https://roastidio.us/webspace/4172 Roastidio.us in webspace https://en.wikipedia.org/ https://en.wikipedia.org/wiki/Liability_insurance NRohYoW6QRysXmcQl_epZyxaTAgzrF1Lro3HvQ== Tue, 15 Sep 2026 09:36:34 +0000 Market <div><h2>Market</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Liability_insurance&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><table><tbody><tr><td></td><td><div>This section <b>may be too technical for most readers to understand</b>.<span> Please <a href="https://en.wikipedia.org/w/index.php?title=Liability_insurance&amp;action=edit">help improve it</a> to <a href="https://en.wikipedia.org/wiki/Wikipedia:Make_technical_articles_understandable">make it understandable to non-experts</a>, without removing the technical details.</span> <span><i>(<span>September 2020</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>Commercial liability is an important segment for the insurance industry. With premium income of US$160 billion in 2013, it accounted for 10% of global non-life premiums of US$1,550 billion, or 23% of the global commercial premiums.^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i><span>]</span>} Liability insurance is far more prevalent in advanced than in emerging markets. The advanced markets accounted for 93% of global liability premiums in 2013, while their share of global non-life premiums was 79%.^{<span><span>[</span>2<span>]</span></span>}</p><p>The <a href="https://en.wikipedia.org/wiki/Insurance_in_the_United_States">US is by far the largest market</a>, with 51% of the global liability premiums written in 2013. This is due to the size of the US economy and the high penetration of liability insurance (0.5% of GDP). In 2013, US businesses spent US$84 billion on commercial liability covers, of which US$50 billion was on general liability, including US$12 billion for <a href="https://en.wikipedia.org/wiki/Professional_liability_insurance">Errors and Omissions</a> (E&amp;O) and US$5.4 billion for <a href="https://en.wikipedia.org/wiki/Directors_and_officers_liability_insurance">Directors and Officers</a> (D&amp;O). US businesses spent another US$13 billion on the liability portion of commercial multi-peril policies, US$9.5 billion for medical malpractice, and US$3 billion for product liability covers.</p><p>The <a href="https://en.wikipedia.org/wiki/Insurance_in_the_United_Kingdom">UK is the world&#39;s second largest market</a> for liability insurance, with US$9.9 billion of liability premiums in 2013. The largest sub-line of business is public and product liability. This is followed by professional indemnity and employers’ liability (cover for employment-related accidents and illnesses). There has been a significant shift in the sub-segments of UK liability insurance. In the last decade, the share of professional indemnity has increased from about 14% to 32%, highlighting the shift towards a more services-driven economy. Manufacturing, meanwhile, comprises a lower share of liability claims as accidents related to injuries and property damages have declined.</p><p>In continental Europe, the largest liability insurance markets are Germany, France, Italy, and Spain. Together they made up almost US$22 billion of global liability premiums in 2013. Typically governed by civil law systems, these markets rely on local conditions and historical experience to determine which liability policies and covers are available. Penetration ranges from 0.16% to 0.25%, which is low compared to the common law countries such as the US, the UK and Australia.</p><p>Japan and Australia are the largest markets in the Asia Pacific region, with commercial liability premiums of US$6.0 billion and US$4.8 billion, respectively, in 2013. At 0.12% of GDP, liability insurance penetration in Japan is much lower than in other advanced economies. In Australia, penetration is much higher at 0.32% of GDP. This is due to the country&#39;s English law-derived legal framework, which has increased demand for employers’ liability insurance. Australia has mandatory covers for aviation, maritime oil pollution, and residential construction and, in certain states, for medical practitioners, property brokers, and stock brokers. Liability insurance premiums have grown at an average annual rate of 11% since 2000.</p><p>China is the ninth largest commercial liability market globally, with premiums of US$3.5 billion in 2013 and strong annual average growth of 22% since 2000. However, penetration remains low at 0.04% of GDP. Growth has been driven by increasing risk awareness and regulatory changes.</p> https://en.wikipedia.org/wiki/Pantry CHjxvNLpnaIoOGNVTYqW7EFUttTVb6-rZm8WlQ== Tue, 15 Sep 2026 09:19:58 +0000 History in Europe and United States <div><h2>History in Europe and United States</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Pantry&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><section><div><h3>Late Middle Ages</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Pantry&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <p>In a <a href="https://en.wikipedia.org/wiki/Late_Middle_Ages">late</a> <a href="https://en.wikipedia.org/wiki/Middle_Ages">medieval</a> <a href="https://en.wikipedia.org/wiki/Hall_(concept)">hall</a>, there were separate rooms for the various service functions and <a href="https://en.wikipedia.org/wiki/Food_storage">food storage</a>. The pantry was a dry room where <a href="https://en.wikipedia.org/wiki/Bread">bread</a> was kept and food preparation was done. The head of the office who is responsible for this room is referred to as a <i>pantler.</i> There were similar rooms for cooler storage of <a href="https://en.wikipedia.org/wiki/Meat">meats</a> and lard/butter (<a href="https://en.wikipedia.org/wiki/Larder">larder</a>), <a href="https://en.wikipedia.org/wiki/Alcoholic_beverage">alcoholic beverages</a> (<a href="https://en.wikipedia.org/wiki/Buttery_(shop)">buttery</a>, known for the &quot;butts&quot;, or barrels, stored there), and cooking (<a href="https://en.wikipedia.org/wiki/Kitchen">kitchen</a>).^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i><span>]</span>}</p> <figure><a href="https://en.wikipedia.org/wiki/File:Museu_Romàntic_Can_Papiol_(Vilanova_i_la_Geltrú)_-_8.jpg"></a><figcaption>Nineteenth-century pantry in Museu Romàntic Can Papiol in <a href="https://en.wikipedia.org/wiki/Vilanova_i_la_Geltrú">Vilanova i la Geltrú</a></figcaption></figure> </section><section><div><h3>Colonial Era</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Pantry&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <p>In the <a href="https://en.wikipedia.org/wiki/United_States">United States</a>, pantries evolved from early <a href="https://en.wikipedia.org/wiki/Colonial_history_of_the_United_States">Colonial American</a> &quot;<a href="https://en.wikipedia.org/wiki/Buttery_(room)">butteries</a>&quot;, built in a cold north corner of a colonial home (more commonly referred to and spelled as &quot;butt&#39;ry&quot;), into a variety of pantries in self-sufficient <a href="https://en.wikipedia.org/wiki/Farmsteads">farmsteads</a>. Butler&#39;s pantries, or China pantries, were built between the dining room and kitchen of a middle-class American home, especially in the latter part of the 19th into the early 20th centuries. Great estates, such as the <a href="https://en.wikipedia.org/wiki/Biltmore_Estate">Biltmore Estate</a> in <a href="https://en.wikipedia.org/wiki/Asheville,_North_Carolina">Asheville, North Carolina</a> or <a href="https://en.wikipedia.org/wiki/Stan_Hywet_Hall">Stan Hywet Hall</a> in <a href="https://en.wikipedia.org/wiki/Akron,_Ohio">Akron, Ohio</a>, had many pantries and other domestic &quot;offices&quot;, echoing their British &quot;<a href="https://en.wikipedia.org/wiki/Great_house">great house</a>&quot; counterparts.^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i><span>]</span>}</p> </section><section><div><h3>Victorian Era</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Pantry&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <p>By the <a href="https://en.wikipedia.org/wiki/Victorian_era">Victorian era</a>, large houses and estates in Britain maintained the use of separate rooms, each one dedicated to distinct stages of food preparation and cleanup. The kitchen was for cooking, while food was stored in a storeroom, pantry or cellar. Meat preparation was done in a <a href="https://en.wikipedia.org/wiki/Larder">larder</a> as game would come in undressed, fish unfilleted, and meat in half or quarter carcasses. Vegetable cleaning and preparation would be done in the <a href="https://en.wikipedia.org/wiki/Scullery_(room)">scullery</a>. Dishwashing was done in a scullery or butler&#39;s pantry, &quot;depending on the type of dish and level of dirt&quot;.^{<span><span>[</span>2<span>]</span></span>}</p> <p>Since the scullery was the room with running water with a sink, it was where the messiest food preparation took place, such as cleaning fish and cutting raw meat. The pantry was where <a href="https://en.wikipedia.org/wiki/Tableware">tableware</a> was stored, such as China, <a href="https://en.wikipedia.org/wiki/Glassware">glassware</a>, and <a href="https://en.wikipedia.org/wiki/List_of_eating_utensils">silverware</a>. If the pantry had a sink for washing tableware, it was a wooden sink lined with lead to prevent chipping the China and glassware while they were being washed. In some middle-class houses, the larder, pantry, and storeroom might simply be large wooden cupboards, each with its exclusive purpose.^{<span><span>[</span>3<span>]</span></span>}</p> </section> https://en.wikipedia.org/wiki/Willem_de_Ridder KiwolUjKQyS-mdFFI2tKb9esveCp1aLfg9mejQ== Tue, 15 Sep 2026 08:58:44 +0000 Dutch artist and anarchist <section><div>Dutch artist and anarchist</div> <p> </p> <table><tbody><tr><th colspan="2"><div>Willem de Ridder</div></th></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Willem_de_Ridder.jpg"></a></span><div>de Ridder in 1968</div></td></tr><tr><th>Born</th><td><span>(<span>1939-10-14</span>)</span>October 14, 1939^{<span><span>[</span>1<span>]</span></span>}<br/><div><a href="https://en.wikipedia.org/wiki/&#39;s-Hertogenbosch">&#39;s-Hertogenbosch</a>, the Netherlands^{<span><span>[</span>2<span>]</span></span>}</div></td></tr><tr><th>Died</th><td>December 29, 2022<span>(2022-12-29)</span> (aged<span> </span>83)</td></tr><tr><th>Occupation</th><td>Artist</td></tr><tr><th>Known<span> </span>for</th><td><a href="https://en.wikipedia.org/wiki/Fluxus">Fluxus</a></td></tr></tbody></table> <p><b>Willem de Ridder</b> (14 October 1939^{<span><span>[</span>3<span>]</span></span>} – 29 December 2022) was a Dutch anarchist^{<span><span>[</span>4<span>]</span></span>} and artist, known as a founder of <a href="https://en.wikipedia.org/wiki/Fluxus">Fluxus</a>.^{<span><span>[</span>5<span>]</span></span>} He was the foremost Fluxus member in the Netherlands. He showed and sold Fluxus works in his gallery, Amstel 47, and shops Fluxshop and European Mail-Order Warehouse. He organized Dutch Fluxus festivals with <a href="https://en.wikipedia.org/wiki/Wim_T._Schippers">Wim T. Schippers</a> in 1963 and 1964.^{<span><span>[</span>3<span>]</span></span>}</p> <p>De Ridder&#39;s Amsterdam club, Provadya, was a center for the city&#39;s <a href="https://en.wikipedia.org/wiki/Counterculture">counterculture</a>.^{<span><span>[</span>6<span>]</span></span>}</p> <p>He graduated from the Academy of Arts in Den Bosch. After finishing his studies, he decided to stop painting.^{<span><span>[</span>7<span>]</span></span>}</p> <p>He was part of the Sexual Egalitarian and Libertarian Fraternity (SELF), a group that edited <i><a href="https://en.wikipedia.org/wiki/Suck:_The_First_European_Sex_Paper">Suck: The First European Sex Paper</a></i> and organized the first international erotic film festival, the <a href="https://en.wikipedia.org/wiki/Wet_Dream_Festival?action=edit&amp;redlink=1">Wet Dream Festival</a>.^{<span><span>[</span>8<span>]</span></span>} He later influenced <a href="https://en.wikipedia.org/wiki/Annie_Sprinkle">Annie Sprinkle</a>.^{<span><span>[</span>9<span>]</span></span>}</p> </section><section><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Willem_de_Ridder&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div> <div> <div><ol><li><span><span>↑</span></span> <span><cite><a href="https://www.concertzender.nl/programma/pakrammel_533029/">&quot;Pakrammel&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Concertzender">Concertzender</a></i>. 2019<span>. Retrieved <span>April 4,</span> 2021</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>de Ridder, Willem (November 2, 2016). <a href="https://flash---art.com/article/fluxus-tales/">&quot;Fluxus Tales&quot;</a>. <i>Flash Art</i><span>. Retrieved <span>January 26,</span> 2020</span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Muller, Sheila D. (July 4, 2013). <a href="https://books.google.com/books?id=ZPhLoy0FICMC&amp;pg=PA141">&quot;Fluxus&quot;</a>. <i>Dutch Art: An Encyclopedia</i>. Routledge. pp.<span> </span><span>140–</span>141. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-135-49574-9"><bdi>978-1-135-49574-9</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Christgau, Robert (April 27, 1997). <a href="https://www.nytimes.com/1997/04/27/books/the-pleasure-seekers.html">&quot;The Pleasure Seekers&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/The_New_York_Times">The New York Times</a></i>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0362-4331">0362-4331</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Dunning, Jennifer (November 3, 1994). <a href="https://www.nytimes.com/1994/11/03/theater/dance-review-nude-cellist-and-video-chaos-in-reprise.html">&quot;DANCE REVIEW; Nude Cellist and Video Chaos, in Reprise&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/The_New_York_Times">The New York Times</a></i>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0362-4331">0362-4331</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>&quot;Prog&#39;s: never-Netherlands&quot;. <i>Record Collector</i>. No.<span> </span>430. August 2014. pp.<span> </span>32–. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0261-250X">0261-250X</a>. <a href="https://en.wikipedia.org/wiki/Gale_(publisher)">Gale</a><span> </span><a href="https://go.gale.com/ps/anonymous?id=GALE%7CA404271428">A404271428</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.willemderidder.com/eng/page.htm">&quot;www.willemderidder.com - De Willem de Ridder website&quot;</a>. <i>www.willemderidder.com</i><span>. Retrieved <span>July 20,</span> 2020</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Gorfinkel, Elena (2006). &quot;Wet Dreams: Erotic Film Festivals of the Early 1970s and the Utopian Sexual Public Sphere&quot;. <i>Framework: The Journal of Cinema and Media</i>. <b>47</b> (2): <span>59–</span>86. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1353%2Ffrm.2006.0012">10.1353/frm.2006.0012</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0306-7661">0306-7661</a>. <a href="https://en.wikipedia.org/wiki/JSTOR_(identifier)">JSTOR</a><span> </span><a href="https://www.jstor.org/stable/41552463">41552463</a>. <a href="https://en.wikipedia.org/wiki/Gale_(publisher)">Gale</a><span> </span><a href="https://go.gale.com/ps/anonymous?id=GALE%7CA159028320">A159028320</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Kostelanetz, Richard (November 15, 2018). <a href="https://books.google.com/books?id=kDZ7DwAAQBAJ&amp;pg=PT892">&quot;Annie Sprinkle&quot;</a>. <i>A Dictionary of the Avant-Gardes</i>. Taylor &amp; Francis. pp.<span> </span><span>891–</span>892. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-351-26710-6"><bdi>978-1-351-26710-6</bdi></a>.</cite></span></li> </ol></div></div> </section><section><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Willem_de_Ridder&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div> <div> <ul><li><cite>Heidenry, John (March 22, 2002). <a href="https://books.google.com/books?id=DJtDSjG8BYQC&amp;pg=PA141"><i>What Wild Ecstasy</i></a>. Simon and Schuster. pp.<span> </span>141–. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-7432-4184-7"><bdi>978-0-7432-4184-7</bdi></a>.</cite></li> <li><cite>Ruhé, Harry; Dekeukeleire, Jeannette (2017). <a href="https://books.google.com/books?id=WMCVtAEACAAJ"><i>The Adventures of Willem de Ridder</i></a>. CultClub Edition. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-90-812458-8-3"><bdi>978-90-812458-8-3</bdi></a>.</cite></li> <li><cite>&quot;Willem de Ridder&quot;. <i>Contemporary Music Review</i>. <b>25</b> (5/6): 397. October 2006. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1080%2F07494460600989721">10.1080/07494460600989721</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0749-4467">0749-4467</a>. <a href="https://en.wikipedia.org/wiki/EBSCOhost_(identifier)">EBSCO<i>host</i></a><span> </span><a href="http://search.ebscohost.com/login.aspx?direct=true&amp;AN=23479883">23479883</a>.</cite></li></ul> </div> </section><section><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Willem_de_Ridder&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://www.willemderidder.com/eng/page.htm">Official website</a></li> <li><a href="https://www.harvardartmuseums.org/collections/person/25856">Harvard Art Museums Profile Page</a></li></ul> <div><span><a href="https://en.wikipedia.org/wiki/Wikipedia:Contents/Portals">Portals</a>:</span><ul><li><span><span><a href="https://en.wikipedia.org/wiki/File:BlackFlagSymbol.svg"></a></span> </span><a href="https://en.wikipedia.org/wiki/Portal:Anarchism">Anarchism</a></li><li> <a href="https://en.wikipedia.org/wiki/Portal:Biography">Biography</a></li><li><span><span><a href="https://en.wikipedia.org/wiki/File:WPVA-khamsa.svg"></a></span> </span><a href="https://en.wikipedia.org/wiki/Portal:Visual_arts">Visual arts</a></li></ul></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/Q2460190#identifiers"></a></span></div></th></tr><tr><th>International</th><td><div><ul><li><span><a href="https://viaf.org/viaf/288187660">VIAF</a></span></li><li><span><a href="https://d-nb.info/gnd/139837639">GND</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=500100363">ULAN</a></span></li><li><span><a href="https://rkd.nl/en/explore/artists/487295">RKD Artists</a></span></li><li><span><a href="https://www.moma.org/artists/35728">Museum of Modern Art</a></span></li></ul></div></td></tr></tbody></table></div> <div><table><tbody><tr><td><span><a href="https://en.wikipedia.org/wiki/File:Voltairine_de_Cleyre_(1891).gif"></a></span></td><td><p>This biographical article about an anarchist is a <a href="https://en.wikipedia.org/wiki/Wikipedia:Stub">stub</a>. You can help Wikipedia by <a href="https://en.wikipedia.org/w/index.php?title=Willem_de_Ridder&amp;action=edit">adding missing information</a>.</p></td></tr></tbody></table><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Anarchist-stub"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Anarchist-stub"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Anarchist-stub"><abbr>e</abbr></a></li></ul></div></div> <div><table><tbody><tr><td><span><a href="https://en.wikipedia.org/wiki/File:Vincent_Willem_van_Gogh_107.jpg"></a></span></td><td><p>This article about a Dutch painter is a <a href="https://en.wikipedia.org/wiki/Wikipedia:Stub">stub</a>. You can help Wikipedia by <a href="https://en.wikipedia.org/w/index.php?title=Willem_de_Ridder&amp;action=edit">adding missing information</a>.</p></td></tr></tbody></table><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Netherlands-painter-stub"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Netherlands-painter-stub"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Netherlands-painter-stub"><abbr>e</abbr></a></li></ul></div></div></section> https://en.wikipedia.org/wiki/Thomas_Szasz d0wYvMfil6k64m19klH8wP1XoiJIsCdFswMKug== Tue, 15 Sep 2026 08:58:38 +0000 Hungarian-American psychiatrist and activist (1920–2012) <div>Hungarian-American psychiatrist and activist (1920–2012)</div><p> </p><table><tbody><tr><td></td><td><div><div><b>This article has multiple issues.</b> Please help <b><a href="https://en.wikipedia.org/wiki/Special:EditPage/Thomas_Szasz">improve it</a></b> or discuss these issues on the <b><a href="https://en.wikipedia.org/wiki/Talk:Thomas_Szasz">talk page</a></b>. <small><i>(<a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove these messages</a>)</i></small> <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 <a href="https://en.wikipedia.org/wiki/Wikipedia:Verifiability">more citations</a></b>.<span> Please help <a href="https://en.wikipedia.org/wiki/Special:EditPage/Thomas_Szasz">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 <a href="https://en.wikipedia.org/wiki/Wikipedia:Verifiability#Burden_of_evidence">removed</a>.<br/><small><span><i>Find sources:</i><span> </span><a href="https://www.google.com/search?as_eq=wikipedia&amp;q=%22Thomas+Szasz%22">&quot;Thomas Szasz&quot;</a><span> </span>–<span> </span><a href="https://www.google.com/search?tbm=nws&amp;q=%22Thomas+Szasz%22+-wikipedia&amp;tbs=ar:1">news</a> <b>·</b> <a href="https://www.google.com/search?&amp;q=%22Thomas+Szasz%22&amp;tbs=bkt:s&amp;tbm=bks">newspapers</a> <b>·</b> <a href="https://www.google.com/search?tbs=bks:1&amp;q=%22Thomas+Szasz%22+-wikipedia">books</a> <b>·</b> <a href="https://scholar.google.com/scholar?q=%22Thomas+Szasz%22">scholar</a> <b>·</b> <a href="https://www.jstor.org/action/doBasicSearch?Query=%22Thomas+Szasz%22&amp;acc=on&amp;wc=on">JSTOR</a></span></small></span> <span><i>(<span>May 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><table><tbody><tr><td></td><td><div>This article <b>may contain <a href="https://en.wikipedia.org/wiki/Wikipedia:No_original_research">original research</a></b>.<span> Please <a href="https://en.wikipedia.org/w/index.php?title=Thomas_Szasz&amp;action=edit">improve it</a> by <a href="https://en.wikipedia.org/wiki/Wikipedia:Verifiability">verifying</a> the claims made and adding <a href="https://en.wikipedia.org/wiki/Wikipedia:Citing_sources#Inline_citations">inline citations</a>. Statements consisting only of original research should be removed.