, R1(B)<sub>initial read</sub>, W1(B), Com1, R2(B)<sub>written by T1</sub>, W2(B)<sub>final write</sub>, Com2</li> <li>S3: R1(A)<sub>initial read</sub>, W1(A), R2(A)<sub>written by T1</sub>, W2(A)<sub>final write</sub>, <b>R2(B)<sub>initial read</sub>, W2(B), R1(B)<sub>written by T2</sub>, W1(B)<sub>final write</sub>,</b> Com1, Com2</li></ul><div><h4>View-serializable</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><p>A schedule is <b>view-serializable</b> if it is view-equivalent to some serial schedule. Note that by definition, all conflict-serializable schedules are view-serializable. </p><p>Notice that the above example (which is the same as the example in the discussion of conflict-serializable) is both view-serializable and conflict-serializable at the same time. There are however view-serializable schedules that are not conflict-serializable: those schedules with a transaction performing a <a href="https://en.wikipedia.org/wiki/Blind_write">blind write</a>: </p><p>The above example is not conflict-serializable, but it is view-serializable since it has a view-equivalent serial schedule &lt;T1,| T2,| T3&gt;. </p><p>Since determining whether a schedule is view-serializable is <a href="https://en.wikipedia.org/wiki/NP-complete">NP-complete</a>, view-serializability has little practical interest.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup> </p><div><h3>Recoverable</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><p>In a <b>recoverable schedule</b>, transactions only commit after all transactions whose changes they read have committed. A schedule becomes <b>unrecoverable</b> if a transaction <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8dd1c50cb9436474f83624c3f679ccf3eebbfef" alt="{\displaystyle T_{i}}" title=""/></span> reads and relies on changes from another transaction <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27cdb9041c8aa769beb9153a48f41002297faacc" alt="{\displaystyle T_{j}}" title=""/></span>, and then <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8dd1c50cb9436474f83624c3f679ccf3eebbfef" alt="{\displaystyle T_{i}}" title=""/></span> commits and <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>T</mi> <mrow> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle T_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27cdb9041c8aa769beb9153a48f41002297faacc" alt="{\displaystyle T_{j}}" title=""/></span> aborts. </p><p>These schedules are recoverable. The schedule F is recoverable because T1 commits before T2, that makes the value read by T2 correct. Then T2 can commit itself. In the F2 schedule, if T1 aborted, T2 has to abort because the value of A it read is incorrect. In both cases, the database is left in a consistent state. </p><p>Schedule J is unrecoverable because T2 committed before T1 despite previously reading the value written by T1. Because T1 aborted after T2 committed, the value read by T2 is wrong. Because a transaction cannot be rolled-back after it commits, the schedule is unrecoverable. </p><div><h4>Cascadeless</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><p><b>Cascadeless schedules</b> (a.k.a. &quot;Avoiding Cascading Aborts (ACA) schedules&quot;) are schedules which avoid cascading aborts by disallowing <a href="https://en.wikipedia.org/wiki/Write%E2%80%93read_conflict">dirty reads</a>. <b>Cascading aborts</b> occur when one transaction&#39;s abort causes another transaction to abort because it read and relied on the first transaction&#39;s changes to an object. A <b>dirty read</b> occurs when a transaction reads data from uncommitted write in another transaction.<sup><span>[</span>9<span>]</span></sup> </p><p>The following examples are the same as the ones in the discussion on recoverable: </p><p>In this example, although F2 is recoverable, it does not avoid cascading aborts. It can be seen that if T1 aborts, T2 will have to be aborted too in order to maintain the correctness of the schedule as T2 has already read the uncommitted value written by T1. </p><p>The following is a recoverable schedule which avoids cascading abort. Note, however, that the update of A by T1 is always lost (since T1 is aborted). </p><p>Note that this Schedule would not be serializable if T1 would be committed. Cascading aborts avoidance is sufficient but not necessary for a schedule to be recoverable. </p><div><h4>Strict</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><p>A schedule is <b>strict</b> if for any two transactions T1, T2, if a write operation of T1 precedes a <i>conflicting</i> operation of T2 (either read or write), then the commit or abort event of T1 also precedes that conflicting operation of T2. For example, the schedule F3 above is strict. </p><p>Any strict schedule is cascade-less, but not the converse. Strictness allows efficient recovery of databases from failure. </p><div><h2>Serializability class relationships</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div><p>The following expressions illustrate the hierarchical (containment) relationships between <a href="https://en.wikipedia.org/wiki/Serializability">serializability</a> and <a href="https://en.wikipedia.org/wiki/Serializability#Correctness_-_recoverability">recoverability</a> classes: </p><ul><li>Serial ⊂ conflict-serializable ⊂ view-serializable ⊂ all schedules</li> <li>Serial ⊂ strict ⊂ cascadeless (ACA) ⊂ recoverable ⊂ all schedules</li></ul><p>The <a href="https://en.wikipedia.org/wiki/Venn_diagram">Venn diagram</a> (below) illustrates the above clauses graphically. </p><figure><a href="https://en.wikipedia.org/wiki/File:Schedule-serializability.png"></a><figcaption>Venn diagram for serializability and recoverability classes</figcaption></figure><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Schedule_(project_management)">Schedule (project management)</a></li> <li><a href="https://en.wikipedia.org/wiki/Two-phase_locking">Strong strict two-phase locking</a> (SS2PL or Rigorousness).</li> <li><a href="https://en.wikipedia.org/wiki/Snapshot_isolation#Making_Snapshot_Isolation_Serializable">Making snapshot isolation serializable</a><sup><span>[</span>8<span>]</span></sup> in <a href="https://en.wikipedia.org/wiki/Snapshot_isolation">Snapshot isolation</a>.</li> <li><a href="https://en.wikipedia.org/wiki/Global_serializability">Global serializability</a>, where the <i>Global serializability problem</i> and its proposed solutions are described.</li> <li><a href="https://en.wikipedia.org/wiki/Linearizability">Linearizability</a>, a more general concept in <a href="https://en.wikipedia.org/wiki/Concurrent_computing">concurrent computing</a>.</li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Database_transaction_schedule&amp;action=edit&amp;section=17"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span><a href="https://en.wikipedia.org/wiki/Phil_Bernstein">Philip A. Bernstein</a>, Vassos Hadzilacos, Nathan Goodman (1987): <a href="http://research.microsoft.com/en-us/people/philbe/ccontrol.aspx"><i>Concurrency Control and Recovery in Database Systems</i></a> (free PDF download), Addison Wesley Publishing Company, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-201-10715-5"><bdi>0-201-10715-5</bdi></a></span> </li> <li><span><b>^</b></span> <span><a href="https://en.wikipedia.org/wiki/Gerhard_Weikum">Gerhard Weikum</a>, Gottfried Vossen (2001): <a href="http://www.elsevier.com/wps/find/bookdescription.cws_home/677937/description#description"><i>Transactional Information Systems</i></a>, Elsevier, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/1-55860-508-8"><bdi>1-55860-508-8</bdi></a></span> </li> <li><span><b>^</b></span> <span><a href="https://en.wikipedia.org/wiki/Maurice_Herlihy">Maurice Herlihy</a> and J. Eliot B. Moss. <i>Transactional memory: architectural support for lock-free data structures.</i> Proceedings of the 20th annual international symposium on Computer architecture (ISCA &#39;93). Volume 21, Issue 2, May 1993.</span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://www.geeksforgeeks.org/conflict-serializability-in-dbms/">&quot;Conflict Serializability in DBMS&quot;</a>. <i>GeeksforGeeks</i>. 2015-12-29<span>. Retrieved <span>2023-11-27</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Silberschatz, Abraham; Korth, Henry F.; Sudarshan, S. (2020). <i>Database system concepts</i> (Seventh ed.). New York, NY: McGraw-Hill Education. p. 814. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-260-08450-4"><bdi>978-1-260-08450-4</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Ramakrishnan, Raghu; Gehrke, Johannes (2000). <i>Database management systems</i>. Computer science series (2nd ed.). Boston: McGraw-Hill. p. 540. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-07-232206-4"><bdi>978-0-07-232206-4</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Garcia-Molina, Hector; Ullman, Jeffrey D.; Widom, Jennifer (2009). <i>Database systems: the complete book</i>. Pearson international edition (2nd ed.). Upper Saddle River, NJ: Pearson/Prentice Hall. pp. <span>891–</span>892. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-13-187325-4"><bdi>978-0-13-187325-4</bdi></a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>Michael J. Cahill, Uwe Röhm, Alan D. Fekete (2008): <a href="http://portal.acm.org/citation.cfm?id=1376690">&quot;Serializable isolation for snapshot databases&quot;</a>, <i>Proceedings of the 2008 ACM SIGMOD international conference on Management of data</i>, pp. 729-738, Vancouver, Canada, June 2008, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-60558-102-6"><bdi>978-1-60558-102-6</bdi></a> (SIGMOD 2008 best paper award)</span> </li> <li><span><b>^</b></span> <span><cite><a href="https://www.geeksforgeeks.org/cascadeless-in-dbms/">&quot;Cascadeless in DBMS&quot;</a>. <i>GeeksforGeeks</i>. 2019-08-06<span>. Retrieved <span>2023-11-29</span></span>.</cite></span> </li> </ol></div></div> Isolation (database systems) - Wikipedia https://en.wikipedia.org/wiki/Isolation_(database_systems) FHxLZlHKujci3C_xw7DYFnV5o7_bcsJFjUxoPw== Fri, 08 May 2026 09:28:39 +0000 Database transaction integrity concept <div>Database transaction integrity concept</div><table><tbody><tr><td><div><span><a href="https://en.wikipedia.org/wiki/File:Question_book-new.svg"></a></span></div></td><td><div>This article <b>needs additional citations for <a href="https://en.wikipedia.org/wiki/Wikipedia:Verifiability">verification</a></b>.<span> Please help <a href="https://en.wikipedia.org/wiki/Special:EditPage/Isolation_(database_systems)">improve this article</a> by <a href="https://en.wikipedia.org/wiki/Help:Referencing_for_beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br/><small><span><i>Find sources:</i> <a href="https://www.google.com/search?as_eq=wikipedia&amp;q=%22Isolation%22+database+systems">&quot;Isolation&quot; database systems</a> – <a href="https://www.google.com/search?tbm=nws&amp;q=%22Isolation%22+database+systems+-wikipedia&amp;tbs=ar:1">news</a> <b>·</b> <a href="https://www.google.com/search?&amp;q=%22Isolation%22+database+systems&amp;tbs=bkt:s&amp;tbm=bks">newspapers</a> <b>·</b> <a href="https://www.google.com/search?tbs=bks:1&amp;q=%22Isolation%22+database+systems+-wikipedia">books</a> <b>·</b> <a href="https://scholar.google.com/scholar?q=%22Isolation%22+database+systems">scholar</a> <b>·</b> <a href="https://www.jstor.org/action/doBasicSearch?Query=%22Isolation%22+database+systems&amp;acc=on&amp;wc=on">JSTOR</a></span></small></span> <span><i>(<span>January 2009</span>)</i></span><span><i> (<small><a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table><p>In <a href="https://en.wikipedia.org/wiki/Database">database</a> systems, <b>isolation</b> is one of the <a href="https://en.wikipedia.org/wiki/ACID">ACID</a> (<i><a href="https://en.wikipedia.org/wiki/Atomicity_(database_systems)">Atomicity</a>, <a href="https://en.wikipedia.org/wiki/Consistency_(database_systems)">Consistency</a>, Isolation, <a href="https://en.wikipedia.org/wiki/Durability_(database_systems)">Durability</a></i>) <a href="https://en.wikipedia.org/wiki/Database_transaction">transaction</a> properties. It determines how <a href="https://en.wikipedia.org/wiki/Database_transaction">transaction</a> integrity is visible to other users and systems. A lower isolation level increases the ability of many users to access the same data at the same time, but also increases the number of <a href="https://en.wikipedia.org/wiki/Concurrency_(computer_science)">concurrency</a> effects (such as <a href="https://en.wikipedia.org/wiki/Write%E2%80%93read_conflict"> dirty reads</a> or <a href="https://en.wikipedia.org/wiki/Lost_update">lost updates</a>) users might encounter. Conversely, a higher isolation level reduces the types of concurrency effects that users may encounter, but requires more system resources and increases the chances that one transaction will block another.<sup><span>[</span>1<span>]</span></sup> </p><div><h2>DBMS concurrency control</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p><a href="https://en.wikipedia.org/wiki/Concurrency_control">Concurrency control</a> comprises the underlying mechanisms in a <a href="https://en.wikipedia.org/wiki/DBMS">DBMS</a> which handle isolation and guarantee related correctness. It is heavily used by the database and storage engines both to guarantee the correct execution of concurrent transactions, and (via different mechanisms) the correctness of other DBMS processes. The transaction-related mechanisms typically constrain the database data access operations&#39; timing (<a href="https://en.wikipedia.org/wiki/Database_transaction_schedule">transaction schedules</a>) to certain orders characterized as the <a href="https://en.wikipedia.org/wiki/Serializability">serializability</a> and <a href="https://en.wikipedia.org/wiki/Recoverability">recoverability</a> schedule properties. Constraining database access operation execution typically means reduced performance (measured by rates of execution), and thus concurrency control mechanisms are typically designed to provide the best performance possible under the constraints. Often, when possible without harming correctness, the serializability property is compromised for better performance. However, recoverability cannot be compromised, since such typically results in a <a href="https://en.wikipedia.org/wiki/Data_integrity">database integrity violation</a>. </p><p><a href="https://en.wikipedia.org/wiki/Two-phase_locking">Two-phase locking</a> is the most common transaction concurrency control method in DBMSs, used to provide both serializability and recoverability for correctness. In order to access a database object a transaction first needs to acquire a <a href="https://en.wikipedia.org/wiki/Lock_(database)">lock</a> for this object. Depending on the access operation type (e.g., reading or writing an object) and on the lock type, acquiring the lock may be blocked and postponed, if another transaction is holding a lock for that object. </p><div><h2>Client-side isolation</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>Isolation is typically enforced at the database level. However, various client-side systems can also be used. It can be controlled in application frameworks or runtime containers such as <a href="https://en.wikipedia.org/wiki/J2EE">J2EE</a> <a href="https://en.wikipedia.org/wiki/Entity_Bean">Entity Beans</a><sup><span>[</span>2<span>]</span></sup> On older systems, it may be implemented systemically (by the application developers), for example through the use of temporary tables.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Verifiability"><span>failed verification</span></a></i>]</sup> In two-tier, three-tier, or <a href="https://en.wikipedia.org/wiki/Multitier_architecture">n-tier</a> web applications a <a href="https://en.wikipedia.org/wiki/Transaction_manager">transaction manager</a> can be used to maintain isolation. A transaction manager is <a href="https://en.wikipedia.org/wiki/Middleware_(distributed_applications)">middleware</a> which sits between an app service (back-end application service) and the <a href="https://en.wikipedia.org/wiki/Operating_system">operating system</a>. A transaction manager can provide global isolation and atomicity. It tracks when new servers join a transaction and coordinates an <a href="https://en.wikipedia.org/wiki/Atomic_commit">atomic commit</a> protocol among the servers. The details are abstracted from the app, making transactions simpler and easier to code. A <a href="https://en.wikipedia.org/wiki/Transaction_processing_system">transaction processing monitor</a> (TPM) is a collection of middle-ware including a transaction manager. A TPM might provide local isolation to an app with a lock manager.<sup><span>[</span>2<span>]</span></sup> </p><div><h2>Read phenomena</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>The ANSI/ISO standard SQL 92 refers to three different <i>read phenomena</i> when a transaction retrieves data that another transaction might have updated. </p><p>In the following examples, two transactions take place. In transaction 1, a query is performed, then in transaction 2, an update is performed, and finally in transaction 1, the same query is performed again. </p><p>The examples use the following relation: </p><div><h3>Dirty reads</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Write-read_conflict">Write-read conflict</a></div><p>A <i>dirty read</i> (aka <i>uncommitted dependency</i>) occurs when a transaction retrieves a row that has been updated by another transaction that is not yet committed. </p><p>In this example, transaction 1 retrieves the row with id 1, then transaction 2 updates the row with id 1, and finally transaction 1 retrieves the row with id 1 again. Now if transaction 2 rolls back its update (already retrieved by transaction 1) or performs other updates, then the view of the row may be wrong in transaction 1. At the READ UNCOMMITTED isolation level, the second SELECT in transaction 1 retrieves the updated row: this is a dirty read. At the READ COMMITTED, REPEATABLE READ, and SERIALIZABLE isolation levels, the second SELECT in transaction 1 retrieves the initial row. </p><table> <tbody><tr> <th>Transaction 1 </th> <th>Transaction 2 </th></tr> <tr> <td><div><pre><span>BEGIN</span><span>;</span> <span>SELECT</span> <span>age</span> <span>FROM</span> <span>users</span> <span>WHERE</span> <span>id</span> <span>=</span> <span>1</span><span>;</span> <span>-- retrieves 20</span> </pre></div> </td> <td> </td></tr> <tr> <td> </td> <td><div><pre><span>BEGIN</span><span>;</span> <span>UPDATE</span> <span>users</span> <span>SET</span> <span>age</span> <span>=</span> <span>21</span> <span>WHERE</span> <span>id</span> <span>=</span> <span>1</span><span>;</span> <span>-- no commit here</span> </pre></div> </td></tr> <tr> <td><div><pre><span>SELECT</span> <span>age</span> <span>FROM</span> <span>users</span> <span>WHERE</span> <span>id</span> <span>=</span> <span>1</span><span>;</span> <span>-- READ UNCOMMITTED retrieves 21 (dirty read)</span> <span>-- READ COMMITTED retrieves 20 (dirty read has been avoided)</span> <span>-- REPEATABLE READ retrieves 20 (dirty read has been avoided)</span> <span>-- SERIALIZABLE retrieves 20 (dirty read has been avoided)</span> <span>COMMIT</span><span>;</span> </pre></div> </td> <td> </td></tr> <tr> <td> </td> <td><div><pre><span>ROLLBACK</span><span>;</span> </pre></div> </td></tr></tbody></table><div><h3>Non-repeatable reads</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>A <i>non-repeatable read</i> occurs when a transaction retrieves a row twice and that row is updated by another transaction that is committed in between. </p><p>In this example, transaction 1 retrieves the row with id 1, then transaction 2 updates the row with id 1 and is committed, and finally transaction 1 retrieves the row with id 1 again. At the READ UNCOMMITTED and READ COMMITTED isolation levels, the second SELECT in transaction 1 retrieves the updated row: this is a non-repeatable read. At the REPEATABLE READ and SERIALIZABLE isolation levels, the second SELECT in transaction 1 retrieves the initial row. </p><table> <tbody><tr> <th>Transaction 1 </th> <th>Transaction 2 </th></tr> <tr> <td><div><pre><span>BEGIN</span><span>;</span> <span>SELECT</span> <span>age</span> <span>FROM</span> <span>users</span> <span>WHERE</span> <span>id</span> <span>=</span> <span>1</span><span>;</span> <span>-- retrieves 20</span> </pre></div> </td> <td> </td></tr> <tr> <td> </td> <td><div><pre><span>BEGIN</span><span>;</span> <span>UPDATE</span> <span>users</span> <span>SET</span> <span>age</span> <span>=</span> <span>21</span> <span>WHERE</span> <span>id</span> <span>=</span> <span>1</span><span>;</span> <span>COMMIT</span><span>;</span> </pre></div> </td></tr> <tr> <td><div><pre><span>SELECT</span> <span>age</span> <span>FROM</span> <span>users</span> <span>WHERE</span> <span>id</span> <span>=</span> <span>1</span><span>;</span> <span>-- READ UNCOMMITTED retrieves 21 (non-repeatable read)</span> <span>-- READ COMMITTED retrieves 21 (non-repeatable read)</span> <span>-- REPEATABLE READ retrieves 20 (non-repeatable read has been avoided)</span> <span>-- SERIALIZABLE retrieves 20 (non-repeatable read has been avoided)</span> <span>COMMIT</span><span>;</span> </pre></div> </td></tr></tbody></table><div><h3>Phantom reads</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>A <i>phantom read</i> occurs when a transaction retrieves a set of rows twice and new rows are inserted into or removed from that set by another transaction that is committed in between. </p><p>In this example, transaction 1 retrieves the set of rows with age greater than 17, then transaction 2 inserts a row with age 26 and is committed, and finally transaction 1 retrieves the set of rows with age greater than 17 again. At the READ UNCOMMITTED, READ COMMITTED, and REPEATABLE READ isolation levels, the second SELECT in transaction 1 retrieves the new set of rows that includes the inserted row: this is a phantom read. At the SERIALIZABLE isolation level, the second SELECT in transaction 1 retrieves the initial set of rows. </p><table> <tbody><tr> <th>Transaction 1 </th> <th>Transaction 2 </th></tr> <tr> <td><div><pre><span>BEGIN</span><span>;</span> <span>SELECT</span> <span>name</span> <span>FROM</span> <span>users</span> <span>WHERE</span> <span>age</span> <span>&gt;</span> <span>17</span><span>;</span> <span>-- retrieves Alice and Bob</span> </pre></div> </td> <td> </td></tr> <tr> <td> </td> <td><div><pre><span>BEGIN</span><span>;</span> <span>INSERT</span> <span>INTO</span> <span>users</span> <span>VALUES</span> <span>(</span><span>3</span><span>,</span> <span>&#39;Carol&#39;</span><span>,</span> <span>26</span><span>);</span> <span>COMMIT</span><span>;</span> </pre></div> </td></tr> <tr> <td><div><pre><span>SELECT</span> <span>name</span> <span>FROM</span> <span>users</span> <span>WHERE</span> <span>age</span> <span>&gt;</span> <span>17</span><span>;</span> <span>-- READ UNCOMMITTED retrieves Alice, Bob and Carol (phantom read)</span> <span>-- READ COMMITTED retrieves Alice, Bob and Carol (phantom read)</span> <span>-- REPEATABLE READ retrieves Alice, Bob and Carol (phantom read)</span> <span>-- SERIALIZABLE retrieves Alice and Bob (phantom read has been avoided)</span> <span>COMMIT</span><span>;</span> </pre></div> </td></tr></tbody></table><p>There are two basic strategies used to prevent non-repeatable reads and phantom reads. In the first strategy, <i>lock-based concurrency control</i>, transaction 2 is committed after transaction 1 is committed or rolled back. It produces the serial <a href="https://en.wikipedia.org/wiki/Database_transaction_schedule">schedule</a> <i>T1, T2</i>. In the other strategy, <i><a href="https://en.wikipedia.org/wiki/Multiversion_concurrency_control">multiversion concurrency control</a></i>, transaction 2 is committed immediately while transaction 1, which started before transaction 2, continues to operate on an old snapshot of the database taken at the start of transaction 1, and when transaction 1 eventually tries to commit, if the result of committing would be equivalent to the serial schedule <i>T1, T2</i>, then transaction 1 is committed; otherwise, there is a commit conflict and transaction 1 is rolled back with a serialization failure. </p><p>Under lock-based concurrency control, non-repeatable reads and phantom reads may occur when read locks are not acquired when performing a SELECT, or when the acquired locks on affected rows are released as soon as the SELECT is performed. Under multiversion concurrency control, non-repeatable reads and phantom reads may occur when the requirement that a transaction affected by a commit conflict must be rolled back is relaxed. </p><div><h2>Isolation levels</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><p>Of the four <a href="https://en.wikipedia.org/wiki/ACID">ACID</a> properties in a <a href="https://en.wikipedia.org/wiki/Database_management_system">DBMS</a> (Database Management System), the isolation property is the one most often relaxed. When attempting to maintain the highest level of isolation, a DBMS usually acquires <a href="https://en.wikipedia.org/wiki/Lock_(database)">locks</a> on data which may result in a loss of <a href="https://en.wikipedia.org/wiki/Concurrency_(computer_science)">concurrency</a>, or implements <a href="https://en.wikipedia.org/wiki/Multiversion_concurrency_control">multiversion concurrency control</a>. This requires adding logic for the <a href="https://en.wikipedia.org/wiki/Software_application">application</a> to function correctly. </p><p>Most DBMSs offer a number of <i>transaction isolation levels</i>, which control the degree of locking that occurs when selecting data. For many database applications, the majority of database transactions can be constructed to avoid requiring high isolation levels (e.g. SERIALIZABLE level), thus reducing the locking overhead for the system. The programmer must carefully analyze database access code to ensure that any relaxation of isolation does not cause software bugs that are difficult to find. Conversely, if higher isolation levels are used, the possibility of <a href="https://en.wikipedia.org/wiki/Deadlock_(computer_science)">deadlock</a> is increased, which also requires careful analysis and programming techniques to avoid. </p><p>Since each isolation level is stronger than those below, in that no higher isolation level allows an action forbidden by a lower one, the standard permits a DBMS to run a transaction at an isolation level stronger than that requested (e.g., a &quot;Read committed&quot; transaction may actually be performed at a &quot;Repeatable read&quot; isolation level). </p><p>The isolation levels defined by the <a href="https://en.wikipedia.org/wiki/American_National_Standards_Institute">ANSI</a>/<a href="https://en.wikipedia.org/wiki/International_Organization_for_Standardization">ISO</a> <a href="https://en.wikipedia.org/wiki/SQL">SQL</a> standard are listed as follows. </p><div><h3>Serializable</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>This is the <i>highest</i> isolation level. </p><p>With a lock-based <a href="https://en.wikipedia.org/wiki/Concurrency_control">concurrency control</a> DBMS implementation, <a href="https://en.wikipedia.org/wiki/Serializability">serializability</a> requires read and write locks (acquired on selected data) to be released at the end of the transaction. Also <i>range-locks</i> must be acquired when a <a href="https://en.wikipedia.org/wiki/Select_(SQL)">SELECT</a> query uses a ranged <i>WHERE</i> clause, especially to avoid the <i><b>phantom reads</b></i> phenomenon. </p><p>When using non-lock based concurrency control, no locks are acquired; however, if the system detects a <i>write collision</i> among several concurrent transactions, only one of them is allowed to commit. See <i><a href="https://en.wikipedia.org/wiki/Snapshot_isolation">snapshot isolation</a></i> for more details on this topic. </p><p>From : (Second Informal Review Draft) ISO/IEC 9075:1992, Database Language SQL- July 30, 1992: <i>The execution of concurrent SQL-transactions at isolation level SERIALIZABLE is guaranteed to be serializable. A serializable execution is defined to be an execution of the operations of concurrently executing SQL-transactions that produces the same effect as some serial execution of those same SQL-transactions. A serial execution is one in which each SQL-transaction executes to completion before the next SQL-transaction begins.</i> </p><div><h3>Repeatable reads</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>In this isolation level, a lock-based <a href="https://en.wikipedia.org/wiki/Concurrency_control">concurrency control</a> DBMS implementation keeps read and write locks (acquired on selected data) until the end of the transaction. However, <i>range-locks</i> are not managed, so <i><b>phantom reads</b></i> can occur. </p><p>Write skew is possible at this isolation level in some systems. Write skew is a phenomenon where two writes are allowed to the same column(s) in a table by two different writers (who have previously read the columns they are updating), resulting in the column having data that is a mix of the two transactions.<sup><span>[</span>3<span>]</span></sup><sup><span>[</span>4<span>]</span></sup> </p><div><h3>Read committed</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><p>In this isolation level, a lock-based <a href="https://en.wikipedia.org/wiki/Concurrency_control">concurrency control</a> DBMS implementation keeps write locks (acquired on selected data) until the end of the transaction, but read locks are released as soon as the <a href="https://en.wikipedia.org/wiki/Select_(SQL)">SELECT</a> operation is performed (so the <i><b>non-repeatable reads phenomenon</b></i> can occur in this isolation level). As in the previous level, <i>range-locks</i> are not managed. </p><p>Putting it in simpler words, read committed is an isolation level that guarantees that any data read is committed at the moment it is read. It simply restricts the reader from seeing any intermediate, uncommitted, &#39;dirty&#39; read. It makes no promise whatsoever that if the transaction re-issues the read, it will find the same data; data is free to change after it is read. </p><div><h3>Read uncommitted</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><p>This is the <i>lowest</i> isolation level. In this level, <i><b>dirty reads</b></i> are allowed, so one transaction may see <i>not-yet-committed</i> changes made by other transactions. </p><div><h2>Default isolation level</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><p>The <i>default isolation level</i> of different <a href="https://en.wikipedia.org/wiki/Database_management_system">DBMS</a>&#39;s varies quite widely. Most databases that feature transactions allow the user to set any isolation level. Some DBMS&#39;s also require additional syntax when performing a SELECT statement to acquire locks (e.g. <i>SELECT ... FOR UPDATE</i> to acquire exclusive write locks on accessed rows). </p><p>However, the definitions above have been criticized as being ambiguous, and as not accurately reflecting the isolation provided by many databases: </p><dl><dd>This paper shows a number of weaknesses in the anomaly approach to defining isolation levels. The three ANSI phenomena are ambiguous, and even in their loosest interpretations do not exclude some anomalous behavior ... This leads to some counter-intuitive results. In particular, lock-based isolation levels have different characteristics than their ANSI equivalents. This is disconcerting because commercial database systems typically use locking implementations. Additionally, the ANSI phenomena do not distinguish between a number of types of isolation level behavior that are popular in commercial systems.<sup><span>[</span>5<span>]</span></sup></dd></dl><p>There are also other criticisms concerning ANSI SQL&#39;s isolation definition, in that it encourages implementors to do &quot;bad things&quot;: </p><dl><dd>... it relies in subtle ways on an assumption that a locking schema is used for concurrency control, as opposed to an optimistic or multi-version concurrency scheme. This implies that the proposed semantics are <i>ill-defined</i>.<sup><span>[</span>6<span>]</span></sup></dd></dl><div><h2>Isolation levels vs read phenomena</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><p>Anomaly serializable is not the same as serializable. That is, it is necessary, but not sufficient that a serializable schedule should be free of all three phenomena types.<sup><span>[</span>5<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/Atomicity_(database_systems)">Atomicity</a></li> <li><a href="https://en.wikipedia.org/wiki/Consistency_(database_systems)">Consistency</a></li> <li><a href="https://en.wikipedia.org/wiki/Durability_(database_systems)">Durability</a></li> <li><a href="https://en.wikipedia.org/wiki/Lock_(database)">Lock (database)</a></li> <li><a href="https://en.wikipedia.org/wiki/Optimistic_concurrency_control">Optimistic concurrency control</a></li> <li><a href="https://en.wikipedia.org/wiki/Relational_Database_Management_System">Relational Database Management System</a></li> <li><a href="https://en.wikipedia.org/wiki/Snapshot_isolation">Snapshot isolation</a></li></ul><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span>&quot;Isolation Levels in the Database Engine&quot;, TechNet, Microsoft, <a href="https://technet.microsoft.com/en-us/library/ms189122(v=SQL.105).aspx">https://technet.microsoft.com/en-us/library/ms189122(v=SQL.105).aspx</a></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>&quot;The Architecture of Transaction Processing Systems&quot;, Chapter 23, Evolution of Processing Systems, Department of Computer Science, Stony Brook University, retrieved 20 March 2014, <a href="http://www.cs.sunysb.edu/~liu/cse315/23.pdf">http://www.cs.sunysb.edu/~liu/cse315/23.pdf</a></span> </li> <li><span><b>^</b></span> <span><cite>Vlad Mihalcea (2015-10-20). <a href="https://vladmihalcea.com/2015/10/20/a-beginners-guide-to-read-and-write-skew-phenomena/">&quot;A beginner&#39;s guide to read and write skew phenomena&quot;</a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://wiki.postgresql.org/wiki/SSI#Simple_Write_Skew">&quot;Postgresql wiki - SSI&quot;</a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span> <cite><a href="http://www.cs.umb.edu/~poneil/iso.pdf">&quot;A Critique of ANSI SQL Isolation Levels&quot;</a> <span>(PDF)</span><span>. Retrieved <span>29 July</span> 2012</span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>salesforce (2010-12-06). <a href="https://www.youtube.com/v/7J61pPG9j90?version=3">&quot;Customer testimonials (SimpleGeo, CLOUDSTOCK 2010)&quot;</a>. www.DataStax.com: DataStax<span>. Retrieved <span>2010-03-09</span></span>. <q>(see above at about 13:30 minutes of the webcast!)</q></cite></span> </li> </ol></div></div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Isolation_(database_systems)&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div><ul><li><a href="http://docs.oracle.com/cd/B12037_01/server.101/b10743/toc.htm">Oracle® Database Concepts</a>, <a href="http://docs.oracle.com/cd/B12037_01/server.101/b10743/consist.htm#sthref1919">chapter 13 Data Concurrency and Consistency, Preventable Phenomena and Transaction Isolation Levels</a></li> <li><a href="http://docs.oracle.com/cd/B19306_01/server.102/b14200/toc.htm">Oracle® Database SQL Reference</a>, <a href="http://docs.oracle.com/cd/B19306_01/server.102/b14200/statements_10.htm#i2068385">chapter 19 SQL Statements: SAVEPOINT to UPDATE</a>, <a href="http://docs.oracle.com/cd/B19306_01/server.102/b14200/statements_10005.htm#i2067247">SET TRANSACTION</a></li> <li>in <a href="https://en.wikipedia.org/wiki/Java_Database_Connectivity">JDBC</a>: <a href="http://docs.oracle.com/javase/7/docs/api/java/sql/Connection.html#field_summary">Connection constant fields</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/sql/Connection.html#getTransactionIsolation()">Connection.getTransactionIsolation()</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/sql/Connection.html#setTransactionIsolation(int)">Connection.setTransactionIsolation(int)</a></li> <li>in <a href="https://en.wikipedia.org/wiki/Spring_Framework">Spring Framework</a>: <a href="http://static.springsource.org/spring/docs/current/javadoc-api/org/springframework/transaction/annotation/Transactional.html">@Transactional</a><sup><span>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Link_rot"><span>dead link</span></a></i>]</span></sup>, <a href="http://static.springsource.org/spring/docs/current/javadoc-api/org/springframework/transaction/annotation/Isolation.html">Isolation</a><sup><span>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Link_rot"><span>dead link</span></a></i>]</span></sup></li> <li><a href="http://www.bailis.org/blog/when-is-acid-acid-rarely/">P.Bailis. When is &quot;ACID&quot; ACID? Rarely</a></li></ul><div><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q1674485#identifiers"></a></span></th><td><div><ul><li><span><a href="https://d-nb.info/gnd/4704495-0">GND</a></span></li></ul></div></td></tr></tbody></table></div> Schwartz–Zippel lemma - Wikipedia https://en.wikipedia.org/wiki/Schwartz%E2%80%93Zippel_lemma p6v9NvTOXZqzEeEraROd-T06j8g7P_J7TajY2Q== Fri, 08 May 2026 09:28:11 +0000 Tool used in probabilistic polynomial identity testing <div>Tool used in probabilistic polynomial identity testing</div><p>In mathematics, the <b>Schwartz–Zippel lemma</b> (also called the <b>DeMillo–Lipton–Schwartz–Zippel lemma</b>) is a tool commonly used in probabilistic <a href="https://en.wikipedia.org/wiki/Polynomial_identity_testing">polynomial identity testing</a>. Identity testing is the problem of determining whether a given multivariate <a href="https://en.wikipedia.org/wiki/Polynomial">polynomial</a> is the 0-polynomial, the polynomial that ignores all its variables and always returns zero. The lemma states that evaluating a nonzero polynomial on inputs chosen randomly from a large-enough set is likely to find an input that produces a nonzero output. </p><p>it was discovered independently by <a href="https://en.wikipedia.org/wiki/Jack_Schwartz">Jack Schwartz</a>,<sup><span>[</span>1<span>]</span></sup> <a href="https://en.wikipedia.org/w/index.php?title=Richard_Zippel&amp;action=edit&amp;redlink=1">Richard Zippel</a>,<sup><span>[</span>2<span>]</span></sup> and <a href="https://en.wikipedia.org/wiki/Richard_DeMillo">Richard DeMillo</a> and <a href="https://en.wikipedia.org/wiki/Richard_J._Lipton">Richard J. Lipton</a>, although DeMillo and Lipton&#39;s version was shown a year prior to Schwartz and Zippel&#39;s result.<sup><span>[</span>3<span>]</span></sup> The <a href="https://en.wikipedia.org/wiki/Finite_field">finite field</a> version of this bound was proved by <a href="https://en.wikipedia.org/wiki/%C3%98ystein_Ore">Øystein Ore</a> in 1922.<sup><span>[</span>4<span>]</span></sup> </p><div><h2>Statement and proof of the lemma</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Schwartz%E2%80%93Zippel_lemma&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p><b>Theorem 1</b> (Schwartz, Zippel). <i>Let</i> </p><p><i>Equivalently, the Lemma states that for any finite subset S of R, if Z(P) is the zero set of P, then</i> </p><dl><dd><span><span><math> <semantics> <mrow> <mstyle> <mrow> <mtable> <mtr> <mtd> <mo>Pr</mo> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mtd> <mtd> <mo>=</mo> <mo>Pr</mo> <mo>[</mo> <mi>A</mi> <mo>∩</mo> <mi>B</mi> <mo>]</mo> <mo>+</mo> <mo>Pr</mo> <mo>[</mo> <mi>A</mi> <mo>∩</mo> <msup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> </msup> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mo>Pr</mo> <mo>[</mo> <mi>B</mi> <mo>]</mo> <mo>Pr</mo> <mo>[</mo> <mi>A</mi> <mrow> <mo>|</mo> </mrow> <mi>B</mi> <mo>]</mo> <mo>+</mo> <mo>Pr</mo> <mo>[</mo> <msup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> </msup> <mo>]</mo> <mo>Pr</mo> <mo>[</mo> <mi>A</mi> <mrow> <mo>|</mo> </mrow> <msup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> </msup> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mo>≤</mo> <mo>Pr</mo> <mo>[</mo> <mi>B</mi> <mo>]</mo> <mo>+</mo> <mo>Pr</mo> <mo>[</mo> <mi>A</mi> <mrow> <mo>|</mo> </mrow> <msup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> </msup> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mo>≤</mo> <mrow> <mfrac> <mrow> <mi>d</mi> <mo>−</mo> <mi>i</mi> </mrow> <mrow> <mrow> <mo>|</mo> </mrow> <mi>S</mi> <mrow> <mo>|</mo> </mrow> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow> <mfrac> <mi>i</mi> <mrow> <mrow> <mo>|</mo> </mrow> <mi>S</mi> <mrow> <mo>|</mo> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow> <mfrac> <mi>d</mi> <mrow> <mrow> <mo>|</mo> </mrow> <mi>S</mi> <mrow> <mo>|</mo> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\begin{aligned}\Pr[A]&amp;=\Pr[A\cap B]+\Pr[A\cap B^{c}]\\&amp;=\Pr[B]\Pr[A|B]+\Pr[B^{c}]\Pr[A|B^{c}]\\&amp;\leq \Pr[B]+\Pr[A|B^{c}]\\&amp;\leq {\frac {d-i}{|S|}}+{\frac {i}{|S|}}={\frac {d}{|S|}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e9838641759db8e41a529b4166427d72d8e5dc2" alt="{\displaystyle {\begin{aligned}\Pr[A]&amp;=\Pr[A\cap B]+\Pr[A\cap B^{c}]\\&amp;=\Pr[B]\Pr[A|B]+\Pr[B^{c}]\Pr[A|B^{c}]\\&amp;\leq \Pr[B]+\Pr[A|B^{c}]\\&amp;\leq {\frac {d-i}{|S|}}+{\frac {i}{|S|}}={\frac {d}{|S|}}\end{aligned}}}" title=""/></span></dd></dl><p><i>Remark.</i> The Schwartz-Zippel lemma is tight in the following sense. Let <span><span><math> <semantics> <mrow> <mstyle> <mi>S</mi> <mo>⊆</mo> <mi>R</mi> </mstyle> </mrow> <annotation>{\displaystyle S\subseteq R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9a9719c1e3e0e1ba37e28af70f70851bdd099a4" alt="{\displaystyle S\subseteq R}" title=""/></span> be a finite subset and let <span><span><math> <semantics> <mrow> <mstyle> <mi>d</mi> <mo>≤</mo> <mrow> <mo>|</mo> </mrow> <mi>S</mi> <mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle d\leq |S|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7baf201b998a35a38f50060a4efd98f82b97ba23" alt="{\displaystyle d\leq |S|}" title=""/></span>. Choose any <span><span><math> <semantics> <mrow> <mstyle> <mi>d</mi> </mstyle> </mrow> <annotation>{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" alt="{\displaystyle d}" title=""/></span> distinct elements <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>s</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>s</mi> <mrow> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle s_{1},\ldots ,s_{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3495e05534aac7517139407f2533d738a1b3177" alt="{\displaystyle s_{1},\ldots ,s_{d}}" title=""/></span> from <span><span><math> <semantics> <mrow> <mstyle> <mi>S</mi> </mstyle> </mrow> <annotation>{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" alt="{\displaystyle S}" title=""/></span>. Then define <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>∈</mo> <mi>R</mi> <mo>[</mo> <msub> <mi>x</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>n</mi> </mrow> </msub> <mo>]</mo> </mstyle> </mrow> <annotation>{\displaystyle P\in R[x_{1},\ldots ,x_{n}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29b6df1e577fcd5d042cde7993b68585dc173435" alt="{\displaystyle P\in R[x_{1},\ldots ,x_{n}]}" title=""/></span> by <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>n</mi> </mrow> </msub> <mo>)</mo> <mo>=</mo> <munderover> <mo>∏</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>d</mi> </mrow> </munderover> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>s</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle P(x_{1},\ldots ,x_{n})=\prod _{i=1}^{d}(x_{1}-s_{i})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8268adcdd56280c2ec1d5e51a55792891bdf5d41" alt="{\displaystyle P(x_{1},\ldots ,x_{n})=\prod _{i=1}^{d}(x_{1}-s_{i})}" title=""/></span>. Let <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>r</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>r</mi> <mrow> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle r_{1},\ldots ,r_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52dfb1691f61905ec0a447728fc01781fcc71205" alt="{\displaystyle r_{1},\ldots ,r_{n}}" title=""/></span> be selected uniformly at random from <span><span><math> <semantics> <mrow> <mstyle> <mi>S</mi> </mstyle> </mrow> <annotation>{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" alt="{\displaystyle S}" title=""/></span>. Then <span><span><math> <semantics> <mrow> <mstyle> <mo>Pr</mo> <mo>[</mo> <mi>P</mi> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>r</mi> <mrow> <mi>n</mi> </mrow> </msub> <mo>)</mo> <mo>=</mo> <mn>0</mn> <mo>]</mo> <mo>=</mo> <mo>Pr</mo> <mo>[</mo> <msub> <mi>r</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>∈</mo> <mo>{</mo> <msub> <mi>s</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>s</mi> <mrow> <mi>d</mi> </mrow> </msub> <mo>}</mo> <mo>]</mo> <mo>=</mo> <mrow> <mfrac> <mi>d</mi> <mrow> <mrow> <mo>|</mo> </mrow> <mi>S</mi> <mrow> <mo>|</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation>{\displaystyle \Pr[P(r_{1},\ldots ,r_{n})=0]=\Pr[r_{1}\in \{s_{1},\ldots ,s_{d}\}]={\frac {d}{|S|}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4948a279322fcdc97138b9cb3fbaf7c07a5e7273" alt="{\displaystyle \Pr[P(r_{1},\ldots ,r_{n})=0]=\Pr[r_{1}\in \{s_{1},\ldots ,s_{d}\}]={\frac {d}{|S|}}}" title=""/></span> so that the bound stated in the Schwartz-Zippel lemma is exactly matched. </p><div><h2>Applications</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Schwartz%E2%80%93Zippel_lemma&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><p>The Schwartz–Zippel lemma is used to obtain algorithms for problems which are reducible to <a href="https://en.wikipedia.org/wiki/Polynomial_identity_testing">polynomial identity testing</a>. </p><div><h3>Zero testing</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Schwartz%E2%80%93Zippel_lemma&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>One of the most common applications of the Schwartz-Zippel lemma in <a href="https://en.wikipedia.org/wiki/Theoretical_computer_science">theoretical computer science</a> is to testing whether a polynomial (given in terms of an <a href="https://en.wikipedia.org/wiki/Arithmetic_circuit">arithmetic circuit</a> or formula) is identically 0. For example, consider asking whether the arithmetic formula below is identically 0 </p><p>To solve this problem deterministically, we can multiply all the terms and check whether the coefficient of every monomial is nonzero. However, this can take <a href="https://en.wikipedia.org/wiki/Exponential_time">exponential time</a> in the number of variables <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span> since a degree <span><span><math> <semantics> <mrow> <mstyle> <mi>d</mi> </mstyle> </mrow> <annotation>{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" alt="{\displaystyle d}" title=""/></span> polynomial in <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span> variables has up to <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mrow> <mo>(</mo> </mrow> <mfrac> <mrow> <mi>n</mi> <mo>+</mo> <mi>d</mi> </mrow> <mi>d</mi> </mfrac> <mrow> <mo>)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\binom {n+d}{d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf56c7f07120a0387b8527602b15689a7723715" alt="{\displaystyle {\binom {n+d}{d}}}" title=""/></span> monomials. Instead, we can evaluate the polynomial at a random <a href="https://en.wikipedia.org/wiki/Tuple">tuple</a> of points over a sufficiently large field and if the result is indeed 0, we can use the Schwartz-Zippel lemma to conclude the formula is identically 0 with high probability. </p><div><h3>Comparison of two polynomials</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Schwartz%E2%80%93Zippel_lemma&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><p>Hence if we can determine that </p><p>where </p><p>then we can determine whether the two polynomials are equivalent. </p><p>Comparison of polynomials has applications for branching programs (also called <a href="https://en.wikipedia.org/wiki/Binary_decision_diagram">binary decision diagrams</a>). A read-once branching program can be represented by a <a href="https://en.wikipedia.org/wiki/Multilinear_polynomial">multilinear polynomial</a> which computes (over any field) on {0,1}-inputs the same <a href="https://en.wikipedia.org/wiki/Boolean_function">Boolean function</a> as the branching program, and two branching programs compute the same function if and only if the corresponding polynomials are equal. Thus, identity of Boolean functions computed by read-once branching programs can be reduced to polynomial identity testing. </p><p>Comparison of two polynomials (and therefore testing polynomial identities) also has applications in 2D-compression, where the problem of finding the equality of two 2D-texts <i>A</i> and <i>B</i> is reduced to the problem of comparing equality of two polynomials <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>p</mi> <mrow> <mi>A</mi> </mrow> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle p_{A}(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87fe609db8df2e2d48d73d6cda48e734d0361276" alt="{\displaystyle p_{A}(x,y)}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>p</mi> <mrow> <mi>B</mi> </mrow> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle p_{B}(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8e3ca64cfe7fc69bf7b736d6226fe60e85a4bff" alt="{\displaystyle p_{B}(x,y)}" title=""/></span>. </p><div><h3>Primality testing</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Schwartz%E2%80%93Zippel_lemma&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><p>They propose that all prime numbers <i>n</i> (and only prime numbers) satisfy the following polynomial identity: </p><p>This is a consequence of the <a href="https://en.wikipedia.org/wiki/Frobenius_endomorphism">Frobenius endomorphism</a>. </p><p>Let </p><p>Then <span><span><math> <semantics> <mrow> <mstyle> <msub> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> <mrow> <mi>n</mi> </mrow> </msub> <mo>(</mo> <mi>z</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> <mo>(</mo> <mrow> <mstyle> <mtext>mod</mtext> </mstyle> </mrow> <mi>n</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle {\mathcal {P}}_{n}(z)=0\;({\mbox{mod}}\;n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7647bba6ab010bf9240402dd058e827704c9e0a" alt="{\displaystyle {\mathcal {P}}_{n}(z)=0\;({\mbox{mod}}\;n)}" title=""/></span> <i><a href="https://en.wikipedia.org/wiki/Iff">iff</a> n is prime</i>. The proof can be found in [4]. However, since this polynomial has degree <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span>, where <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span> may or may not be a prime, the Schwartz–Zippel method would not work. Agrawal and Biswas use a more sophisticated technique, which divides <span><span><math> <semantics> <mrow> <mstyle> <msub> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle {\mathcal {P}}_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18b28e0cb7064400f07370c0d35d46b6875e17e1" alt="{\displaystyle {\mathcal {P}}_{n}}" title=""/></span> by a random <a href="https://en.wikipedia.org/wiki/Monic_polynomial">monic polynomial</a> of small degree. The <a href="https://en.wikipedia.org/wiki/AKS_primality_test">AKS algorithm</a> uses a similar technique but runs in <a href="https://en.wikipedia.org/wiki/P_(complexity)">deterministic polynomial time</a>. </p><p>Prime numbers are used in a number of applications such as <a href="https://en.wikipedia.org/wiki/Hash_table">hash table</a> sizing, <a href="https://en.wikipedia.org/wiki/Pseudorandom">pseudorandom</a> number generators and in key generation for <a href="https://en.wikipedia.org/wiki/Cryptography">cryptography</a>. Therefore, finding very large prime numbers (on the order of (at least) <span><span><math> <semantics> <mrow> <mstyle> <msup> <mn>10</mn> <mrow> <mn>350</mn> </mrow> </msup> <mo>≈</mo> <msup> <mn>2</mn> <mrow> <mn>1024</mn> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle 10^{350}\approx 2^{1024}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6d4494bef0d698b0444bb856d8cd2d213378fb7" alt="{\displaystyle 10^{350}\approx 2^{1024}}" title=""/></span>) becomes very important and efficient primality testing algorithms are required. </p><div><h3>Perfect matching</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Schwartz%E2%80%93Zippel_lemma&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p><b>Theorem 2</b> (Tutte 1947): <i>A <a href="https://en.wikipedia.org/wiki/Tutte_matrix">Tutte matrix</a> determinant is not a <span>0</span>-polynomial <a href="https://en.wikipedia.org/wiki/If_and_only_if">if and only if</a> there exists a perfect matching.