</span> <span><i>(<span>May 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> </div> </div><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><table><tbody><tr><th colspan="2"><div>Thomas Szasz</div></th></tr><tr><td colspan="2"><div>Szász Tamás István</div></td></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Dr_Thomas_S_Szasz_(cropped).jpg"></a></span><div>Szasz in 2010</div></td></tr><tr><th>Born</th><td><div>Szász Tamás István</div><br/><span>(<span>1920-04-15</span>)</span>April 15, 1920<br/><div><a href="https://en.wikipedia.org/wiki/Budapest">Budapest</a>, <a href="https://en.wikipedia.org/wiki/Kingdom_of_Hungary_(1920–46)">Kingdom of Hungary</a></div></td></tr><tr><th>Died</th><td>September 8, 2012<span>(2012-09-08)</span> (aged<span> </span>92)<br/><div><a href="https://en.wikipedia.org/wiki/Manlius,_New_York">Manlius, New York</a>, U.S.^{<span><span>[</span>1<span>]</span></span>}</div></td></tr><tr><th>Citizenship</th><td>Hungary, United States</td></tr><tr><th>Education</th><td><a href="https://en.wikipedia.org/wiki/University_of_Cincinnati">University of Cincinnati</a></td></tr><tr><th>Known<span> </span>for</th><td>Criticism of psychiatry</td></tr><tr><th>Spouse</th><td> <div><div>Rosine Loshkajian</div> <div><span>​</span></div> <div><span>​</span></div><span>(</span><abbr>m.</abbr><span> </span>1951<span>;</span> died<span> </span>1971<span>)</span><span>​</span></div></td></tr><tr><th>Children</th><td>2</td></tr><tr><td colspan="2"><b>Scientific career</b></td></tr><tr><th>Fields</th><td><a href="https://en.wikipedia.org/wiki/Psychiatry">Psychiatry</a></td></tr><tr><th>Workplaces</th><td><a href="https://en.wikipedia.org/wiki/State_University_of_New_York_Upstate_Medical_University">State University of New York Upstate Medical University</a></td></tr><tr><td colspan="2"> </td></tr><tr><th>Website</th><td><span>szasz.com</span></td></tr></tbody></table><p><b>Thomas Stephen Szasz</b> (<span><span><a href="https://en.wikipedia.org/wiki/Help:IPA/English">/<span><span>s</span><span>ɑː</span><span>s</span></span>/</a></span></span> <a href="https://en.wikipedia.org/wiki/Help:Pronunciation_respelling_key"><i><span>SAHSS</span></i></a>; <a href="https://en.wikipedia.org/wiki/Hungarian_language">Hungarian</a><span>: </span><i>Szász Tamás István</i> <span><a href="https://en.wikipedia.org/wiki/Help:IPA/Hungarian"><span>[</span>saːs<span>]</span></a></span>; 15 April 1920 – 8 September 2012) was a Hungarian-American academic and <a href="https://en.wikipedia.org/wiki/Psychiatrist">psychiatrist</a>. He served for most of his career as professor of psychiatry at the <a href="https://en.wikipedia.org/wiki/State_University_of_New_York_Upstate_Medical_University">State University of New York Upstate Medical University</a>.^{<span><span>[</span>2<span>]</span></span>} A distinguished lifetime fellow of the <a href="https://en.wikipedia.org/wiki/American_Psychiatric_Association">American Psychiatric Association</a> and a life member of the <a href="https://en.wikipedia.org/wiki/American_Psychoanalytic_Association">American Psychoanalytic Association</a>, he was best known as a <a href="https://en.wikipedia.org/wiki/Social_critic">social critic</a> of the moral and scientific foundations of <a href="https://en.wikipedia.org/wiki/Psychiatry">psychiatry</a>, as what he saw as the <a href="https://en.wikipedia.org/wiki/Social_control">social control</a> aims of medicine in modern society, as well as <a href="https://en.wikipedia.org/wiki/Scientism">scientism</a>.</p><p>Szasz maintained throughout his career that he was not <a href="https://en.wikipedia.org/wiki/Anti-psychiatry">anti-psychiatry</a> but rather that he opposed coercive psychiatry. He was a staunch opponent of <a href="https://en.wikipedia.org/wiki/Civil_commitment">civil commitment</a> and involuntary psychiatric treatment but believed in and practiced psychiatry and <a href="https://en.wikipedia.org/wiki/Psychotherapy">psychotherapy</a> that involved <a href="https://en.wikipedia.org/wiki/Informed_consent">consenting</a> adults.</p> https://en.wikipedia.org/wiki/R._D._Laing I6FiyFT-3r2h8T-NmiXevxKZh_76Zl8cEtLYFw== Tue, 15 Sep 2026 08:58:38 +0000 Unorthodox Scottish psychiatrist (1927–1989) <section><div>Unorthodox Scottish psychiatrist (1927–1989)</div> <div>This article is about the psychiatrist. For the American comedian, see <a href="https://en.wikipedia.org/wiki/Artie_Lange">Artie Lange</a>.</div> <p> </p> <table><tbody><tr><th colspan="2"><div>Ronald David Laing</div></th></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Ronald_D._Laing.jpg"></a></span><div>Laing in 1983, perusing<br/><i><a href="https://en.wikipedia.org/wiki/The_Ashley_Book_of_Knots">The Ashley Book of Knots</a></i> (1944)</div></td></tr><tr><th>Born</th><td><div>Ronald David Laing</div><br/><span>(<span>1927-10-07</span>)</span>7 October 1927<br/><div><a href="https://en.wikipedia.org/wiki/Govanhill">Govanhill</a>, Glasgow, Scotland</div></td></tr><tr><th>Died</th><td>23 August 1989<span>(1989-08-23)</span> (aged<span> </span>61)<br/><div><a href="https://en.wikipedia.org/wiki/Saint-Tropez">Saint-Tropez</a>, France</div></td></tr><tr><th>Known<span> </span>for</th><td><a href="https://en.wikipedia.org/wiki/Medical_model">Medical model</a></td></tr><tr><th>Spouse(s)</th><td> <div><div>Anne Hearne</div> <div><span>​</span></div> <div><span>​</span></div><span>(</span><abbr>m.</abbr><span> </span>1952<span>;</span> <abbr>div.</abbr><span> </span>1966<span>)</span><span>​</span></div><br/> <div><div>Jutta Werner</div> <div><span>​</span></div> <div><span>​</span></div><span>(</span><abbr>m.</abbr><span> </span>1974<span>;</span> <abbr>div.</abbr><span> </span>1986<span>)</span><span>​</span></div></td></tr><tr><th>Children</th><td>10</td></tr><tr><td colspan="2"><b>Scientific career</b></td></tr><tr><th>Fields</th><td>Psychiatry</td></tr><tr><td colspan="2"> </td></tr></tbody></table> <p><b>Ronald David Laing</b> (7 October 1927<span> </span>– 23 August 1989) was a Scottish <a href="https://en.wikipedia.org/wiki/Psychiatrist">psychiatrist</a> who wrote extensively on <a href="https://en.wikipedia.org/wiki/Mental_illness">mental illness</a>, particularly <a href="https://en.wikipedia.org/wiki/Psychosis">psychosis</a> and <a href="https://en.wikipedia.org/wiki/Schizophrenia">schizophrenia</a>.^{<span><span>[</span>1<span>]</span></span>} Politically, Laing was regarded as a thinker of the <a href="https://en.wikipedia.org/wiki/New_Left">New Left</a>. He has been theatrically portrayed by Mike Maran, Alan Cox, Billy Mack, and David Tennant in the 2017 film <i>Mad to Be Normal</i>.^{<span><span>[</span>2<span>]</span></span>}</p> <p>Laing&#39;s views on the causes and treatment of psychopathological phenomena were influenced by his study of <a href="https://en.wikipedia.org/wiki/Existentialism">existential philosophy</a> and ran counter to the chemical and electroshock methods that had become psychiatric orthodoxy. Laing took the expressed <a href="https://en.wikipedia.org/wiki/Emotion">feelings</a> of the individual patient or client as valid descriptions of personal experience rather than simply as symptoms of mental illness. Although associated in the public mind with the <a href="https://en.wikipedia.org/wiki/Anti-psychiatry">anti-psychiatry</a> movement, he rejected the label.^{<span><span>[</span>3<span>]</span></span>} Laing regarded <a href="https://en.wikipedia.org/wiki/Schizophrenia">schizophrenia</a> as the normal psychological adjustment to a dysfunctional social context.^{<span><span>[</span>4<span>]</span></span>}</p> </section><section><div><h2>Early years</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div> <p>Laing was born in the <a href="https://en.wikipedia.org/wiki/Govanhill">Govanhill</a> district of <a href="https://en.wikipedia.org/wiki/Glasgow">Glasgow</a> on 7 October 1927, the only child of civil engineer David Park MacNair Laing and Amelia Glen Laing (née Kirkwood).^{<span><span>[</span>5<span>]</span></span>} Laing described his parents, particularly his mother, as being somewhat anti-social, and demanding the maximum achievement from him. Adrian, his son and biographer, discounted much of Laing&#39;s published childhood account, and an obituary by an acquaintance of Laing asserted that, of his parents, &quot;the full truth he told only to a few close friends&quot;.^{<span><span>[</span>6<span>]</span></span>}^{<span><span>[</span>7<span>]</span></span>}</p> <p>He was educated initially at Sir John Neilson Cuthbertson Public School and after four years transferred to <a href="https://en.wikipedia.org/wiki/Hutchesons&#39;_Grammar_School">Hutchesons&#39; Grammar School</a>. Described variously as clever, competitive or precocious, he studied <a href="https://en.wikipedia.org/wiki/Classics">classics</a>, particularly <a href="https://en.wikipedia.org/wiki/Philosophy">philosophy</a>, including through reading books from the local <a href="https://en.wikipedia.org/wiki/Library">library</a>. Small and slightly built, Laing participated in distance running; he was also a musician, being made an Associate of the <a href="https://en.wikipedia.org/wiki/Royal_College_of_Music">Royal College of Music</a>. He studied <a href="https://en.wikipedia.org/wiki/Medicine">medicine</a> at the <a href="https://en.wikipedia.org/wiki/University_of_Glasgow">University of Glasgow</a>. During his time in Glasgow, he set up a &quot;Socratic Club&quot;, of which the philosopher <a href="https://en.wikipedia.org/wiki/Bertrand_Russell">Bertrand Russell</a> agreed to be president. Laing failed his final exams. In a partial autobiography, <i>Wisdom, Madness and Folly,</i> Laing said he felt remarks he made under the influence of alcohol at a university function had offended the staff and led to him being failed on every subject including some he was sure he had passed. After spending six months working in a psychiatric unit, Laing passed the re-sits in 1951 to qualify as a medical doctor.^{<span><span>[</span>8<span>]</span></span>}</p> </section><section><div><h2>Career</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div> <p>Laing spent a couple of years as a psychiatrist in the <a href="https://en.wikipedia.org/wiki/British_Army">British Army</a> <a href="https://en.wikipedia.org/wiki/Netley_Hospital">Psychiatric Unit at Netley</a>, where, as he later recalled, those trying to fake <a href="https://en.wikipedia.org/wiki/Schizophrenia">schizophrenia</a> to get a lifelong <a href="https://en.wikipedia.org/wiki/Disability_pension">disability pension</a> were likely to get more than they had bargained for as <a href="https://en.wikipedia.org/wiki/Insulin_shock_therapy">insulin shock therapy</a> was being used.^{<span><span>[</span>9<span>]</span></span>} In 1953, Laing returned to Glasgow, participated in an existentialism-oriented discussion group, and worked at the <a href="https://en.wikipedia.org/wiki/Gartnavel_Royal_Hospital">Glasgow Royal Mental Hospital</a>.^{<span><span>[</span>10<span>]</span></span>} The hospital was influenced by <a href="https://en.wikipedia.org/wiki/David_Henderson_(psychiatrist)">David Henderson</a>&#39;s school of thought, which may have exerted an unacknowledged influence on Laing; he became the youngest <a href="https://en.wikipedia.org/wiki/Consultant">consultant</a> in the country.^{<span><span>[</span>11<span>]</span></span>}^{<span><span>[</span>8<span>]</span></span>} Laing&#39;s colleagues characterised him as &quot;conservative&quot; for his opposition to <a href="https://en.wikipedia.org/wiki/Electroconvulsive_therapy">electroconvulsive therapy</a> and the new drugs that were being introduced.^{<span><span>[</span>11<span>]</span></span>}</p> <p>In 1956, Laing went to train on a grant at the <a href="https://en.wikipedia.org/wiki/Tavistock_Clinic">Tavistock Clinic</a> in London, widely known as a centre for the study and practice of <a href="https://en.wikipedia.org/wiki/Psychotherapy">psychotherapy</a> (particularly <a href="https://en.wikipedia.org/wiki/Psychoanalysis">psychoanalysis</a>). At this time, he was associated with <a href="https://en.wikipedia.org/wiki/John_Bowlby">John Bowlby</a>, <a href="https://en.wikipedia.org/wiki/Donald_Winnicott">D. W. Winnicott</a> and his training analyst, <a href="https://en.wikipedia.org/wiki/Charles_Rycroft">Charles Rycroft</a>. He remained at the Tavistock Clinic until 1964.^{<span><span>[</span>12<span>]</span></span>} In 1965, Laing and a group of colleagues, most notably Sid Briskin, created the <a href="https://en.wikipedia.org/wiki/Philadelphia_Association">Philadelphia Association</a> and started a psychiatric community project at <a href="https://en.wikipedia.org/wiki/Kingsley_Hall">Kingsley Hall</a>, where patients and therapists lived together.^{<span><span>[</span>13<span>]</span></span>} The Norwegian author <a href="https://en.wikipedia.org/wiki/Axel_Jensen">Axel Jensen</a> contacted Laing at Kingsley Hall after reading his book <i>The Divided Self</i>, which had been given to him by <a href="https://en.wikipedia.org/wiki/Noel_Cobb">Noel Cobb</a>. Laing treated Jensen, and subsequently, they became close friends. Laing often visited Jensen on board his ship <i><a href="https://en.wikipedia.org/wiki/S/Y_Shanti_Devi">Shanti Devi</a></i>, which was his home in <a href="https://en.wikipedia.org/wiki/Stockholm">Stockholm</a>.^{<span><span>[</span>14<span>]</span></span>}</p> <p>In 1967, Laing appeared on the BBC programme <i>Your Witness</i>, chaired by <a href="https://en.wikipedia.org/wiki/Ludovic_Kennedy">Ludovic Kennedy</a>, on which, alongside <a href="https://en.wikipedia.org/wiki/Jonathan_Aitken">Jonathan Aitken</a> and G.P. Ian Dunbar, he argued for the legalisation of <a href="https://en.wikipedia.org/wiki/Cannabis">cannabis</a> in the first live television debate on the subject.^{<span><span>[</span>15<span>]</span></span>} In the same years, his views were explored in the television play <i><a href="https://en.wikipedia.org/wiki/In_Two_Minds">In Two Minds</a></i>, written by <a href="https://en.wikipedia.org/wiki/David_Mercer_(playwright)">David Mercer</a>. In October 1972, Laing met <a href="https://en.wikipedia.org/wiki/Arthur_Janov">Arthur Janov</a>, author of the popular book <i><a href="https://en.wikipedia.org/wiki/The_Primal_Scream">The Primal Scream</a></i>. Although Laing found Janov modest and unassuming, he considered him a &quot;jig man&quot; (someone who knows a lot about a little). Laing sympathized with Janov but regarded his <a href="https://en.wikipedia.org/wiki/Primal_therapy">primal therapy</a> as a lucrative business—one which required no more than obtaining a suitable space and letting people &quot;hang it all out&quot;.^{<span><span>[</span>16<span>]</span></span>} Inspired by the work of American psychotherapist Elizabeth Fehr, Laing began to develop a team offering &quot;rebirthing workshops&quot; in which one designated person chooses to re-experience the struggle of trying to break out of the birth canal represented by the remaining members of the group who surround him or her.^{<span><span>[</span>17<span>]</span></span>}</p> </section><section><div><h2>Laing and anti-psychiatry</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <div> <blockquote> <p>If the human race survives, future men will, I suspect, look back on our enlightened epoch as a veritable age of Darkness. They will presumably be able to savour the irony of the situation with more amusement than we can extract from it. The laugh’s on us. They will see that what we call &quot;schizophrenia&quot; was one of the forms in which, often through quite ordinary people, the light began to break through the cracks in our all-too-closed minds.</p> </blockquote> <div><cite>—<span> </span>R. D. Laing, <i><a href="https://en.wikipedia.org/wiki/The_Politics_of_Experience">The Politics of Experience</a></i>, p. 107</cite></div> </div> <p>Laing was seen as an important figure in the <a href="https://en.wikipedia.org/wiki/Anti-psychiatry">anti-psychiatry</a> movement, along with <a href="https://en.wikipedia.org/wiki/David_Cooper_(psychiatrist)">David Cooper</a>, although he never denied the value of treating mental distress. He also challenged psychiatric diagnosis itself, arguing that the diagnosis of a mental disorder contradicted accepted medical procedure: the diagnosis was made on the basis of behaviour or conduct of an examination, and tests that traditionally precede the diagnosis of such viable pathologies as broken bones or pneumonia occurred after the diagnosis of mental disorder, if at all. Hence, according to Laing, psychiatry was founded on a false <a href="https://en.wikipedia.org/wiki/Epistemology">epistemology</a>: illness diagnosed by conduct but treated biologically. Laing maintained that <a href="https://en.wikipedia.org/wiki/Schizophrenia">schizophrenia</a> was &quot;a theory not a fact&quot;; he believed leading medical geneticists did not accept the models of genetically inherited schizophrenia being promoted by biologically based psychiatry.^{<span><span>[</span>18<span>]</span></span>} He rejected the &quot;medical model of <a href="https://en.wikipedia.org/wiki/Mental_illness">mental illness</a>&quot;—according to Laing, diagnosis of mental illness did not follow a traditional medical model—and this led him to question the use of medication such as <a href="https://en.wikipedia.org/wiki/Antipsychotics">antipsychotics</a> by psychiatry. His attitude to recreational <a href="https://en.wikipedia.org/wiki/Drug">drugs</a> was quite different; privately, he advocated an anarchy of experience.^{<span><span>[</span>19<span>]</span></span>} Politically, Laing was regarded as a thinker of the <a href="https://en.wikipedia.org/wiki/New_Left">New Left</a>.^{<span><span>[</span>20<span>]</span></span>}</p> </section><section><div><h2>Works</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <p>In 1913, psychiatrist and philosopher <a href="https://en.wikipedia.org/wiki/Karl_Jaspers">Karl Jaspers</a> had pronounced in his work <a href="https://en.wikipedia.org/wiki/Karl_Jaspers#Contributions_to_psychiatry"><i>General Psychopathology</i></a> that many of the symptoms of mental illness (and particularly of <a href="https://en.wikipedia.org/wiki/Delusion">delusions</a>) were &quot;un-understandable&quot;, and were therefore worthy of little consideration except as a sign of some other underlying primary disorder. Then, in 1956, <a href="https://en.wikipedia.org/wiki/Gregory_Bateson">Gregory Bateson</a> and his colleagues <a href="https://en.wikipedia.org/wiki/Donald_deAvila_Jackson">Donald Jackson</a> and <a href="https://en.wikipedia.org/wiki/Jay_Haley">Jay Haley</a> articulated a theory of schizophrenia as stemming from <a href="https://en.wikipedia.org/wiki/Double_bind">double bind</a> situations where a person receives different or contradictory messages.^{<span><span>[</span>21<span>]</span></span>}</p> <p>The perceived symptoms of schizophrenia were therefore an expression of this distress, and should be valued as a <a href="https://en.wikipedia.org/wiki/Catharsis">cathartic</a> and transformative experience. Laing argued a similar account for psychoses: that the strange behavior and seemingly confused speech of people undergoing a <a href="https://en.wikipedia.org/wiki/Psychosis">psychotic</a> episode were ultimately understandable as an attempt to communicate worries and concerns, often in situations where this was not possible or not permitted. Laing stressed the role of society, and particularly the <a href="https://en.wikipedia.org/wiki/Family">family</a>, in the development of &quot;madness&quot; (his term). Laing saw <a href="https://en.wikipedia.org/wiki/Psychopathology">psychopathology</a> as being seated not in biological or psychic organs—whereby environment is relegated to playing at most an accidental role as immediate trigger of disease (the &quot;stress diathesis model&quot; of the nature and causes of psychopathology)—but rather in the social cradle, the urban home, that cultivates it. This re-evaluation of the locus of the disease process, and consequent shift in forms of treatment, was in stark contrast to psychiatric orthodoxy. Laing was revolutionary in valuing the content of psychotic behaviour and speech as a valid expression of distress, albeit wrapped in an enigmatic language of personal symbolism which is meaningful only from within the subject&#39;s situation. Laing expanded the view of the &quot;<a href="https://en.wikipedia.org/wiki/Double_bind">double bind</a>&quot; hypothesis put forth by Bateson and his team, and came up with a new concept to describe the highly complex situation that unfolds in the process of &quot;going mad&quot;: an &quot;incompatible knot&quot;. Laing never denied the existence of mental illness, but viewed it in a radically different light from his contemporaries. For Laing, mental illness could be a transformative episode whereby the process of undergoing mental distress was compared to a <a href="https://en.wikipedia.org/wiki/Shaman">shamanic</a> journey. The traveller could return from the journey with important insights, and may have become (in the views of Laing and his followers) a wiser and more grounded person as a result.^{<span><span>[</span>22<span>]</span></span>}^{<span><span>[</span>23<span>]</span></span>}</p> <p>In <i>The Divided Self</i> (1960), Laing contrasts the experience of the &quot;<a href="https://en.wikipedia.org/wiki/Ontological_security">ontologically secure</a>&quot; person with that of a person who &quot;cannot take the realness, aliveness, autonomy and identity of himself and others for granted&quot; and who consequently contrives strategies to avoid &quot;losing his self&quot;.^{<span><span>[</span>24<span>]</span></span>} This concept is used to develop a <a href="https://en.wikipedia.org/wiki/Psychodynamics">psychodynamic</a> model of the mind to explain psychosis and schizophrenia.^{<span><span>[</span>24<span>]</span></span>}^{<span><span>:</span><span> </span>137<span> </span></span>} Laing&#39;s theories resemble later ideas about <a href="https://en.wikipedia.org/wiki/Self-disorder">self-disorder</a> as a core characteristic of schizophrenia.^{<span><span>[</span>25<span>]</span></span>} In <i><a href="https://en.wikipedia.org/wiki/The_Self_and_Others">The Self and Others</a></i> (1961), Laing&#39;s definition of normality shifted somewhat. Laing also wrote poetry and his poetry publications include <i>Knots</i> (1970, published by <a href="https://en.wikipedia.org/wiki/Penguin_Books">Penguin</a>) and <i>Sonnets</i> (1979, published by <a href="https://en.wikipedia.org/wiki/Michael_Joseph_(publisher)">Michael Joseph</a>). Laing appears, alongside his son Adam, on the 1980 album <i>Miniatures – a sequence of fifty-one tiny masterpieces</i> edited by <a href="https://en.wikipedia.org/wiki/Morgan_Fisher">Morgan Fisher</a>, performing the song &quot;<a href="https://en.wikipedia.org/wiki/It&#39;s_a_Long_Way_to_Tipperary">Tipperary</a>&quot;.