</i> </p><dl><dd><dl><dd><dl><dd><span><span><math> <semantics> <mrow> <mstyle> <mi>A</mi> <mo>=</mo> <mrow> <mrow> <mo>[</mo> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mn>11</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>12</mn> </mrow> </msub> </mtd> <mtd> <mo>⋯</mo> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mn>21</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>22</mn> </mrow> </msub> </mtd> <mtd> <mo>⋯</mo> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>⋮</mo> </mtd> <mtd> <mo>⋮</mo> </mtd> <mtd> <mo>⋱</mo> </mtd> <mtd> <mo>⋮</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mo>…</mo> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mrow> <mi>n</mi> <mi>n</mi> </mrow> </mrow> </msub> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation>{\displaystyle A={\begin{bmatrix}a_{11}&amp;a_{12}&amp;\cdots &amp;a_{1{\mathit {n}}}\\a_{21}&amp;a_{22}&amp;\cdots &amp;a_{2{\mathit {n}}}\\\vdots &amp;\vdots &amp;\ddots &amp;\vdots \\a_{{\mathit {n}}1}&amp;a_{{\mathit {n}}2}&amp;\ldots &amp;a_{\mathit {nn}}\end{bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b793a484353b0628c08cd2b27706d7d4ae42262d" alt="{\displaystyle A={\begin{bmatrix}a_{11}&amp;a_{12}&amp;\cdots &amp;a_{1{\mathit {n}}}\\a_{21}&amp;a_{22}&amp;\cdots &amp;a_{2{\mathit {n}}}\\\vdots &amp;\vdots &amp;\ddots &amp;\vdots \\a_{{\mathit {n}}1}&amp;a_{{\mathit {n}}2}&amp;\ldots &amp;a_{\mathit {nn}}\end{bmatrix}}}" title=""/></span></dd></dl></dd></dl></dd></dl><p>where </p><p>The Tutte matrix determinant (in the variables <i>x<sub>ij</sub></i>, <span>⁠<span><span><math> <semantics> <mrow> <mstyle> <mi>i</mi> <mo>&lt;</mo> <mi>j</mi> </mstyle> </mrow> <annotation>{\displaystyle i&lt;j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e60ff2d1b23e30fb2979e8c1536da03493f943cf" alt="{\displaystyle i&lt;j}" title=""/></span>⁠</span> ) is then defined as the <a href="https://en.wikipedia.org/wiki/Determinant">determinant</a> of this <a href="https://en.wikipedia.org/wiki/Skew-symmetric_matrix">skew-symmetric matrix</a> which coincides with the square of the <a href="https://en.wikipedia.org/wiki/Pfaffian">pfaffian</a> of the matrix <i>A</i> and is non-zero (as polynomial) if and only if a perfect matching exists. One can then use polynomial identity testing to find whether <span>G</span> contains a perfect matching. There exists a deterministic black-box algorithm for graphs with polynomially bounded permanents (Grigoriev &amp; Karpinski 1987).<sup><span>[</span>5<span>]</span></sup> </p><p>if the first <i>m</i> rows (resp. columns) are indexed with the first subset of the bipartition and the last <i>m</i> rows with the complementary subset. In this case the pfaffian coincides with the usual determinant of the <i>m</i> × <i>m</i> matrix <i>X</i> (up to sign). Here <i>X</i> is the <a href="https://en.wikipedia.org/wiki/Edmonds_matrix">Edmonds matrix</a>. </p><div><h2>Notes</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Schwartz%E2%80%93Zippel_lemma&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Schwartz%E2%80%93Zippel_lemma&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><div> <ul><li><cite>Agrawal, Manindra; Biswas, Somenath (2003-02-21). <a href="https://ieeexplore.ieee.org/document/814592">&quot;Primality and Identity Testing via Chinese Remaindering&quot;</a>. <i>Journal of the ACM</i>. <b>50</b> (4): <span>429–</span>443. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1145%2F792538.792540">10.1145/792538.792540</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:13145079">13145079</a><span>. Retrieved <span>2008-06-15</span></span>.</cite></li> <li><cite>Berman, Piotr; <a href="https://en.wikipedia.org/wiki/Marek_Karpinski">Karpinski, Marek</a>; Larmore, Lawrence L.; Plandowski, Wojciech; <a href="https://en.wikipedia.org/wiki/Wojciech_Rytter">Rytter, Wojciech</a> (2002). <span><a href="http://www.egr.unlv.edu/~larmore/Research/pattern.ps.gz">&quot;On the Complexity of Pattern Matching for Highly Compressed Two-Dimensional Texts&quot;</a></span> <span>(ps)</span>. <i>Journal of Computer and System Sciences</i>. <b>65</b> (2): <span>332–</span>350. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1006%2Fjcss.2002.1852">10.1006/jcss.2002.1852</a></span><span>. Retrieved <span>2008-06-15</span></span>.</cite></li> <li><cite>Grigoriev, Dima; Karpinski, Marek (1987). &quot;The matching problem for bipartite graphs with polynomially bounded permanents is in NC&quot;. <i>Proceedings of the 28th Annual Symposium on Foundations of Computer Science (FOCS 1987), Los Angeles, California, USA, 27-29 October 1987</i>. IEEE Computer Society. pp. <span>166–</span>172. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1109%2FSFCS.1987.56">10.1109/SFCS.1987.56</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8186-0807-0"><bdi>978-0-8186-0807-0</bdi></a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:14476361">14476361</a>.</cite></li> <li><a href="https://en.wikipedia.org/wiki/Dana_Moshkovitz">Moshkovitz, Dana</a> (2010). An Alternative Proof of The Schwartz-Zippel Lemma. <a href="https://en.wikipedia.org/wiki/Electronic_Colloquium_on_Computational_Complexity">ECCC</a> <a href="https://eccc.weizmann.ac.il/report/2010/096/">TR10-096</a></li> <li><cite><a href="https://en.wikipedia.org/wiki/Richard_DeMillo">DeMillo, Richard A.</a>; <a href="https://en.wikipedia.org/wiki/Richard_Lipton">Lipton, Richard J.</a> (1978). &quot;A probabilistic remark on algebraic program testing&quot;. <i>Information Processing Letters</i>. <b>7</b> (4): <span>193–</span>195. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1016%2F0020-0190%2878%2990067-4">10.1016/0020-0190(78)90067-4</a>.</cite></li> <li><cite>Rudich, Steven (2004). AMS (ed.). <i>Computational Complexity Theory</i>. IAS/Park City Mathematics Series. Vol. 10. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-2872-4"><bdi>978-0-8218-2872-4</bdi></a>.</cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/Jacob_T._Schwartz">Schwartz, Jacob T.</a> (October 1980). <a href="http://delivery.acm.org/10.1145/330000/322225/p701-schwartz.pdf">&quot;Fast probabilistic algorithms for verification of polynomial identities&quot;</a> <span>(PDF)</span>. <i>Journal of the ACM</i>. <b>27</b> (4): <span>701–</span>717. <a href="https://en.wikipedia.org/wiki/CiteSeerX_(identifier)">CiteSeerX</a> <span><a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.391.1254">10.1.1.391.1254</a></span>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1145%2F322217.322225">10.1145/322217.322225</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:8314102">8314102</a><span>. Retrieved <span>2008-06-15</span></span>.</cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/W._T._Tutte">Tutte, W.T.</a> (April 1947). &quot;The factorization of linear graphs&quot;. <i>J. London Math. Soc</i>. <b>22</b> (2): <span>107–</span>111. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1112%2Fjlms%2Fs1-22.2.107">10.1112/jlms/s1-22.2.107</a>. <a href="https://en.wikipedia.org/wiki/Hdl_(identifier)">hdl</a>:<a href="https://hdl.handle.net/10338.dmlcz%2F128215">10338.dmlcz/128215</a>.</cite></li> <li><cite>Zippel, Richard (1979). &quot;Probabilistic algorithms for sparse polynomials&quot;. In Ng, Edward W. (ed.). <i>Symbolic and Algebraic Computation, EUROSAM &#39;79, An International Symposiumon Symbolic and Algebraic Computation, Marseille, France, June 1979, Proceedings</i>. Lecture Notes in Computer Science. Vol. 72. Springer. pp. <span>216–</span>226. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2F3-540-09519-5_73">10.1007/3-540-09519-5_73</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-3-540-09519-4"><bdi>978-3-540-09519-4</bdi></a>.</cite></li> <li><cite>Zippel, Richard (February 1989). <a href="http://historical.ncstrl.org/tr/ps/cornellcs/TR89-965.ps">&quot;An Explicit Separation of Relativised Random Polynomial Time and Relativised Deterministic Polynomial Time&quot;</a> <span>(ps)</span><span>. Retrieved <span>2008-06-15</span></span>.</cite></li> <li><cite>Zippel, Richard (1993). Springer (ed.). <a href="https://www.springer.com/computer/mathematics/book/978-0-7923-9375-7"><i>Effective Polynomial Computation</i></a>. The Springer International Series in Engineering and Computer Science. Vol. 241. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-7923-9375-7"><bdi>978-0-7923-9375-7</bdi></a>.</cite></li></ul> </div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Schwartz%E2%80%93Zippel_lemma&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><ul><li><a href="http://rjlipton.wordpress.com/2009/11/30/the-curious-history-of-the-schwartz-zippel-lemma">The Curious History of the Schwartz–Zippel Lemma</a>, by <a href="https://en.wikipedia.org/wiki/Richard_J._Lipton">Richard J. Lipton</a></li></ul> Polynomial - Wikipedia https://en.wikipedia.org/wiki/Polynomial SkZXW1KXmBr6xYwA8I0JGrTXkfTIRsOD33n8Ow== Fri, 08 May 2026 09:28:11 +0000 Type of mathematical expression <div>Type of mathematical expression</div><div>This article is about the expressions themselves. For the related topic in algebra, see <a href="https://en.wikipedia.org/wiki/Polynomial_ring">Polynomial ring</a>.</div><p>In <a href="https://en.wikipedia.org/wiki/Mathematics">mathematics</a>, a <b>polynomial</b> is a <a href="https://en.wikipedia.org/wiki/Expression_(mathematics)">mathematical expression</a> consisting of <a href="https://en.wikipedia.org/wiki/Indeterminate_(variable)">indeterminates</a> (also called <a href="https://en.wikipedia.org/wiki/Variable_(mathematics)">variables</a>) and <a href="https://en.wikipedia.org/wiki/Coefficient">coefficients</a>, that involves only the operations of <a href="https://en.wikipedia.org/wiki/Addition">addition</a>, <a href="https://en.wikipedia.org/wiki/Subtraction">subtraction</a>, <a href="https://en.wikipedia.org/wiki/Multiplication">multiplication</a> and <a href="https://en.wikipedia.org/wiki/Exponentiation">exponentiation</a> to <a href="https://en.wikipedia.org/wiki/Nonnegative_integer">nonnegative integer</a> powers, and has a finite number of terms.<sup><span>[</span>1<span>]</span></sup><sup><span>[</span>2<span>]</span></sup><sup><span>[</span>3<span>]</span></sup><sup><span>[</span>4<span>]</span></sup><sup><span>[</span>5<span>]</span></sup> An example of a polynomial of a single indeterminate <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is <span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> <mi>x</mi> <mo>+</mo> <mn>7</mn> </mstyle> </mrow> <annotation>{\displaystyle x^{2}-4x+7}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2d99eaca8e062e6b74d4545fa56eebec5f54a08" alt="{\displaystyle x^{2}-4x+7}" title=""/></span>. An example with three indeterminates is <span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>x</mi> <mrow> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>x</mi> <mi>y</mi> <msup> <mi>z</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>y</mi> <mi>z</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation>{\displaystyle x^{3}+2xyz^{2}-yz+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65877105acf1ba0ae77f5a46371df0f55027ded7" alt="{\displaystyle x^{3}+2xyz^{2}-yz+1}" title=""/></span>. </p><p>Polynomials appear in many areas of mathematics and <a href="https://en.wikipedia.org/wiki/Science">science</a>. For example, they are used to form <a href="https://en.wikipedia.org/wiki/Polynomial_equation">polynomial equations</a>, which encode a wide range of problems, from elementary <a href="https://en.wikipedia.org/wiki/Word_problem_(mathematics_education)">word problems</a> to complicated scientific problems; they are used to define <b>polynomial functions</b>, which appear in settings ranging from basic <a href="https://en.wikipedia.org/wiki/Chemistry">chemistry</a> and <a href="https://en.wikipedia.org/wiki/Physics">physics</a> to <a href="https://en.wikipedia.org/wiki/Economics">economics</a> and <a href="https://en.wikipedia.org/wiki/Social_science">social science</a>; and they are used in <a href="https://en.wikipedia.org/wiki/Calculus">calculus</a> and <a href="https://en.wikipedia.org/wiki/Numerical_analysis">numerical analysis</a> to approximate other functions. In advanced mathematics, polynomials are used to construct <a href="https://en.wikipedia.org/wiki/Polynomial_ring">polynomial rings</a> and <a href="https://en.wikipedia.org/wiki/Algebraic_variety">algebraic varieties</a>, which are central concepts in <a href="https://en.wikipedia.org/wiki/Algebra">algebra</a> and <a href="https://en.wikipedia.org/wiki/Algebraic_geometry">algebraic geometry</a>. </p><div><h2>Etymology</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>The word <i>polynomial</i> <a href="https://en.wikipedia.org/wiki/Hybrid_word">joins two diverse roots</a>: the Greek <i>poly</i>, meaning &quot;many&quot;, and the Latin <i>nomen</i>, or &quot;name&quot;. It was derived from the term <i><a href="https://en.wikipedia.org/wiki/Binomial_(polynomial)">binomial</a></i> by replacing the Latin root <i>bi-</i> with the Greek <i>poly-</i>. That is, it means a sum of many terms (many <a href="https://en.wikipedia.org/wiki/Monomial">monomials</a>). The word <i>polynomial</i> was first used in the 17th century.<sup><span>[</span>6<span>]</span></sup> </p><div><h2>Notation and terminology</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Polynomialdeg3.svg"></a><figcaption>The <a href="https://en.wikipedia.org/wiki/Graph_of_a_function">graph</a> of a polynomial function of degree 3</figcaption></figure><p>The <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> occurring in a polynomial is commonly called a <i>variable</i> or an <i>indeterminate</i>. When the polynomial is considered as an expression, <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is a fixed symbol which does not have any value (its value is &quot;indeterminate&quot;). However, when one considers the <a href="https://en.wikipedia.org/wiki/Function_(mathematics)">function</a> defined by the polynomial, then <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> represents the argument of the function, and is therefore called a &quot;variable&quot;. Many authors use these two words interchangeably. </p><p>A polynomial <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> </mstyle> </mrow> <annotation>{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" alt="{\displaystyle P}" title=""/></span> in the indeterminate <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is commonly denoted either as <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> </mstyle> </mrow> <annotation>{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" alt="{\displaystyle P}" title=""/></span> or as <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle P(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89833156eff2c51bfb8750db3306a0544ce34e14" alt="{\displaystyle P(x)}" title=""/></span>. Formally, the name of the polynomial is <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> </mstyle> </mrow> <annotation>{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" alt="{\displaystyle P}" title=""/></span>, not <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle P(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89833156eff2c51bfb8750db3306a0544ce34e14" alt="{\displaystyle P(x)}" title=""/></span>, but the use of the <a href="https://en.wikipedia.org/wiki/Functional_notation">functional notation</a> <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle P(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89833156eff2c51bfb8750db3306a0544ce34e14" alt="{\displaystyle P(x)}" title=""/></span> dates from a time when the distinction between a polynomial and the associated function was unclear. Moreover, the functional notation is often useful for specifying, in a single phrase, a polynomial and its indeterminate. For example, &quot;let <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle P(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89833156eff2c51bfb8750db3306a0544ce34e14" alt="{\displaystyle P(x)}" title=""/></span> be a polynomial&quot; is a shorthand for &quot;let <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> </mstyle> </mrow> <annotation>{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" alt="{\displaystyle P}" title=""/></span> be a polynomial in the indeterminate <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>&quot;. On the other hand, when it is not necessary to emphasize the name of the indeterminate, many formulas are much simpler and easier to read if the name(s) of the indeterminate(s) do not appear at each occurrence of the polynomial. </p><p>The ambiguity of having two notations for a single mathematical object may be formally resolved by considering the general meaning of the functional notation for polynomials. If <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> </mstyle> </mrow> <annotation>{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" alt="{\displaystyle a}" title=""/></span> denotes a number, a variable, another polynomial, or, more generally, any expression, then <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle P(a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87843d318d662e597ebd3c0260bcb2727707009d" alt="{\displaystyle P(a)}" title=""/></span> denotes, by convention, the result of substituting <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> </mstyle> </mrow> <annotation>{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" alt="{\displaystyle a}" title=""/></span> for <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> in <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> </mstyle> </mrow> <annotation>{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" alt="{\displaystyle P}" title=""/></span>. Thus, the polynomial <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> </mstyle> </mrow> <annotation>{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" alt="{\displaystyle P}" title=""/></span> defines the function <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> <mo>↦</mo> <mi>P</mi> <mo>(</mo> <mi>a</mi> <mo>)</mo> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle a\mapsto P(a),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80ac11962a475fafca00dce1ecc1524986b5afbd" alt="{\displaystyle a\mapsto P(a),}" title=""/></span> which is the <i>polynomial function</i> associated to <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> </mstyle> </mrow> <annotation>{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" alt="{\displaystyle P}" title=""/></span>. Frequently, when using this notation, one supposes that <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> </mstyle> </mrow> <annotation>{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" alt="{\displaystyle a}" title=""/></span> is a number. However, one may use it over any domain where addition and multiplication are defined (that is, any <a href="https://en.wikipedia.org/wiki/Ring_(mathematics)">ring</a>). In particular, if <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> </mstyle> </mrow> <annotation>{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" alt="{\displaystyle a}" title=""/></span> is a polynomial then <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle P(a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87843d318d662e597ebd3c0260bcb2727707009d" alt="{\displaystyle P(a)}" title=""/></span> is also a polynomial. </p><p>More specifically, when <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> </mstyle> </mrow> <annotation>{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" alt="{\displaystyle a}" title=""/></span> is the indeterminate <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>, then the <a href="https://en.wikipedia.org/wiki/Image_(mathematics)">image</a> of <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> by this function is the polynomial <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> </mstyle> </mrow> <annotation>{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" alt="{\displaystyle P}" title=""/></span> itself (substituting <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> for <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> does not change anything). In other words, <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>P</mi> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle P(x)=P,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb7117c512c36d059063286480e1d9ef81310030" alt="{\displaystyle P(x)=P,}" title=""/></span> which justifies formally the existence of two notations for the same polynomial. </p><div><h2>Definition</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><p>A <i>polynomial expression</i> is an <a href="https://en.wikipedia.org/wiki/Expression_(mathematics)">expression</a> that can be built from <a href="https://en.wikipedia.org/wiki/Constant_(mathematics)">constants</a> and symbols called <i>variables</i> or <i>indeterminates</i> by means of <a href="https://en.wikipedia.org/wiki/Addition">addition</a>, <a href="https://en.wikipedia.org/wiki/Multiplication">multiplication</a> and <a href="https://en.wikipedia.org/wiki/Exponentiation">exponentiation</a> to a <a href="https://en.wikipedia.org/wiki/Non-negative_integer">non-negative integer</a> power. The constants are generally <a href="https://en.wikipedia.org/wiki/Number">numbers</a>, but may be any expression that do not involve the indeterminates, and represent <a href="https://en.wikipedia.org/wiki/Mathematical_object">mathematical objects</a> that can be added and multiplied. Two polynomial expressions are considered as defining the same <i>polynomial</i> if they may be transformed, one to the other, by applying the usual properties of <a href="https://en.wikipedia.org/wiki/Commutative_property">commutativity</a>, <a href="https://en.wikipedia.org/wiki/Associative_property">associativity</a> and <a href="https://en.wikipedia.org/wiki/Distributive_property">distributivity</a> of addition and multiplication. For example <span><span><math> <semantics> <mrow> <mstyle> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle (x-1)(x-2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8531d6e3eb9f6d3a798cf9593ff8dfeda8475446" alt="{\displaystyle (x-1)(x-2)}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>3</mn> <mi>x</mi> <mo>+</mo> <mn>2</mn> </mstyle> </mrow> <annotation>{\displaystyle x^{2}-3x+2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a41e6650022d8d264fa45b1eeb530c85d6c8235" alt="{\displaystyle x^{2}-3x+2}" title=""/></span> are two polynomial expressions that represent the same polynomial; so, one has the <a href="https://en.wikipedia.org/wiki/Equality_(mathematics)">equality</a> <span><span><math> <semantics> <mrow> <mstyle> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mo>)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>3</mn> <mi>x</mi> <mo>+</mo> <mn>2</mn> </mstyle> </mrow> <annotation>{\displaystyle (x-1)(x-2)=x^{2}-3x+2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe365de84c197cf23ea2aacbe83154f42103c474" alt="{\displaystyle (x-1)(x-2)=x^{2}-3x+2}" title=""/></span>. </p><p>A polynomial in a single indeterminate <span><i>x</i></span> can always be written (or rewritten) in the form <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> </mrow> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e90604c4b13e7695572308d60f7ecc889484108c" alt="{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0},}" title=""/></span> where <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle a_{0},\ldots ,a_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/403d004cd76aacd38b6432fdc449ddbc226075f7" alt="{\displaystyle a_{0},\ldots ,a_{n}}" title=""/></span> are constants that are called the <i>coefficients</i> of the polynomial, and <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is the indeterminate.<sup><span>[</span>7<span>]</span></sup> The word &quot;indeterminate&quot; means that <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> represents no particular value, although any value may be substituted for it. The mapping that associates the result of this substitution to the substituted value is a <a href="https://en.wikipedia.org/wiki/Function_(mathematics)">function</a>, called a <i>polynomial function</i>. </p><p>This can be expressed more concisely by using <a href="https://en.wikipedia.org/wiki/Summation#Capital-sigma_notation">summation notation</a>: <span><span><math> <semantics> <mrow> <mstyle> <munderover> <mo>∑</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> </mrow> </munderover> <msub> <mi>a</mi> <mrow> <mi>k</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>k</mi> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle \sum _{k=0}^{n}a_{k}x^{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09ed204b80acdcf6f853e704999d24d8a7d4a076" alt="{\displaystyle \sum _{k=0}^{n}a_{k}x^{k}}" title=""/></span> That is, a polynomial can either be zero or can be written as the sum of a finite number of non-zero <a href="https://en.wikipedia.org/wiki/Summand">terms</a>. Each term consists of the product of a number – called the <a href="https://en.wikipedia.org/wiki/Coefficient">coefficient</a> of the term<sup><span>[</span>a<span>]</span></sup> – and a finite number of indeterminates, raised to non-negative integer powers. </p><div><h2>Classification</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><div>Further information: <a href="https://en.wikipedia.org/wiki/Degree_of_a_polynomial">Degree of a polynomial</a></div><p>The exponent on an indeterminate in a term is called the degree of that indeterminate in that term; the degree of the term is the sum of the degrees of the indeterminates in that term, and the degree of a polynomial is the largest degree of any term with nonzero coefficient.<sup><span>[</span>8<span>]</span></sup> Because <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> <mo>=</mo> <msup> <mi>x</mi> <mrow> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle x=x^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5435a16e253d6087aaea2e5db93af527003d717e" alt="{\displaystyle x=x^{1}}" title=""/></span>, the degree of an indeterminate without a written exponent is one. </p><p> A term with no indeterminates and a polynomial with no indeterminates are called, respectively, a <a href="https://en.wikipedia.org/wiki/Constant_term">constant term</a> and a <b>constant polynomial</b>.<sup><span>[</span>b<span>]</span></sup> The degree of a constant term and of a nonzero constant polynomial is <span><span><math> <semantics> <mrow> <mstyle> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" alt="{\displaystyle 0}" title=""/></span>. The degree of the zero polynomial <span><span><math> <semantics> <mrow> <mstyle> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" alt="{\displaystyle 0}" title=""/></span> (which has no terms at all) is generally treated as not defined (but see below).<sup><span>[</span>9<span>]</span></sup> </p><p>For example: <span><span><math> <semantics> <mrow> <mstyle> <mo>−</mo> <mn>5</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mi>y</mi> </mstyle> </mrow> <annotation>{\displaystyle -5x^{2}y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8437cbad6fdcaf0ccbbc33654f5203b8358f3daf" alt="{\displaystyle -5x^{2}y}" title=""/></span> is a term. The coefficient is <span><span><math> <semantics> <mrow> <mstyle> <mo>−</mo> <mn>5</mn> </mstyle> </mrow> <annotation>{\displaystyle -5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffa50dcaacd32d77fb512af521f6066839464c82" alt="{\displaystyle -5}" title=""/></span>, the indeterminates are <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>y</mi> </mstyle> </mrow> <annotation>{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" alt="{\displaystyle y}" title=""/></span>, the degree of <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is two, while the degree of <span><span><math> <semantics> <mrow> <mstyle> <mi>y</mi> </mstyle> </mrow> <annotation>{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" alt="{\displaystyle y}" title=""/></span> is one. The degree of the entire term is the sum of the degrees of each indeterminate in it, so in this example the degree is <span><span><math> <semantics> <mrow> <mstyle> <mn>2</mn> <mo>+</mo> <mn>1</mn> <mo>=</mo> <mn>3</mn> </mstyle> </mrow> <annotation>{\displaystyle 2+1=3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdca0e15ed01800bb3f8a2c4725d8a1bd98429c1" alt="{\displaystyle 2+1=3}" title=""/></span>. </p><p>Forming a sum of several terms produces a polynomial. For example, the following is a polynomial: <span><span><math> <semantics> <mrow> <mstyle> <munder> <mrow> <munder> <mrow> <msub> <mrow> </mrow> </msub> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow> <mstyle> <mtable> <mtr> <mtd> <mrow> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mi>m</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </munder> <munder> <mrow> <munder> <mrow> <msub> <mo>−</mo> <mrow> </mrow> </msub> <mn>5</mn> <mi>x</mi> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow> <mstyle> <mtable> <mtr> <mtd> <mrow> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mi>m</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </munder> <munder> <mrow> <munder> <mrow> <msub> <mo>+</mo> <mrow> </mrow> </msub> <mn>4</mn> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow> <mstyle> <mtable> <mtr> <mtd> <mrow> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mi>m</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>3</mn> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </munder> <mo>.</mo> </mstyle> </mrow> <annotation>{\displaystyle \underbrace {_{\,}3x^{2}} _{\begin{smallmatrix}\mathrm {term} \\\mathrm {1} \end{smallmatrix}}\underbrace {-_{\,}5x} _{\begin{smallmatrix}\mathrm {term} \\\mathrm {2} \end{smallmatrix}}\underbrace {+_{\,}4} _{\begin{smallmatrix}\mathrm {term} \\\mathrm {3} \end{smallmatrix}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/519f66849a58f888a09d7e3e079155885d6f7e72" alt="{\displaystyle \underbrace {_{\,}3x^{2}} _{\begin{smallmatrix}\mathrm {term} \\\mathrm {1} \end{smallmatrix}}\underbrace {-_{\,}5x} _{\begin{smallmatrix}\mathrm {term} \\\mathrm {2} \end{smallmatrix}}\underbrace {+_{\,}4} _{\begin{smallmatrix}\mathrm {term} \\\mathrm {3} \end{smallmatrix}}.}" title=""/></span> It consists of three terms: the first is degree two, the second is degree one, and the third is degree zero. </p><p>Polynomials of small degree have been given specific names. A polynomial of degree zero is a <i><a href="https://en.wikipedia.org/wiki/Constant_polynomial">constant polynomial</a></i>, or simply a <i>constant</i>. Polynomials of degree one, two or three are respectively <i><a href="https://en.wikipedia.org/wiki/Linear_polynomial">linear polynomials</a>,</i> <i><a href="https://en.wikipedia.org/wiki/Quadratic_polynomial">quadratic polynomials</a></i> and <i><a href="https://en.wikipedia.org/wiki/Cubic_polynomial">cubic polynomials</a></i>.<sup><span>[</span>8<span>]</span></sup> For higher degrees, the specific names are not commonly used, although <i>quartic polynomial</i> (for degree four) and <i>quintic polynomial</i> (for degree five) are sometimes used. The names for the degrees may be applied to the polynomial or to its terms. For example, the term <span><span><math> <semantics> <mrow> <mstyle> <mn>2</mn> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle 2x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e50b849d3a7cd902f0ae3fa6ad6d1cad49987c39" alt="{\displaystyle 2x}" title=""/></span> in <span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation>{\displaystyle x^{2}+2x+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/044d597c158b2f1106185cdb438c5785f7c21514" alt="{\displaystyle x^{2}+2x+1}" title=""/></span> is a linear term in a quadratic polynomial. </p><p>The polynomial <span><span><math> <semantics> <mrow> <mstyle> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" alt="{\displaystyle 0}" title=""/></span>, which may be considered to have no terms at all, is called the <b>zero polynomial</b>. Unlike other constant polynomials, its degree is not zero. Rather, the degree of the zero polynomial is either left explicitly undefined, or defined as negative (either −1 or <span><span><math> <semantics> <mrow> <mstyle> <mo>−</mo> <mi>∞</mi> </mstyle> </mrow> <annotation>{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" alt="{\displaystyle -\infty }" title=""/></span>).<sup><span>[</span>10<span>]</span></sup> The zero polynomial is also unique in that it is the only polynomial in one indeterminate that has an infinite number of <a href="https://en.wikipedia.org/wiki/Root_of_a_function">roots</a>. The graph of the zero polynomial, <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle f(x)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf85883d74b75fe35ca8d3f2b44802df078e4fa1" alt="{\displaystyle f(x)=0}" title=""/></span>, is the <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>-axis. </p><p>In the case of polynomials in more than one indeterminate, a polynomial is called <i>homogeneous</i> of degree <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span> if <i>all</i> of its non-zero terms have degree <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span>. The zero polynomial is homogeneous, and, as a homogeneous polynomial, its degree is undefined.<sup><span>[</span>c<span>]</span></sup> For example, <span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>x</mi> <mrow> <mn>3</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>7</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>5</mn> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle x^{3}y^{2}+7x^{2}y^{3}-3x^{5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dc39ffcb09900ddf537ae7ab0621408ef9f27f0" alt="{\displaystyle x^{3}y^{2}+7x^{2}y^{3}-3x^{5}}" title=""/></span> is homogeneous of degree <span><span><math> <semantics> <mrow> <mstyle> <mn>5</mn> </mstyle> </mrow> <annotation>{\displaystyle 5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29483407999b8763f0ea335cf715a6a5e809f44b" alt="{\displaystyle 5}" title=""/></span>. For more details, see <a href="https://en.wikipedia.org/wiki/Homogeneous_polynomial">homogeneous polynomials</a>. </p><p>The <a href="https://en.wikipedia.org/wiki/Commutative_law">commutative law</a> of addition can be used to rearrange terms into any preferred order. In polynomials with one indeterminate, the terms are usually ordered according to degree, either in &quot;descending powers of <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>&quot;, with the term of largest degree first, or in &quot;ascending powers of <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>&quot;. The polynomial <span><span><math> <semantics> <mrow> <mstyle> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>5</mn> <mi>x</mi> <mo>+</mo> <mn>4</mn> </mstyle> </mrow> <annotation>{\displaystyle 3x^{2}-5x+4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74a60231435dc750928f5a961e6781371298c903" alt="{\displaystyle 3x^{2}-5x+4}" title=""/></span> is written in descending powers of <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>. The first term has coefficient <span><span><math> <semantics> <mrow> <mstyle> <mn>3</mn> </mstyle> </mrow> <annotation>{\displaystyle 3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/991e33c6e207b12546f15bdfee8b5726eafbbb2f" alt="{\displaystyle 3}" title=""/></span>, indeterminate <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>, and exponent <span><span><math> <semantics> <mrow> <mstyle> <mn>2</mn> </mstyle> </mrow> <annotation>{\displaystyle 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/901fc910c19990d0dbaaefe4726ceb1a4e217a0f" alt="{\displaystyle 2}" title=""/></span>. In the second term, the coefficient is <span><span><math> <semantics> <mrow> <mstyle> <mo>−</mo> <mn>5</mn> </mstyle> </mrow> <annotation>{\displaystyle -5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffa50dcaacd32d77fb512af521f6066839464c82" alt="{\displaystyle -5}" title=""/></span>. The third term is a constant. Because the <i>degree</i> of a non-zero polynomial is the largest degree of any one term, this polynomial has degree two.<sup><span>[</span>11<span>]</span></sup> </p><p>Two terms with the same indeterminates raised to the same powers are called &quot;similar terms&quot; or &quot;like terms&quot;, and they can be combined, using the <a href="https://en.wikipedia.org/wiki/Distributive_law">distributive law</a>, into a single term whose coefficient is the sum of the coefficients of the terms that were combined. It may happen that this makes the coefficient <span><span><math> <semantics> <mrow> <mstyle> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" alt="{\displaystyle 0}" title=""/></span>.<sup><span>[</span>12<span>]</span></sup> </p><p>Polynomials can be classified by the number of terms with nonzero coefficients, so that a one-term polynomial is called a <a href="https://en.wikipedia.org/wiki/Monomial">monomial</a>,<sup><span>[</span>d<span>]</span></sup> a two-term polynomial is called a <a href="https://en.wikipedia.org/wiki/Binomial_(polynomial)">binomial</a>, and a three-term polynomial is called a <a href="https://en.wikipedia.org/wiki/Trinomial">trinomial</a>. A polynomial with two or more terms is also called a <b>multinomial</b>.<sup><span>[</span>13<span>]</span></sup><sup><span>[</span>14<span>]</span></sup> </p><p>A <b>real polynomial</b> is a polynomial with <a href="https://en.wikipedia.org/wiki/Real_number">real</a> coefficients. When it is used to define a <a href="https://en.wikipedia.org/wiki/Function_(mathematics)">function</a>, the <a href="https://en.wikipedia.org/wiki/Domain_(function)">domain</a> is not so restricted. However, a <b>real polynomial function</b> is a function from the reals to the reals that is defined by a real polynomial. Similarly, an <b>integer polynomial</b> is a polynomial with <a href="https://en.wikipedia.org/wiki/Integer">integer</a> coefficients, and a <b>complex polynomial</b> is a polynomial with <a href="https://en.wikipedia.org/wiki/Complex_number">complex</a> coefficients. </p><p>A polynomial in one indeterminate is called a <b>univariate polynomial</b>, a polynomial in more than one indeterminate is called a <b>multivariate polynomial</b>.<sup><span>[</span>15<span>]</span></sup> A polynomial with two indeterminates is called a <b>bivariate polynomial</b>.<sup><span>[</span>7<span>]</span></sup> These notions refer more to the kind of polynomials one is generally working with than to individual polynomials; for instance, when working with univariate polynomials, one does not exclude constant polynomials (which may result from the subtraction of non-constant polynomials), although strictly speaking, constant polynomials do not contain any indeterminates at all. It is possible to further classify multivariate polynomials as <i>bivariate</i>, <i>trivariate</i>, and so on, according to the maximum number of indeterminates allowed. Again, so that the set of objects under consideration be closed under subtraction, a study of trivariate polynomials usually allows bivariate polynomials, and so on. It is also common to say simply &quot;polynomials in <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mstyle> </mrow> <annotation>{\displaystyle x,y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ea0abffd33a692ded22accc104515a032851dff" alt="{\displaystyle x,y}" title=""/></span>, and <span><span><math> <semantics> <mrow> <mstyle> <mi>z</mi> </mstyle> </mrow> <annotation>{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" alt="{\displaystyle z}" title=""/></span>&quot;, listing the indeterminates allowed. </p><div><h2>Operations</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><div><h3>Addition and subtraction</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div><p>Polynomials can be added using the <a href="https://en.wikipedia.org/wiki/Associative_law">associative law</a> of addition (grouping all their terms together into a single sum), possibly followed by reordering (using the <a href="https://en.wikipedia.org/wiki/Commutative_law">commutative law</a>) and combining of like terms.<sup><span>[</span>12<span>]</span></sup><sup><span>[</span>16<span>]</span></sup> For example, if <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>=</mo> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>5</mn> <mi>x</mi> <mi>y</mi> <mo>−</mo> <mn>2</mn> </mstyle> </mrow> <annotation>{\displaystyle P=3x^{2}-2x+5xy-2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd58f2a5833b24767d967d92202ca5d97c64f87f" alt="{\displaystyle P=3x^{2}-2x+5xy-2}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>Q</mi> <mo>=</mo> <mo>−</mo> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>3</mn> <mi>x</mi> <mo>+</mo> <mn>4</mn> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>8</mn> </mstyle> </mrow> <annotation>{\displaystyle Q=-3x^{2}+3x+4y^{2}+8}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63df111693a9c14a89bbac05fe75f5f76530e2e4" alt="{\displaystyle Q=-3x^{2}+3x+4y^{2}+8}" title=""/></span> then the sum <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>+</mo> <mi>Q</mi> <mo>=</mo> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>5</mn> <mi>x</mi> <mi>y</mi> <mo>−</mo> <mn>2</mn> <mo>−</mo> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>3</mn> <mi>x</mi> <mo>+</mo> <mn>4</mn> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>8</mn> </mstyle> </mrow> <annotation>{\displaystyle P+Q=3x^{2}-2x+5xy-2-3x^{2}+3x+4y^{2}+8}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab6ced222ea3f8d5ae591a7b02dfebaf6ea1338e" alt="{\displaystyle P+Q=3x^{2}-2x+5xy-2-3x^{2}+3x+4y^{2}+8}" title=""/></span> can be reordered and regrouped as <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>+</mo> <mi>Q</mi> <mo>=</mo> <mo>(</mo> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>)</mo> <mo>+</mo> <mo>(</mo> <mo>−</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>3</mn> <mi>x</mi> <mo>)</mo> <mo>+</mo> <mn>5</mn> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mn>4</mn> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo>(</mo> <mn>8</mn> <mo>−</mo> <mn>2</mn> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle P+Q=(3x^{2}-3x^{2})+(-2x+3x)+5xy+4y^{2}+(8-2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cfa0581ff9256f598e15df43b2d26e95229453c" alt="{\displaystyle P+Q=(3x^{2}-3x^{2})+(-2x+3x)+5xy+4y^{2}+(8-2)}" title=""/></span> and then simplified to <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>+</mo> <mi>Q</mi> <mo>=</mo> <mi>x</mi> <mo>+</mo> <mn>5</mn> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mn>4</mn> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>6.</mn> </mstyle> </mrow> <annotation>{\displaystyle P+Q=x+5xy+4y^{2}+6.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e1ff44450f1e8474afdf0451800d4a128fa075d" alt="{\displaystyle P+Q=x+5xy+4y^{2}+6.}" title=""/></span> When polynomials are added together, the result is another polynomial.<sup><span>[</span>17<span>]</span></sup> </p><p>Subtraction of polynomials is similar. </p><div><h3>Multiplication</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div><div>Further information: <a href="https://en.wikipedia.org/wiki/Polynomial_expansion">Polynomial expansion</a></div><p>Polynomials can also be multiplied. To expand the <a href="https://en.wikipedia.org/wiki/Product_(mathematics)">product</a> of two polynomials into a sum of terms, the distributive law is repeatedly applied, which results in each term of one polynomial being multiplied by every term of the other.