^{<span><span>[</span>26<span>]</span></span>}</p> <p><i>The Divided Self</i> was listed by the David Bowie Estate as one of David Bowie&#39;s top 100 books he had read.^{<span><span>[</span>27<span>]</span></span>}</p> </section><section><div><h2>Personal life</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <p>In his early life, Laing&#39;s father, David, an electrical engineer who had served in the <a href="https://en.wikipedia.org/wiki/Royal_Flying_Corps">Royal Flying Corps</a>,^{<span><span>[</span>28<span>]</span></span>} seems often to have come to blows with his own brother, and had a breakdown himself for three months when Laing was a teenager. His mother Amelia, according to Adrian Laing had &quot;an inability to express affection to... her only child&quot;.^{<span><span>[</span>29<span>]</span></span>} Laing was troubled by his own personal problems, suffering from both episodic <a href="https://en.wikipedia.org/wiki/Alcoholism">alcoholism</a> and <a href="https://en.wikipedia.org/wiki/Clinical_depression">clinical depression</a>, according to his <a href="https://en.wikipedia.org/wiki/Self-diagnosis">self-diagnosis</a> in a BBC Radio interview with <a href="https://en.wikipedia.org/wiki/Anthony_Clare">Anthony Clare</a> in 1983,^{<span><span>[</span>30<span>]</span></span>} although he reportedly was free of both in the years before his death. These admissions were to have serious consequences for Laing as they formed part of the case against him by the <a href="https://en.wikipedia.org/wiki/General_Medical_Council">General Medical Council</a> which led him to voluntarily withdraw his name from the Medical Register on 20 May 1987.^{<span><span>[</span>31<span>]</span></span>}</p> <p>Laing fathered six sons and four daughters by four women. After his rise as a celebrity, Laing left his first wife Anne Hearne, a former nurse (m. 1952–1966) and their five children, and moved into Kingsley Hall. Subsequently, he married German graphic designer Jutta Werner (m. 1974–1986) with whom he fathered three children. His ninth child, Benjamin, with German therapist Sue Sünkel, was born in 1984. In 1988, Laing&#39;s partner until his death, Marguerite, gave birth to his tenth child, Charles. Laing died 19 months later of a heart attack at the age of 61 while playing tennis.^{<span><span>[</span>32<span>]</span></span>}^{<span><span>[</span>33<span>]</span></span>}</p> <p>In September 2008, his lawyer son Adrian, said, &quot;It was ironic that my father became well known as a family psychiatrist, when, in the meantime, he had nothing to do with his own family.&quot;^{<span><span>[</span>34<span>]</span></span>} His second daughter Susan died in 1976, aged 21, of <a href="https://en.wikipedia.org/wiki/Leukemia">leukemia</a>.^{<span><span>[</span>35<span>]</span></span>} His third daughter Karen was born in Glasgow in 1955 and became a psychotherapist. Adam, his oldest son by his second marriage, who had been in an increasingly melancholic and fragile state of mind, was found dead in May 2008 in a tent on the island of <a href="https://en.wikipedia.org/wiki/Formentera">Formentera</a>. He had died of a heart attack, aged 41.^{<span><span>[</span>33<span>]</span></span>} R.D Laing&#39;s fourth daughter from his second marriage, Natascha, died of cancer in 2018 aged 48.</p> </section><section><div><h2>Death and legacy</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div> <p>Laing died on 23 August 1989 at the age of 61 from a heart attack while playing tennis in <a href="https://en.wikipedia.org/wiki/Saint-Tropez">Saint-Tropez</a>.^{<span><span>[</span>33<span>]</span></span>}^{<span><span>[</span>36<span>]</span></span>}^{<span><span>[</span>37<span>]</span></span>} He was described as a &quot;pioneer on schizophrenia&quot;.^{<span><span>[</span>38<span>]</span></span>} In 1965, Laing had co-founded, along with Sid Briskin and others,^{<span><span>[</span>39<span>]</span></span>} the UK charity the <a href="https://en.wikipedia.org/wiki/Philadelphia_Association">Philadelphia Association</a> concerned with the understanding and relief of mental suffering, which he also chaired.^{<span><span>[</span>40<span>]</span></span>} His work influenced the wider movement of <a href="https://en.wikipedia.org/wiki/Therapeutic_communities">therapeutic communities</a>, operating in less &quot;confrontational&quot; (in a Laingian perspective) psychiatric settings. Other organizations created in a Laingian tradition are the Arbours Association,^{<span><span>[</span>41<span>]</span></span>} the New School of Psychotherapy and Counselling in London,^{<span><span>[</span>42<span>]</span></span>} and the R. D. Laing in the 21st Century Symposium, held annually at <a href="https://en.wikipedia.org/wiki/Esalen_Institute">Esalen Institute</a>, where Laing frequently taught.^{<span><span>[</span>43<span>]</span></span>}</p> </section><section><div><h2>Films, sound recordings, and plays about Laing</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div> <ul><li><i>Ah, Sunflower</i> (1967). Short film by Robert Klinkert and <a href="https://en.wikipedia.org/wiki/Iain_Sinclair">Iain Sinclair</a>, filmed around the <a href="https://en.wikipedia.org/wiki/Dialectics_of_Liberation">Dialectics of Liberation</a> conference and featuring Laing, <a href="https://en.wikipedia.org/wiki/Allen_Ginsberg">Allen Ginsberg</a>, <a href="https://en.wikipedia.org/wiki/Stokely_Carmichael">Stokely Carmichael</a> and others.</li> <li><i>Cain’s Film</i> (1969). Short film by Jamie Wadhawan on <a href="https://en.wikipedia.org/wiki/Alexander_Trocchi">Alexander Trocchi</a>, featuring other <a href="https://en.wikipedia.org/wiki/Counter-culture">counter-cultural</a> figures in London at the time including Laing, <a href="https://en.wikipedia.org/wiki/William_Burroughs">William Burroughs</a> and <a href="https://en.wikipedia.org/wiki/Davy_Graham">Davy Graham</a>.</li> <li><i><a href="https://en.wikipedia.org/wiki/Family_Life_(1971_British_film)">Family Life</a></i> (1971). Reworking of <i><a href="https://en.wikipedia.org/wiki/The_Wednesday_Play">The Wednesday Play</a></i>: <i><a href="https://en.wikipedia.org/wiki/In_Two_Minds">In Two Minds</a></i> (1967) that &quot;explored the issue of schizophrenia and the ideas of the radical psychiatrist R. D. Laing&quot;.^{<span><span>[</span>44<span>]</span></span>} Both were directed by <a href="https://en.wikipedia.org/wiki/Ken_Loach">Ken Loach</a> from scripts by <a href="https://en.wikipedia.org/wiki/David_Mercer_(playwright)">David Mercer</a>.</li> <li><i><a href="https://en.wikipedia.org/wiki/Asylum_(1972_documentary_film)">Asylum</a></i> (1972). Documentary directed by Peter Robinson showing Laing&#39;s psychiatric community project where patients and therapists lived together. Laing also appears in the film.</li> <li><i>Knots</i> (1975). Film adapted from Laing&#39;s 1970 book and <a href="https://en.wikipedia.org/wiki/Edward_Petherbridge">Edward Petherbridge</a>&#39;s play.</li> <li><i>How Does It Feel?</i> (1976). Documentary on physical senses and creativity featuring Laing, <a href="https://en.wikipedia.org/wiki/Joseph_Beuys">Joseph Beuys</a>, <a href="https://en.wikipedia.org/wiki/David_Hockney">David Hockney</a>, <a href="https://en.wikipedia.org/wiki/Elkie_Brooks">Elkie Brooks</a>, <a href="https://en.wikipedia.org/wiki/Michael_Tippett">Michael Tippett</a> and <a href="https://en.wikipedia.org/wiki/Richard_Gregory">Richard Gregory</a>.</li> <li><i>Birth with R. D. Laing</i> (1978). Documentary on the &quot;institutionalization of childbirth practices in Western society&quot;.^{<span><span>[</span>45<span>]</span></span>}</li> <li>The play <i><a href="https://en.wikipedia.org/wiki/Mary_Barnes_(artist)">Mary Barnes</a></i> by <a href="https://en.wikipedia.org/wiki/David_Edgar_(playwright)">David Edgar</a> (1978) was a theatrical indictment of traditional psychiatry, chronicling the six-year journey through the illness of Barnes, a middle-aged former nurse diagnosed as schizophrenic, kept in padded cells and drugged and shocked into numbness. Set in 1960s London and based on the personal accounts of Barnes and therapist <a href="https://en.wikipedia.org/wiki/Joseph_Berke">Joseph Berke</a>, the play follows her years as a resident of Kingsley Hall, where the innovative treatment approach begins her path to recovery. The play premiered at the Birmingham Rep in 1978, with Patti Love in the title role, Simon Callow as Berke, plus Timothy Spall and Roger Allam in the cast.^{<span><span>[</span>46<span>]</span></span>} It was broadcast in a radio adaptation as The Monday Play on BBC Radio on 26 June 1995.^{<span><span>[</span>47<span>]</span></span>}</li> <li><i>R. D. Laing’s Glasgow</i> (1979). An episode of the Canadian TV series <i><a href="https://en.wikipedia.org/wiki/Cities_(TV_series)">Cities</a></i>.</li> <li><i>Did You Used to be R. D. Laing?</i> (1989). Documentary portrait of Laing by Kirk Tougas and Tom Shandel.</li> <li><i>Eros, Love &amp; Lies</i> (1990). Documentary on Laing.</li> <li><i>What You See Is Where You’re At</i> (2001). A collage of found footage by <a href="https://en.wikipedia.org/wiki/Luke_Fowler">Luke Fowler</a> on Laing&#39;s experiment in alternative therapy at Kingsley Hall.</li> <li><a href="https://en.wikipedia.org/wiki/The_Trap_(British_TV_series)"><i>The Trap</i></a>, part 1 (2007). Covering Laings&#39; modeling of familial interactions using game theory.</li> <li><i>All Divided Selves</i> (2011). Another collage of archive material and new footage by <a href="https://en.wikipedia.org/wiki/Luke_Fowler">Luke Fowler</a>.</li> <li><i>The Divided Laing or The Two Ronnies</i> by Patrick Marmion was performed between 17 November and 12 December 2015 at the Arcola Theatre, Dalston London. This riotous play by Patrick Marmion, starring Alan Cox, captured the conflicts and tension between Aaron Esterson, David Cooper, Joe Berke, Mary Barnes, and Laing during the early Kingsley Hall days in the mid-1960s.</li> <li><i><a href="https://en.wikipedia.org/wiki/Mad_to_Be_Normal">Mad to Be Normal</a></i> (2017). A fictionalised account of the Kingsley Hall project, starring <a href="https://en.wikipedia.org/wiki/David_Tennant">David Tennant</a> as Laing and directed by <a href="https://en.wikipedia.org/wiki/Robert_Mullan">Robert Mullan</a>.^{<span><span>[</span>48<span>]</span></span>}</li> <li><a href="https://www.bbc.co.uk/programmes/b0bcgslz">BBC Radio 4: <i>Unforgettable</i> – R. D. Laing &amp; Adrian Laing</a> (2018).</li> <li><i>Divided</i> by Ian Pattison is a powerful play by Ian Pattison which sheds a sharp light on the events surrounding the death of Laing&#39;s second daughter, Susie, in 1976. The play was first staged at the Oran Mor in Glasgow&#39;s West End in 2013 and more recently from 14 October to 19 October 2019. Billy Mack played Laing.</li></ul> </section><section><div><h2>Selected bibliography</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div> <section><div><h3>Laing&#39;s publications</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div> <ul><li>Laing, R. D. (1960). <i><a href="https://en.wikipedia.org/wiki/The_Divided_Self">The Divided Self</a>: An Existential Study in Sanity and Madness</i>. London: Tavistock Publications, 1959; republished with a new preface, Harmondsworth: Penguin Books, 1965.</li> <li>Laing, R. D. (1961). <i><a href="https://en.wikipedia.org/wiki/The_Self_and_Others">The Self and Others</a></i>. London: <a href="https://en.wikipedia.org/wiki/Tavistock_Publications">Tavistock Publications</a>.^{<span><span>[</span>49<span>]</span></span>}</li> <li>Laing, R. D. and <a href="https://en.wikipedia.org/wiki/Aaron_Esterson">Esterson, A.</a> (1964). <i>Sanity, Madness and the Family</i>. London: Penguin Books.</li> <li>Laing, R. D. and Cooper, D.G. (1964). <i>Reason and Violence: A Decade of Sartre&#39;s Philosophy</i>. (2nd ed.) London: Tavistock Publications Ltd.</li> <li>Laing, R. D., Phillipson, H. and Lee, A.R. (1966). <i>Interpersonal Perception: A Theory and a Method of Research</i>. London: Tavistock Publications.</li> <li>Laing, R. D. (1967). <i><a href="https://en.wikipedia.org/wiki/The_Politics_of_Experience_and_The_Bird_of_Paradise">The Politics of Experience and The Bird of Paradise</a></i>. Harmondsworth: Penguin.</li> <li>Laing, R. D. (1970). <i>Knots</i>. London: Penguin. <a href="http://www.oikos.org/knotpageen.htm">Excerpt</a> (<a href="https://web.archive.org/web/20081114005752/http://www.oikos.org/knotpageen.htm">Archived</a><span> 14 November 2008 at the </span><a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a>); <a href="https://www.imdb.com/title/tt0434128/"><i>Knots</i></a><span> at </span><a href="https://en.wikipedia.org/wiki/IMDb_(identifier)">IMDb</a>.</li> <li>Laing, R. D. (1971). <i>The Politics of the Family and Other Essays</i>. London: Tavistock Publications.</li> <li>Laing, R. D. (1972). <i>Knots</i>. New York: <a href="https://en.wikipedia.org/wiki/Vintage_Press">Vintage Press</a>.</li> <li>Laing, R. D. (1976). <i>Do You Love Me? An Entertainment in Conversation and Verse</i>. New York: Pantheon Books.</li> <li>Laing, R. D. (1976). <i>Sonnets</i>. London: Michael Joseph.</li> <li>Laing, R. D. (1976). <i>The Facts of Life</i>. London: Penguin.</li> <li>Laing, R. D. (1977). <i>Conversations with Adam and Natasha</i>. New York: Pantheon.</li> <li>Laing, R. D. (1982). <i>The Voice of Experience: Experience, Science and Psychiatry</i>. Harmondsworth: Penguin.</li> <li>Laing, R. D. (1985). <i>Wisdom, Madness and Folly: The Making of a Psychiatrist 1927–1957</i>. London: <a href="https://en.wikipedia.org/wiki/Macmillan_Publishers">Macmillan</a>.</li></ul> </section><section><div><h3>On Laing by others</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div> <ul><li><i>R. D. Laing: A Life</i>, HarperCollins 1997. The most authoritative biography of Laing written by his second son, Adrian Laing.</li> <li>Caretti, V. and R. D. Laing (2022). <i>Dialogues on Madness and Wisdom: In Conservation with R. D. Laing</i>. Edited by Groth, M. and D. Serra. London: The Society for Existential Analysis.</li> <li>Mott, F. J. and R. D. Laing (2014). <a href="https://www.amazon.co.uk/Mythology-Prenatal-Life-Francis-Mott/dp/0955823188/"><i>Mythology of the Prenatal Life</i></a>. London: Starwalker Press. (Hand-written annotations [c. 1977] by R. D. Laing are included in the text, revealing Laing&#39;s own thoughts and associative material on prenatal psychology as he studied this book.^{<span><span>[</span>50<span>]</span></span>}</li> <li>Mullan, B. (1995). <i>Mad to be Normal: Conversations with R. D. Laing</i>. London: <a href="https://en.wikipedia.org/wiki/Free_Association_Books">Free Association Books</a>.</li> <li>Russell, R.; Laing, R. D. (1992). <i>R. D. Laing and Me: Lessons in Love</i> (free download). New York: Hillgarth Press.</li></ul> </section></section><section><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/Alice_Miller_(psychologist)">Alice Miller</a> – psychologist who was similar in influence to Laing</li> <li><a href="https://en.wikipedia.org/wiki/David_Smail_(psychologist)">David Smail</a> – more modern writer with similarly unconventional views</li> <li><a href="https://en.wikipedia.org/wiki/Dream_speech">Dream speech</a> – Emil Kraepelin&#39;s enigmatic dream speech, analogous to psychotic speech</li> <li><a href="https://en.wikipedia.org/wiki/Emmy_van_Deurzen">Emmy van Deurzen</a> – existential therapist and psychologist who worked with Laing</li> <li><a href="https://en.wikipedia.org/wiki/Eugène_Minkowski">Eugène Minkowski</a> – psychiatrist commended by Laing</li> <li><a href="https://en.wikipedia.org/wiki/Existential_therapy">Existential therapy</a> – form of psychotherapy focused on the client&#39;s lived experience of their subjective reality</li> <li><a href="https://en.wikipedia.org/wiki/Family_nexus">Family nexus</a> – term coined by Laing</li> <li><a href="https://en.wikipedia.org/wiki/Joseph_Berke">Joseph Berke</a> – psychoanalyst and therapist to Mary Barnes</li> <li><a href="https://en.wikipedia.org/wiki/Martti_Olavi_Siirala">Martti Olavi Siirala</a> – psychiatrist, psychoanalyst, and philosopher similar to Laing</li> <li><a href="https://en.wikipedia.org/wiki/Stephen_Ticktin">Stephen Ticktin</a> – psychiatrist, therapist, lecturer, and prominent figure in the anti-psychiatry movement</li> <li><i><a href="https://en.wikipedia.org/wiki/The_Trap_(British_TV_series)">The Trap</a></i> – three-part <a href="https://en.wikipedia.org/wiki/BBC">BBC</a> series that in its first episode concentrates on Laing&#39;s work</li> <li><a href="https://en.wikipedia.org/wiki/Serial_Experiments_Lain">Serial Experiments Lain</a> – anime series portraying Laing&#39;s interpretations on psychosis, and schizophrenia; Lain is also the eponymous namesake of Laing</li></ul> </section><section><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div> <div><ol><li><span><span>↑</span></span> <span><cite><a href="https://www.britannica.com/biography/R-D-Laing">&quot;R. D. Laing&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Encyclopædia_Britannica">Encyclopædia Britannica</a></i>. <a href="https://web.archive.org/web/20230727143523/https://www.britannica.com/biography/R-D-Laing">Archived</a> from the original on 27 July 2023<span>. Retrieved <span>9 August</span> 2023</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.rdlaingofficial.com/news-and-events/">&quot;News and events&quot;</a>. <i>Iaing enterprises</i>. 2015<span>. Retrieved <span>26 March</span> 2026</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Laing, Adrian C. (1997). <i>R. D. Laing: a life</i>. London: HarperCollins. pp.<span> </span><span>137–</span>139. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0-00-638829-9"><bdi>0-00-638829-9</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>McGeachan, C. (2014). <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4230397">&quot;&#39;The world is full of big bad wolves&#39;: investigating the experimental therapeutic spaces of R. D. Laing and Aaron Esterson&quot;</a>. <i>History of Psychiatry</i>. <b>25</b> (3). NIH National Library of Medicine: <span>283–</span>298. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1177%2F0957154X14529222">10.1177/0957154X14529222</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a><span> </span><span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4230397">4230397</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a><span> </span><a href="https://pubmed.ncbi.nlm.nih.gov/25114145">25114145</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Laing, Ronald D. (1985). <i>Wisdom, madness and folly: the making of a psychiatrist, 1927–1957</i>. London: Macmillan. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0333370759"><bdi>0333370759</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Laing, Adrian Charles (1995). <i>R. D. Laing: A Biography</i>. Peter Owen Ltd. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0720609349"><bdi>978-0720609349</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span>Obituary of R. D. Laing by Joseph Berke; <i>Daily Telegraph</i>, 25 August 1989.</span></li> <li><span><span>1</span> <span>2</span></span> <span>Beveridge, A. (2011) <a href="https://books.google.com/books?id=JKlnhKRlrqUC">Portrait of the Psychiatrist as a Young Man: The Early Writing and Work of R. D. Laing, 1927–1960</a> Oxford University Press</span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/David_Kynaston">Kynaston, David</a> (2009). <a href="https://archive.org/details/familybritain1950000kyna/page/97"><i>Family Britain 1951-7</i></a>. London: Bloomsbury. p.<span> </span><a href="https://archive.org/details/familybritain1950000kyna/page/97">97</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/9780747583851"><bdi>9780747583851</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Turnbull, Ronnie; Beveridge, Craig (1988), &quot;R. D. Laing and Scottish Philosophy&quot;, <i>Edinburgh Review</i>, <b><span>78–</span>9</b>: <span>126–</span>127, <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0267-6672">0267-6672</a></cite></span></li> <li><span><span>1</span> <span>2</span></span> <span>Mad to be Normal: Conversations with R. D. Laing [Paperback]</span></li> <li><span><span>↑</span></span> <span><cite>Itten, Theodor, <a href="https://web.archive.org/web/20071016084554/http://laingsociety.org/colloquia/psychotherapy/ittensoulmaking.htm"><i>The Paths of Soul Making</i></a>, archived from <a href="http://laingsociety.org/colloquia/psychotherapy/ittensoulmaking.htm">the original</a> on 16 October 2007<span>, retrieved <span>17 October</span> 2007</span></cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://web.archive.org/web/20080509060104/http://www.philadelphia-association.co.uk/Kingsley-Hall.html">&quot;Kingsley Hall&quot;</a>. Philadelphia Association. Archived from <a href="http://www.philadelphia-association.co.uk/Kingsley-Hall.html">the original</a> on 9 May 2008<span>. Retrieved <span>13 September</span> 2008</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Axel_Jensen">Axel Jensen</a>. <i>Axel Jensen, Livet sett fra Nimbus (&quot;Life as seen from Nimbus&quot;): a biography as told to Petter Mejlænder</i> (in Norwegian). Oslo: Norway: Spartacus forlag (Spartacus Publishing).</cite></span></li> <li><span><span>↑</span></span> <span><cite>Dunbar, Ian (2009). <a href="https://books.google.com/books?id=MdAhAgAAQBAJ"><i>More Than a Puff of Smoke</i></a>. Lulu Enterprises Incorporated. p.<span> </span>82. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-1-409-29409-2"><bdi>978-1-409-29409-2</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Laing, Adrian (1994). <i>R. D. Laing: A Life</i>. London: HarperCollinsPublishers. pp.<span> </span><span>165–</span>166. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0-00-638829-9"><bdi>0-00-638829-9</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Miller, Russell (12 April 2009), <a href="https://web.archive.org/web/20110615193523/http://women.timesonline.co.uk/tol/life_and_style/women/families/article6058901.ece">&quot;RD Laing: The abominable family man&quot;</a>, <i>The Sunday Times</i>, London, archived from <a href="http://women.timesonline.co.uk/tol/life_and_style/women/families/article6058901.ece">the original</a> on 15 June 2011<span>, retrieved <span>8 August</span> 2011</span></cite></span></li> <li><span><span>↑</span></span> <span>Mad to be Normal: Conversations with R. D. Laing <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/1853433950"><bdi>1853433950</bdi></a>[Paperback]</span></li> <li><span><span>↑</span></span> <span>Obituary of R. D. Laing by Joseph Berke; <i>Daily Telegraph</i>, 25 August 1989</span></li> <li><span><span>↑</span></span> <span>&quot;R. D. Laing&quot;, in <i>The New Left</i>, edited by Maurice Cranston, The Library Press, 1971, pp. 179–208. &quot;Ronald Laing must be accounted one of the main contributors to the theoretical and rhetorical armoury of the contemporary Left&quot;.</span></li> <li><span><span>↑</span></span> <span>Bateson, G., Jackson, D. D., Haley, J. &amp; Weakland, J., 1956, Toward a theory of schizophrenia. (in: <i><a href="https://en.wikipedia.org/wiki/Systems_Research_and_Behavioral_Science">Behavioral Science</a></i>, Vol.1, pp. 251–264)</span></li> <li><span><span>↑</span></span> <span><cite>Lewis, Bradley (2006). <a href="https://web.english.upenn.edu/~cavitch/pdf-library/Lewis_Postpsychiatry.pdf"><i>Moving Beyond Prozac, DSM, and the New Psychiatry</i></a> <span>(PDF)</span>. Ann Arbor: University of Michigan Press. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.3998%2Fmpub.93209">10.3998/mpub.93209</a><span>. Retrieved <span>26 March</span> 2026</span> <span>–</span> via Department of English at the University of Pennsylvania.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Diller, Lawrence (19 November 2007). <span><a href="https://journals.sagepub.com/doi/10.1177/1087054707305104?icid=int.sj-abstract.similar-articles.1">&quot;Book Review: Lewis, B. (2006). Moving Beyond Prozac, DSM, and the New Psychiatry: The Birth of Postpsychiatry. Ann Arbor: University of Michigan Press&quot;</a></span>. <i>Journal of Attention Disorders</i>. <b>11</b> (5). <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1177%2F1087054707305104">10.1177/1087054707305104</a><span>. Retrieved <span>26 March</span> 2026</span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Laing, R. D. (1965). <i>The Divided Self</i>. Pelican. pp.<span> </span><span>41–</span>43. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0-14-020734-1"><bdi>0-14-020734-1</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Nour, Matthew M.; Barrera, Alvaro (November 2015). <a href="https://academic.oup.com/schizophreniabulletin/article-lookup/doi/10.1093/schbul/sbv035">&quot;Schizophrenia, Subjectivity, and Mindreading&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Schizophrenia_Bulletin">Schizophrenia Bulletin</a></i>. <b>41</b> (6): <span>1214–</span>1219. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1093%2Fschbul%2Fsbv035">10.1093/schbul/sbv035</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0586-7614">0586-7614</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a><span> </span><span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4601706">4601706</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a><span> </span><a href="https://pubmed.ncbi.nlm.nih.gov/25848120">25848120</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.discogs.com/Various-Miniatures-A-Sequence-Of-Fifty-One-Tiny-Masterpieces-Edited-By-Morgan-Fisher/release/347586">&quot;Various – Miniatures (A Sequence of Fifty-One Tiny Masterpieces Edited by Morgan Fisher) (Vinyl, LP, Album)&quot;</a>. <i>discogs.com</i>. <a href="https://en.wikipedia.org/wiki/Discogs">Discogs</a>. 1980<span>. Retrieved <span>4 October</span> 2016</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>&quot;David Bowie&quot;. <i>David Bowie</i><span>. Retrieved <span>3 May</span> 2026</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Laing, Adrian C. (1997). <i>R. D. Laing: a life</i>. London: HarperCollins. p.<span> </span>19. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0-00-638829-9"><bdi>0-00-638829-9</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Laing, Adrian C. (1997). <i>R. D. Laing: a life</i>. London: HarperCollins. p.<span> </span>22. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0-00-638829-9"><bdi>0-00-638829-9</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="http://special.lib.gla.ac.uk/manuscripts/search/detaild.cfm?DID=77056"><i>University of Glasgow Special Collection: Document Details</i></a><span>, retrieved <span>17 October</span> 2007</span></cite></span></li> <li><span><span>↑</span></span> <span><cite>Laing, Adrian C. (1997). <i>R. D. Laing: a life</i>. London: HarperCollins. pp.<span> </span><span>228–</span>229. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0-00-638829-9"><bdi>0-00-638829-9</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://spartacus-educational.com/R_D_Laing.htm">&quot;R. D. Laing&quot;</a>. <i>Spartacus Educational</i><span>. Retrieved <span>26 January</span> 2020</span>.</cite></span></li> <li><span><span>1</span> <span>2</span> <span>3</span></span> <span><cite>Day, Elizabeth; Keeley, Graham (1 June 2008). <a href="https://www.theguardian.com/books/2008/jun/01/mentalhealth.society">&quot;My father, RD Laing: &#39;he solved other people&#39;s problems – but not his own&#39;&quot;</a>. <i>The Observer</i><span>. Retrieved <span>10 November</span> 2022</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Day, Elizabeth; Keeley, Graham (31 May 2008). <a href="https://www.theguardian.com/books/2008/jun/01/mentalhealth.society">&quot;My father, RD Laing: &#39;he solved other people&#39;s problems - but not his own&#39;&quot;</a>. <i>The Guardian</i><span>. Retrieved <span>26 March</span> 2026</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Laing, Adrian C. (1997). <i>R. D. Laing: a life</i>. London: HarperCollins. pp.<span> </span><span>181–</span>183. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0-00-638829-9"><bdi>0-00-638829-9</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://spartacus-educational.com/R_D_Laing.htm">&quot;R. D. Laing&quot;</a>. <i>Spartacus Educational</i><span>. Retrieved <span>26 January</span> 2020</span>.</cite></span></li> <li><span><span>↑</span></span> <span> <cite><a href="https://www.thetimes.com/travel/destinations/uk-travel/scotland-travel/rd-laing-the-abominable-family-man-mqkbxw8jj2x">&quot;RD Laing: The abominable family man&quot;</a>. <i>The Times</i>. 12 April 2009<span>. Retrieved <span>26 March</span> 2026</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>McQuiston, John T. (25 August 1989). <a href="https://www.nytimes.com/1989/08/25/obituaries/rd-laing-rebel-and-pioneer-on-schizophrenia-is-dead-at-61.html">&quot;R. D. Laing, Rebel and Pioneer on Schizophrenia, Is Dead at 61&quot;</a>. <i>The New York Times</i><span>. Retrieved <span>26 March</span> 2026</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Laing, Adrian C. (1997). <i>R. D. Laing: a life</i>. London: HarperCollins. pp.<span> </span><span>101–</span>117. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0-00-638829-9"><bdi>0-00-638829-9</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://web.archive.org/web/20081206073355/http://www.philadelphia-association.co.uk/the-history.html">&quot;The Philadelphia Association: Philosophical Perspective&quot;</a>. Philadelphia Association. Archived from <a href="http://www.philadelphia-association.co.uk/the-history.html">the original</a> on 6 December 2008<span>. Retrieved <span>7 September</span> 2008</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Coltart, Nina (1990). <a href="http://www3.interscience.wiley.com/cgi-bin/fulltext/119999330/PDFSTART">&quot;ARBOURS ASSOCIATION 20TH ANNIVERSARY LECTURE&quot;</a>. British Journal of Psychotherapy. p.<span> </span>165<span>. Retrieved <span>7 September</span> 2008</span>.</cite>^{<span><span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Link_rot"><span>dead link</span></a></i><span>]</span></span>}</span></li> <li><span><span>↑</span></span> <span><cite><a href="https://web.archive.org/web/20081226132758/http://www.nspc.org.uk/html/5b_therapy.htm">&quot;Existential Counselling and Psychotherapy, and the New School&quot;</a>. New School of Psychotherapy and Counselling. Archived from <a href="http://www.nspc.org.uk/html/5b_therapy.htm">the original</a> on 26 December 2008<span>. Retrieved <span>7 September</span> 2008</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>&quot;RD Laing in the 21st Century Symposium&quot;. RD Laing in the 21s Century Symposium<span>. Retrieved <span>30 July</span> 2018</span>.</cite></span></li> <li><span><span>↑</span></span> <span>Cooke, Lez <a href="http://www.screenonline.org.uk/people/id/458945/">&quot;BFI Screenonline: Loach, Ken (1936–) Biography&quot;</a>, accessed 7 July 2011.</span></li> <li><span><span>↑</span></span> <span>IMDB, <a href="https://www.imdb.com/title/tt0968255/">&quot;Birth (1977)&quot;</a>, accessed 7 July 2011.</span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.birmingham-rep.co.uk/about-us/50-years-of-history/">&quot;50 Years of History&quot;</a>. <i>Birmingham Rep</i><span>. Retrieved <span>9 May</span> 2026</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://suttonelms.org.uk/monday-play.html">&quot;The Monday Play&quot;</a>. <i>Diversity Website</i><span>. Retrieved <span>9 May</span> 2026</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="http://gizmofilms.com/home/features/">&quot;Current Features – Mad to be Normal&quot;</a>. <i>www.gizmofilms.com</i>. Gizmo Films<span>. Retrieved <span>31 January</span> 2016</span>.</cite></span></li> <li><span><span>↑</span></span> <span><a href="http://www.pep-web.org/document.php?id=joap.007.0172a">Psychoanalytic Electronic Publishing</a>. Retrieved on 16 October 2008</span></li> <li><span><span>↑</span></span> <span>Original is located in the R. D. Laing Special Collection, Glasgow University Library. <cite><a href="https://web.archive.org/web/20170630072559/http://special.lib.gla.ac.uk/manuscripts/search/detail_c.cfm?ID=60234">&quot;MS Laing V51&quot;</a>. <i>University of Glasgow<span> </span>:: Manuscripts Catalogue</i>. Archived from <a href="http://special.lib.gla.ac.uk/manuscripts/search/detail_c.cfm?ID=60234">the original</a> on 30 June 2017.</cite> See also <cite><a href="https://web.archive.org/web/20170630071251/http://special.lib.gla.ac.uk/manuscripts/search/detail_c.cfm?ID=77629">&quot;MS Laing A578&quot;</a>. University of Glasgow Manuscripts Catalogue. Archived from <a href="http://special.lib.gla.ac.uk/manuscripts/search/detail_c.cfm?ID=77629">the original</a> on 30 June 2017.</cite></span></li> </ol></div> </section><section><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=13"><span>edit</span></a><span>]</span></span></div> <div> <ul><li>Laing, A. (1997) <i>R. D. Laing: A Life</i>: London, HarperCollins.</li> <li>Boyers, R. and R. Orrill, Eds. (1971) <i>Laing and Anti-Psychiatry</i>. New York: Salamagundi Press.</li> <li>Burston, D. (1996) <i>The Wing of Madness: The Life and Work of R. D. Laing</i>. Cambridge, MA: Harvard University Press.</li> <li>Burston, D. (2000) <i>The Crucible of Experience: R. D. Laing and the Crisis of Psychotherapy</i>. Cambridge, MA: Harvard University Press.</li> <li>Clay, J. (1996) <i>R. D. Laing: A Divided Self</i>. London: Hodder &amp; Stoughton.</li> <li>Collier, A. (1977) <i>R. D. Laing: The Philosophy and Politics of Psychotherapy</i>. New York: Pantheon.</li> <li>Evans, R. I. (1976) <i>R. D. Laing, The Man and His Ideas</i>. New York: E. P. Dutton.</li> <li>Friedenberg, E. Z. (1973) <i>R. D. Laing</i>. New York: Viking Press.</li> <li>Itten, T. &amp; Young, C. (Ed.) (2012) R. D. Laing – 50 Years since The Divieded Self. Ross-on-Wye, PCCS-Books</li> <li>Miller, G. (2004) <i>R. D. Laing</i>. Edinburgh: Edinburgh University Press.</li> <li>Kotowicz, Z. (1997) <i>R. D. Laing and the Paths of Anti-Psychiatry</i>. London: Taylor &amp; Francis.</li> <li>Mullan, B., Ed. (1997) <i>R. D. Laing: Creative Destroyer</i>. London: Cassell &amp; Co.</li> <li>Mullan, B. (1999) <i>R. D. Laing: A Personal View</i>. London: Duckworth.</li> <li>Raschid, S., Ed. (2005) <i>R. D. Laing: Contemporary Perspectives</i>. London: <a href="https://en.wikipedia.org/wiki/Free_Association_Books">Free Association Books</a>.</li></ul> </div> </section><section><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=R._D._Laing&amp;action=edit&amp;section=14"><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/R.%20D.%20Laing">R. D. Laing</a></b></i>.</div></div> </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 <a href="https://commons.wikimedia.org/wiki/Category:Ronald%20David%20Laing"><span>R. D. Laing</span></a>.</div></div> </div> <ul><li>R. D. Laing Estate Website</li> <li><a href="https://web.archive.org/web/20070302173147/http://laingsociety.org/biograph.htm">Biography at The Society for Laingian Studies</a></li> <li><a href="http://www.janushead.org/4-1/index.cfm">Special Issue of Janus Head</a> <a href="https://web.archive.org/web/20060616014602/http://janushead.org/4-1/index.cfm">Archived</a><span> 16 June 2006 at the </span><a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a>, Edited by Daniel Burston</li> <li>The Philadelphia Association</li> <li><a href="http://www.mindfortherapy.com/laing-and-family-therapy.html">Historical documents including correspondence with Gregory Bateson</a> <a href="https://web.archive.org/web/20090802191814/http://www.mindfortherapy.com/laing-and-family-therapy.html">Archived</a><span> 2 August 2009 at the </span><a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a></li> <li><a href="https://web.archive.org/web/20110615193523/http://women.timesonline.co.uk/tol/life_and_style/women/families/article6058901.ece">RD Laing: The Abominable Family Man</a> from The Sunday Times</li> <li>Life before Death – 1978 album of sonnets and other poems performed by R. D. Laing to an original musical score</li> <li><a href="https://www.youtube.com/watch?v=FiCOazoizjU"><span>Leo Matos and R. D. Laing: Transpersonal Psychology</span></a><span> on </span><a href="https://en.wikipedia.org/wiki/YouTube_video_(identifier)">YouTube</a>: St Görans Lecture, Stockholm, 10 February 1982.</li> <li><a href="https://www.gla.ac.uk/collections/#/details?irn=251370&amp;catType=C">Papers of Ronald David Laing, psychotherapist, 1928-1989 (GB 247 MS Laing) Archives &amp; Special Collections, University of Glasgow</a></li></ul> <p><a href="https://en.wikipedia.org/wiki/Octopus_(Gentle_Giant_album)">Octopus</a></p> <div><table><tbody><tr><th colspan="2"><div>Links to related articles</div></th></tr><tr><td colspan="2"><div> <div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Anti-psychiatry"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Anti-psychiatry"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Anti-psychiatry"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Anti-psychiatry">Anti-psychiatry</a></div></th></tr><tr><th>Topics</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Biopsychiatry_controversy">Biopsychiatry controversy</a></li> <li><a href="https://en.wikipedia.org/wiki/Controversies_about_psychiatry">Controversies about psychiatry</a></li> <li><a href="https://en.wikipedia.org/wiki/Critical_Psychiatry_Network">Critical psychiatry</a></li> <li><a href="https://en.wikipedia.org/wiki/Hearing_Voices_Movement">Hearing Voices Movement</a></li> <li><a href="https://en.wikipedia.org/wiki/History_of_mental_disorders">History of mental disorders</a></li> <li><a href="https://en.wikipedia.org/wiki/Involuntary_commitment">Involuntary commitment</a></li> <li><a href="https://en.wikipedia.org/wiki/Involuntary_treatment">Involuntary treatment</a></li> <li><a href="https://en.wikipedia.org/wiki/Martha_Mitchell_effect">Martha Mitchell effect</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_medical_ethics_cases">Medical ethics</a></li> <li><a href="https://en.wikipedia.org/wiki/Medicalization">Medicalization</a> <ul><li><a href="https://en.wikipedia.org/wiki/Medicalisation_of_sexuality">of sexuality</a></li> <li><a href="https://en.wikipedia.org/wiki/Medical_model">medical model</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Nouthetic_counseling">Nouthetic counseling</a></li> <li><a href="https://en.wikipedia.org/wiki/Outline_of_the_psychiatric_survivors_movement">Outline of the psychiatric survivors movement</a></li> <li><a href="https://en.wikipedia.org/wiki/Political_abuse_of_psychiatry">Political abuse of psychiatry</a></li> <li><a href="https://en.wikipedia.org/wiki/Positive_disintegration">Positive disintegration</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychiatric_survivors_movement">Psychiatric survivors movement</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychoanalytic_theory">Psychoanalytic theory</a></li> <li><a href="https://en.wikipedia.org/wiki/Recovery_model">Recovery model</a></li> <li><a href="https://en.wikipedia.org/wiki/Rhetoric_of_therapy">Rhetoric of therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Rosenhan_experiment">Rosenhan experiment</a></li> <li><a href="https://en.wikipedia.org/wiki/Self-help_groups_for_mental_health">Self-help groups for mental health</a></li> <li><a href="https://en.wikipedia.org/wiki/Therapeutic_community">Therapeutic community</a></li></ul> </div></td></tr><tr><th>Organizations</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/American_Association_for_the_Abolition_of_Involuntary_Mental_Hospitalization">American Association for the Abolition of Involuntary Mental Hospitalization</a></li> <li><a href="https://en.wikipedia.org/wiki/Aspies_For_Freedom">Aspies For Freedom</a></li> <li><a href="https://en.wikipedia.org/wiki/Autism_Network_International">Autism Network International</a></li> <li><a href="https://en.wikipedia.org/wiki/Bazelon_Center_for_Mental_Health_Law">Bazelon Center for Mental Health Law</a></li> <li><a href="https://en.wikipedia.org/wiki/Citizens_Commission_on_Human_Rights">Citizens Commission on Human Rights</a></li> <li><a href="https://en.wikipedia.org/wiki/Critical_Psychiatry_Network">Critical Psychiatry Network</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_Rights_International">Disability Rights International</a></li> <li><a href="https://en.wikipedia.org/wiki/Hearing_Voices_Network">Hearing Voices Network</a></li> <li><a href="https://en.wikipedia.org/wiki/Icarus_Project">Icarus Project</a></li> <li><a href="https://en.wikipedia.org/wiki/International_Disability_Alliance">International Disability Alliance</a></li> <li><a href="https://en.wikipedia.org/wiki/Learning_Disability_Coalition">Learning Disability Coalition</a></li> <li><a href="https://en.wikipedia.org/wiki/Mad_Pride">Mad Pride</a></li> <li><a href="https://en.wikipedia.org/wiki/MindFreedom_International">MindFreedom International</a></li> <li><a href="https://en.wikipedia.org/wiki/National_Empowerment_Center">National Empowerment Center</a></li> <li><a href="https://en.wikipedia.org/wiki/Radical_Psychology_Network">Radical Psychology Network</a></li> <li><a href="https://en.wikipedia.org/wiki/Rehabilitation_International">Rehabilitation International</a></li> <li><a href="https://en.wikipedia.org/wiki/Disability_Rights_UK">Royal Association for Disability Rights</a></li> <li>Paranoia Network</li> <li><a href="https://en.wikipedia.org/wiki/Soteria_(psychiatric_treatment)">Soteria</a></li> <li><a href="https://en.wikipedia.org/wiki/Socialist_Patients&#39;_Collective">Socialist Patients&#39; Collective</a></li> <li><a href="https://en.wikipedia.org/wiki/World_Network_of_Users_and_Survivors_of_Psychiatry">World Network of Users and Survivors of Psychiatry</a></li></ul> </div></td></tr><tr><th>People</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Linda_Andre">Linda Andre</a></li> <li><a href="https://en.wikipedia.org/wiki/Giorgio_Antonucci">Giorgio Antonucci</a></li> <li><a href="https://en.wikipedia.org/wiki/Franco_Basaglia">Franco Basaglia</a></li> <li><a href="https://en.wikipedia.org/wiki/Ernest_Becker">Ernest Becker</a></li> <li><a href="https://en.wikipedia.org/wiki/Lauretta_Bender">Lauretta Bender</a></li> <li><a href="https://en.wikipedia.org/wiki/Richard_Bentall">Richard Bentall</a></li> <li><a href="https://en.wikipedia.org/wiki/Peter_Breggin">Peter Breggin</a></li> <li><a href="https://en.wikipedia.org/wiki/Paula_Caplan">Paula Caplan</a></li> <li><a href="https://en.wikipedia.org/wiki/Ted_Chabasinski">Ted Chabasinski</a></li> <li><a href="https://en.wikipedia.org/wiki/Judi_Chamberlin">Judi Chamberlin</a></li> <li><a href="https://en.wikipedia.org/wiki/David_Cooper_(psychiatrist)">David Cooper</a></li> <li><a href="https://en.wikipedia.org/wiki/Lyn_Duff">Lyn Duff</a></li> <li><a href="https://en.wikipedia.org/wiki/Michel_Foucault">Michel Foucault</a></li> <li><a href="https://en.wikipedia.org/wiki/Leonard_Roy_Frank">Leonard Roy Frank</a></li> <li><a href="https://en.wikipedia.org/wiki/Erving_Goffman">Erving Goffman</a></li> <li><a href="https://en.wikipedia.org/wiki/James_Gottstein">James Gottstein</a></li> <li><a href="https://en.wikipedia.org/wiki/Peter_C._Gøtzsche">Peter C. Gøtzsche</a></li> <li><a href="https://en.wikipedia.org/wiki/Félix_Guattari">Félix Guattari</a></li> <li><a href="https://en.wikipedia.org/wiki/Jacques_Lacan">Jacques Lacan</a></li> <li><a href="https://en.wikipedia.org/wiki/R._D._Laing">R. D. Laing</a></li> <li><a href="https://en.wikipedia.org/wiki/Peter_Lehmann_(author)">Peter Lehmann</a></li> <li><a href="https://en.wikipedia.org/wiki/Kate_Millett">Kate Millett</a></li> <li><a href="https://en.wikipedia.org/wiki/Loren_Mosher">Loren Mosher</a></li> <li><a href="https://en.wikipedia.org/wiki/Joanna_Moncrieff">Joanna Moncrieff</a></li> <li><a href="https://en.wikipedia.org/wiki/David_Oaks">David Oaks</a></li> <li><a href="https://en.wikipedia.org/wiki/Elizabeth_Packard">Elizabeth Packard</a></li> <li><a href="https://en.wikipedia.org/wiki/Sascha_Altman_DuBrul">Sascha Scatter</a></li> <li><a href="https://en.wikipedia.org/wiki/David_Smail_(psychologist)">David Smail</a></li> <li><a href="https://en.wikipedia.org/wiki/Thomas_Szasz">Thomas Szasz</a></li> <li><a href="https://en.wikipedia.org/wiki/Stephen_Ticktin">Stephen Ticktin</a></li> <li><a href="https://en.wikipedia.org/wiki/Robert_Whitaker_(author)">Robert Whitaker</a></li></ul> </div></td></tr><tr><th>Publications</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Anatomy_of_an_Epidemic">Anatomy of an Epidemic</a></li> <li><a href="https://en.wikipedia.org/wiki/Anti-Oedipus">Anti-Oedipus</a></li> <li><a href="https://en.wikipedia.org/wiki/Asylums_(book)">Asylums</a></li> <li><a href="https://en.wikipedia.org/wiki/Crazy_Therapies">Crazy