<sup><span>[</span>12<span>]</span></sup> For example, if <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mtable> <mtr> <mtd> <mstyle> <mi>P</mi> </mstyle> </mtd> <mtd> <mstyle> <mrow> <mo>=</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>3</mn> <mi>y</mi> <mo>+</mo> <mn>5</mn> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle> <mi>Q</mi> </mstyle> </mtd> <mtd> <mrow> <mstyle> <mrow> <mo>=</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>5</mn> <mi>y</mi> <mo>+</mo> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mn>1</mn> </mrow> </mstyle> </mrow> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\begin{aligned}\color {Red}P\,&amp;\color {Red}{=2x+3y+5}\\\color {Blue}Q\,&amp;{\color {Blue}{=2x+5y+xy+1}},\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/364c643faa5f3127a34cd5e661c0b9a403a42178" alt="{\displaystyle {\begin{aligned}\color {Red}P\,&amp;\color {Red}{=2x+3y+5}\\\color {Blue}Q\,&amp;{\color {Blue}{=2x+5y+xy+1}},\end{aligned}}}" title=""/></span> then <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mtable> <mtr> <mtd> <mrow> <mstyle> <mrow> <mi>P</mi> </mrow> </mstyle> </mrow> <mrow> <mstyle> <mrow> <mi>Q</mi> </mrow> </mstyle> </mrow> </mtd> <mtd> <mrow> <mo>=</mo> </mrow> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>2</mn> <mi>x</mi> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mn>2</mn> <mi>x</mi> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>2</mn> <mi>x</mi> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mn>5</mn> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>2</mn> <mi>x</mi> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>2</mn> <mi>x</mi> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mn>1</mn> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>3</mn> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mn>2</mn> <mi>x</mi> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>3</mn> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mn>5</mn> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>3</mn> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>3</mn> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mn>1</mn> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>5</mn> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mn>2</mn> <mi>x</mi> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>5</mn> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mn>5</mn> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>5</mn> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mrow> <mstyle> <mrow> <mn>5</mn> </mrow> </mstyle> </mrow> <mo>⋅</mo> <mrow> <mstyle> <mrow> <mn>1</mn> </mrow> </mstyle> </mrow> <mo>)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\begin{array}{rccrcrcrcr}{\color {Red}{P}}{\color {Blue}{Q}}&amp;{=}&amp;&amp;({\color {Red}{2x}}\cdot {\color {Blue}{2x}})&amp;+&amp;({\color {Red}{2x}}\cdot {\color {Blue}{5y}})&amp;+&amp;({\color {Red}{2x}}\cdot {\color {Blue}{xy}})&amp;+&amp;({\color {Red}{2x}}\cdot {\color {Blue}{1}})\\&amp;&amp;+&amp;({\color {Red}{3y}}\cdot {\color {Blue}{2x}})&amp;+&amp;({\color {Red}{3y}}\cdot {\color {Blue}{5y}})&amp;+&amp;({\color {Red}{3y}}\cdot {\color {Blue}{xy}})&amp;+&amp;({\color {Red}{3y}}\cdot {\color {Blue}{1}})\\&amp;&amp;+&amp;({\color {Red}{5}}\cdot {\color {Blue}{2x}})&amp;+&amp;({\color {Red}{5}}\cdot {\color {Blue}{5y}})&amp;+&amp;({\color {Red}{5}}\cdot {\color {Blue}{xy}})&amp;+&amp;({\color {Red}{5}}\cdot {\color {Blue}{1}})\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc195210ff9c8de159f149cc8592d152491d73d5" alt="{\displaystyle {\begin{array}{rccrcrcrcr}{\color {Red}{P}}{\color {Blue}{Q}}&amp;{=}&amp;&amp;({\color {Red}{2x}}\cdot {\color {Blue}{2x}})&amp;+&amp;({\color {Red}{2x}}\cdot {\color {Blue}{5y}})&amp;+&amp;({\color {Red}{2x}}\cdot {\color {Blue}{xy}})&amp;+&amp;({\color {Red}{2x}}\cdot {\color {Blue}{1}})\\&amp;&amp;+&amp;({\color {Red}{3y}}\cdot {\color {Blue}{2x}})&amp;+&amp;({\color {Red}{3y}}\cdot {\color {Blue}{5y}})&amp;+&amp;({\color {Red}{3y}}\cdot {\color {Blue}{xy}})&amp;+&amp;({\color {Red}{3y}}\cdot {\color {Blue}{1}})\\&amp;&amp;+&amp;({\color {Red}{5}}\cdot {\color {Blue}{2x}})&amp;+&amp;({\color {Red}{5}}\cdot {\color {Blue}{5y}})&amp;+&amp;({\color {Red}{5}}\cdot {\color {Blue}{xy}})&amp;+&amp;({\color {Red}{5}}\cdot {\color {Blue}{1}})\end{array}}}" title=""/></span> Carrying out the multiplication in each term produces <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mtable> <mtr> <mtd> <mi>P</mi> <mi>Q</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mn>4</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>10</mn> <mi>x</mi> <mi>y</mi> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>2</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mi>y</mi> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>2</mn> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> </mtd> <mtd> <mn>6</mn> <mi>x</mi> <mi>y</mi> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>15</mn> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>3</mn> <mi>x</mi> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>3</mn> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> </mtd> <mtd> <mn>10</mn> <mi>x</mi> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>25</mn> <mi>y</mi> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>5</mn> <mi>x</mi> <mi>y</mi> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>5.</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\begin{array}{rccrcrcrcr}PQ&amp;=&amp;&amp;4x^{2}&amp;+&amp;10xy&amp;+&amp;2x^{2}y&amp;+&amp;2x\\&amp;&amp;+&amp;6xy&amp;+&amp;15y^{2}&amp;+&amp;3xy^{2}&amp;+&amp;3y\\&amp;&amp;+&amp;10x&amp;+&amp;25y&amp;+&amp;5xy&amp;+&amp;5.\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9f082545d28b0eff0d4e39f45fd96cb8621d5fd" alt="{\displaystyle {\begin{array}{rccrcrcrcr}PQ&amp;=&amp;&amp;4x^{2}&amp;+&amp;10xy&amp;+&amp;2x^{2}y&amp;+&amp;2x\\&amp;&amp;+&amp;6xy&amp;+&amp;15y^{2}&amp;+&amp;3xy^{2}&amp;+&amp;3y\\&amp;&amp;+&amp;10x&amp;+&amp;25y&amp;+&amp;5xy&amp;+&amp;5.\end{array}}}" title=""/></span> Combining similar terms yields <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mtable> <mtr> <mtd> <mi>P</mi> <mi>Q</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mn>4</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mn>10</mn> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mn>6</mn> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mn>5</mn> <mi>x</mi> <mi>y</mi> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>2</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mi>y</mi> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>10</mn> <mi>x</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> </mtd> <mtd> <mn>15</mn> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>3</mn> <mi>x</mi> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mo>(</mo> <mn>3</mn> <mi>y</mi> <mo>+</mo> <mn>25</mn> <mi>y</mi> <mo>)</mo> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>5</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\begin{array}{rcccrcrcrcr}PQ&amp;=&amp;&amp;4x^{2}&amp;+&amp;(10xy+6xy+5xy)&amp;+&amp;2x^{2}y&amp;+&amp;(2x+10x)\\&amp;&amp;+&amp;15y^{2}&amp;+&amp;3xy^{2}&amp;+&amp;(3y+25y)&amp;+&amp;5\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a456c047e979efaf41ecc8b0fae753a03675ad3" alt="{\displaystyle {\begin{array}{rcccrcrcrcr}PQ&amp;=&amp;&amp;4x^{2}&amp;+&amp;(10xy+6xy+5xy)&amp;+&amp;2x^{2}y&amp;+&amp;(2x+10x)\\&amp;&amp;+&amp;15y^{2}&amp;+&amp;3xy^{2}&amp;+&amp;(3y+25y)&amp;+&amp;5\end{array}}}" title=""/></span> which can be simplified to <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mi>Q</mi> <mo>=</mo> <mn>4</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>21</mn> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mn>2</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mi>y</mi> <mo>+</mo> <mn>12</mn> <mi>x</mi> <mo>+</mo> <mn>15</mn> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>3</mn> <mi>x</mi> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>28</mn> <mi>y</mi> <mo>+</mo> <mn>5.</mn> </mstyle> </mrow> <annotation>{\displaystyle PQ=4x^{2}+21xy+2x^{2}y+12x+15y^{2}+3xy^{2}+28y+5.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6792dbf53f6399df0dac6e1fd7845c9de08b54e" alt="{\displaystyle PQ=4x^{2}+21xy+2x^{2}y+12x+15y^{2}+3xy^{2}+28y+5.}" title=""/></span> As in the example, the product of polynomials is always a polynomial.<sup><span>[</span>17<span>]</span></sup><sup><span>[</span>9<span>]</span></sup> </p><div><h3>Composition</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div><p>Given a polynomial <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> </mstyle> </mrow> <annotation>{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" alt="{\displaystyle f}" title=""/></span> of a single variable and another polynomial <span><span><math> <semantics> <mrow> <mstyle> <mi>g</mi> </mstyle> </mrow> <annotation>{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" alt="{\displaystyle g}" title=""/></span> of any number of variables, the <a href="https://en.wikipedia.org/wiki/Function_composition">composition</a> <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> <mo>∘</mo> <mi>g</mi> </mstyle> </mrow> <annotation>{\displaystyle f\circ g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2f61ca7838709fbae07dce9c0d513770f10cfae" alt="{\displaystyle f\circ g}" title=""/></span> is obtained by substituting each copy of the variable of the first polynomial by the second polynomial.<sup><span>[</span>9<span>]</span></sup> For example, if <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle f(x)=x^{2}+2x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1639b5547d4cf9dcb437dd018495c196f1a513f0" alt="{\displaystyle f(x)=x^{2}+2x}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>g</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mn>3</mn> <mi>x</mi> <mo>+</mo> <mn>2</mn> </mstyle> </mrow> <annotation>{\displaystyle g(x)=3x+2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d540741ace96ba0a52e9553d483449e75f6b42dd" alt="{\displaystyle g(x)=3x+2}" title=""/></span> then <span><span><math> <semantics> <mrow> <mstyle> <mo>(</mo> <mi>f</mi> <mo>∘</mo> <mi>g</mi> <mo>)</mo> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>f</mi> <mo>(</mo> <mi>g</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>3</mn> <mi>x</mi> <mo>+</mo> <mn>2</mn> <msup> <mo>)</mo> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo>(</mo> <mn>3</mn> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mo>)</mo> <mo>.</mo> </mstyle> </mrow> <annotation>{\displaystyle (f\circ g)(x)=f(g(x))=(3x+2)^{2}+2(3x+2).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf202107201c88255c32126879d7fa0b174fef2a" alt="{\displaystyle (f\circ g)(x)=f(g(x))=(3x+2)^{2}+2(3x+2).}" title=""/></span> A composition may be expanded to a sum of terms using the rules for multiplication and division of polynomials. The composition of two polynomials is another polynomial.<sup><span>[</span>18<span>]</span></sup> </p><div><h3>Division</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div><p>The division of one polynomial by another is not typically a polynomial. Instead, such ratios are a more general family of objects, called <i><a href="https://en.wikipedia.org/wiki/Rational_fraction">rational fractions</a></i>, <i>rational expressions</i>, or <i><a href="https://en.wikipedia.org/wiki/Rational_function">rational functions</a></i>, depending on context.<sup><span>[</span>19<span>]</span></sup> This is analogous to the fact that the ratio of two <a href="https://en.wikipedia.org/wiki/Integer">integers</a> is a <a href="https://en.wikipedia.org/wiki/Rational_number">rational number</a>, not necessarily an integer.<sup><span>[</span>20<span>]</span></sup><sup><span>[</span>21<span>]</span></sup> For example, the fraction <span><span><math> <semantics> <mrow> <mstyle> <mn>1</mn> <mrow> <mo>/</mo> </mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle 1/(x^{2}+1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9ec9419665a9cd331882bbd9b3549d924711cf4" alt="{\displaystyle 1/(x^{2}+1)}" title=""/></span> is not a polynomial, and it cannot be written as a finite sum of powers of the variable <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span>. </p><p>For polynomials in one variable, there is a notion of <a href="https://en.wikipedia.org/wiki/Euclidean_division_of_polynomials">Euclidean division of polynomials</a>, generalizing the <a href="https://en.wikipedia.org/wiki/Euclidean_division">Euclidean division</a> of integers.<sup><span>[</span>e<span>]</span></sup> This notion of the division <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mrow> <mo>/</mo> </mrow> <mi>b</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle a(x)/b(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67f9a98af5529962941dc949aaeb328cc19ad063" alt="{\displaystyle a(x)/b(x)}" title=""/></span> results in two polynomials, a <i>quotient</i> <span><span><math> <semantics> <mrow> <mstyle> <mi>q</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle q(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c38bbafe34a043d284f19231b946a76c0a4b16b4" alt="{\displaystyle q(x)}" title=""/></span> and a <i>remainder</i> <span><span><math> <semantics> <mrow> <mstyle> <mi>r</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle r(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d457e88abd861f46ede37d27c4669c747367109" alt="{\displaystyle r(x)}" title=""/></span>, such that <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> <mo>=</mo> <mi>b</mi> <mi>q</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation>{\displaystyle a=bq+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff37cbe024f8cc6ff961323bde02fb9c5d32066e" alt="{\displaystyle a=bq+r}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>deg</mi> <mo>⁡</mo> <mo>(</mo> <mi>r</mi> <mo>)</mo> <mo>&lt;</mo> <mi>deg</mi> <mo>⁡</mo> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle \deg(r)&lt;\deg(b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d9626ecbc070959c64ec611c286d1eb494ebdd0" alt="{\displaystyle \deg(r)&lt;\deg(b)}" title=""/></span>, where <span><span><math> <semantics> <mrow> <mstyle> <mi>deg</mi> <mo>⁡</mo> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle \deg(p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ace8b1213962bf7c065bd6dd11775a7acdfe711" alt="{\displaystyle \deg(p)}" title=""/></span> is the degree of <span><span><math> <semantics> <mrow> <mstyle> <mi>p</mi> </mstyle> </mrow> <annotation>{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" alt="{\displaystyle p}" title=""/></span>. The quotient and remainder may be computed by any of several algorithms, including <a href="https://en.wikipedia.org/wiki/Polynomial_long_division">polynomial long division</a> and <a href="https://en.wikipedia.org/wiki/Synthetic_division">synthetic division</a>.<sup><span>[</span>22<span>]</span></sup> </p><p>When the denominator <span><span><math> <semantics> <mrow> <mstyle> <mi>b</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle b(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97e149d1ad9ac13aa08fe1230a622e06d2dde3a0" alt="{\displaystyle b(x)}" title=""/></span> is <a href="https://en.wikipedia.org/wiki/Monic_polynomial">monic</a> and linear, that is, <span><span><math> <semantics> <mrow> <mstyle> <mi>b</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>x</mi> <mo>−</mo> <mi>c</mi> </mstyle> </mrow> <annotation>{\displaystyle b(x)=x-c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb083621571682cc6e7e206506542a206197ab6e" alt="{\displaystyle b(x)=x-c}" title=""/></span> for some constant <span><span><math> <semantics> <mrow> <mstyle> <mi>c</mi> </mstyle> </mrow> <annotation>{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" alt="{\displaystyle c}" title=""/></span>, then the <a href="https://en.wikipedia.org/wiki/Polynomial_remainder_theorem">polynomial remainder theorem</a> asserts that the remainder of the division of <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle a(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d685172ca5d7f10d1e9dfd16cffc5a54bf1301a" alt="{\displaystyle a(x)}" title=""/></span> by <span><span><math> <semantics> <mrow> <mstyle> <mi>b</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle b(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97e149d1ad9ac13aa08fe1230a622e06d2dde3a0" alt="{\displaystyle b(x)}" title=""/></span> is the evaluation <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle a(c)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6357292aab06d2b76509f0877c093cb14d328da8" alt="{\displaystyle a(c)}" title=""/></span>.<sup><span>[</span>21<span>]</span></sup> In this case, the quotient may be computed by <a href="https://en.wikipedia.org/wiki/Ruffini%27s_rule">Ruffini&#39;s rule</a>, a special case of synthetic division.<sup><span>[</span>23<span>]</span></sup> </p><div><h3>Factoring</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div><p>All polynomials with coefficients in a <a href="https://en.wikipedia.org/wiki/Unique_factorization_domain">unique factorization domain</a> (for example, the integers or a <a href="https://en.wikipedia.org/wiki/Field_(mathematics)">field</a>) also have a factored form in which the polynomial is written as a product of <a href="https://en.wikipedia.org/wiki/Irreducible_polynomial">irreducible polynomials</a> and a constant. This factored form is unique up to the order of the factors and their multiplication by an invertible constant. In the case of the field of <a href="https://en.wikipedia.org/wiki/Complex_number">complex numbers</a>, the irreducible factors are linear. Over the <a href="https://en.wikipedia.org/wiki/Real_number">real numbers</a>, they have the degree either one or two. Over the integers and the <a href="https://en.wikipedia.org/wiki/Rational_number">rational numbers</a> the irreducible factors may have any degree.<sup><span>[</span>24<span>]</span></sup> For example, the factored form of<span><span><math> <semantics> <mrow> <mstyle> <mn>5</mn> <msup> <mi>x</mi> <mrow> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>5</mn> </mstyle> </mrow> <annotation>{\displaystyle 5x^{3}-5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db4d1e50aa4cca56c80a7d53c8af5b2fc7140557" alt="{\displaystyle 5x^{3}-5}" title=""/></span> is <span><span><math> <semantics> <mrow> <mstyle> <mn>5</mn> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> <mrow> <mo>(</mo> <mrow> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle 5(x-1)\left(x^{2}+x+1\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b1545345384719a509f7ec5d5b2507d3c785b45" alt="{\displaystyle 5(x-1)\left(x^{2}+x+1\right)}" title=""/></span> over the integers and the reals, and <span><span><math> <semantics> <mrow> <mstyle> <mn>5</mn> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>+</mo> <mrow> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>i</mi> <mrow> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>+</mo> <mrow> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mi>i</mi> <mrow> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle 5(x-1)\left(x+{\frac {1+i{\sqrt {3}}}{2}}\right)\left(x+{\frac {1-i{\sqrt {3}}}{2}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/286cd27fa6537dfce68f8621ff6cebb373994446" alt="{\displaystyle 5(x-1)\left(x+{\frac {1+i{\sqrt {3}}}{2}}\right)\left(x+{\frac {1-i{\sqrt {3}}}{2}}\right)}" title=""/></span> over the complex numbers. </p><p>The computation of the factored form, called <i>factorization</i> is, in general, too difficult to be done by hand-written computation. However, efficient <a href="https://en.wikipedia.org/wiki/Factorization_of_polynomials">polynomial factorization</a> <a href="https://en.wikipedia.org/wiki/Algorithm">algorithms</a> are available in most <a href="https://en.wikipedia.org/wiki/Computer_algebra_system">computer algebra systems</a>. </p><div><h3>Calculus</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Calculus_with_polynomials">Calculus with polynomials</a></div><p>Calculating <a href="https://en.wikipedia.org/wiki/Derivative">derivatives</a> and <a href="https://en.wikipedia.org/wiki/Integral">integrals</a> of polynomials is particularly simple, compared to other kinds of functions. The <a href="https://en.wikipedia.org/wiki/Derivative">derivative</a> of the polynomial <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>=</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> </mrow> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> </mrow> </munderover> <msub> <mi>a</mi> <mrow> <mi>i</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>i</mi> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle P=a_{n}x^{n}+a_{n-1}x^{n-1}+\dots +a_{2}x^{2}+a_{1}x+a_{0}=\sum _{i=0}^{n}a_{i}x^{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/628d133fbe28d6dfec79d2632a2b972ac133eb10" alt="{\displaystyle P=a_{n}x^{n}+a_{n-1}x^{n-1}+\dots +a_{2}x^{2}+a_{1}x+a_{0}=\sum _{i=0}^{n}a_{i}x^{i}}" title=""/></span> with respect to <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" alt="{\displaystyle x}" title=""/></span> is the polynomial <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mn>2</mn> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> </mrow> </munderover> <mi>i</mi> <msub> <mi>a</mi> <mrow> <mi>i</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation>{\displaystyle na_{n}x^{n-1}+(n-1)a_{n-1}x^{n-2}+\dots +2a_{2}x+a_{1}=\sum _{i=1}^{n}ia_{i}x^{i-1}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cf6926cde23aa4aafe0289c42b5ed85d6f6f540" alt="{\displaystyle na_{n}x^{n-1}+(n-1)a_{n-1}x^{n-2}+\dots +2a_{2}x+a_{1}=\sum _{i=1}^{n}ia_{i}x^{i-1}.}" title=""/></span> Similarly, the general <a href="https://en.wikipedia.org/wiki/Antiderivative">antiderivative</a> (or indefinite integral) of <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> </mstyle> </mrow> <annotation>{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" alt="{\displaystyle P}" title=""/></span> is <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mfrac> <mrow> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow> <mfrac> <mrow> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> </mrow> </msup> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow> <mfrac> <mrow> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mn>3</mn> </mrow> </msup> </mrow> <mn>3</mn> </mfrac> </mrow> <mo>+</mo> <mrow> <mfrac> <mrow> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> <mi>x</mi> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mi>c</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> </mrow> </munderover> <mrow> <mfrac> <mrow> <msub> <mi>a</mi> <mrow> <mi>i</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\frac {a_{n}x^{n+1}}{n+1}}+{\frac {a_{n-1}x^{n}}{n}}+\dots +{\frac {a_{2}x^{3}}{3}}+{\frac {a_{1}x^{2}}{2}}+a_{0}x+c=c+\sum _{i=0}^{n}{\frac {a_{i}x^{i+1}}{i+1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b459ca530b63bd0a93139abd04299297cb833c4" alt="{\displaystyle {\frac {a_{n}x^{n+1}}{n+1}}+{\frac {a_{n-1}x^{n}}{n}}+\dots +{\frac {a_{2}x^{3}}{3}}+{\frac {a_{1}x^{2}}{2}}+a_{0}x+c=c+\sum _{i=0}^{n}{\frac {a_{i}x^{i+1}}{i+1}}}" title=""/></span> where <span><span><math> <semantics> <mrow> <mstyle> <mi>c</mi> </mstyle> </mrow> <annotation>{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" alt="{\displaystyle c}" title=""/></span> is an arbitrary constant. For example, antiderivatives of <span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation>{\displaystyle x^{2}+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92a3a8d23f9f8123651e496dcf8490990c65cf9a" alt="{\displaystyle x^{2}+1}" title=""/></span> have the form <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <msup> <mi>x</mi> <mrow> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mi>x</mi> <mo>+</mo> <mi>c</mi> </mstyle> </mrow> <annotation>{\displaystyle {\frac {1}{3}}x^{3}+x+c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15f9260740dd1ed87bc87e9893c5efbbd47ec7ff" alt="{\displaystyle {\frac {1}{3}}x^{3}+x+c}" title=""/></span>. </p><p>For polynomials whose coefficients come from more abstract settings (for example, if the coefficients are integers <a href="https://en.wikipedia.org/wiki/Modular_arithmetic">modulo</a> some <a href="https://en.wikipedia.org/wiki/Prime_number">prime number</a> <span><span><math> <semantics> <mrow> <mstyle> <mi>p</mi> </mstyle> </mrow> <annotation>{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" alt="{\displaystyle p}" title=""/></span>, or elements of an arbitrary ring), the formula for the derivative can still be interpreted formally, with the coefficient <span><span><math> <semantics> <mrow> <mstyle> <mi>k</mi> <msub> <mi>a</mi> <mrow> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle ka_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/009ce105d9cb94c62a03e4e14f668c40e2b7d88d" alt="{\displaystyle ka_{k}}" title=""/></span> understood to mean the sum of <span><span><math> <semantics> <mrow> <mstyle> <mi>k</mi> </mstyle> </mrow> <annotation>{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" alt="{\displaystyle k}" title=""/></span> copies of <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>a</mi> <mrow> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle a_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05e256a120c3ab9f8958de71acdf81cd75065e3b" alt="{\displaystyle a_{k}}" title=""/></span>. For example, over the integers modulo <span><span><math> <semantics> <mrow> <mstyle> <mi>p</mi> </mstyle> </mrow> <annotation>{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" alt="{\displaystyle p}" title=""/></span>, the derivative of the polynomial <span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>x</mi> <mrow> <mi>p</mi> </mrow> </msup> <mo>+</mo> <mi>x</mi> </mstyle> </mrow> <annotation>{\displaystyle x^{p}+x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3a44db4aa79034efc76a73a510e32b23f76cfcd" alt="{\displaystyle x^{p}+x}" title=""/></span> is the polynomial <span><span><math> <semantics> <mrow> <mstyle> <mn>1</mn> </mstyle> </mrow> <annotation>{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" alt="{\displaystyle 1}" title=""/></span>.<sup><span>[</span>25<span>]</span></sup> </p><div><h2>Polynomial functions</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div><div>See also: <a href="https://en.wikipedia.org/wiki/Ring_of_polynomial_functions">Ring of polynomial functions</a></div><p>A <i>polynomial function</i> is a function that can be defined by evaluating a polynomial. More precisely, a function <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> </mstyle> </mrow> <annotation>{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" alt="{\displaystyle f}" title=""/></span> of one <a href="https://en.wikipedia.org/wiki/Argument_of_a_function">argument</a> from a given domain is a polynomial function if there exists a polynomial <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> </mrow> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{2}x^{2}+a_{1}x+a_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8d770b4e9a5584c7ffed4fbef6136f5ec9c6ef6" alt="{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{2}x^{2}+a_{1}x+a_{0}}" title=""/></span> that evaluates to <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" alt="{\displaystyle f(x)}" title=""/></span> for all <span>x</span> in the <a href="https://en.wikipedia.org/wiki/Domain_of_a_function">domain</a> of <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> </mstyle> </mrow> <annotation>{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" alt="{\displaystyle f}" title=""/></span> (here, <span><span><math> <semantics> <mrow> <mstyle> <mi>n</mi> </mstyle> </mrow> <annotation>{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" alt="{\displaystyle n}" title=""/></span> is a non-negative integer and <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle a_{0},a_{1},a_{2},\ldots ,a_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e5b3a7818b9c6eef31df3b0671f6d77c1ae495b" alt="{\displaystyle a_{0},a_{1},a_{2},\ldots ,a_{n}}" title=""/></span> are constant coefficients).<sup><span>[</span>26<span>]</span></sup> Generally, unless otherwise specified, polynomial functions have <a href="https://en.wikipedia.org/wiki/Complex_number">complex</a> coefficients, arguments, and values. In particular, a polynomial, restricted to have real coefficients, defines a function from the complex numbers to the complex numbers. If the domain of this function is also <a href="https://en.wikipedia.org/wiki/Restriction_of_a_function">restricted</a> to the reals, the resulting function is a <a href="https://en.wikipedia.org/wiki/Real_function">real function</a> that maps reals to reals. </p><p>For example, the function <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> </mstyle> </mrow> <annotation>{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" alt="{\displaystyle f}" title=""/></span>, defined by <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mi>x</mi> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle f(x)=x^{3}-x,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39f8e8e71eba342e6991cb75d37a9b27e76195fb" alt="{\displaystyle f(x)=x^{3}-x,}" title=""/></span> is a polynomial function of one variable. Polynomial functions of several variables are similarly defined, using polynomials in more than one indeterminate, as in <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mo>=</mo> <mn>2</mn> <msup> <mi>x</mi> <mrow> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mi>y</mi> <mo>+</mo> <mi>x</mi> <msup> <mi>y</mi> <mrow> <mn>5</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>7.</mn> </mstyle> </mrow> <annotation>{\displaystyle f(x,y)=2x^{3}+4x^{2}y+xy^{5}+y^{2}-7.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4a86d490b7f529b65aa3643e151129c513494f5" alt="{\displaystyle f(x,y)=2x^{3}+4x^{2}y+xy^{5}+y^{2}-7.}" title=""/></span> According to the definition of polynomial functions, there may be expressions that obviously are not polynomials but nevertheless define polynomial functions. An example is the expression <span><span><math> <semantics> <mrow> <mstyle> <msup> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>)</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle \left({\sqrt {1-x^{2}}}\right)^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc70da8873463de7c113e184750c55c152996f75" alt="{\displaystyle \left({\sqrt {1-x^{2}}}\right)^{2},}" title=""/></span> which takes the same values as the polynomial <span><span><math> <semantics> <mrow> <mstyle> <mn>1</mn> <mo>−</mo> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle 1-x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/462243d841fc40a3fe3f8f05c2cf637ea867ad41" alt="{\displaystyle 1-x^{2}}" title=""/></span> on the interval <span><span><math> <semantics> <mrow> <mstyle> <mo>[</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mstyle> </mrow> <annotation>{\displaystyle [-1,1]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51e3b7f14a6f70e614728c583409a0b9a8b9de01" alt="{\displaystyle [-1,1]}" title=""/></span>, and thus both expressions define the same polynomial function on this interval. </p><p>Every polynomial function is <a href="https://en.wikipedia.org/wiki/Continuous_function">continuous</a>, <a href="https://en.wikipedia.org/wiki/Smooth_function">smooth</a>, and <a href="https://en.wikipedia.org/wiki/Entire_function">entire</a>. </p><p>The <a href="https://en.wikipedia.org/wiki/Polynomial_evaluation"><b>evaluation</b></a> of a polynomial is the computation of the corresponding polynomial function; that is, the evaluation consists of substituting a numerical value to each indeterminate and carrying out the indicated multiplications and additions. </p><p>For polynomials in one indeterminate, the evaluation is usually more efficient (lower number of arithmetic operations to perform) using <a href="https://en.wikipedia.org/wiki/Horner%27s_method">Horner&#39;s method</a>, which consists of rewriting the polynomial as <span><span><math> <semantics> <mrow> <mstyle> <mo>(</mo> <mo>(</mo> <mo>(</mo> <mo>(</mo> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mi>x</mi> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>3</mn> </mrow> </msub> <mo>)</mo> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation>{\displaystyle (((((a_{n}x+a_{n-1})x+a_{n-2})x+\dotsb +a_{3})x+a_{2})x+a_{1})x+a_{0}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad945524d5308fc2cfc2682d5fd6f118e2977e2a" alt="{\displaystyle (((((a_{n}x+a_{n-1})x+a_{n-2})x+\dotsb +a_{3})x+a_{2})x+a_{1})x+a_{0}.}" title=""/></span> </p><div><h3>Graphs</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div><div> <ul> <li> <div><span><a href="https://en.wikipedia.org/wiki/File:Algebra1_fnz_fig037_pc.svg"></a></span></div> <div>Polynomial of degree 0:<br/><small><span><i>f</i>(<i>x</i>) = 2</span></small></div> </li> <li> <div><span><a href="https://en.wikipedia.org/wiki/File:Fonction_de_Sophie_Germain.png"></a></span></div> <div>Polynomial of degree 1:<br/><small><span><i>f</i>(<i>x</i>) = 2<i>x</i> + 1</span></small></div> </li> <li> <div><span><a href="https://en.wikipedia.org/wiki/File:Polynomialdeg2.svg"></a></span></div> <div>Polynomial of degree 2:<br/><small><span><i>f</i>(<i>x</i>) = <i>x</i><sup>2</sup> − <i>x</i> − 2</span><br/><span>= (<i>x</i> + 1)(<i>x</i> − 2)</span></small></div> </li> <li> <div><span><a href="https://en.wikipedia.org/wiki/File:Polynomialdeg3.svg"></a></span></div> <div>Polynomial of degree 3:<br/><small><span><i>f</i>(<i>x</i>) = <i>x</i><sup>3</sup>/4 + 3<i>x</i><sup>2</sup>/4 − 3<i>x</i>/2 − 2</span><br/><span>= 1/4 (<i>x</i> + 4)(<i>x</i> + 1)(<i>x</i> − 2)</span></small></div> </li> <li> <div><span><a href="https://en.wikipedia.org/wiki/File:Polynomialdeg4.svg"></a></span></div> <div>Polynomial of degree 4:<br/><small><span><i>f</i>(<i>x</i>) = 1/14 (<i>x</i> + 4)(<i>x</i> + 1)(<i>x</i> − 1)(<i>x</i> − 3) <br/>+ 0.5</span></small></div> </li> <li> <div><span><a href="https://en.wikipedia.org/wiki/File:Quintic_polynomial.svg"></a></span></div> <div>Polynomial of degree 5:<br/><small><span><i>f</i>(<i>x</i>) = 1/20 (<i>x</i> + 4)(<i>x</i> + 2)(<i>x</i> + 1)(<i>x</i> − 1)<br/>(<i>x</i> − 3) + 2</span></small></div> </li> <li> <div><span><a href="https://en.wikipedia.org/wiki/File:Sextic_Graph.svg"></a></span></div> <div>Polynomial of degree 6:<br/><small><span><i>f</i>(<i>x</i>) = 1/100 (<i>x</i><sup>6</sup> − 2<i>x</i> <sup>5</sup> − 26<i>x</i><sup>4</sup> + 28<i>x</i><sup>3</sup></span><br/><span>+ 145<i>x</i><sup>2</sup> − 26<i>x</i> − 80)</span></small></div> </li> <li> <div><span><a href="https://en.wikipedia.org/wiki/File:Septic_graph.svg"></a></span></div> <div>Polynomial of degree 7:<br/><small><span><i>f</i>(<i>x</i>) = (<i>x</i> − 3)(<i>x</i> − 2)(<i>x</i> − 1)(<i>x</i>)(<i>x</i> + 1)(<i>x</i> + 2)</span><br/><span>(<i>x</i> + 3)</span></small></div> </li> </ul> </div><p>A polynomial function in one real variable can be represented by a <a href="https://en.wikipedia.org/wiki/Graph_of_a_function">graph</a>. </p><ul> <li> The graph of the zero polynomial <div><span><i>f</i>(<i>x</i>) = 0</span></div> is the <span><i>x</i></span>-axis. </li> <li> The graph of a degree 0 polynomial <div><span><i>f</i>(<i>x</i>) = <i>a</i><sub>0</sub></span>, where <span><i>a</i><sub>0</sub> ≠ 0</span>,</div> is a horizontal line with <span><span><i>y</i></span>-intercept <span><i>a</i><sub>0</sub></span></span> </li> <li> The graph of a degree 1 polynomial (or linear function) <div><span><i>f</i>(<i>x</i>) = <i>a</i><sub>0</sub> + <i>a</i><sub>1</sub><i>x</i></span>, where <span><i>a</i><sub>1</sub> ≠ 0</span>,</div> is an oblique line with <span><span><i>y</i></span>-intercept <span><i>a</i><sub>0</sub></span></span> and <a href="https://en.wikipedia.org/wiki/Slope">slope</a> <span><i>a</i><sub>1</sub></span>. </li> <li> The graph of a degree 2 polynomial <div><span><i>f</i>(<i>x</i>) = <i>a</i><sub>0</sub> + <i>a</i><sub>1</sub><i>x</i> + <i>a</i><sub>2</sub><i>x</i><sup>2</sup></span>, where <span><i>a</i><sub>2</sub> ≠ 0</span></div> is a <a href="https://en.wikipedia.org/wiki/Parabola">parabola</a>. </li> <li> The graph of a degree 3 polynomial <div><span><i>f</i>(<i>x</i>) = <i>a</i><sub>0</sub> + <i>a</i><sub>1</sub><i>x</i> + <i>a</i><sub>2</sub><i>x</i><sup>2</sup> + <i>a</i><sub>3</sub><i>x</i><sup>3</sup></span>, where <span><i>a</i><sub>3</sub> ≠ 0</span></div> is a <a href="https://en.wikipedia.org/wiki/Cubic_equation">cubic curve</a>. </li> <li> The graph of any polynomial with degree 2 or greater <div><span><i>f</i>(<i>x</i>) = <i>a</i><sub>0</sub> + <i>a</i><sub>1</sub><i>x</i> + <i>a</i><sub>2</sub><i>x</i><sup>2</sup> + ⋯ + <i>a</i><sub><i>n</i></sub><i>x</i><sup><i>n</i></sup></span>, where <span><i>a</i><sub><i>n</i></sub> ≠ 0 and <i>n</i> ≥ 2</span></div> is a continuous non-linear curve. </li> </ul><p>A non-constant polynomial function <a href="https://en.wikipedia.org/wiki/Infinity#Calculus">tends to infinity</a> when the variable increases indefinitely (in <a href="https://en.wikipedia.org/wiki/Absolute_value">absolute value</a>). If the degree is higher than one, the graph does not have any <a href="https://en.wikipedia.org/wiki/Asymptote">asymptote</a>. It has two <a href="https://en.wikipedia.org/wiki/Parabolic_branch">parabolic branches</a> with vertical direction (one branch for positive <span><i>x</i></span> and one for negative <span><i>x</i></span>). </p><p>Polynomial graphs are analyzed in calculus using intercepts, slopes, concavity, and end behavior. </p><div><h2>Equations</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Algebraic_equation">Algebraic equation</a></div><p>A <i>polynomial equation</i>, also called an <i><a href="https://en.wikipedia.org/wiki/Algebraic_equation">algebraic equation</a></i>, is an <a href="https://en.wikipedia.org/wiki/Equation">equation</a> of the form<sup><span>[</span>27<span>]</span></sup> <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> </mrow> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation>{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0}=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/864e0906d8d2aa277214b8d0e96311fdab22bae7" alt="{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0}=0.}" title=""/></span> For example, <span><span><math> <semantics> <mrow> <mstyle> <mn>3</mn> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <mi>x</mi> <mo>−</mo> <mn>5</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle 3x^{2}+4x-5=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c3986a6188aeb755a27bf49f2838fc06fd19881" alt="{\displaystyle 3x^{2}+4x-5=0}" title=""/></span>is a polynomial equation. </p><p>When considering equations, the indeterminates (variables) of polynomials are also called <a href="https://en.wikipedia.org/wiki/Variable_(mathematics)">unknowns</a>, and the <i>solutions</i> are the possible values of the unknowns for which the equality is true (in general more than one solution may exist). A polynomial equation stands in contrast to a <i>polynomial <a href="https://en.wikipedia.org/wiki/Identity_(mathematics)">identity</a></i> like <span><span><math> <semantics> <mrow> <mstyle> <mo>(</mo> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo>)</mo> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> <mo>)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>y</mi> <mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle (x+y)(x-y)=x^{2}-y^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/addbb8b37188b7f10b8d3ba5e83ec0fd72e3f963" alt="{\displaystyle (x+y)(x-y)=x^{2}-y^{2}}" title=""/></span>, where both expressions represent the same polynomial in different forms, and as a consequence any evaluation of both members gives a valid equality. </p><p>In elementary <a href="https://en.wikipedia.org/wiki/Algebra">algebra</a>, methods such as the <a href="https://en.wikipedia.org/wiki/Quadratic_formula">quadratic formula</a> are taught for solving all first degree and second degree polynomial equations in one variable. There are also formulas for the <a href="https://en.wikipedia.org/wiki/Cubic_equation">cubic</a> and <a href="https://en.wikipedia.org/wiki/Quartic_equation">quartic equations</a>. For higher degrees, the <a href="https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem">Abel–Ruffini theorem</a> asserts that there can not exist a general formula in radicals. However, <a href="https://en.wikipedia.org/wiki/Root-finding_algorithm">root-finding algorithms</a> may be used to find <a href="https://en.wikipedia.org/wiki/Numerical_approximation">numerical approximations</a> of the roots of a polynomial expression of any degree. </p><p>The number of solutions of a polynomial equation with real coefficients may not exceed the degree, and equals the degree when the <a href="https://en.wikipedia.org/wiki/Complex_number">complex</a> solutions are counted with their <a href="https://en.wikipedia.org/wiki/Multiplicity_(mathematics)">multiplicity</a>. This fact is called the <a href="https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra">fundamental theorem of algebra</a>. </p><div><h3>Solving equations </h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Algebraic_equation">Algebraic equation</a></div><div>See also: <a href="https://en.wikipedia.org/wiki/Root-finding_of_polynomials">Root-finding of polynomials</a> and <a href="https://en.wikipedia.org/wiki/Properties_of_polynomial_roots">Properties of polynomial roots</a></div><div>&quot;Simple root&quot; redirects here. For simple roots in a root system, see <a href="https://en.wikipedia.org/wiki/Root_system#Positive_roots_and_simple_roots">Root system § Positive roots and simple roots</a>.</div><p>A <i>root</i> of a nonzero univariate polynomial <span><i>P</i></span> is a value <span>a</span> of <span>x</span> such that <span><i>P</i>(<i>a</i>) = 0</span>. In other words, a root of <span>P</span> is a solution of the <a href="https://en.wikipedia.org/wiki/Polynomial_equation">polynomial equation</a> <span><i>P</i>(<i>x</i>) = 0</span> or a <a href="https://en.wikipedia.org/wiki/Zero_of_a_function">zero</a> of the polynomial function defined by <span><i>P</i></span>. In the case of the zero polynomial, every number is a zero of the corresponding function, and the concept of root is rarely considered. </p><p>A number <span><i>a</i></span> is a root of a polynomial <span><i>P</i></span> if and only if the linear polynomial <span><i>x</i> − <i>a</i></span> divides <span><i>P</i></span>, that is if there is another polynomial <span><i>Q</i></span> such that <span><i>P</i> = (<i>x</i> − <i>a</i>) Q</span>. It may happen that a power (greater than <span>1</span>) of <span><i>x</i> − <i>a</i></span> divides <span><i>P</i></span>; in this case, <span><i>a</i></span> is a <i>multiple root</i> of <span><i>P</i></span>, and otherwise <span><i>a</i></span> is a <b>simple root</b> of <span><i>P</i></span>. If <span><i>P</i></span> is a nonzero polynomial, there is a highest power <span><i>m</i></span> such that <span>(<i>x</i> − <i>a</i>)<sup><i>m</i></sup></span> divides <span><i>P</i></span>, which is called the <i>multiplicity</i> of <span><i>a</i></span> as a root of <span><i>P</i></span>. The number of roots of a nonzero polynomial <span><i>P</i></span>, counted with their respective multiplicities, cannot exceed the degree of <span><i>P</i></span>,<sup><span>[</span>28<span>]</span></sup> and equals this degree if all <a href="https://en.wikipedia.org/wiki/Complex_number">complex</a> roots are considered (this is a consequence of the <a href="https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra">fundamental theorem of algebra</a>). The coefficients of a polynomial and its roots are related by <a href="https://en.wikipedia.org/wiki/Vieta%27s_formulas">Vieta&#39;s formulas</a>. </p><p>Some polynomials, such as <span><i>x</i><sup>2</sup> + 1</span>, do not have any roots among the <a href="https://en.wikipedia.org/wiki/Real_number">real numbers</a>. If, however, the set of accepted solutions is expanded to the <a href="https://en.wikipedia.org/wiki/Complex_number">complex numbers</a>, every non-constant polynomial has at least one root; this is the <a href="https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra">fundamental theorem of algebra</a>. By successively dividing out factors <span><i>x</i> − <i>a</i></span>, one sees that any polynomial with complex coefficients can be written as a constant (its leading coefficient) times a product of such polynomial factors of degree 1; as a consequence, the number of (complex) roots counted with their multiplicities is exactly equal to the degree of the polynomial. </p><p>There may be several meanings of <a href="https://en.wikipedia.org/wiki/Equation_solving">&quot;solving an equation&quot;</a>. One may want to express the solutions as explicit numbers; for example, the unique solution of <span>2<i>x</i> − 1 = 0</span> is <span>1/2</span>. This is, in general, impossible for equations of degree greater than one, and, since the ancient times, mathematicians have searched to express the solutions as <a href="https://en.wikipedia.org/wiki/Algebraic_expression">algebraic expressions</a>; for example, the <a href="https://en.wikipedia.org/wiki/Golden_ratio">golden ratio</a> <span>(1+<span>√<span>5</span></span>)/2</span> is the unique positive solution of <span><i>x</i><sup>2</sup> − <i>x</i> − 1 = 0</span> In the ancient times, they succeeded only for degrees one and two. For <a href="https://en.wikipedia.org/wiki/Quadratic_equation">quadratic equations</a>, the <a href="https://en.wikipedia.org/wiki/Quadratic_formula">quadratic formula</a> provides such expressions of the solutions. Since the 16th century, similar formulas (using cube roots in addition to square roots), although much more complicated, are known for equations of degree three and four (see <a href="https://en.wikipedia.org/wiki/Cubic_equation">cubic equation</a> and <a href="https://en.wikipedia.org/wiki/Quartic_equation">quartic equation</a>). But formulas for degree 5 and higher eluded researchers for several centuries. In 1824, <a href="https://en.wikipedia.org/wiki/Niels_Henrik_Abel">Niels Henrik Abel</a> proved the striking result that there are equations of degree 5 whose solutions cannot be expressed by a (finite) formula, involving only arithmetic operations and radicals (see <a href="https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem">Abel–Ruffini theorem</a>). In 1830, <a href="https://en.wikipedia.org/wiki/%C3%89variste_Galois">Évariste Galois</a> proved that most equations of degree higher than four cannot be solved by radicals, and showed that for each equation, one may decide whether it is solvable by radicals, and, if it is, solve it. This result marked the start of <a href="https://en.wikipedia.org/wiki/Galois_theory">Galois theory</a> and <a href="https://en.wikipedia.org/wiki/Group_theory">group theory</a>, two important branches of modern <a href="https://en.wikipedia.org/wiki/Algebra">algebra</a>. Galois himself noted that the computations implied by his method were impracticable. Nevertheless, formulas for solvable equations of degrees 5 and 6 have been published (see <a href="https://en.wikipedia.org/wiki/Quintic_function">quintic function</a> and <a href="https://en.wikipedia.org/wiki/Sextic_equation">sextic equation</a>). </p><p>When there is no algebraic expression for the roots, and when such an algebraic expression exists but is too complicated to be useful, the unique way of solving it is to compute <a href="https://en.wikipedia.org/wiki/Numerical_approximation">numerical approximations</a> of the solutions.<sup><span>[</span>29<span>]</span></sup> There are many methods for that; some are restricted to polynomials and others may apply to any <a href="https://en.wikipedia.org/wiki/Continuous_function">continuous function</a>. The most efficient <a href="https://en.wikipedia.org/wiki/Algorithm">algorithms</a> allow solving easily (on a <a href="https://en.wikipedia.org/wiki/Computer">computer</a>) polynomial equations of degree higher than 1,000 (see <i><a href="https://en.wikipedia.org/wiki/Root-finding_algorithm">Root-finding algorithm</a></i>). </p><p>For polynomials with more than one indeterminate, the combinations of values for the variables for which the polynomial function takes the value zero are generally called <i>zeros</i> instead of &quot;roots&quot;. The study of the sets of zeros of polynomials is the object of <a href="https://en.wikipedia.org/wiki/Algebraic_geometry">algebraic geometry</a>. For a set of polynomial equations with several unknowns, there are <a href="https://en.wikipedia.org/wiki/Algorithm">algorithms</a> to decide whether they have a finite number of <a href="https://en.wikipedia.org/wiki/Complex_number">complex</a> solutions, and, if this number is finite, for computing the solutions. See <a href="https://en.wikipedia.org/wiki/System_of_polynomial_equations">System of polynomial equations</a>. </p><p>The special case where all the polynomials are of degree one is called a <a href="https://en.wikipedia.org/wiki/System_of_linear_equations">system of linear equations</a>, for which another range of different <a href="https://en.wikipedia.org/wiki/System_of_linear_equations#Solving_a_linear_system">solution methods</a> exist, including the classical <a href="https://en.wikipedia.org/wiki/Gaussian_elimination">Gaussian elimination</a>. </p><p>A polynomial equation for which one is interested only in the solutions which are <a href="https://en.wikipedia.org/wiki/Integer">integers</a> is called a <a href="https://en.wikipedia.org/wiki/Diophantine_equation">Diophantine equation</a>. Solving Diophantine equations is generally a very hard task. It has been proved that there cannot be any general <a href="https://en.wikipedia.org/wiki/Algorithm">algorithm</a> for solving them, or even for deciding whether the set of solutions is empty (see <a href="https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem">Hilbert&#39;s tenth problem</a>). Some of the most famous problems that have been solved during the last fifty years are related to Diophantine equations, such as <a href="https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem">Fermat&#39;s Last Theorem</a>. </p><div><h2>Polynomial expressions</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div><p> </p><p>Polynomials where indeterminates are substituted for some other mathematical objects are often considered, and sometimes have a special name. </p><div><h3>Trigonometric polynomials</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=17"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Trigonometric_polynomial">Trigonometric polynomial</a></div><p>If sin(<i>nx</i>) and cos(<i>nx</i>) are expanded in terms of sin(<i>x</i>) and cos(<i>x</i>), a trigonometric polynomial becomes a polynomial in the two variables sin(<i>x</i>) and cos(<i>x</i>) (using the <a href="https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Multiple-angle_formulae">multiple-angle formulae</a>). Conversely, every polynomial in sin(<i>x</i>) and cos(<i>x</i>) may be converted, with <a href="https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities">Product-to-sum identities</a>, into a linear combination of functions sin(<i>nx</i>) and cos(<i>nx</i>). This equivalence explains why linear combinations are called polynomials. </p><p>For <a href="https://en.wikipedia.org/wiki/Complex_number">complex coefficients</a>, there is no difference between such a function and a finite <a href="https://en.wikipedia.org/wiki/Fourier_series">Fourier series</a>. </p><p>Trigonometric polynomials are widely used, for example in <a href="https://en.wikipedia.org/wiki/Trigonometric_interpolation">trigonometric interpolation</a> applied to the <a href="https://en.wikipedia.org/wiki/Interpolation">interpolation</a> of <a href="https://en.wikipedia.org/wiki/Periodic_function">periodic functions</a>. They are also used in the <a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform">discrete Fourier transform</a>. </p><div><h3>Matrix polynomials</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=18"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Matrix_polynomial">Matrix polynomial</a></div><p>A <a href="https://en.wikipedia.org/wiki/Matrix_polynomial">matrix polynomial</a> is a polynomial with <a href="https://en.wikipedia.org/wiki/Square_matrix">square matrices</a> as variables.