Therapies</a></li> <li><a href="https://en.wikipedia.org/wiki/Doctoring_the_Mind">Doctoring the Mind</a></li> <li><a href="https://en.wikipedia.org/wiki/Interpretation_of_Schizophrenia">Interpretation of Schizophrenia</a></li> <li><a href="https://en.wikipedia.org/wiki/Liberation_by_Oppression">Liberation by Oppression</a></li> <li><a href="https://en.wikipedia.org/wiki/Mad_in_America">Mad in America</a></li> <li><a href="https://en.wikipedia.org/wiki/Madness_and_Civilization">Madness and Civilization</a></li> <li><a href="https://en.wikipedia.org/wiki/Radical_Psychology_Network">Radical Psychology</a></li> <li><a href="https://en.wikipedia.org/wiki/The_Gene_Illusion">The Gene Illusion</a></li> <li><a href="https://en.wikipedia.org/wiki/The_Myth_of_Mental_Illness">The Myth of Mental Illness</a></li> <li><a href="https://en.wikipedia.org/wiki/The_Politics_of_Experience_and_The_Bird_of_Paradise">The Politics of Experience and The Bird of Paradise</a></li> <li><a href="https://en.wikipedia.org/wiki/The_Protest_Psychosis">The Protest Psychosis</a></li> <li><a href="https://en.wikipedia.org/wiki/The_Radical_Therapist">The Radical Therapist</a></li></ul> </div></td></tr><tr><td colspan="2"><div><a href="https://en.wikipedia.org/wiki/Portal:Psychiatry">Psychiatry portal</a></div></td></tr></tbody></table></div> <div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Psychotherapy"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Psychotherapy"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Psychotherapy"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Psychotherapy">Psychotherapy</a></div></th></tr><tr><th>Schools</th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Psychodynamic_psychotherapy">Psychodynamic</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Adlerian">Adlerian therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Analytical_psychology">Analytical therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Mentalization-based_treatment">Mentalization-based treatment</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychoanalysis">Psychoanalysis</a></li> <li><a href="https://en.wikipedia.org/wiki/Transference_focused_psychotherapy">Transference focused psychotherapy</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Behavioral_psychotherapy">Cognitive and <br/>behavioral</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Clinical_behavior_analysis">Clinical behavior analysis</a> <ul><li><a href="https://en.wikipedia.org/wiki/Acceptance_and_commitment_therapy">Acceptance and commitment therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Functional_analytic_psychotherapy">Functional analytic psychotherapy</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Cognitive_behavioral_therapy">Cognitive behavioral therapy</a> <ul><li><a href="https://en.wikipedia.org/wiki/Cognitive_therapy">Cognitive therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Dialectical_behavior_therapy">Dialectical behavior therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Mindfulness-based_cognitive_therapy">Mindfulness-based cognitive therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Rational_emotive_behavior_therapy">Rational emotive behavior therapy</a></li></ul></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Humanistic_psychology">Humanistic</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Emotionally_focused_therapy">Emotionally focused therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Existential_therapy">Existential therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Focusing_(psychotherapy)">Focusing</a></li> <li><a href="https://en.wikipedia.org/wiki/Gestalt_therapy">Gestalt therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Logotherapy">Logotherapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Person-centered_therapy">Person-centered therapy</a></li></ul> </div></td></tr><tr><th>Other</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Art_therapy">Art therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Dance_therapy">Dance therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Feminist_therapy">Feminist therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Music_therapy">Music therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Narrative_therapy">Narrative therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Play_therapy">Play therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Reality_therapy">Reality therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Systemic_therapy_(psychotherapy)">Systemic therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Transactional_analysis">Transactional analysis</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_psychotherapies">List</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Integrative_psychotherapy">Integrative</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Eclectic_psychotherapy">Eclectic psychotherapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Multimodal_therapy">Multimodal therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Transtheoretical_model">Transtheoretical model</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Approaches</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Brief_psychotherapy">Brief psychotherapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Counseling_psychology">Counseling</a></li> <li><a href="https://en.wikipedia.org/wiki/Online_counseling">Online therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Telephone_counseling">Telephone therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Residential_treatment_center">Residential treatment</a></li> <li><a href="https://en.wikipedia.org/wiki/Self-help">Self-help</a></li> <li><a href="https://en.wikipedia.org/wiki/Support_group">Support group</a></li></ul> </div></td></tr><tr><th>Research</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Clinical_formulation">Clinical formulation</a></li> <li><a href="https://en.wikipedia.org/wiki/Clinical_pluralism">Clinical pluralism</a></li> <li><a href="https://en.wikipedia.org/wiki/Common_factors_theory">Common factors theory</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychotherapy_discontinuation">Discontinuation</a></li> <li><a href="https://en.wikipedia.org/wiki/History_of_psychotherapy">History</a></li> <li><a href="https://en.wikipedia.org/wiki/Practitioner–scholar_model">Practitioner–scholar model</a></li></ul> </div></td></tr><tr><th>Techniques</th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Behaviour_therapy">Behavior therapy</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Aversion_therapy">Aversion therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Chaining">Chaining</a></li> <li><a href="https://en.wikipedia.org/wiki/Contingency_management">Contingency management</a> <ul><li><a href="https://en.wikipedia.org/wiki/Shaping_(psychology)">Shaping</a></li> <li><a href="https://en.wikipedia.org/wiki/Stimulus_control">Stimulus control</a></li> <li><a href="https://en.wikipedia.org/wiki/Token_economy">Token economy</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Counterconditioning">Counterconditioning</a></li> <li><a href="https://en.wikipedia.org/wiki/Desensitization_(psychology)">Desensitization</a>/<a href="https://en.wikipedia.org/wiki/Exposure_therapy">Exposure therapy</a> <ul><li><a href="https://en.wikipedia.org/wiki/Systematic_desensitization">Systematic desensitization</a></li></ul></li></ul> </div></td></tr><tr><th>Other individual therapy</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Autogenic_training">Autogenic training</a></li> <li><a href="https://en.wikipedia.org/wiki/Biofeedback">Biofeedback</a></li> <li><a href="https://en.wikipedia.org/wiki/Clean_language">Clean language</a></li> <li><a href="https://en.wikipedia.org/wiki/Cognitive_restructuring">Cognitive restructuring</a></li> <li><a href="https://en.wikipedia.org/wiki/Emotional_self-regulation">Emotion regulation</a> <ul><li><a href="https://en.wikipedia.org/wiki/Affect_labeling">Affect labeling</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Free_association_(psychology)">Free association</a></li> <li><a href="https://en.wikipedia.org/wiki/Homework_in_psychotherapy">Homework</a></li> <li><a href="https://en.wikipedia.org/wiki/Hypnotherapy">Hypnotherapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Modeling_(psychology)">Modeling</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Group_psychotherapy">Group psychotherapy</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Co-therapy">Co-therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Couples_therapy">Couples therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Family_therapy">Family therapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychodrama">Psychodrama</a></li> <li><a href="https://en.wikipedia.org/wiki/Sensitivity_training">Sensitivity training</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>People</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Philippe_Pinel">Philippe Pinel</a></li> <li><a href="https://en.wikipedia.org/wiki/Josef_Breuer">Josef Breuer</a></li> <li><a href="https://en.wikipedia.org/wiki/Sigmund_Freud">Sigmund Freud</a></li> <li><a href="https://en.wikipedia.org/wiki/Pierre_Janet">Pierre Janet</a></li> <li><a href="https://en.wikipedia.org/wiki/Alfred_Adler">Alfred Adler</a></li> <li><a href="https://en.wikipedia.org/wiki/Sándor_Ferenczi">Sándor Ferenczi</a></li> <li><a href="https://en.wikipedia.org/wiki/Carl_Jung">Carl Jung</a></li> <li><a href="https://en.wikipedia.org/wiki/Ludwig_Binswanger">Ludwig Binswanger</a></li> <li><a href="https://en.wikipedia.org/wiki/Melanie_Klein">Melanie Klein</a></li> <li><a href="https://en.wikipedia.org/wiki/Otto_Rank">Otto Rank</a></li> <li><a href="https://en.wikipedia.org/wiki/Karen_Horney">Karen Horney</a></li> <li><a href="https://en.wikipedia.org/wiki/Harry_Stack_Sullivan">Harry Stack Sullivan</a></li> <li><a href="https://en.wikipedia.org/wiki/Fritz_Perls">Fritz Perls</a></li> <li><a href="https://en.wikipedia.org/wiki/Anna_Freud">Anna Freud</a></li> <li><a href="https://en.wikipedia.org/wiki/Donald_Winnicott">Donald Winnicott</a></li> <li><a href="https://en.wikipedia.org/wiki/Wilhelm_Reich">Wilhelm Reich</a></li> <li><a href="https://en.wikipedia.org/wiki/Milton_H._Erickson">Milton H. Erickson</a></li> <li><a href="https://en.wikipedia.org/wiki/Jacques_Lacan">Jacques Lacan</a></li> <li><a href="https://en.wikipedia.org/wiki/Erik_Erikson">Erik Erikson</a></li> <li><a href="https://en.wikipedia.org/wiki/Carl_Rogers">Carl Rogers</a></li> <li><a href="https://en.wikipedia.org/wiki/Viktor_Frankl">Viktor Frankl</a></li> <li><a href="https://en.wikipedia.org/wiki/George_Kelly_(psychologist)">George Kelly</a></li> <li><a href="https://en.wikipedia.org/wiki/Rollo_May">Rollo May</a></li> <li><a href="https://en.wikipedia.org/wiki/Virginia_Axline">Virginia Axline</a></li> <li><a href="https://en.wikipedia.org/wiki/Carl_Whitaker">Carl Whitaker</a></li> <li><a href="https://en.wikipedia.org/wiki/Albert_Ellis">Albert Ellis</a></li> <li><a href="https://en.wikipedia.org/wiki/Silvano_Arieti">Silvano Arieti</a></li> <li><a href="https://en.wikipedia.org/wiki/James_Bugental">James Bugental</a></li> <li><a href="https://en.wikipedia.org/wiki/Joseph_Wolpe">Joseph Wolpe</a></li> <li><a href="https://en.wikipedia.org/wiki/Virginia_Satir">Virginia Satir</a></li> <li><a href="https://en.wikipedia.org/wiki/Aaron_Beck">Aaron Beck</a></li> <li><a href="https://en.wikipedia.org/wiki/Salvador_Minuchin">Salvador Minuchin</a></li> <li><a href="https://en.wikipedia.org/wiki/Paul_Watzlawick">Paul Watzlawick</a></li> <li><a href="https://en.wikipedia.org/wiki/Haim_Ginott">Haim Ginott</a></li> <li><a href="https://en.wikipedia.org/wiki/Ogden_Lindsley">Ogden Lindsley</a></li> <li><a href="https://en.wikipedia.org/wiki/Paul_Watzlawick">Paul Watzlawick</a></li> <li><a href="https://en.wikipedia.org/wiki/Arthur_Janov">Arthur Janov</a></li> <li><a href="https://en.wikipedia.org/wiki/Eugene_Gendlin">Eugene Gendlin</a></li> <li><a href="https://en.wikipedia.org/wiki/R._D._Laing">R. D. Laing</a></li> <li><a href="https://en.wikipedia.org/wiki/Jean_Baker_Miller">Jean Baker Miller</a></li> <li><a href="https://en.wikipedia.org/wiki/Otto_F._Kernberg">Otto F. Kernberg</a></li> <li><a href="https://en.wikipedia.org/wiki/Nathan_Azrin">Nathan Azrin</a></li> <li><a href="https://en.wikipedia.org/wiki/Irvin_D._Yalom">Irvin D. Yalom</a></li> <li><a href="https://en.wikipedia.org/wiki/Arnold_Lazarus">Arnold Lazarus</a></li> <li><a href="https://en.wikipedia.org/wiki/Lorna_Smith_Benjamin">Lorna Smith Benjamin</a></li> <li><a href="https://en.wikipedia.org/wiki/Marsha_M._Linehan">Marsha M. Linehan</a></li> <li><a href="https://en.wikipedia.org/wiki/Vittorio_Guidano">Vittorio Guidano</a></li> <li><a href="https://en.wikipedia.org/wiki/Les_Greenberg">Les Greenberg</a></li> <li><a href="https://en.wikipedia.org/wiki/William_Richard_Miller">William R. Miller</a></li> <li><a href="https://en.wikipedia.org/wiki/Steven_C._Hayes">Steven C. Hayes</a></li> <li><a href="https://en.wikipedia.org/wiki/Michael_White_(psychotherapist)">Michael White</a></li> <li><a href="https://en.wikipedia.org/wiki/Jeffrey_Young_(psychologist)">Jeffrey Young</a></li> <li><a href="https://en.wikipedia.org/wiki/Peter_Fonagy">Peter Fonagy</a></li></ul> </div></td></tr><tr><th>Associations</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Association_for_the_Advancement_of_Psychotherapy">Association for the Advancement of Psychotherapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Association_for_Applied_Psychophysiology_and_Biofeedback">Association for Applied Psychophysiology and Biofeedback</a></li> <li><a href="https://en.wikipedia.org/wiki/Association_for_Behavioral_and_Cognitive_Therapies">Association for Behavioral and Cognitive Therapies</a></li> <li><a href="https://en.wikipedia.org/wiki/Association_for_Behavior_Analysis_International">Association for Behavior Analysis International</a></li> <li><a href="https://en.wikipedia.org/wiki/European_Association_for_Psychotherapy">European Association for Psychotherapy</a></li> <li><a href="https://en.wikipedia.org/wiki/Society_for_Psychotherapy_Research">Society for Psychotherapy Research</a></li> <li><a href="https://en.wikipedia.org/wiki/World_Council_for_Psychotherapy">World Council for Psychotherapy</a></li></ul> </div></td></tr><tr><td colspan="2"><div> <a href="https://en.wikipedia.org/wiki/Category:Psychotherapy">Category</a></div></td></tr></tbody></table></div></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/Q238584#identifiers"></a></span></div></th></tr><tr><th>International</th><td><div><ul><li><span><a href="https://isni.org/isni/0000000083394180">ISNI</a></span></li><li><span><a href="https://viaf.org/viaf/14772266">VIAF</a></span></li><li><span><a href="https://d-nb.info/gnd/118568779">GND</a></span></li><li><span><a href="https://id.worldcat.org/fast/1717157">FAST</a></span></li><li><span><a href="https://id.oclc.org/worldcat/entity/E39PBJqVWfRTMQ6DBChjby3mh3">WorldCat</a></span></li></ul></div></td></tr><tr><th>National</th><td><div><ul><li><span><a href="https://id.loc.gov/authorities/n80005655">United States</a></span></li><li><span><a href="https://catalogue.bnf.fr/ark:/12148/cb11910720m">France</a></span></li><li><span><a href="https://data.bnf.fr/ark:/12148/cb11910720m">BnF data</a></span></li><li><span><a href="https://id.ndl.go.jp/auth/ndlna/00446672">Japan</a></span></li><li><span><span><a href="https://opac.sbn.it/nome/CFIV017895">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=xx0004924&amp;CON_LNG=ENG">Czech Republic</a></span></li><li><span><a href="https://datos.bne.es/resource/XX992534">Spain</a></span></li><li><span><a href="http://id.bnportugal.gov.pt/aut/catbnp/59750">Portugal</a></span></li><li><span><a href="http://data.bibliotheken.nl/id/thes/p068512120">Netherlands</a></span></li><li><span><a href="https://authority.bibsys.no/authority/rest/authorities/html/90084081">Norway</a></span></li><li><span><span><a href="https://kopkatalogs.lv/F?func=direct&amp;local_base=lnc10&amp;doc_number=000056741&amp;P_CON_LNG=ENG">Latvia</a></span></span></li><li><span><a href="https://catalogue.nlg.gr/cgi-bin/koha/opac-authoritiesdetail.pl?authid=86717">Greece</a></span></li><li><span><a href="https://lod.nl.go.kr/resource/KAC2018P3909">Korea</a></span></li><li><span><a href="https://libris.kb.se/b8nqrg3v137p87x">Sweden</a></span></li><li><span><a href="https://dbn.bn.org.pl/descriptor-details/9810638311505606">Poland</a></span></li><li><span><span>Vatican</span></span></li><li><span><a href="https://www.nli.org.il/en/authorities/987007278582605171">Israel</a></span></li><li><span><a href="https://cantic.bnc.cat/registre/981058518640906706">Catalonia</a></span></li><li><span><a href="https://bukinet-mreza.primo.exlibrisgroup.com/discovery/authfulldisplay?&amp;context=L&amp;vid=385BUKINET_NETWORK:VU1_UNION&amp;lang=en&amp;docid=981005663154809366">Croatia</a></span></li></ul></div></td></tr><tr><th>Academics</th><td><div><ul><li><span><a href="https://ci.nii.ac.jp/author/DA0031622X?l=en">CiNii</a></span></li></ul></div></td></tr><tr><th>Artists</th><td><div><ul><li><span><a href="https://musicbrainz.org/artist/6ae91c45-b30d-48b9-806b-ee83a2bc845e">MusicBrainz</a></span><ul><li><span><span><a href="https://musicbrainz.org/artist/fc745f24-d127-4171-8d63-22a2e566cea2">2</a></span></span></li></ul></li></ul></div></td></tr><tr><th>People</th><td><div><ul><li><span><a href="https://trove.nla.gov.au/people/898680">Trove</a></span></li><li><span><a href="https://www.deutsche-biographie.de/118568779.html?language=en">Deutsche Biographie</a></span></li><li><span><a href="https://www.deutsche-digitale-bibliothek.de/person/gnd/118568779">DDB</a></span></li></ul></div></td></tr><tr><th>Other</th><td><div><ul><li><span><a href="https://www.idref.fr/026961245">IdRef</a></span></li><li><span><span><a href="https://openlibrary.org/works/OL44765A?mode=all">Open Library</a></span></span></li><li><span><a href="https://snaccooperative.org/ark:/99166/w6n58krc">SNAC</a></span></li><li><span><a href="https://lux.collections.yale.edu/view/person/7549f78d-a640-4bc1-9021-f45dec3da073">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div> </section> https://en.wikipedia.org/wiki/David_Rosenhan SZy9aACCjMpbszqCgdcefcwN2DBs-3-6T2duUw== Tue, 15 Sep 2026 08:58:38 +0000 Research <div><h2>Research</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=David_Rosenhan&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div><table><tbody><tr><td></td><td><div><div><b>This section has multiple issues.</b> Please help <b><a href="https://en.wikipedia.org/wiki/Special:EditPage/David_Rosenhan">improve it</a></b> or discuss these issues on the <b><a href="https://en.wikipedia.org/wiki/Talk:David_Rosenhan">talk page</a></b>. <small><i>(<a href="https://en.wikipedia.org/wiki/Help:Maintenance_template_removal">Learn how and when to remove these messages</a>)</i></small> <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 scientific article <b>needs additional <a href="https://en.wikipedia.org/wiki/Wikipedia:Scientific_citation_guidelines">citations</a> to <a href="https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources#Scholarship">secondary or tertiary sources</a></b>.<span> Help add sources such as review articles, monographs, or textbooks. Please also establish the relevance for any <a href="https://en.wikipedia.org/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources">primary research articles</a> cited. Unsourced or poorly sourced material may be challenged and removed.</span> <span><i>(<span>November 2019</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><table><tbody><tr><td><div><span><a href="https://en.wikipedia.org/wiki/File:Wiki_letter_w_cropped.svg"></a></span></div></td><td><div>This section <b>needs expansion</b> with: a more complete, sourced description of the research emphases reflected in the subject&#39;s obituaries and publication list. You can help by <a href="https://en.wikipedia.org/w/index.php?title=David_Rosenhan&amp;action=edit&amp;section=">adding missing information</a>. <span><i>(<span>November 2019</span>)</i></span></div></td></tr></tbody></table> </div> </div><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>Rosenhan believed that there are seven main features of psychological abnormality: suffering; maladaptiveness; vividness and unconventionality; unpredictability and loss of control; irrationality and incomprehensibility; observer discomfort; and violation of moral and ideal standards.^{<span><span>[</span>6<span>]</span></span>}</p><p>In 1973, Rosenhan published &quot;On Being Sane In Insane Places&quot;,^{<span><span>[</span>7<span>]</span></span>} which describes what is now known as the <a href="https://en.wikipedia.org/wiki/Rosenhan_experiment">Rosenhan experiment</a>. In this study report, Rosenhan uses &quot;hard labeling&quot;^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Please_clarify"><span>clarification needed</span></a></i><span>]</span>} to argue that mental illnesses are manifested solely as a result of societal influence.^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i><span>]</span>} The study experiments arranged for eight individuals with no history of psychopathology to attempt admission into twelve psychiatric hospitals, all with the purpose of obtaining admission with a diagnosis of schizophrenia or bipolar disorder.^{<span><span>[</span>8<span>]</span></span>} The report describes psychiatrists then attempting to treat the individuals using psychiatric medications; all eight were described as being self-discharged within 7 to 52 days, with an average stay of 19 days, after having stated that they accepted their diagnosis.^{<span><span>[</span>8<span>]</span></span>} Later,^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items"><span>when?</span></a></i><span>]</span>} a research and teaching hospital challenged Rosenhan to perform a similar experiment involving its own diagnosis and admission procedures, where psychiatric staff were warned that at least one pseudo-patient might be sent to their institution.^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i><span>]</span>} In that study, 41 out of 193 new patients were believed by at least one staff member to be actors; in fact, Rosenhan reports not having sent any actors.