<sup><span>[</span>31<span>]</span></sup> Given an ordinary, scalar-valued polynomial <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> </mrow> </munderover> <mrow> <msub> <mi>a</mi> <mrow> <mi>i</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>i</mi> </mrow> </msup> </mrow> <mo>=</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle P(x)=\sum _{i=0}^{n}{a_{i}x^{i}}=a_{0}+a_{1}x+a_{2}x^{2}+\cdots +a_{n}x^{n},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fedf00e6d1e4f4c50a92e35bf3fac3c489d1eef2" alt="{\displaystyle P(x)=\sum _{i=0}^{n}{a_{i}x^{i}}=a_{0}+a_{1}x+a_{2}x^{2}+\cdots +a_{n}x^{n},}" title=""/></span> this polynomial evaluated at a matrix <i>A</i> is <span><span><math> <semantics> <mrow> <mstyle> <mi>P</mi> <mo>(</mo> <mi>A</mi> <mo>)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> </mrow> </munderover> <mrow> <msub> <mi>a</mi> <mrow> <mi>i</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow> <mi>i</mi> </mrow> </msup> </mrow> <mo>=</mo> <msub> <mi>a</mi> <mrow> <mn>0</mn> </mrow> </msub> <mi>I</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> </mrow> </msub> <mi>A</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> </mrow> </msub> <msup> <mi>A</mi> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow> <mi>n</mi> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle P(A)=\sum _{i=0}^{n}{a_{i}A^{i}}=a_{0}I+a_{1}A+a_{2}A^{2}+\cdots +a_{n}A^{n},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66dc9788b5ccf460b7cb64a24fad0592e552ce66" alt="{\displaystyle P(A)=\sum _{i=0}^{n}{a_{i}A^{i}}=a_{0}I+a_{1}A+a_{2}A^{2}+\cdots +a_{n}A^{n},}" title=""/></span> where <i>I</i> is the <a href="https://en.wikipedia.org/wiki/Identity_matrix">identity matrix</a>.<sup><span>[</span>32<span>]</span></sup> </p><p>A <b>matrix polynomial equation</b> is an equality between two matrix polynomials, which holds for the specific matrices in question. A <b>matrix polynomial identity</b> is a matrix polynomial equation which holds for all matrices <i>A</i> in a specified <a href="https://en.wikipedia.org/wiki/Matrix_ring">matrix ring</a> <i>M<sub>n</sub></i>(<i>R</i>). </p><div><h3>Exponential polynomials</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=19"><span>edit</span></a><span>]</span></span></div><p>A bivariate polynomial where the second variable is substituted for an exponential function applied to the first variable, for example <span><i>P</i>(<i>x</i>, <i>e</i><sup><i>x</i></sup>)</span>, may be called an <a href="https://en.wikipedia.org/wiki/Exponential_polynomial">exponential polynomial</a>. </p><div><h2>Related concepts</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=20"><span>edit</span></a><span>]</span></span></div><div><h3>Rational functions</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=21"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Rational_function">Rational function</a></div><p>A <a href="https://en.wikipedia.org/wiki/Rational_fraction">rational fraction</a> is the <a href="https://en.wikipedia.org/wiki/Quotient">quotient</a> (<a href="https://en.wikipedia.org/wiki/Algebraic_fraction">algebraic fraction</a>) of two polynomials. Any <a href="https://en.wikipedia.org/wiki/Algebraic_expression">algebraic expression</a> that can be rewritten as a rational fraction is a <a href="https://en.wikipedia.org/wiki/Rational_function">rational function</a>. </p><p>While polynomial functions are defined for all values of the variables, a rational function is defined only for the values of the variables for which the denominator is not zero. </p><p>The rational fractions include the Laurent polynomials, but do not limit denominators to powers of an indeterminate. </p><div><h3>Laurent polynomials</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=22"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Laurent_polynomial">Laurent polynomial</a></div><p><a href="https://en.wikipedia.org/wiki/Laurent_polynomial">Laurent polynomials</a> are like polynomials, but allow negative powers of the variable(s) to occur. </p><div><h3>Power series</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=23"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Formal_power_series">Formal power series</a></div><p><a href="https://en.wikipedia.org/wiki/Formal_power_series">Formal power series</a> are like polynomials, but allow infinitely many non-zero terms to occur, so that they do not have finite degree. Unlike polynomials they cannot in general be explicitly and fully written down (just like <a href="https://en.wikipedia.org/wiki/Irrational_number">irrational numbers</a> cannot), but the rules for manipulating their terms are the same as for polynomials. Non-formal <a href="https://en.wikipedia.org/wiki/Power_series">power series</a> also generalize polynomials, but the multiplication of two power series may not converge. </p><div><h2>Polynomial ring</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=24"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Polynomial_ring">Polynomial ring</a></div><p>A <i>polynomial</i> <span><i>f</i></span> over a <a href="https://en.wikipedia.org/wiki/Commutative_ring">commutative ring</a> <span><i>R</i></span> is a polynomial all of whose coefficients belong to <span><i>R</i></span>. It is straightforward to verify that the polynomials in a given set of indeterminates over <span><i>R</i></span> form a commutative ring, called the <i>polynomial ring</i> in these indeterminates, denoted <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>]</mo> </mstyle> </mrow> <annotation>{\displaystyle R[x]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ce54622cb380383ab3a42441b056626ea0d2440" alt="{\displaystyle R[x]}" title=""/></span> in the univariate case and <span><span><math> <semantics> <mrow> <mstyle> <mi>R</mi> <mo>[</mo> <msub> <mi>x</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>n</mi> </mrow> </msub> <mo>]</mo> </mstyle> </mrow> <annotation>{\displaystyle R[x_{1},\ldots ,x_{n}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58c388e003e234e12fb55533e35a211c8cf295e5" alt="{\displaystyle R[x_{1},\ldots ,x_{n}]}" title=""/></span> in the multivariate case. </p><p>One can think of the ring <span><i>R</i>[<i>x</i>]</span> as arising from <span><i>R</i></span> by adding one new element <i>x</i> to <i>R</i>, and extending in a minimal way to a ring in which <span><i>x</i></span> satisfies no other relations than the obligatory ones, plus commutation with all elements of <span><i>R</i></span> (that is <span><i>xr</i> = <i>rx</i></span>). To do this, one must add all powers of <span><i>x</i></span> and their linear combinations as well. </p><p>Formation of the polynomial ring, together with forming factor rings by factoring out <a href="https://en.wikipedia.org/wiki/Ideal_(ring_theory)">ideals</a>, are important tools for constructing new rings out of known ones. For instance, the ring (in fact field) of complex numbers, which can be constructed from the polynomial ring <span><i>R</i>[<i>x</i>]</span> over the real numbers by factoring out the ideal of multiples of the polynomial <span><i>x</i><sup>2</sup> + 1</span>. Another example is the construction of <a href="https://en.wikipedia.org/wiki/Finite_field">finite fields</a>, which proceeds similarly, starting out with the field of integers modulo some <a href="https://en.wikipedia.org/wiki/Prime_number">prime number</a> as the coefficient ring <span><i>R</i></span> (see <a href="https://en.wikipedia.org/wiki/Modular_arithmetic">modular arithmetic</a>). </p><p>If <span><i>R</i></span> is commutative, then one can associate with every polynomial <span><i>P</i></span> in <span><i>R</i>[<i>x</i>]</span> a <i>polynomial function</i> <span><i>f</i></span> with domain and range equal to <span><i>R</i></span>. (More generally, one can take domain and range to be any same <a href="https://en.wikipedia.org/wiki/Unital_algebra">unital</a> <a href="https://en.wikipedia.org/wiki/Associative_algebra">associative algebra</a> over <span><i>R</i></span>.) One obtains the value <span><i>f</i>(<i>r</i>)</span> by <a href="https://en.wikipedia.org/wiki/Substitution_(algebra)">substitution</a> of the value <span><i>r</i></span> for the symbol <span><i>x</i></span> in <span><i>P</i></span>. One reason to distinguish between polynomials and polynomial functions is that, over some rings, different polynomials may give rise to the same polynomial function (see <a href="https://en.wikipedia.org/wiki/Fermat%27s_little_theorem">Fermat&#39;s little theorem</a> for an example where <span><i>R</i></span> is the integers modulo <span><i>p</i></span>). This is not the case when <span><i>R</i></span> is the real or complex numbers, whence the two concepts are not always distinguished in <a href="https://en.wikipedia.org/wiki/Analysis_(mathematics)">analysis</a>. An even more important reason to distinguish between polynomials and polynomial functions is that many operations on polynomials (like <a href="https://en.wikipedia.org/wiki/Euclidean_division">Euclidean division</a>) require looking at what a polynomial is composed of as an expression rather than evaluating it at some constant value for <span><i>x</i></span>. </p><div><h3>Divisibility</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=25"><span>edit</span></a><span>]</span></span></div><div>Main articles: <a href="https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor">Polynomial greatest common divisor</a> and <a href="https://en.wikipedia.org/wiki/Factorization_of_polynomials">Factorization of polynomials</a></div><p>If <span><i>R</i></span> is an <a href="https://en.wikipedia.org/wiki/Integral_domain">integral domain</a> and <span><i>f</i></span> and <span><i>g</i></span> are polynomials in <span><i>R</i>[<i>x</i>]</span>, it is said that <span><i>f</i></span> <i>divides</i> <span><i>g</i></span> or <span><i>f</i></span> is a divisor of <span><i>g</i></span> if there exists a polynomial <span><i>q</i></span> in <span><i>R</i>[<i>x</i>]</span> such that <span><i>f</i> <i>q</i> = <i>g</i></span>. If <span><span><math> <semantics> <mrow> <mstyle> <mi>a</mi> <mo>∈</mo> <mi>R</mi> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle a\in R,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e60ad1d63f653a7249204f2f0f1330a542e0e581" alt="{\displaystyle a\in R,}" title=""/></span> then <span>a</span> is a root of <span>f</span> if and only <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> <mo>−</mo> <mi>a</mi> </mstyle> </mrow> <annotation>{\displaystyle x-a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e32f42f9f52615f0186e3c8f2c25d7cd6f7bd6aa" alt="{\displaystyle x-a}" title=""/></span> divides <span>f</span>. In this case, the quotient can be computed using the <a href="https://en.wikipedia.org/wiki/Polynomial_long_division">polynomial long division</a>.<sup><span>[</span>33<span>]</span></sup><sup><span>[</span>34<span>]</span></sup> </p><p>If <span><i>F</i></span> is a <a href="https://en.wikipedia.org/wiki/Field_(mathematics)">field</a> and <span><i>f</i></span> and <span><i>g</i></span> are polynomials in <span><i>F</i>[<i>x</i>]</span> with <span><i>g</i> ≠ 0</span>, then there exist unique polynomials <span><i>q</i></span> and <span><i>r</i></span> in <span><i>F</i>[<i>x</i>]</span> with <span><span><math> <semantics> <mrow> <mstyle> <mi>f</mi> <mo>=</mo> <mi>q</mi> <mi>g</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation>{\displaystyle f=q\,g+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd736cabd100d712293746d60defd82f495f8347" alt="{\displaystyle f=q\,g+r}" title=""/></span>and such that the degree of <span><i>r</i></span> is smaller than the degree of <span><i>g</i></span> (using the convention that the polynomial 0 has a negative degree). The polynomials <span><i>q</i></span> and <span><i>r</i></span> are uniquely determined by <span><i>f</i></span> and <span><i>g</i></span>. This is called <i><a href="https://en.wikipedia.org/wiki/Euclidean_division_of_polynomials">Euclidean division</a>, division with remainder</i> or <i>polynomial long division</i> and shows that the ring <span><i>F</i>[<i>x</i>]</span> is a <a href="https://en.wikipedia.org/wiki/Euclidean_domain">Euclidean domain</a>. </p><p>Analogously, <i>prime polynomials</i> (more correctly, <i><a href="https://en.wikipedia.org/wiki/Irreducible_polynomial">irreducible polynomials</a></i>) can be defined as <i>non-zero polynomials which cannot be factorized into the product of two non-constant polynomials</i>. In the case of coefficients in a ring, <i>&quot;non-constant&quot;</i> must be replaced by <i>&quot;non-constant or non-<a href="https://en.wikipedia.org/wiki/Unit_(ring_theory)">unit</a>&quot;</i> (both definitions agree in the case of coefficients in a field). Any polynomial may be decomposed into the product of an invertible constant by a product of irreducible polynomials. If the coefficients belong to a field or a <a href="https://en.wikipedia.org/wiki/Unique_factorization_domain">unique factorization domain</a> this decomposition is unique up to the order of the factors and the multiplication of any non-unit factor by a unit (and division of the unit factor by the same unit). When the coefficients belong to integers, rational numbers or a finite field, there are algorithms to test irreducibility and to compute the factorization into irreducible polynomials (see <i><a href="https://en.wikipedia.org/wiki/Factorization_of_polynomials">Factorization of polynomials</a></i>). These algorithms are not practicable for hand-written computation, but are available in any <a href="https://en.wikipedia.org/wiki/Computer_algebra_system">computer algebra system</a>. <a href="https://en.wikipedia.org/wiki/Eisenstein%27s_criterion">Eisenstein&#39;s criterion</a> can also be used in some cases to determine irreducibility. </p><div><h2>Applications</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=26"><span>edit</span></a><span>]</span></span></div><div><h3>Positional notation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=27"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/Positional_notation">Positional notation</a></div><p>In modern positional numbers systems, such as the <a href="https://en.wikipedia.org/wiki/Decimal">decimal system</a>, the digits and their positions in the representation of an integer, for example, 45, are a shorthand notation for a polynomial in the <a href="https://en.wikipedia.org/wiki/Radix">radix</a> or base, in this case, <span>4 × 10<sup>1</sup> + 5 × 10<sup>0</sup></span>. As another example, in radix 5, a string of digits such as 132 denotes the (decimal) number <span>1 × 5<sup>2</sup> + 3 × 5<sup>1</sup> + 2 × 5<sup>0</sup></span> = 42. This representation is unique. Let <i>b</i> be a positive integer greater than 1. Then every positive integer <i>a</i> can be expressed uniquely in the form </p><div><h3>Interpolation and approximation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=28"><span>edit</span></a><span>]</span></span></div><div>See also: <a href="https://en.wikipedia.org/wiki/Polynomial_interpolation">Polynomial interpolation</a>, <a href="https://en.wikipedia.org/wiki/Orthogonal_polynomials">Orthogonal polynomials</a>, <a href="https://en.wikipedia.org/wiki/B-spline">B-spline</a>, and <a href="https://en.wikipedia.org/wiki/Spline_interpolation">spline interpolation</a></div><p>The simple structure of polynomial functions makes them quite useful in analyzing general functions using polynomial approximations. An important example in <a href="https://en.wikipedia.org/wiki/Calculus">calculus</a> is <a href="https://en.wikipedia.org/wiki/Taylor%27s_theorem">Taylor&#39;s theorem</a>, which roughly states that every <a href="https://en.wikipedia.org/wiki/Differentiable_function">differentiable function</a> locally looks like a polynomial function, and the <a href="https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem">Stone–Weierstrass theorem</a>, which states that every <a href="https://en.wikipedia.org/wiki/Continuous_function">continuous function</a> defined on a <a href="https://en.wikipedia.org/wiki/Compact_space">compact</a> <a href="https://en.wikipedia.org/wiki/Interval_(mathematics)">interval</a> of the real axis can be approximated on the whole interval as closely as desired by a polynomial function. Practical methods of approximation include <a href="https://en.wikipedia.org/wiki/Polynomial_interpolation">polynomial interpolation</a> and the use of <a href="https://en.wikipedia.org/wiki/Spline_(mathematics)">splines</a>.<sup><span>[</span>36<span>]</span></sup> </p><div><h3>Other applications</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=29"><span>edit</span></a><span>]</span></span></div><p>Polynomials are frequently used to encode information about some other object. The <a href="https://en.wikipedia.org/wiki/Characteristic_polynomial">characteristic polynomial</a> of a matrix or linear operator contains information about the operator&#39;s <a href="https://en.wikipedia.org/wiki/Eigenvalue">eigenvalues</a>. The <a href="https://en.wikipedia.org/wiki/Minimal_polynomial_(field_theory)">minimal polynomial</a> of an <a href="https://en.wikipedia.org/wiki/Algebraic_element">algebraic element</a> records the simplest algebraic relation satisfied by that element. The <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">chromatic polynomial</a> of a <a href="https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)">graph</a> counts the number of proper colourings of that graph. </p><p>The term &quot;polynomial&quot;, as an adjective, can also be used for quantities or functions that can be written in polynomial form. For example, in <a href="https://en.wikipedia.org/wiki/Computational_complexity_theory">computational complexity theory</a> the phrase <i><a href="https://en.wikipedia.org/wiki/Polynomial_time">polynomial time</a></i> means that the time it takes to complete an <a href="https://en.wikipedia.org/wiki/Algorithm">algorithm</a> is bounded by a polynomial function of some variable, such as the size of the input. </p><div><h2>History</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=30"><span>edit</span></a><span>]</span></span></div><div>Main articles: <a href="https://en.wikipedia.org/wiki/Cubic_function#History">Cubic function § History</a>, <a href="https://en.wikipedia.org/wiki/Quartic_function#History">Quartic function § History</a>, and <a href="https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem#History">Abel–Ruffini theorem § History</a></div><p>Determining the roots of polynomials, or &quot;solving algebraic equations&quot;, is among the oldest problems in mathematics. However, the notation we use today only developed beginning in the 15th century. Before that, equations were written out in words. For example, an algebra problem from the Chinese <a href="https://en.wikipedia.org/wiki/The_Nine_Chapters_on_the_Mathematical_Art">Arithmetic in Nine Sections</a>, <abbr>c.</abbr><span> 200 BCE</span>, begins &quot;Three sheafs of good crop, two sheafs of mediocre crop, and one sheaf of bad crop are sold for 29 dou.&quot; We would write <span>3<i>x</i> + 2<i>y</i> + <i>z</i> = 29</span>. </p><div><h3>History of the notation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=31"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/History_of_mathematical_notation">History of mathematical notation</a></div><p>The earliest known use of the equal sign is in <a href="https://en.wikipedia.org/wiki/Robert_Recorde">Robert Recorde</a>&#39;s <i><a href="https://en.wikipedia.org/wiki/The_Whetstone_of_Witte">The Whetstone of Witte</a></i>, 1557. The signs + for addition, − for subtraction, and the use of a letter for an unknown appear in <a href="https://en.wikipedia.org/wiki/Michael_Stifel">Michael Stifel</a>&#39;s <i>Arithemetica integra</i>, 1544. <a href="https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes">René Descartes</a>, in <i>La géometrie</i>, 1637, introduced the concept of the graph of a polynomial equation. He popularized the use of letters from the beginning of the alphabet to denote constants and letters from the end of the alphabet to denote variables, as can be seen above, in the general formula for a polynomial in one variable, where the <span><i>a</i></span>s denote constants and <span><i>x</i></span> denotes a variable. Descartes introduced the use of superscripts to denote exponents as well.<sup><span>[</span>37<span>]</span></sup> </p><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=32"><span>edit</span></a><span>]</span></span></div><ul><li><a href="https://en.wikipedia.org/wiki/List_of_polynomial_topics">List of polynomial topics</a></li></ul><div><h2>Footnotes</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=33"><span>edit</span></a><span>]</span></span></div><div> <div><ol> <li><span><b>^</b></span> <span>The coefficient of a term may be any number from a specified set. If that set is the set of real numbers, we speak of &quot;polynomials over the reals&quot;. Other common kinds of polynomials are polynomials with integer coefficients, polynomials with complex coefficients, and polynomials with coefficients that are integers <a href="https://en.wikipedia.org/wiki/Modular_arithmetic">modulo</a> some <a href="https://en.wikipedia.org/wiki/Prime_number">prime number</a> <span><span><math> <semantics> <mrow> <mstyle> <mi>p</mi> </mstyle> </mrow> <annotation>{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" alt="{\displaystyle p}" title=""/></span>.</span> </li> <li><span><b>^</b></span> <span>This terminology dates from the time when the distinction was not clear between a polynomial and the function that it defines: a constant term and a constant polynomial define <a href="https://en.wikipedia.org/wiki/Constant_function">constant functions</a>.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup></span> </li> <li><span><b>^</b></span> <span>In fact, as a <a href="https://en.wikipedia.org/wiki/Homogeneous_function">homogeneous function</a>, it is homogeneous of <i>every</i> degree.<sup>[<i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i>]</sup></span> </li> <li><span><b>^</b></span> <span>Some authors use &quot;monomial&quot; to mean &quot;<a href="https://en.wikipedia.org/wiki/Monic_polynomial">monic</a> monomial&quot;. See <cite>Knapp, Anthony W. (2007). <i>Advanced Algebra: Along with a Companion Volume Basic Algebra</i>. Springer. p. 457. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8176-4522-9"><bdi>978-0-8176-4522-9</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span>This paragraph assumes that the polynomials have coefficients in a <a href="https://en.wikipedia.org/wiki/Field_(mathematics)">field</a>.</span> </li> </ol></div></div><div><h2>Notes</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=34"><span>edit</span></a><span>]</span></span></div><div><ol> <li><span><b>^</b></span> <span>Beauregard &amp; Fraleigh (1973, p. 153)</span> </li> <li><span><b>^</b></span> <span>Burden &amp; Faires (1993, p. 96)</span> </li> <li><span><b>^</b></span> <span>Fraleigh (1976, p. 245)</span> </li> <li><span><b>^</b></span> <span>McCoy (1968, p. 190)</span> </li> <li><span><b>^</b></span> <span>Moise (1967, p. 82)</span> </li> <li><span><b>^</b></span> <span>See &quot;polynomial&quot; and &quot;binomial&quot;, <i>Compact Oxford English Dictionary</i></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite>Weisstein, Eric W. <a href="https://mathworld.wolfram.com/Polynomial.html">&quot;Polynomial&quot;</a>. <i>mathworld.wolfram.com</i><span>. Retrieved <span>2020-08-28</span></span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://brilliant.org/wiki/polynomials/">&quot;Polynomials | Brilliant Math &amp; Science Wiki&quot;</a>. <i>brilliant.org</i><span>. Retrieved <span>2020-08-28</span></span>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span>Barbeau 2003, pp. <a href="https://books.google.com/books?id=CynRMm5qTmQC&amp;pg=PA1">1</a>–2</span> </li> <li><span><b>^</b></span> <span><span><cite><a href="https://en.wikipedia.org/wiki/Eric_W._Weisstein">Weisstein, Eric W.</a> <a href="https://mathworld.wolfram.com/ZeroPolynomial.html">&quot;Zero Polynomial&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/MathWorld">MathWorld</a></i>.</cite></span></span> </li> <li><span><b>^</b></span> <span>Edwards 1995, p. <a href="https://books.google.com/books?id=ylFR4h5BIDEC&amp;pg=PA78">78</a></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup> <sup><i><b>c</b></i></sup></span> <span><cite>Edwards, Harold M. (1995). <a href="https://books.google.com/books?id=ylFR4h5BIDEC&amp;pg=PA47"><i>Linear Algebra</i></a>. Springer. p. 47. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8176-3731-6"><bdi>978-0-8176-3731-6</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Weisstein, Eric W. <a href="https://mathworld.wolfram.com/Multinomial.html">&quot;Multinomial&quot;</a>. <i>mathworld.wolfram.com</i><span>. Retrieved <span>2025-08-26</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Clapham, Christopher; Nicholson, James (2009). <a href="https://www.google.ae/books/edition/The_Concise_Oxford_Dictionary_of_Mathema/ZsiSvE0Z3s4C"><i>The Concise Oxford Dictionary of Mathematics</i></a> (4th ed.). United States: Oxford University Press. p. 303. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9780199235940"><bdi>9780199235940</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Weisstein, Eric W. <a href="https://mathworld.wolfram.com/MultivariatePolynomial.html">&quot;Multivariate Polynomial&quot;</a>. <i>mathworld.wolfram.com</i><span>. Retrieved <span>2025-08-26</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Salomon, David (2006). <a href="https://books.google.com/books?id=Zr9bjEpXKnIC&amp;pg=PA459"><i>Coding for Data and Computer Communications</i></a>. Springer. p. 459. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-387-23804-3"><bdi>978-0-387-23804-3</bdi></a>.</cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span><cite><a href="https://books.google.com/books?id=PagNAQAAIAAJ&amp;q=the+addition+of+polynomials+is+an+operation+that+takes+any+two+polynomials+and+produce+always+another+polynomial,"><i>Introduction to Algebra</i></a>. Yale University Press. 1965. p. 621. <q>Any two such polynomials can be added, subtracted, or multiplied. Furthermore, the result in each case is another polynomial</q></cite></span> </li> <li><span><b>^</b></span> <span><cite>Kriete, Hartje (1998-05-20). <a href="https://books.google.com/books?id=HwqjxJOLLOoC&amp;q=The+composition+of+two+polynomials+is+always+another+polynomial.&amp;pg=PA159"><i>Progress in Holomorphic Dynamics</i></a>. CRC Press. p. 159. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-582-32388-9"><bdi>978-0-582-32388-9</bdi></a>. <q>This class of endomorphisms is closed under composition,</q></cite></span> </li> <li><span><b>^</b></span> <span><cite>Marecek, Lynn; Mathis, Andrea Honeycutt (6 May 2020). <a href="https://openstax.org/details/books/intermediate-algebra-2e"><i>Intermediate Algebra 2e</i></a>. <a href="https://en.wikipedia.org/wiki/OpenStax">OpenStax</a>. §7.1.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Haylock, Derek; Cockburn, Anne D. (2008-10-14). <a href="https://books.google.com/books?id=hgAr3maZeQUC&amp;q=division+integers+not+closed&amp;pg=PA49"><i>Understanding Mathematics for Young Children: A Guide for Foundation Stage and Lower Primary Teachers</i></a>. SAGE. p. 49. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-4462-0497-9"><bdi>978-1-4462-0497-9</bdi></a>. <q>We find that the set of integers is not closed under this operation of division.</q></cite></span> </li> <li><span>^ <sup><i><b>a</b></i></sup> <sup><i><b>b</b></i></sup></span> <span>Marecek &amp; Mathis 2020, §5.4]</span> </li> <li><span><b>^</b></span> <span><cite>Selby, Peter H.; Slavin, Steve (1991). <i>Practical Algebra: A Self-Teaching Guide</i> (2nd ed.). Wiley. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-471-53012-1"><bdi>978-0-471-53012-1</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Weisstein, Eric W. <a href="https://mathworld.wolfram.com/RuffinisRule.html">&quot;Ruffini&#39;s Rule&quot;</a>. <i>mathworld.wolfram.com</i><span>. Retrieved <span>2020-07-25</span></span>.</cite></span> </li> <li><span><b>^</b></span> <span>Barbeau 2003, pp. <a href="https://books.google.com/books?id=CynRMm5qTmQC&amp;pg=PA80">80</a>–2</span> </li> <li><span><b>^</b></span> <span>Barbeau 2003, pp. <a href="https://books.google.com/books?id=CynRMm5qTmQC&amp;pg=PA64">64</a>–5</span> </li> <li><span><b>^</b></span> <span>Varberg, Purcell &amp; Rigdon 2007, p. <a href="https://archive.org/details/matematika-a-purcell-calculus-9th-ed/page/38/mode/1up?view=theater&amp;q=polynomial">38</a>.</span> </li> <li><span><b>^</b></span> <span><cite>Proskuryakov, I.V. (1994). <a href="https://books.google.com/books?id=PE1a-EIG22kC&amp;pg=PA88">&quot;Algebraic equation&quot;</a>. In <a href="https://en.wikipedia.org/wiki/Michiel_Hazewinkel">Hazewinkel, Michiel</a> (ed.). <i>Encyclopaedia of Mathematics</i>. Vol. 1. Springer. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-55608-010-4"><bdi>978-1-55608-010-4</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Leung, Kam-tim; et al. (1992). <a href="https://books.google.com/books?id=v5uXkwIUbC8C&amp;pg=PA134"><i>Polynomials and Equations</i></a>. Hong Kong University Press. p. 134. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9789622092716"><bdi>9789622092716</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>McNamee, J.M. (2007). <a href="https://books.google.com/books?id=4PMqxwG-eqQC"><i>Numerical Methods for Roots of Polynomials, Part 1</i></a>. Elsevier. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-08-048947-6"><bdi>978-0-08-048947-6</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite><a href="https://en.wikipedia.org/wiki/Michael_J._D._Powell">Powell, Michael J. D.</a> (1981). <i>Approximation Theory and Methods</i>. <a href="https://en.wikipedia.org/wiki/Cambridge_University_Press">Cambridge University Press</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-521-29514-7"><bdi>978-0-521-29514-7</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Gohberg, Israel; Lancaster, Peter; Rodman, Leiba (2009) [1982]. <i>Matrix Polynomials</i>. Classics in Applied Mathematics. Vol. 58. Lancaster, PA: <a href="https://en.wikipedia.org/wiki/Society_for_Industrial_and_Applied_Mathematics">Society for Industrial and Applied Mathematics</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-89871-681-8"><bdi>978-0-89871-681-8</bdi></a>. <a href="https://en.wikipedia.org/wiki/Zbl_(identifier)">Zbl</a> <a href="https://zbmath.org/?format=complete&amp;q=an:1170.15300">1170.15300</a>.</cite></span> </li> <li><span><b>^</b></span> <span>Horn &amp; Johnson 1990, p. 36.</span> </li> <li><span><b>^</b></span> <span><cite>Irving, Ronald S. (2004). <a href="https://books.google.com/books?id=B4k6ltaxm5YC&amp;pg=PA129"><i>Integers, Polynomials, and Rings: A Course in Algebra</i></a>. Springer. p. 129. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-387-20172-6"><bdi>978-0-387-20172-6</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Jackson, Terrence H. (1995). <a href="https://books.google.com/books?id=LCEOri2-doMC&amp;pg=PA143"><i>From Polynomials to Sums of Squares</i></a>. CRC Press. p. 143. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-7503-0329-3"><bdi>978-0-7503-0329-3</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span>McCoy 1968, p. 75</span> </li> <li><span><b>^</b></span> <span><cite>de Villiers, Johann (2012). <a href="https://books.google.com/books?id=l5mIro_6RlUC"><i>Mathematics of Approximation</i></a>. Springer. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9789491216503"><bdi>9789491216503</bdi></a>.</cite></span> </li> <li><span><b>^</b></span> <span><cite>Eves, Howard (1990). <i>An Introduction to the History of Mathematics</i> (6th ed.). Saunders. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-03-029558-0"><bdi>0-03-029558-0</bdi></a>.</cite></span> </li> </ol></div><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=35"><span>edit</span></a><span>]</span></span></div><div> <ul><li><cite>Barbeau, E.J. (2003). <a href="https://books.google.com/books?id=CynRMm5qTmQC"><i>Polynomials</i></a>. Springer. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-387-40627-5"><bdi>978-0-387-40627-5</bdi></a>.</cite></li> <li><cite>Beauregard, Raymond A.; Fraleigh, John B. (1973), <i>A First Course In Linear Algebra: with Optional Introduction to Groups, Rings, and Fields</i>, Boston: <a href="https://en.wikipedia.org/wiki/Houghton_Mifflin_Company">Houghton Mifflin Company</a>, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-395-14017-X"><bdi>0-395-14017-X</bdi></a></cite></li> <li><cite>Bronstein, Manuel; et al., eds. (2006). <a href="https://books.google.com/books?id=aIlSmBV3yf8C"><i>Solving Polynomial Equations: Foundations, Algorithms, and Applications</i></a>. Springer. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-3-540-27357-8"><bdi>978-3-540-27357-8</bdi></a>.</cite></li> <li><cite>Burden, Richard L.; Faires, J. Douglas (1993), <i>Numerical Analysis</i> (5th ed.), Boston: <a href="https://en.wikipedia.org/w/index.php?title=Prindle,_Weber_and_Schmidt&amp;action=edit&amp;redlink=1">Prindle, Weber and Schmidt</a>, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-534-93219-3"><bdi>0-534-93219-3</bdi></a></cite></li> <li><cite>Cahen, Paul-Jean; Chabert, Jean-Luc (1997). <a href="https://books.google.com/books?id=AlAluH5is6AC"><i>Integer-Valued Polynomials</i></a>. American Mathematical Society. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-0388-2"><bdi>978-0-8218-0388-2</bdi></a>.</cite></li> <li><cite>Fraleigh, John B. (1976), <i>A First Course In Abstract Algebra</i> (2nd ed.), Reading: <a href="https://en.wikipedia.org/wiki/Addison-Wesley">Addison-Wesley</a>, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/0-201-01984-1"><bdi>0-201-01984-1</bdi></a></cite></li> <li><cite>Horn, Roger A.; Johnson, Charles R. (1990). <i>Matrix Analysis</i>. <a href="https://en.wikipedia.org/wiki/Cambridge_University_Press">Cambridge University Press</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-521-38632-6"><bdi>978-0-521-38632-6</bdi></a>.</cite>.</li> <li><cite><a href="https://en.wikipedia.org/wiki/Serge_Lang">Lang, Serge</a> (2002), <i><a href="https://en.wikipedia.org/wiki/Algebra_(Lang)">Algebra</a></i>, <a href="https://en.wikipedia.org/wiki/Graduate_Texts_in_Mathematics">Graduate Texts in Mathematics</a>, vol. 211 (Revised third ed.), New York: Springer-Verlag, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-387-95385-4"><bdi>978-0-387-95385-4</bdi></a>, <a href="https://en.wikipedia.org/wiki/MR_(identifier)">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=1878556">1878556</a></cite>. This classical book covers most of the content of this article.</li> <li><cite>Leung, Kam-tim; et al. (1992). <a href="https://books.google.com/books?id=v5uXkwIUbC8C"><i>Polynomials and Equations</i></a>. Hong Kong University Press. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/9789622092716"><bdi>9789622092716</bdi></a>.</cite></li> <li><cite>Mayr, K. (1937). &quot;Über die Auflösung algebraischer Gleichungssysteme durch hypergeometrische Funktionen&quot;. <i>Monatshefte für Mathematik und Physik</i>. <b>45</b>: <span>280–</span>313. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2FBF01707992">10.1007/BF01707992</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:197662587">197662587</a>.</cite></li> <li><cite>McCoy, Neal H. (1968), <i>Introduction To Modern Algebra, Revised Edition</i>, Boston: <a href="https://en.wikipedia.org/wiki/Allyn_and_Bacon">Allyn and Bacon</a>, <a href="https://en.wikipedia.org/wiki/LCCN_(identifier)">LCCN</a> <a href="https://lccn.loc.gov/68015225">68015225</a></cite></li> <li><cite>Moise, Edwin E. (1967), <i>Calculus: Complete</i>, Reading: <a href="https://en.wikipedia.org/wiki/Addison-Wesley">Addison-Wesley</a></cite></li> <li><cite>Prasolov, Victor V. (2005). <a href="https://books.google.com/books?id=qIJPxdwSqlcC"><i>Polynomials</i></a>. Springer. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-3-642-04012-2"><bdi>978-3-642-04012-2</bdi></a>.</cite></li> <li><cite>Sethuraman, B.A. (1997). <a href="https://books.google.com/books?id=yWnTIqmUOFgC&amp;pg=PA119">&quot;Polynomials&quot;</a>. <span><a href="https://archive.org/details/ringsfieldsvecto0000seth"><i>Rings, Fields, and Vector Spaces: An Introduction to Abstract Algebra Via Geometric Constructibility</i></a></span>. Springer. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-387-94848-5"><bdi>978-0-387-94848-5</bdi></a>.</cite></li> <li><cite>Toth, Gabor (2021). <a href="https://books.google.com/books?id=bJhEEAAAQBAJ&amp;pg=PA263">&quot;Polynomial Expressions&quot;</a>. <i>Elements of Mathematics</i>. Undergraduate Texts in Mathematics. pp. <span>263–</span>318. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2F978-3-030-75051-0_6">10.1007/978-3-030-75051-0_6</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-3-030-75050-3"><bdi>978-3-030-75050-3</bdi></a>.</cite></li> <li><cite>Umemura, H. (2012) [1984]. <a href="https://books.google.com/books?id=xaNCAAAAQBAJ&amp;pg=PA261">&quot;Resolution of algebraic equations by theta constants&quot;</a>. In Mumford, David (ed.). <i>Tata Lectures on Theta II: Jacobian theta functions and differential equations</i>. Springer. pp. 261–. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8176-4578-6"><bdi>978-0-8176-4578-6</bdi></a>.</cite></li> <li><cite>Varberg, Dale E.; Purcell, Edwin J.; Rigdon, Steven E. (2007). <i>Calculus</i> (9th ed.). <a href="https://en.wikipedia.org/wiki/Pearson_Prentice_Hall">Pearson Prentice Hall</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a> <a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0131469686"><bdi>978-0131469686</bdi></a>.</cite></li> <li><cite>von Lindemann, F. (1884). <a href="https://eudml.org/doc/180024">&quot;Ueber die Auflösung der algebraischen Gleichungen durch transcendente Functionen&quot;</a>. <i>Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen</i>. <b>1884</b>: <span>245–</span>8.</cite></li> <li><cite>von Lindemann, F. (1892). <a href="https://eudml.org/doc/180353">&quot;Ueber die Auflösung der algebraischen Gleichungen durch transcendente Functionen. II&quot;</a>. <i>Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen</i>. <b>1892</b>: <span>245–</span>8.</cite></li></ul> </div><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Polynomial&amp;action=edit&amp;section=36"><span>edit</span></a><span>]</span></span></div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Commons-logo.svg"></a></span></div> <div>Wikimedia Commons has media related to <span><a href="https://commons.wikimedia.org/wiki/Category:Polynomials">Polynomials</a></span>.</div></div> </div><div> <div> <div><span><a href="https://en.wikipedia.org/wiki/File:Wiktionary-logo-en-v2.svg"></a></span></div> <div>Look up <i><b><a href="https://en.wiktionary.org/wiki/polynomial">polynomial</a></b></i> in Wiktionary, the free dictionary.</div></div> </div><ul><li><cite>Markushevich, A.I. (2001) [1994], <a href="https://www.encyclopediaofmath.org/index.php?title=Polynomial&amp;oldid=36519">&quot;Polynomial&quot;</a>, <i><a href="https://en.wikipedia.org/wiki/Encyclopedia_of_Mathematics">Encyclopedia of Mathematics</a></i>, <a href="https://en.wikipedia.org/wiki/European_Mathematical_Society">EMS Press</a></cite></li> <li><cite><a href="https://web.archive.org/web/20120924140505/http://mathdl.maa.org/mathDL/46/?pa=content&amp;sa=viewDocument&amp;nodeId=640&amp;pf=1">&quot;Euler&#39;s Investigations on the Roots of Equations&quot;</a>. Archived from <a href="http://mathdl.maa.org/mathDL/46/?pa=content&amp;sa=viewDocument&amp;nodeId=640&amp;pf=1">the original</a> on September 24, 2012.</cite></li></ul><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Polynomials"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Polynomials"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Polynomials"><abbr>e</abbr></a></li></ul></div><div>Polynomials and <a href="https://en.wikipedia.org/wiki/Polynomial_function">polynomial functions</a> and <a href="https://en.wikipedia.org/wiki/Polynomial_equation">polynomial equations</a></div></th></tr><tr><th>By <a href="https://en.wikipedia.org/wiki/Degree_of_a_polynomial">degree</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Zero_polynomial">Zero polynomial (degree undefined or −1 or −∞)</a></li> <li><a href="https://en.wikipedia.org/wiki/Constant_function">Constant function (0)</a></li> <li><a href="https://en.wikipedia.org/wiki/Linear_function_(calculus)">Linear function (1)</a> <ul><li><a href="https://en.wikipedia.org/wiki/Linear_equation">Linear equation</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Quadratic_function">Quadratic function (2)</a> <ul><li><a href="https://en.wikipedia.org/wiki/Quadratic_equation">Quadratic equation</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Cubic_function">Cubic function (3)</a> <ul><li><a href="https://en.wikipedia.org/wiki/Cubic_equation">Cubic equation</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Quartic_function">Quartic function (4)</a> <ul><li><a href="https://en.wikipedia.org/wiki/Quartic_equation">Quartic equation</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Quintic_function">Quintic function (5)</a></li> <li><a href="https://en.wikipedia.org/wiki/Sextic_equation">Sextic equation (6)</a></li> <li><a href="https://en.wikipedia.org/wiki/Septic_equation">Septic equation (7)</a></li></ul> </div></td></tr><tr><th>By properties</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Univariate_polynomial">Univariate</a></li> <li><a href="https://en.wikipedia.org/wiki/Bivariate_polynomial">Bivariate</a></li> <li><a href="https://en.wikipedia.org/wiki/Multivariate_polynomial">Multivariate</a></li> <li><a href="https://en.wikipedia.org/wiki/Monomial">Monomial</a></li> <li><a href="https://en.wikipedia.org/wiki/Binomial_(polynomial)">Binomial</a></li> <li><a href="https://en.wikipedia.org/wiki/Trinomial">Trinomial</a></li> <li><a href="https://en.wikipedia.org/wiki/Irreducible_polynomial">Irreducible</a></li> <li><a href="https://en.wikipedia.org/wiki/Square-free_polynomial">Square-free</a></li> <li><a href="https://en.wikipedia.org/wiki/Homogeneous_polynomial">Homogeneous</a></li> <li><a href="https://en.wikipedia.org/wiki/Quasi-homogeneous_polynomial">Quasi-homogeneous</a></li></ul> </div></td></tr><tr><th>Tools and algorithms</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Factorization_of_polynomials">Factorization</a></li> <li><a href="https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor">Greatest common divisor</a></li> <li><a href="https://en.wikipedia.org/wiki/Polynomial_long_division">Division</a></li> <li><a href="https://en.wikipedia.org/wiki/Horner%27s_method">Horner&#39;s method of evaluation</a></li> <li><a href="https://en.wikipedia.org/wiki/Polynomial_identity_testing">Polynomial identity testing</a></li> <li><a href="https://en.wikipedia.org/wiki/Polynomial_resultant">Resultant</a></li> <li><a href="https://en.wikipedia.org/wiki/Discriminant">Discriminant</a></li> <li><a href="https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis">Gröbner basis</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Functions_navbox"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Functions_navbox"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Functions_navbox"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Function_(mathematics)">Function</a></div></th></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/History_of_the_function_concept">History</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_mathematical_functions">List of specific functions</a></li></ul> </div></td></tr><tr><th>Types by domain,<br/>codomain</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Boolean-valued_function"><span>X → 𝔹</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Ordered_pair"><span>𝔹 → X</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Boolean_function"><span>𝔹ⁿ → 𝔹</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Integer-valued_function"><span>X → ℤ</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Sequence"><span>ℤ → X</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Real-valued_function"><span>X → ℝ</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Function_of_a_real_variable"><span>ℝ → X</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Function_of_several_real_variables"><span>ℝⁿ → X</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Complex-valued_function"><span>X → ℂ</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Function_of_a_complex_variable"><span>ℂ → X</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Function_of_several_complex_variables"><span>ℂⁿ → X</span></a></li></ul> </div></td></tr><tr><th>Classes,<br/>properties</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Constant_function">Constant</a></li> <li><a href="https://en.wikipedia.org/wiki/Identity_function">Identity</a></li> <li><a href="https://en.wikipedia.org/wiki/Linear_map">Linear</a></li> <li>Polynomial</li> <li><a href="https://en.wikipedia.org/wiki/Rational_function">Rational</a></li> <li><a href="https://en.wikipedia.org/wiki/Algebraic_function">Algebraic</a></li> <li><a href="https://en.wikipedia.org/wiki/Analytic_function">Analytic</a></li> <li><a href="https://en.wikipedia.org/wiki/Smooth_function">Smooth</a></li> <li><a href="https://en.wikipedia.org/wiki/Continuous_function">Continuous</a></li> <li><a href="https://en.wikipedia.org/wiki/Measurable_function">Measurable</a></li> <li><a href="https://en.wikipedia.org/wiki/Injective_function">Injective</a></li> <li><a href="https://en.wikipedia.org/wiki/Surjective_function">Surjective</a></li> <li><a href="https://en.wikipedia.org/wiki/Bijection">Bijective</a></li></ul> </div></td></tr><tr><th>Constructions</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Restriction_(mathematics)">Restriction</a></li> <li><a href="https://en.wikipedia.org/wiki/Function_composition">Composition</a></li> <li><a href="https://en.wikipedia.org/wiki/Lambda_calculus">λ</a></li> <li><a href="https://en.wikipedia.org/wiki/Inverse_function">Inverse</a></li></ul> </div></td></tr><tr><th>Generalizations</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Relation_(mathematics)">Relation</a> (<a href="https://en.wikipedia.org/wiki/Binary_relation">Binary relation</a>)</li> <li><a href="https://en.wikipedia.org/wiki/Set-valued_function">Set-valued</a></li> <li><a href="https://en.wikipedia.org/wiki/Multivalued_function">Multivalued</a></li> <li><a href="https://en.wikipedia.org/wiki/Partial_function">Partial</a></li> <li><a href="https://en.wikipedia.org/wiki/Implicit_function">Implicit</a></li> <li><a href="https://en.wikipedia.org/wiki/Function_space">Space</a></li> <li><a href="https://en.wikipedia.org/wiki/Higher-order_function">Higher-order</a></li> <li><a href="https://en.wikipedia.org/wiki/Morphism">Morphism</a></li> <li><a href="https://en.wikipedia.org/wiki/Functor">Functor</a></li></ul> </div></td></tr><tr><td colspan="2"><div> <ul><li> <a href="https://en.wikipedia.org/wiki/Category:Functions">Category</a></li></ul> </div></td></tr></tbody></table></div><div><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Help:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q43260#identifiers"></a></span></div></th></tr><tr><th>National</th><td><div><ul><li><span><a href="https://id.loc.gov/authorities/sh85104702">United States</a></span></li><li><span><span><a href="https://catalogue.bnf.fr/ark:/12148/cb119786822">France</a></span></span></li><li><span><span><a href="https://data.bnf.fr/ark:/12148/cb119786822">BnF data</a></span></span></li><li><span><a href="https://id.ndl.go.jp/auth/ndlna/00572625">Japan</a></span></li><li><span><span><a href="https://aleph.nkp.cz/F/?func=find-c&amp;local_base=aut&amp;ccl_term=ica=ph135425&amp;CON_LNG=ENG">Czech Republic</a></span></span></li><li><span><a href="https://www.nli.org.il/en/authorities/987007563144505171">Israel</a></span></li></ul></div></td></tr><tr><th>Other</th><td><div><ul><li><span><a href="https://lux.collections.yale.edu/view/concept/25027523-78b9-483d-9f6f-d18f72298d41">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div>