^{<span><span>[</span>8<span>]</span></span>} From the results of his experiment, Rosenhan concluded that, &quot;It is clear that we cannot distinguish the sane from the insane in psychiatric hospitals&quot;.^{<span><span>[</span>8<span>]</span></span>} Thus, that existing forms of diagnosis were grossly inaccurate in distinguishing individuals without mental disorders from those with mental disorders, a conclusion that resulted in great controversy.^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i><span>]</span>}</p><p>The Rosenhan experiment can be described as addressing the relationship between psychiatric and medical diagnoses and <a href="https://en.wikipedia.org/wiki/Labeling_theory">labeling theory</a>,^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions"><span>according to whom?</span></a></i><span>]</span>} theorising that deviance is a product of external judgements that can modify an individual&#39;s self-identity and change how others respond to the labeled person.^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions"><span>according to whom?</span></a></i><span>]</span>}^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i><span>]</span>} By this description, by negatively labeling those seen as deviant from standard cultural norms, the behavior of individuals may be adjusted to coincide with the terms used to describe them.^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i><span>]</span>} In short, by actively labeling certain acts as deviant and others as normal, distinct stereotypes are created.^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions"><span>according to whom?</span></a></i><span>]</span>}^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span>citation needed</span></a></i><span>]</span>}</p><section><div><h3>Criticism of research</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=David_Rosenhan&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <table><tbody><tr><th colspan="2">External videos</th></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Nuvola_apps_kaboodle.svg"></a></span> <a href="https://www.c-span.org/video/?466007-1/qa-susannah-cahalan"><i>Q&amp;A</i> interview with Susannah Cahalan on <i>The Great Pretender</i>, November 10, 2019</a>, <a href="https://en.wikipedia.org/wiki/C-SPAN">C-SPAN</a></td></tr></tbody></table> <p>In a 2019 book on Rosenhan by author <a href="https://en.wikipedia.org/wiki/Susannah_Cahalan">Susannah Cahalan</a>, <i><a href="https://en.wikipedia.org/wiki/Susannah_Cahalan#Book_about_David_Rosenhan">The Great Pretender</a></i>, the veracity and validity of the Rosenhan experiment were questioned; Cahalan argues that Rosenhan never published further work on the experiment&#39;s data, nor did he produce a book on it that he had promised. Moreover, she presents her inability to find the experiment&#39;s subjects, save two – a Stanford graduate student who had experiences similar to Rosenhan&#39;s, and one whose positive psychiatric hospital experience was excluded from the published results.^{<span><span>[</span>9<span>]</span></span>} As noted by Alison Abbott in a review of the book in the journal <i><a href="https://en.wikipedia.org/wiki/Nature_(journal)">Nature</a></i>, <a href="https://en.wikipedia.org/wiki/Kenneth_J._Gergen">Kenneth J. Gergen</a>, a Stanford University colleague stated that &quot;some people in the department called him a bullshitter&quot;, a conclusion with which Cahalan appeared to be in agreement, although, Abbott writes, &quot;[s]he cannot be completely certain that Rosenhan cheated. But she is confident enough to call her engrossing, dismaying book <i>The Great Pretender</i>.&quot;^{<span><span>[</span>10<span>]</span></span>}</p> <p>Subsequent pseudo-patient studies similar to that of Rosenhan have had significant methodologic and other concerns.^{<span><span>[</span>11<span>]</span></span>}^{<span><span>[</span>12<span>]</span></span>}</p> </section> https://en.wikipedia.org/wiki/Antinomianism I3ioRvmFJSqK_5KoVSFFBGCMXVqleZh1DQkcGQ== Tue, 15 Sep 2026 08:58:38 +0000 Lutheran views <div><h3>Lutheran views</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Antinomianism&amp;action=edit&amp;section=3"><span>edit source</span></a><span>]</span></span></div><p>The term &quot;antinomianism&quot; was coined by Martin Luther during the Reformation, to criticize extreme interpretations of the new Lutheran <a href="https://en.wikipedia.org/wiki/Soteriology">soteriology</a>.^{<span><span>[</span>16<span>]</span></span>} The Lutheran Church benefited from early antinomian controversies by becoming more precise in distinguishing between <a href="https://en.wikipedia.org/wiki/Law_and_gospel">law and gospel</a> and justification and <a href="https://en.wikipedia.org/wiki/Sanctification_in_Christianity">sanctification</a>. Martin Luther developed 258 theses during his six antinomian disputations, which continue to provide doctrinal guidance to Lutherans today.^{<span><span>[</span>16<span>]</span></span>}</p><p>Upon hearing that he was being charged with the rejection of the Old Testament moral law,^{<span><span>[</span>23<span>]</span></span>}^{<span>:</span><span> </span><span>71</span><span> </span>} Luther responded: &quot;And truly, I wonder exceedingly, how it came to be imputed to me, that I should reject the Law or Ten Commandments, there being extant so many of my own expositions (and those of several sorts) upon the Commandments, which also are daily expounded, and used in our Churches, to say nothing of the Confession and Apology, and other books of ours.&quot;^{<span><span>[</span>23<span>]</span></span>} In his &quot;Introduction to Romans&quot;, Luther stated that saving faith is^{<span><span>[</span>24<span>]</span></span>}</p><blockquote><p><span><span> </span></span>... a living, creative, active and powerful thing, this faith. Faith cannot help doing good works constantly. It doesn&#39;t stop to ask if good works ought to be done, but before anyone asks, it already has done them and continues to do them without ceasing. Anyone who does not do good works in this manner is an unbeliever<span><span> </span></span>... Thus, it is just as impossible to separate faith and works as it is to separate heat and light from fire!</p></blockquote><p>The Lutheran Churches teach that God rewards good works done by Christians; the <a href="https://en.wikipedia.org/wiki/Apology_of_the_Augsburg_Confession">Apology of the Augsburg Confession</a> teaches: &quot;We also affirm what we have often said, that although justification and eternal life go along with faith, nevertheless, good works merit other bodily and spiritual rewards and degrees of reward. According to 1 Corinthians 3:8, &#39;Each will receive his wages according to his labor.<span>&#39;</span><span>&quot;</span>^{<span><span>[</span>25<span>]</span></span>}</p><p>The <a href="https://en.wikipedia.org/wiki/Lutheranism">Lutheran Churches</a> label antinomianism as a <a href="https://en.wikipedia.org/wiki/Heresy_in_Christianity">heresy</a>.^{<span><span>[</span>26<span>]</span></span>}</p><section><div><h4>First antinomian controversy</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Antinomianism&amp;action=edit&amp;section=4"><span>edit source</span></a><span>]</span></span></div> <p>As early as 1525, <a href="https://en.wikipedia.org/wiki/Johannes_Agricola">Johannes Agricola</a> advanced his idea, in his commentary on Luke, that the law was a futile attempt of God to work the restoration of mankind. He maintained that non-Christians were still held to the Mosaic law, while Christians were entirely free from it, being under the Gospel alone. He viewed <a href="https://en.wikipedia.org/wiki/Christian_views_on_sin">sin</a> as a malady or impurity rather than an offense that rendered the sinner guilty and damnable before God. The sinner was the subject of God&#39;s pity rather than of his wrath. To Agricola, the purpose of repentance was to abstain from evil rather than the contrition of a guilty conscience. The law had no role in repentance, which came about after one came to faith, and repentance was caused by the knowledge of the love of God alone.^{<span><span>[</span>16<span>]</span></span>}</p> <p>In contrast, <a href="https://en.wikipedia.org/wiki/Philipp_Melanchthon">Philipp Melanchthon</a> urged that repentance must precede <a href="https://en.wikipedia.org/wiki/Faith_in_Christianity#Lutheranism">faith</a> and that knowledge of the moral law is needed to produce repentance.^{<span><span>[</span>20<span>]</span></span>} He later wrote in the <a href="https://en.wikipedia.org/wiki/Augsburg_Confession">Augsburg Confession</a> that repentance has two parts. &quot;One is contrition, that is, terrors smiting the conscience through the knowledge of sin; the other is faith, which is born of the Gospel, or of absolution, and believes that for Christ&#39;s sake, sins are forgiven, comforts the conscience, and delivers it from terrors.&quot;^{<span><span>[</span>27<span>]</span></span>}</p> <p>Shortly after Melanchthon drew up the <i>1527 Articles of Visitation</i> in June, Agricola began to be verbally aggressive toward him, but Martin Luther succeeded in smoothing out the difficulty at <a href="https://en.wikipedia.org/wiki/Torgau">Torgau</a> in December 1527. However, Agricola did not change his ideas and later depicted Luther as disagreeing with him. After Agricola moved to Wittenberg, he maintained that the law must be used in the courthouse but it must not be used in the church. He said that repentance comes from hearing the good news only and does not precede but rather follows faith. He continued to disseminate this doctrine in books, despite receiving various warnings from Luther.^{<span><span>[</span>16<span>]</span></span>}</p> <p>Luther, with reluctance, at last, believed that he had to make a public comment against antinomianism and its promoters in 1538 and 1539. Agricola apparently yielded, and Luther&#39;s book <i>Against the Antinomians</i> (1539)^{<span><span>[</span>23<span>]</span></span>} was to serve as Agricola&#39;s recantation. This was the first use of the term Antinomian.^{<span><span>[</span>19<span>]</span></span>}^{<span><span>[</span>28<span>]</span></span>} But the conflict flared up again, and Agricola sued Luther. He said that Luther had slandered him in his disputations, <i>Against the Antinomians</i>, and in his <i>On the Councils and Churches</i> (1539). But before the case could be brought to trial, Agricola left the city, even though he had bound himself to remain at <a href="https://en.wikipedia.org/wiki/Wittenberg">Wittenberg</a>, and moved to <a href="https://en.wikipedia.org/wiki/Berlin">Berlin</a> where he had been offered a position as preacher to the court. After his arrival there, he made peace with the <a href="https://en.wikipedia.org/wiki/Saxons">Saxons</a>, acknowledged his &quot;error&quot;, and gradually conformed his doctrine to that which he had before opposed and assailed. He still used such terms as &#39;gospel&#39; and &#39;repentance&#39; in a different manner from Luther.^{<span><span>[</span>16<span>]</span></span>}</p> </section><section><div><h4>Second antinomian controversy</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Antinomianism&amp;action=edit&amp;section=5"><span>edit source</span></a><span>]</span></span></div> <p>The antinomian doctrine, however, was not eliminated from Lutheranism. Melanchthon and those who agreed with him, called <a href="https://en.wikipedia.org/wiki/Philippists">Philippists</a>, were checked by the <a href="https://en.wikipedia.org/wiki/Gnesio-Lutherans">Gnesio-Lutherans</a> in the Second Antinomian Controversy during the <a href="https://en.wikipedia.org/wiki/Augsburg_Interim">Augsburg Interim</a>. The Philippists ascribed to the Gospel alone the ability to work repentance, to the exclusion of the law. They blurred the distinction between Law and Gospel by considering the Gospel itself to be a moral law. They did not identify Christ&#39;s fulfillment of the law with the commandments which humans are expected to follow.^{<span><span>[</span>16<span>]</span></span>}</p> <p>As a result, the <a href="https://en.wikipedia.org/wiki/Book_of_Concord">Book of Concord</a> rejects antinomianism in the last confession of faith. The <a href="https://en.wikipedia.org/wiki/Formula_of_Concord">Formula of Concord</a> rejects antinomianism in the fifth article, <i>On the Law and the Gospel</i>^{<span><span>[</span>29<span>]</span></span>} and in the sixth article, <i>On the Third Use of the Law</i>.^{<span><span>[</span>30<span>]</span></span>}</p> </section> https://en.wikipedia.org/wiki/Millennium_Prize_Problems ZSZjH9LbOx-izErDn9wapWhuJz5A7AKWPSzbcw== Tue, 15 Sep 2026 08:48:03 +0000 Seven mathematical problems with a US$1 million prize for each solution <section><div>Seven mathematical problems with a US$1 million prize for each solution</div> <div>This article is about the math prizes. For the technology prize, see <a href="https://en.wikipedia.org/wiki/Millennium_Technology_Prize">Millennium Technology Prize</a>.</div><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Millennium_Prize_Problems">Millennium Prize Problems</a></th></tr><tr><td> <ul><li><a href="https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture">Birch and Swinnerton-Dyer conjecture</a></li> <li><a href="https://en.wikipedia.org/wiki/Hodge_conjecture">Hodge conjecture</a></li> <li><a href="https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness">Navier–Stokes existence and smoothness</a> (solution claimed)</li> <li><a href="https://en.wikipedia.org/wiki/P_versus_NP_problem">P versus NP problem</a></li> <li><a href="https://en.wikipedia.org/wiki/Poincaré_conjecture">Poincaré conjecture</a> (solved)</li> <li><a href="https://en.wikipedia.org/wiki/Riemann_hypothesis">Riemann hypothesis</a></li> <li><a href="https://en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap">Yang–Mills existence and mass gap</a></li></ul></td> </tr><tr><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Millennium_Prize_Problems"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Millennium_Prize_Problems"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Millennium_Prize_Problems"><abbr>e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>Millennium Prize Problems</b> are seven well-known complex mathematical problems selected by the <a href="https://en.wikipedia.org/wiki/Clay_Mathematics_Institute">Clay Mathematics Institute</a> in 2000. The Clay Institute has pledged to pay one million <a href="https://en.wikipedia.org/wiki/United_States_dollar">US dollars</a> for the first correct solution to each problem.</p> <p>The Clay Mathematics Institute officially designated the title <b>Millennium Problem</b> for the seven unsolved mathematical problems, the <a href="https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture">Birch and Swinnerton-Dyer conjecture</a>, <a href="https://en.wikipedia.org/wiki/Hodge_conjecture">Hodge conjecture</a>, <a href="https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness">Navier–Stokes existence and smoothness</a>, <a href="https://en.wikipedia.org/wiki/P_versus_NP_problem">P versus NP problem</a>, <a href="https://en.wikipedia.org/wiki/Riemann_hypothesis">Riemann hypothesis</a>, <a href="https://en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap">Yang–Mills existence and mass gap</a>, and the <a href="https://en.wikipedia.org/wiki/Poincaré_conjecture">Poincaré conjecture</a> at the Millennium Meeting held on May 24, 2000. Thus, on the official website of the Clay Mathematics Institute, these seven problems are officially called the <b>Millennium Problems</b>.</p> <p><span>As of 2026</span>^{<a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit"><span>[</span>update<span>]</span></a>}, the only Millennium Prize problem to have been officially declared solved is the Poincaré conjecture. The Clay Institute awarded the monetary prize to Russian mathematician <a href="https://en.wikipedia.org/wiki/Grigori_Perelman">Grigori Perelman</a> in 2010. However, he declined the award because it was not also offered to <a href="https://en.wikipedia.org/wiki/Richard_S._Hamilton">Richard S. Hamilton</a>, upon whose work Perelman built.^{<span><span>[</span>1<span>]</span></span>}</p> <p>In September 2026, the American <a href="https://en.wikipedia.org/wiki/Artificial_intelligence">artificial intelligence</a> company <a href="https://en.wikipedia.org/wiki/OpenAI">OpenAI</a> presented a proposed counterexample to the Navier–Stokes existence and smoothness problem, saying that they do not intend to claim the Millennium Prize for the result.^{<span><span>[</span>2<span>]</span></span>} As of September 2026, this result has yet to be verified by the Clay Institute, which describes the problem as &quot;active&quot;,^{<span><span>[</span>3<span>]</span></span>} or by the independent mathematical community, and is the subject of a <a href="https://en.wikipedia.org/wiki/Navier–Stokes_priority_controversy">priority dispute</a>.^{<span><span>[</span>4<span>]</span></span>}</p> </section><section><div><h2>Overview</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div> <p>The Clay Institute was inspired by a set of <a href="https://en.wikipedia.org/wiki/Hilbert&#39;s_problems">twenty-three problems</a> organized by the mathematician <a href="https://en.wikipedia.org/wiki/David_Hilbert">David Hilbert</a> in 1900 which were highly influential in driving the progress of mathematics in the twentieth century.^{<span><span>[</span>5<span>]</span></span>} The seven selected problems span a number of mathematical fields, namely <a href="https://en.wikipedia.org/wiki/Algebraic_geometry">algebraic geometry</a>, <a href="https://en.wikipedia.org/wiki/Arithmetic_geometry">arithmetic geometry</a>, <a href="https://en.wikipedia.org/wiki/Geometric_topology">geometric topology</a>, <a href="https://en.wikipedia.org/wiki/Mathematical_physics">mathematical physics</a>, <a href="https://en.wikipedia.org/wiki/Number_theory">number theory</a>, <a href="https://en.wikipedia.org/wiki/Partial_differential_equation">partial differential equations</a>, and <a href="https://en.wikipedia.org/wiki/Theoretical_computer_science">theoretical computer science</a>. Unlike Hilbert&#39;s problems, the problems selected by the Clay Institute were already renowned among professional mathematicians, with many actively working towards their resolution.^{<span><span>[</span>6<span>]</span></span>}</p> <p>The seven problems were officially announced by <a href="https://en.wikipedia.org/wiki/John_Tate_(mathematician)">John Tate</a> and <a href="https://en.wikipedia.org/wiki/Michael_Atiyah">Michael Atiyah</a> during a ceremony held on May 24, 2000 (at the amphithéâtre <a href="https://en.wikipedia.org/wiki/Marguerite_de_Navarre">Marguerite de Navarre</a>) in the <a href="https://en.wikipedia.org/wiki/Collège_de_France">Collège de France</a> in <a href="https://en.wikipedia.org/wiki/Paris">Paris</a>.^{<span><span>[</span>7<span>]</span></span>}</p> <p><a href="https://en.wikipedia.org/wiki/Grigori_Perelman">Grigori Perelman</a>, who had begun work on the <a href="https://en.wikipedia.org/wiki/Poincaré_conjecture">Poincaré conjecture</a> in the 1990s, released his proof in 2002 and 2003. His refusal of the Clay Institute&#39;s monetary prize in 2010 was widely covered in the media. In 2026, OpenAI claimed to resolve the Navier–Stokes existence and smoothness problem using an internal AI model, but this has yet to be independently verified.^{<span><span>[</span>2<span>]</span></span>}^{<span><span>[</span>4<span>]</span></span>} The other five Millennium Prize Problems remain unsolved, despite a large number of unsatisfactory proofs by both amateur and professional mathematicians.</p> <p><a href="https://en.wikipedia.org/wiki/Andrew_Wiles">Andrew Wiles</a>, as part of the Clay Institute&#39;s scientific advisory board, hoped that the choice of <a href="https://en.wikipedia.org/wiki/US$">US$</a>1 million prize money would popularize, among general audiences, both the selected problems as well as the &quot;excitement of mathematical endeavor&quot;.^{<span><span>[</span>8<span>]</span></span>} Another board member, <a href="https://en.wikipedia.org/wiki/Fields_Medal">Fields medalist</a> <a href="https://en.wikipedia.org/wiki/Alain_Connes">Alain Connes</a>, hoped that the publicity around the unsolved problems would help to combat the &quot;wrong idea&quot; among the public that mathematics would be &quot;overtaken by computers&quot;.^{<span><span>[</span>9<span>]</span></span>}</p> <p>Some mathematicians have been more critical. <a href="https://en.wikipedia.org/wiki/Anatoly_Vershik">Anatoly Vershik</a> characterized their monetary prize as &quot;show business&quot; representing the &quot;worst manifestations of present-day mass culture&quot;, and thought that there are more meaningful ways to invest in public appreciation of mathematics.^{<span><span>[</span>10<span>]</span></span>} He viewed the superficial media treatments of Perelman and his work, with disproportionate attention being placed on the prize value itself, as unsurprising. By contrast, Vershik praised the Clay Institute&#39;s direct funding of research conferences and young researchers. Vershik&#39;s comments were later echoed by Fields medalist <a href="https://en.wikipedia.org/wiki/Shing-Tung_Yau">Shing-Tung Yau</a>, who was additionally critical of the idea of a foundation taking actions to &quot;appropriate&quot; fundamental mathematical questions and &quot;attach its name to them&quot;.^{<span><span>[</span>11<span>]</span></span>}</p> </section><section><div><h2>Solved problems</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div> <section><div><h3>Poincaré conjecture</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Poincaré_conjecture">Poincaré conjecture</a></div> <figure><a href="https://en.wikipedia.org/wiki/File:P1S2all.jpg"></a><figcaption>A <a href="https://en.wikipedia.org/wiki/Compact_space">compact</a> 2-dimensional surface without <a href="https://en.wikipedia.org/wiki/Boundary_(topology)">boundary</a> is topologically <a href="https://en.wikipedia.org/wiki/Homeomorphism">homeomorphic</a> to a 2-sphere if every loop can be continuously tightened to a point. The Poincaré conjecture asserts that the same is true for 3-dimensional spaces.</figcaption></figure><p> In the field of <a href="https://en.wikipedia.org/wiki/Geometric_topology">geometric topology</a>, a two-dimensional <a href="https://en.wikipedia.org/wiki/Sphere">sphere</a> is characterized by the fact that it is the only <a href="https://en.wikipedia.org/wiki/Closed_manifold">closed</a> and <a href="https://en.wikipedia.org/wiki/Simply_connected_space">simply connected</a> two-dimensional surface. In 1904, <a href="https://en.wikipedia.org/wiki/Henri_Poincaré">Henri Poincaré</a> posed the question of whether an analogous statement holds true for three-dimensional shapes. This came to be known as the Poincaré conjecture, the precise formulation of which states:^{<span><span>[</span>12<span>]</span></span>}</p><blockquote><p>Any <a href="https://en.wikipedia.org/wiki/3-manifold">three-dimensional topological manifold</a> which is closed and simply-connected must be <a href="https://en.wikipedia.org/wiki/Homeomorphic">homeomorphic</a> to the <a href="https://en.wikipedia.org/wiki/3-sphere">3-sphere</a>.</p></blockquote> <p>Although the conjecture is usually stated in this form, it is equivalent (as was discovered in the 1950s) to pose it in the context of <a href="https://en.wikipedia.org/wiki/Smooth_manifolds">smooth manifolds</a> and <a href="https://en.wikipedia.org/wiki/Diffeomorphism">diffeomorphisms</a>.</p> <p>A proof of this conjecture, together with the more powerful <a href="https://en.wikipedia.org/wiki/Geometrization_conjecture">geometrization conjecture</a>, was given by <a href="https://en.wikipedia.org/wiki/Grigori_Perelman">Grigori Perelman</a> in 2002 and 2003. Perelman&#39;s solution completed <a href="https://en.wikipedia.org/wiki/Richard_S._Hamilton">Richard Hamilton</a>&#39;s program for the solution of the geometrization conjecture, which he had developed over the course of the preceding twenty years. Hamilton and Perelman&#39;s work revolved around Hamilton&#39;s <a href="https://en.wikipedia.org/wiki/Ricci_flow">Ricci flow</a>, which is a complicated system of <a href="https://en.wikipedia.org/wiki/Partial_differential_equation">partial differential equations</a> defined in the field of <a href="https://en.wikipedia.org/wiki/Riemannian_geometry">Riemannian geometry</a>.</p> <p>For his contributions to the theory of Ricci flow, Perelman was awarded the <a href="https://en.wikipedia.org/wiki/Fields_Medal">Fields Medal</a> in 2006. However, he declined to accept the prize.^{<span><span>[</span>13<span>]</span></span>} For his proof of the Poincaré conjecture, Perelman was awarded the Millennium Prize on March 18, 2010.^{<span><span>[</span>14<span>]</span></span>} However, he declined the award and the associated prize money, stating that Hamilton&#39;s contribution was no less than his own.^{<span><span>[</span>1<span>]</span></span>}</p> </section></section><section><div><h2>Active problems</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <section><div><h3>Navier–Stokes existence and smoothness</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness">Navier–Stokes existence and smoothness</a></div> <dl><dd><b><span><span><math> <semantics> <mrow> <mstyle> <mover> <mrow> <mover> <mrow> <munder> <mrow> <munder> <mfrac> <mrow> <mi>∂</mi> <mrow> <mi>u</mi> </mrow> </mrow> <mrow> <mi>∂</mi> <mi>t</mi> </mrow> </mfrac> <mo>⏟</mo> </munder> </mrow> <mrow> <mstyle> <mtable> <mtr> <mtd> <mrow> <mtext>Variation</mtext> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </munder> <mo>+</mo> <munder> <mrow> <munder> <mrow> <mo>(</mo> <mrow> <mi>u</mi> </mrow> <mo>⋅</mo> <mi>∇</mi> <mo>)</mo> <mrow> <mi>u</mi> </mrow> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow> <mstyle> <mtable> <mtr> <mtd> <mrow> <mtext>Convection</mtext> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </munder> </mrow> <mo>⏞</mo> </mover> </mrow> <mrow> <mtext>Inertia (per volume)</mtext> </mrow> </mover> <mover> <mrow> <mover> <mrow> <mrow> </mrow> <mo>−</mo> <munder> <mrow> <munder> <mrow> <mi>ν</mi> <msup> <mi>∇</mi> <mrow> <mn>2</mn> </mrow> </msup> <mrow> <mi>u</mi> </mrow> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow> <mtext>Diffusion</mtext> </mrow> </munder> <mo>=</mo> <munder> <mrow> <munder> <mrow> <mo>−</mo> <mi>∇</mi> <mi>w</mi> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow> <mstyle> <mtable> <mtr> <mtd> <mrow> <mtext>Internal</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mtext>source</mtext> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </munder> </mrow> <mo>⏞</mo> </mover> </mrow> <mrow> <mtext>Divergence of stress</mtext> </mrow> </mover> <mo>+</mo> <munder> <mrow> <munder> <mrow> <mi>g</mi> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow> <mstyle> <mtable> <mtr> <mtd> <mrow> <mtext>External</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mtext>source</mtext> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </munder> <mo>.</mo> </mstyle> </mrow> <annotation>{\displaystyle \overbrace {\underbrace {\frac {\partial \mathbf {u} }{\partial t}} _{\begin{smallmatrix}{\text{Variation}}\end{smallmatrix}}+\underbrace {(\mathbf {u} \cdot \nabla )\mathbf {u} } _{\begin{smallmatrix}{\text{Convection}}\end{smallmatrix}}} ^{\text{Inertia (per volume)}}\overbrace {{}-\underbrace {\nu \,\nabla ^{2}\mathbf {u} } _{\text{Diffusion}}=\underbrace {-\nabla w} _{\begin{smallmatrix}{\text{Internal}}\\{\text{source}}\end{smallmatrix}}} ^{\text{Divergence of stress}}+\underbrace {\mathbf {g} } _{\begin{smallmatrix}{\text{External}}\\{\text{source}}\end{smallmatrix}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aede081639f5810d30a7cf11270090be07145156" alt="{\displaystyle \overbrace {\underbrace {\frac {\partial \mathbf {u} }{\partial t}} _{\begin{smallmatrix}{\text{Variation}}\end{smallmatrix}}+\underbrace {(\mathbf {u} \cdot \nabla )\mathbf {u} } _{\begin{smallmatrix}{\text{Convection}}\end{smallmatrix}}} ^{\text{Inertia (per volume)}}\overbrace {{}-\underbrace {\nu \,\nabla ^{2}\mathbf {u} } _{\text{Diffusion}}=\underbrace {-\nabla w} _{\begin{smallmatrix}{\text{Internal}}\\{\text{source}}\end{smallmatrix}}} ^{\text{Divergence of stress}}+\underbrace {\mathbf {g} } _{\begin{smallmatrix}{\text{External}}\\{\text{source}}\end{smallmatrix}}.}" title=""/></span></b></dd></dl> <p>The <a href="https://en.wikipedia.org/wiki/Navier–Stokes_equations">Navier–Stokes equations</a> describe the motion of <a href="https://en.wikipedia.org/wiki/Fluid">fluids</a>, and are one of the pillars of <a href="https://en.wikipedia.org/wiki/Fluid_mechanics">fluid mechanics</a>. However, theoretical understanding of their solutions is incomplete, despite its importance in science and engineering. For the three-dimensional system of equations, and given some <a href="https://en.wikipedia.org/wiki/Initial_condition">initial conditions</a>, it was conjectured that <a href="https://en.wikipedia.org/wiki/Smooth_function">smooth solutions</a> always exist. This is called the <i><a href="https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness">Navier–Stokes existence and smoothness</a></i> problem. The problem, restricted to the case of an <a href="https://en.wikipedia.org/wiki/Incompressible_flow">incompressible flow</a>, is to prove either that smooth, globally defined solutions exist that meet certain conditions, or that they do not always exist and the equations break down.</p> <p>The official statement of the problem was given by <a href="https://en.wikipedia.org/wiki/Charles_Fefferman">Charles Fefferman</a>.^{<span><span>[</span>15<span>]</span></span>}</p> <section><div><h4>Claimed counter-example</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Navier–Stokes_priority_controversy">Navier–Stokes priority controversy</a></div> <p>On September 8, 2026, <a href="https://en.wikipedia.org/wiki/OpenAI">OpenAI</a> posted a claimed counterexample with a formalized proof. The counterexample awaits <a href="https://en.wikipedia.org/wiki/Scientific_validation">scientific validation</a>, but the Clay Mathematical Institute wrote that &quot;CMI shares in the excitement of the global mathematical community as we contemplate the announcement that the Navier-Stokes problem has apparently been settled.&quot;^{<span><span>[</span>16<span>]</span></span>}</p> <p>A <a href="https://en.wikipedia.org/wiki/Scientific_priority#Priority_disputes">priority dispute</a> started immediately. <a href="https://en.wikipedia.org/wiki/New_York_University">New York University</a> mathematics professor <a href="https://en.wikipedia.org/wiki/Tristan_Buckmaster">Tristan Buckmaster</a> said that OpenAI took advantage of non-public results derived by himself and <a href="https://en.wikipedia.org/wiki/Anthropic">Anthropic</a> mathematician <a href="https://en.wikipedia.org/wiki/Levent_Alpöge">Levent Alpöge</a>. He went on to say that OpenAI may have used his <a href="https://en.wikipedia.org/wiki/OpenAI_Codex_(AI_agent)">Codex</a> chat history. OpenAI denied seeing the work of Buckmaster or Alpöge before it was public, but said in a statement: &quot;While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.&quot;^{<span><span>[</span>17<span>]</span></span>}^{<span><span>[</span>18<span>]</span></span>}^{<span><span>[</span>19<span>]</span></span>} A later update claims that &quot;Following an investigation, we have confirmed that Buckmaster’s Codex prompts over the two months preceding this announcement and paper on September 8, 2026, could not have influenced the system in any way, including through training.&quot;^{<span><span>[</span>20<span>]</span></span>}</p> <p><a href="https://en.wikipedia.org/wiki/Martin_Bridson">Martin Bridson</a>, the president of the Clay Mathematics Institute, stressed that the Institute requires a solution to a Millennium problem to be in the form of <a href="https://en.wikipedia.org/wiki/Peer_review">peer-reviewed</a> publications, which would then be further scrutinised before the prize is awarded.^{<span><span>[</span>21<span>]</span></span>}</p> </section></section></section><section><div><h2>Unsolved problems</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div> <section><div><h3>Birch and Swinnerton-Dyer conjecture</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture">Birch and Swinnerton-Dyer conjecture</a></div> <p>This conjecture, named after <a href="https://en.wikipedia.org/wiki/Bryan_John_Birch">Bryan John Birch</a> and <a href="https://en.wikipedia.org/wiki/Peter_Swinnerton-Dyer">Peter Swinnerton-Dyer</a>, deals with certain types of equations: those defining <a href="https://en.wikipedia.org/wiki/Elliptic_curve">elliptic curves</a> over the <a href="https://en.wikipedia.org/wiki/Rational_number">rational numbers</a>. The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve <span>E</span> has <a href="https://en.wikipedia.org/wiki/Rank_of_an_elliptic_curve">rank</a> <span>r</span>, then the <a href="https://en.wikipedia.org/wiki/Hasse–Weil_zeta_function"><i>L</i>-function</a> <span><i>L</i>(<i>E</i>, <i>s</i>)</span> associated with it <a href="https://en.wikipedia.org/wiki/Order_of_vanishing">vanishes to order</a> <span>r</span> at <span><i>s</i> = 1</span>.</p> <p>The official statement of the <a href="https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture">Birch and Swinnerton-Dyer conjecture</a> was given by <a href="https://en.wikipedia.org/wiki/Andrew_Wiles">Andrew Wiles</a>.^{<span><span>[</span>22<span>]</span></span>}</p> </section><section><div><h3>Hodge conjecture</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Hodge_conjecture">Hodge conjecture</a></div> <p>The Hodge conjecture is that for <a href="https://en.wikipedia.org/wiki/Projective_space">projective</a> <a href="https://en.wikipedia.org/wiki/Algebraic_variety">algebraic varieties</a>, <a href="https://en.wikipedia.org/wiki/Hodge_cycle">Hodge cycles</a> are rational <a href="https://en.wikipedia.org/wiki/Linear_combination">linear combinations</a> of <a href="https://en.wikipedia.org/wiki/Algebraic_cycle">algebraic cycles</a>.</p> <dl><dd><span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>Hdg</mi> <mrow> <mi>k</mi> </mrow> </msup> <mo>⁡</mo> <mo>(</mo> <mi>X</mi> <mo>)</mo> <mo>=</mo> <msup> <mi>H</mi> <mrow> <mn>2</mn> <mi>k</mi> </mrow> </msup> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mrow> <mi>Q</mi> </mrow> <mo>)</mo> <mo>∩</mo> <msup> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> </mrow> </msup> <mo>(</mo> <mi>X</mi> <mo>)</mo> <mo>.</mo> </mstyle> </mrow> <annotation>{\displaystyle \operatorname {Hdg} ^{k}(X)=H^{2k}(X,\mathbb {Q} )\cap H^{k,k}(X).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbc789dc15326adb8dbfe004ead64bbfe0944319" alt="{\displaystyle \operatorname {Hdg} ^{k}(X)=H^{2k}(X,\mathbb {Q} )\cap H^{k,k}(X).}" title=""/></span></dd></dl> <p>We call this the group of <i>Hodge classes</i> of degree 2<i>k</i> on <i>X</i>.</p> <p>The modern statement of the Hodge conjecture is:</p> <dl><dd><dl><dd>Let <i>X</i> be a non-singular complex projective variety. Then every Hodge class on <i>X</i> is a linear combination with rational coefficients of the <a href="https://en.wikipedia.org/wiki/Cohomology">cohomology classes</a> of complex subvarieties of <i>X</i>.</dd></dl></dd></dl> <p>The official statement of the problem was given by <a href="https://en.wikipedia.org/wiki/Pierre_Deligne">Pierre Deligne</a>.^{<span><span>[</span>23<span>]</span></span>}</p> </section><section><div><h3>P versus NP</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/P_versus_NP_problem">P versus NP problem</a></div> <figure><a href="https://en.wikipedia.org/wiki/File:P_np_np-complete_np-hard.svg"></a><figcaption><a href="https://en.wikipedia.org/wiki/Euler_diagram">Euler diagram</a> for <b><a href="https://en.wikipedia.org/wiki/P_(complexity)">P</a></b>, <b><a href="https://en.wikipedia.org/wiki/NP_(complexity)">NP</a></b>, <b>NP</b>-complete, and <b>NP</b>-hard set of problems (excluding the empty language and its complement, which belong to <b>P</b> but are not <b>NP</b>-complete)</figcaption></figure> <p>The question is whether or not, for all problems for which an algorithm can <i>verify</i> a given solution quickly (that is, in <a href="https://en.wikipedia.org/wiki/Polynomial_time#Polynomial_time">polynomial time</a>), an algorithm can also <i>find</i> that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are also in P. This is generally considered one of the most important open questions in <a href="https://en.wikipedia.org/wiki/Mathematics">mathematics</a> and <a href="https://en.wikipedia.org/wiki/Computation">theoretical computer science</a> as it has far-reaching consequences to other problems in <a href="https://en.wikipedia.org/wiki/Mathematics">mathematics</a>, to <a href="https://en.wikipedia.org/wiki/Biology">biology</a>,^{<span><span>[</span>24<span>]</span></span>} <a href="https://en.wikipedia.org/wiki/Philosophy">philosophy</a>^{<span><span>[</span>25<span>]</span></span>} and to <a href="https://en.wikipedia.org/wiki/Cryptography">cryptography</a> (see <a href="https://en.wikipedia.org/wiki/P_versus_NP_problem#Consequences_of_solution">P versus NP problem proof consequences</a>). A common example of an NP problem not known to be in P is the <a href="https://en.wikipedia.org/wiki/Boolean_satisfiability_problem">Boolean satisfiability problem</a>.</p> <p>Most mathematicians and computer scientists expect that P<span> </span>≠<span> </span>NP; however, it remains unproven.^{<span><span>[</span>26<span>]</span></span>}</p> <p>The official statement of the problem was given by <a href="https://en.wikipedia.org/wiki/Stephen_Cook">Stephen Cook</a>.^{<span><span>[</span>27<span>]</span></span>}</p> </section><section><div><h3>Riemann hypothesis</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Riemann_hypothesis">Riemann hypothesis</a></div> <figure><a href="https://en.wikipedia.org/wiki/File:RiemannCriticalLine.svg"></a><figcaption>The real part (red) and imaginary part (blue) of the <a href="https://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann zeta function</a> <span><span><math> <semantics> <mrow> <mstyle> <mi>ζ</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle \zeta (s)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbd45922057e4d7a5718ce5ed703ab493c63897a" alt="{\displaystyle \zeta (s)}" title=""/></span> along the critical line <span><span><math> <semantics> <mrow> <mstyle> <mi>ζ</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle \zeta (s)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbd45922057e4d7a5718ce5ed703ab493c63897a" alt="{\displaystyle \zeta (s)}" title=""/></span> = <span><span>1</span><span>⁄</span><span>2</span></span>. The first nontrivial <a href="https://en.wikipedia.org/wiki/Zero_of_a_function">zeros</a> can be seen at <span><span><math> <semantics> <mrow> <mstyle> <mi>I</mi> <mi>m</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> <mo>=</mo> <mo>±</mo> <mn>14.135</mn> <mo>,</mo> <mo>±</mo> <mn>21.022</mn> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle Im(s)=\pm 14.135,\pm 21.022,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ed9f126f36fd0ad2f87b2299be1a1ec19e3a04e" alt="{\displaystyle Im(s)=\pm 14.135,\pm 21.022,}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mo>±</mo> <mn>25.011</mn> </mstyle> </mrow> <annotation>{\displaystyle \pm 25.011}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8432eda208932f7e2623dd8a9ebed3fbb9c2a03" alt="{\displaystyle \pm 25.011}" title=""/></span>.</figcaption></figure> <p>The <a href="https://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann zeta function</a> <span><span><math> <semantics> <mrow> <mstyle> <mi>ζ</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle \zeta (s)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbd45922057e4d7a5718ce5ed703ab493c63897a" alt="{\displaystyle \zeta (s)}" title=""/></span> is a <a href="https://en.wikipedia.org/wiki/Function_(mathematics)">function</a> whose <a href="https://en.wikipedia.org/wiki/Argument_of_a_function">arguments</a> may be any <a href="https://en.wikipedia.org/wiki/Complex_number">complex number</a> other than 1, and whose values are also complex. This function can be expressed as the infinite sum of the power of a <a href="https://en.wikipedia.org/wiki/Unit_fraction">unit fraction</a>:^{<span><span>[</span>28<span>]</span></span>}<span><span><math> <semantics> <mrow> <mstyle> <mi>ζ</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>∞</mi> </mrow> </munderover> <mrow> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow> <mi>s</mi> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow> <mfrac> <mn>1</mn> <msup> <mn>1</mn> <mrow> <mi>s</mi> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow> <mfrac> <mn>1</mn> <msup> <mn>2</mn> <mrow> <mi>s</mi> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow> <mfrac> <mn>1</mn> <msup> <mn>3</mn> <mrow> <mi>s</mi> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>.</mo> </mstyle> </mrow> <annotation>{\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1^{s}}}+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+\cdots .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9bd691fccd9541432c60dc5ad456a236fcd395b" alt="{\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1^{s}}}+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+\cdots .}" title=""/></span>Its <a href="https://en.wikipedia.org/wiki/Analytical_continuation">analytical continuation</a> has <a href="https://en.wikipedia.org/wiki/Zero_of_a_function">zeros</a> at the negative even integers; that is, <span><span><math> <semantics> <mrow> <mstyle> <mi>ζ</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle \zeta (s)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18590bfd730d03c72bb83e3a7e5affa9388dfc10" alt="{\displaystyle \zeta (s)=0}" title=""/></span> when <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/01d131dfd7673938b947072a13a9744fe997e632" alt="{\displaystyle s}" title=""/></span> is one of <span><span><math> <semantics> <mrow> <mstyle> <mo>−</mo> <mn>2</mn> </mstyle> </mrow> <annotation>{\displaystyle -2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46e5b5b462e546b1d3d7e5f9a23efece405b2e78" alt="{\displaystyle -2}" title=""/></span>, <span><span><math> <semantics> <mrow> <mstyle> <mo>−</mo> <mn>4</mn> </mstyle> </mrow> <annotation>{\displaystyle -4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/addc8519724f81b43a6883c5eb2c996f9fc2996f" alt="{\displaystyle -4}" title=""/></span>, <span><span><math> <semantics> <mrow> <mstyle> <mo>−</mo> <mn>6</mn> </mstyle> </mrow> <annotation>{\displaystyle -6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d4ef97af022d24d218c5548f54aa789fc647237" alt="{\displaystyle -6}" title=""/></span>, and so on. These are called its trivial zeros. However, the negative even integers are not the only values for which the zeta function is zero. The other ones are called nontrivial zeros. The Riemann hypothesis is concerned with the locations of these nontrivial zeros, and states that:</p> <blockquote><p>The real part of every nontrivial zero of the Riemann zeta function is <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation>{\textstyle {\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/990274ef9b8937f955b175041b7cd0d5a2d482ec" alt="{\textstyle {\frac {1}{2}}}" title=""/></span>.</p></blockquote> <p>The Riemann hypothesis is that all <a href="https://en.wikipedia.org/wiki/Triviality_(mathematics)">nontrivial</a> zeros of the <a href="https://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann zeta function</a> have a real part of <span><span>⁠</span><span><span>1</span><span>/</span><span>2</span></span><span>⁠</span></span>. A proof or disproof of this would have far-reaching implications in <a href="https://en.wikipedia.org/wiki/Number_theory">number theory</a>, especially for the distribution of <a href="https://en.wikipedia.org/wiki/Prime_number">prime numbers</a>. This was <a href="https://en.wikipedia.org/wiki/Hilbert&#39;s_eighth_problem">Hilbert&#39;s eighth problem</a>, and is still considered an important <a href="https://en.wikipedia.org/wiki/Open_problem">open problem</a> a century later.</p> <p>The problem has been well known ever since it was originally posed by <a href="https://en.wikipedia.org/wiki/Bernhard_Riemann">Bernhard Riemann</a> in 1859. The Clay Institute&#39;s exposition of the problem was given by <a href="https://en.wikipedia.org/wiki/Enrico_Bombieri">Enrico Bombieri</a>.^{<span><span>[</span>29<span>]</span></span>}</p> </section><section><div><h3>Yang–Mills existence and mass gap</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap">Yang–Mills existence and mass gap</a></div> <p>In <a href="https://en.wikipedia.org/wiki/Quantum_field_theory">quantum field theory</a>, the <a href="https://en.wikipedia.org/wiki/Mass_gap">mass gap</a> is the difference in energy between the vacuum and the next lowest <a href="https://en.wikipedia.org/wiki/Energy_state">energy state</a>. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle.</p> <p>For a given real field <span><span><math> <semantics> <mrow> <mstyle> <mi>ϕ</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle \phi (x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/546b660b2f3cfb5f34be7b3ed8371d54f5c74227" alt="{\displaystyle \phi (x)}" title=""/></span>, we can say that the theory has a mass gap if the <a href="https://en.wikipedia.org/wiki/Correlation_function_(quantum_field_theory)">two-point function</a> has the property</p> <dl><dd><span><span><math> <semantics> <mrow> <mstyle> <mo>⟨</mo> <mi>ϕ</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> <mi>ϕ</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> <mo>⟩</mo> <mo>∼</mo> <munder> <mo>∑</mo> <mrow> <mi>n</mi> </mrow> </munder> <msub> <mi>A</mi> <mrow> <mi>n</mi> </mrow> </msub> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <msub> <mi>Δ</mi> <mrow> <mi>n</mi> </mrow> </msub> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle \langle \phi (0,t)\phi (0,0)\rangle \sim \sum _{n}A_{n}\exp \left(-\Delta _{n}t\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b30c3a13317e64c367221ea3860f26d8589f81f" alt="{\displaystyle \langle \phi (0,t)\phi (0,0)\rangle \sim \sum _{n}A_{n}\exp \left(-\Delta _{n}t\right)}" title=""/></span></dd></dl> <p>with <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>Δ</mi> <mrow> <mn>0</mn> </mrow> </msub> <mo>&gt;</mo> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle \Delta _{0}&gt;0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2060d33ac218f529c9b1f24eab707b22b4842a8" alt="{\displaystyle \Delta _{0}&gt;0}" title=""/></span> being the lowest energy value in the <a href="https://en.wikipedia.org/wiki/Spectrum_(functional_analysis)">spectrum</a> of the <a href="https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)">Hamiltonian</a> and thus the mass gap. This quantity, easy to generalize to other fields, is what is generally measured in lattice computations.</p> <p>Quantum <a href="https://en.wikipedia.org/wiki/Yang–Mills_theory">Yang–Mills theory</a> is the current grounding for the majority of theoretical applications of thought to the reality and potential realities of <a href="https://en.wikipedia.org/wiki/Elementary_particle_physics">elementary particle physics</a>.^{<span><span>[</span>30<span>]</span></span>} The theory is a generalization of the <a href="https://en.wikipedia.org/wiki/James_Clerk_Maxwell">Maxwell</a> theory of <a href="https://en.wikipedia.org/wiki/Electromagnetism">electromagnetism</a> where the <i>chromo</i>-electromagnetic field itself carries charge. As a classical field theory it has solutions which travel at the speed of light so that its quantum version should describe massless particles (<a href="https://en.wikipedia.org/wiki/Gluon">gluons</a>). However, the postulated phenomenon of <a href="https://en.wikipedia.org/wiki/Color_confinement">color confinement</a> permits only bound states of gluons, forming massive particles. This is the <a href="https://en.wikipedia.org/wiki/Mass_gap">mass gap</a>. Another aspect of confinement is <a href="https://en.wikipedia.org/wiki/Asymptotic_freedom">asymptotic freedom</a> which makes it conceivable that <a href="https://en.wikipedia.org/wiki/Quantum_Yang-Mills_theory">quantum Yang–Mills theory</a> exists without restriction to low energy scales. The problem is to establish rigorously the existence of the quantum Yang–Mills theory and a mass gap.</p> <dl><dd><dl><dd>Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on <span><span><math> <semantics> <mrow> <mstyle> <msup> <mrow> <mi>R</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle \mathbb {R} ^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4abb9b9dab94f7b25a4210364f0f9032704bfb9" alt="{\displaystyle \mathbb {R} ^{4}}" title=""/></span> and has a mass gap Δ &gt; 0. Existence includes establishing axiomatic properties at least as strong as those cited in Streater &amp; Wightman (1964),^{<span><span>[</span>31<span>]</span></span>} Osterwalder &amp; Schrader (1973),^{<span><span>[</span>32<span>]</span></span>} and Osterwalder &amp; Schrader (1975).^{<span><span>[</span>33<span>]</span></span>}</dd></dl></dd></dl> <p>The official statement of the problem was given by <a href="https://en.wikipedia.org/wiki/Arthur_Jaffe">Arthur Jaffe</a> and <a href="https://en.wikipedia.org/wiki/Edward_Witten">Edward Witten</a>.^{<span><span>[</span>34<span>]</span></span>}</p> </section></section><section><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div> <div> <div><ol><li><span><span>1</span> <span>2</span></span> <span><cite><a href="https://www.interfax.ru/russia/143603">&quot;Последнее &quot;нет&quot; доктора Перельмана&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Interfax">Interfax</a></i>. July 1, 2010<span>. Retrieved <span>25 January</span> 2024</span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite><a href="https://openai.com/index/navier-stokes-solution/">&quot;On the Navier–Stokes Millennium Prize Problem&quot;</a>. <i>OpenAI</i><span>. Retrieved <span>2026-09-08</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.claymath.org/millennium/navier-stokes-equation/">&quot;Navier-Stokes Equation&quot;</a>. <i>Clay Mathematics Institute</i><span>. Retrieved <span>2026-09-13</span></span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Hayes, Kali (2026-09-08). <a href="https://www.bbc.com/news/articles/cy7zygy3rl2o">&quot;OpenAI says it cracked 90-year-old maths problem in 88 hours&quot;</a>. <i>bbc.com</i><span>. Retrieved <span>2026-09-08</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Jaffe, Arthur M. (June–July 2006). <a href="https://www.ams.org/notices/200606/fea-jaffe.pdf">&quot;The Millennium Grand Challenge in Mathematics&quot;</a> <span>(PDF)</span>. <i>Notices of the American Mathematical Society</i>. <b>53</b> (6): <span>652–</span>660.</cite></span></li> <li><span><span>↑</span></span> <span>Carlson, Jaffe <span>&amp;</span> Wiles (2006)</span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.claymath.org/millennium-problems/">&quot;The Millennium Prize Problems&quot;</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Jackson, Allyn (September 2000). &quot;Million-dollar mathematics prizes announced&quot;. <i>Notices of the American Mathematical Society</i>. <b>47</b> (8): <span>877–</span>879.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Dickson, David (2000). <a href="https://doi.org/10.1038%2F35013216">&quot;Mathematicians chase the seven million-dollar proofs&quot;</a>. <i>Nature</i>. <b>405</b> (383): 383. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1038%2F35013216">10.1038/35013216</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a><span> </span><a href="https://pubmed.ncbi.nlm.nih.gov/10839504">10839504</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a><span> </span><a href="https://api.semanticscholar.org/CorpusID:31169641">31169641</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Anatoly_Vershik">Vershik, Anatoly</a> (January 2007). &quot;What is good for mathematics? Thoughts on the Clay Millennium prizes&quot;. <i>Notices of the American Mathematical Society</i>. <b>54</b> (1): <span>45–</span>47.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Shing-Tung_Yau">Yau, Shing-Tung</a>; Nadis, Steve (2019). <i>The shape of a life. One mathematician&#39;s search for the universe&#39;s hidden geometry</i>. New Haven, CT: Yale University Press. <a href="https://en.wikipedia.org/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2019shli.book.....Y">2019shli.book.....Y</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Przytycki, Józef H.; Bakshi, Rhea Palak (2024). <a href="https://books.google.com/books?id=22X8EAAAQBAJ&amp;pg=PA375"><i>Lectures in Knot Theory: An Exploration of Contemporary Topics</i></a>. Springer. p.<span> </span>375. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-3-031-40044-5"><bdi>978-3-031-40044-5</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://news.bbc.co.uk/2/hi/science/nature/5274040.stm">&quot;Maths genius declines top prize&quot;</a>. <a href="https://en.wikipedia.org/wiki/BBC_News">BBC News</a>. 22 August 2006<span>. Retrieved <span>16 June</span> 2011</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://web.archive.org/web/20100331134628/http://www.claymath.org/poincare/millenniumPrizeFull.pdf">&quot;Prize for Resolution of the Poincaré Conjecture Awarded to Dr. Grigoriy Perelman&quot;</a> <span>(PDF)</span> (Press release). <a href="https://en.wikipedia.org/wiki/Clay_Mathematics_Institute">Clay Mathematics Institute</a>. March 18, 2010. Archived from <a href="http://www.claymath.org/poincare/millenniumPrizeFull.pdf">the original</a> <span>(PDF)</span> on March 31, 2010<span>. Retrieved <span>March 18,</span> 2010</span>. <q>The Clay Mathematics Institute (CMI) announces today that Dr. Grigoriy Perelman of St. Petersburg, Russia, is the recipient of the Millennium Prize for resolution of the Poincaré conjecture.</q></cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Charles_Fefferman">Fefferman, Charles L.</a> (2006). <a href="https://www.claymath.org/wp-content/uploads/2022/06/navierstokes.pdf">&quot;Existence and smoothness of the Navier–Stokes equation&quot;</a> <span>(PDF)</span>. In Carlson, James; <a href="https://en.wikipedia.org/wiki/Arthur_Jaffe">Jaffe, Arthur</a>; <a href="https://en.wikipedia.org/wiki/Andrew_Wiles">Wiles, Andrew</a> (eds.). <i>The millennium prize problems</i>. Providence, RI: American Mathematical Society and Clay Mathematics Institute. pp.<span> </span><span>57–</span>67. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-3679-8"><bdi>978-0-8218-3679-8</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.claymath.org/news/navier-stokes-announcement/">&quot;Navier-Stokes Announcement&quot;</a>. <i>Clay Mathematics Institute</i><span>. Retrieved <span>2026-09-13</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Brandom, Russell (8 September 2026). <a href="https://techcrunch.com/2026/09/08/openai-fought-dirty-on-career-making-math-problem-says-nyu-mathematician/">&quot;OpenAI fought dirty on career-making math problem, says NYU mathematician&quot;</a>. <i>TechCrunch</i><span>. Retrieved <span>8 September</span> 2026</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://openai.com/index/navier-stokes-solution/">&quot;On the Navier–Stokes Millennium Prize Problem&quot;</a>. <i>OpenAI</i>. 2026-09-08<span>. Retrieved <span>2026-09-09</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://web.archive.org/web/20260908171518/https://openai.com/index/navier-stokes-solution/">&quot;On the Navier–Stokes Millennium Prize Problem&quot;</a>. <i>OpenAI</i>. 2026-09-08<span>. Retrieved <span>2026-09-08</span></span>.</cite> (initial announcement)</span></li> <li><span><span>↑</span></span> <span><cite><a href="https://openai.com/index/navier-stokes-solution/">&quot;On the Navier–Stokes Millennium Prize Problem&quot;</a>. <i>OpenAI</i>. 2026-09-08<span>. Retrieved <span>2026-09-12</span></span>.</cite> (updated announcement)</span></li> <li><span><span>↑</span></span> <span><cite>Castelvecchi, Davide (8 September 2026). &quot;OpenAI claims huge maths breakthrough on a famed &#39;Millennium Problem&#39;&quot;. <i><a href="https://en.wikipedia.org/wiki/Nature_(journal)">Nature</a></i>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1038%2Fd41586-026-02842-5">10.1038/d41586-026-02842-5</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.claymath.org/millennium/birch-and-swinnerton-dyer-conjecture/">&quot;Birch and Swinnerton-Dyer Conjecture&quot;</a>. <i>Clay Mathematics Institute</i><span>. Retrieved <span>2024-11-20</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Pierre_Deligne">Deligne, Pierre</a> (2006). <a href="https://www.claymath.org/sites/default/files/hodge.pdf">&quot;The Hodge conjecture&quot;</a> <span>(PDF)</span>. In Carlson, James; <a href="https://en.wikipedia.org/wiki/Arthur_Jaffe">Jaffe, Arthur</a>; <a href="https://en.wikipedia.org/wiki/Andrew_Wiles">Wiles, Andrew</a> (eds.). <i>The millennium prize problems</i>. Providence, Rhode Island: American Mathematical Society and Clay Mathematics Institute. pp.<span> </span><span>45–</span>53. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-3679-8"><bdi>978-0-8218-3679-8</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Rajput, Uday Singh (2016). <a href="http://bharataganitaparisad.com/wp-content/uploads/2016/12/ch8.pdf">&quot;P Versus NP: More than just a prize problem&quot;</a> <span>(PDF)</span>. <i>Ganita</i>. <b>66</b>. Lucknow, India: 90. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0046-5402">0046-5402</a>. <a href="https://web.archive.org/web/20220617115240/http://bharataganitaparisad.com/wp-content/uploads/2016/12/ch8.pdf">Archived</a> <span>(PDF)</span> from the original on 17 June 2022<span>. Retrieved <span>17 June</span> 2022</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Scott_Aaronson">Scott Aaronson</a> (14 August 2011). <a href="http://eccc.hpi-web.de/report/2011/108/">&quot;Why Philosophers Should Care About Computational Complexity&quot;</a>. Technical report.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/William_Gasarch">William Gasarch</a> (June 2002). <a href="http://www.cs.umd.edu/~gasarch/papers/poll.pdf">&quot;The P=?NP poll&quot;</a> <span>(PDF)</span>. <i>SIGACT News</i>. <b>33</b> (2): <span>34–</span>47. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1145%2F1052796.1052804">10.1145/1052796.1052804</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a><span> </span><a href="https://api.semanticscholar.org/CorpusID:18759797">18759797</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Stephen_Cook">Cook, Stephen</a> (2006). <a href="https://www.claymath.org/wp-content/uploads/2022/06/pvsnp.pdf">&quot;The P versus NP problem&quot;</a> <span>(PDF)</span>. In Carlson, James; <a href="https://en.wikipedia.org/wiki/Arthur_Jaffe">Jaffe, Arthur</a>; <a href="https://en.wikipedia.org/wiki/Andrew_Wiles">Wiles, Andrew</a> (eds.). <i>The millennium prize problems</i>. Providence, Rhode Island: American Mathematical Society and Clay Mathematics Institute. pp.<span> </span><span>87–</span>104. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-3679-8"><bdi>978-0-8218-3679-8</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Steuding, Jörn; Suriajaya, Ade Irma (2020). <a href="https://doi.org/10.1007%2Fs40315-020-00316-x">&quot;Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines&quot;</a>. <i>Computational Methods and Function Theory</i>. <b>20</b> (3): <span>389–</span>401. <a href="https://en.wikipedia.org/wiki/ArXiv_(identifier)">arXiv</a>:<span><a href="https://arxiv.org/abs/2007.14661">2007.14661</a></span>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1007%2Fs40315-020-00316-x">10.1007/s40315-020-00316-x</a></span>. <a href="https://en.wikipedia.org/wiki/Hdl_(identifier)">hdl</a>:<span><a href="https://hdl.handle.net/2324%2F4483207">2324/4483207</a></span>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/2195-3724">2195-3724</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a><span> </span><a href="https://api.semanticscholar.org/CorpusID:216323223">216323223</a>. <q>Theorem 2 implies that <span><span><math> <semantics> <mrow> <mstyle> <mi>ζ</mi> </mstyle> </mrow> <annotation>{\displaystyle \zeta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5c3916703cae7938143d38865f78f27faadd4ae" alt="{\displaystyle \zeta }" title=""/></span> has an essential singularity at infinity</q></cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Enrico_Bombieri">Bombieri, Enrico</a> (2006). <a href="https://www.claymath.org/wp-content/uploads/2022/05/riemann.pdf">&quot;The Riemann hypothesis&quot;</a> <span>(PDF)</span>. In Carlson, James; <a href="https://en.wikipedia.org/wiki/Arthur_Jaffe">Jaffe, Arthur</a>; <a href="https://en.wikipedia.org/wiki/Andrew_Wiles">Wiles, Andrew</a> (eds.). <i>The millennium prize problems</i>. Providence, Rhode Island: American Mathematical Society and Clay Mathematics Institute. pp.<span> </span><span>107–</span>124. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-3679-8"><bdi>978-0-8218-3679-8</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.claymath.org/millennium-problems/yang%E2%80%93mills-and-mass-gap">&quot;Yang–Mills and Mass Gap&quot;</a>. <i>www.claymath.org (<a href="https://en.wikipedia.org/wiki/Clay_Mathematics_Institute">Claymath</a>)</i><span>. Retrieved <span>29 June</span> 2021</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><span>↑</span></span> <span><cite>Streater, R.; Wightman, A. (1964). <span><a href="https://archive.org/details/pctspinstatistic0000stre"><i>PCT, Spin and Statistics and all That</i></a></span>. W. A. Benjamin.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Osterwalder, K.; Schrader, R. (1973). <a href="http://projecteuclid.org/euclid.cmp/1103858969">&quot;Axioms for Euclidean Green&#39;s functions&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Communications_in_Mathematical_Physics">Communications in Mathematical Physics</a></i>. <b>31</b> (2): <span>83–</span>112. <a href="https://en.wikipedia.org/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1973CMaPh..31...83O">1973CMaPh..31...83O</a>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2FBF01645738">10.1007/BF01645738</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a><span> </span><a href="https://api.semanticscholar.org/CorpusID:189829853">189829853</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Osterwalder, K.; Schrader, R. (1975). <a href="http://projecteuclid.org/euclid.cmp/1103899050">&quot;Axioms for Euclidean Green&#39;s functions II&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Communications_in_Mathematical_Physics">Communications in Mathematical Physics</a></i>. <b>42</b> (3): <span>281–</span>305. <a href="https://en.wikipedia.org/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1975CMaPh..42..281O">1975CMaPh..42..281O</a>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2FBF01608978">10.1007/BF01608978</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a><span> </span><a href="https://api.semanticscholar.org/CorpusID:119389461">119389461</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Arthur_Jaffe">Jaffe, Arthur</a>; <a href="https://en.wikipedia.org/wiki/Edward_Witten">Witten, Edward</a> (2006). <a href="http://www.claymath.org/sites/default/files/yangmills.pdf">&quot;Quantum Yang–Mills theory&quot;</a> <span>(PDF)</span>. In Carlson, James; <a href="https://en.wikipedia.org/wiki/Arthur_Jaffe">Jaffe, Arthur</a>; <a href="https://en.wikipedia.org/wiki/Andrew_Wiles">Wiles, Andrew</a> (eds.). <i>The millennium prize problems</i>. Providence, Rhode Island: American Mathematical Society and Clay Mathematics Institute. pp.<span> </span><span>129–</span>152. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-3679-8"><bdi>978-0-8218-3679-8</bdi></a>.</cite></span></li> </ol></div></div> <ul><li><i>This article incorporates material from Millennium Problems on <a href="https://en.wikipedia.org/wiki/PlanetMath">PlanetMath</a>, which is licensed under the <a href="https://en.wikipedia.org/wiki/Wikipedia:CC-BY-SA">Creative Commons Attribution/Share-Alike License</a>.</i></li></ul> </section><section><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div> <ul><li><cite>Carlson, James; <a href="https://en.wikipedia.org/wiki/Arthur_Jaffe">Jaffe, Arthur</a>; <a href="https://en.wikipedia.org/wiki/Andrew_Wiles">Wiles, Andrew</a>, eds. (2006). <a href="http://www.claymath.org/library/"><i>The Millennium Prize Problems</i></a>. Providence, Rhode Island: <a href="https://en.wikipedia.org/wiki/American_Mathematical_Society">American Mathematical Society</a> and <a href="https://en.wikipedia.org/wiki/Clay_Mathematics_Institute">Clay Mathematics Institute</a>. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-8218-3679-8"><bdi>978-0-8218-3679-8</bdi></a>.</cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/Keith_Devlin">Devlin, Keith J.</a> (2003) [2002]. <span><a href="https://archive.org/details/millenniumproble00keit"><i>The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time</i></a></span>. New York: Basic Books. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/0-465-01729-0"><bdi>0-465-01729-0</bdi></a>.</cite></li></ul> </section><section><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Millennium_Prize_Problems&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div> <div> <div> <div>Wikiquote has quotations related to <a href="https://en.wikiquote.org/wiki/Millennium%20Prize%20Problems"><b><i>Millennium Prize Problems</i></b></a>.</div></div> </div> <ul><li><a href="http://www.claymath.org/millennium-problems">The Millennium Prize Problems</a></li></ul> <div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Active_inducement_prize_contests"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Active_inducement_prize_contests"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Active_inducement_prize_contests"><abbr>e</abbr></a></li></ul></div><div>Active <a href="https://en.wikipedia.org/wiki/Inducement_prize_contest">inducement prize contests</a></div></th></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Category:Science_and_engineering_awards">Science and engineering awards</a></li> <li><a href="https://en.wikipedia.org/wiki/Category:Challenge_awards">Challenge awards</a></li> <li><a href="https://en.wikipedia.org/wiki/Category:Invention_awards">Invention awards</a></li></ul> </div></td></tr><tr><th>Biology and medicine</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/M-prize">M-prize</a></li> <li><a href="https://en.wikipedia.org/wiki/Prize4Life">Prize4Life</a></li></ul> <ul><li>See also: <a href="https://en.wikipedia.org/wiki/Competitions_and_prizes_in_biotechnology">Competitions and prizes in biotechnology</a></li></ul> </div></td></tr><tr><th>Engineering</th><td><table><tbody><tr><th>Space</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Centennial_Challenges">Centennial Challenges</a></li> <li><a href="https://en.wikipedia.org/wiki/N-Prize">N-Prize</a></li></ul> </div></td></tr><tr><th>Robotics</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Multi_Autonomous_Ground-robotic_International_Challenge">MAGIC</a></li> <li><a href="https://en.wikipedia.org/wiki/Micromouse">Micromouse Contest</a></li> <li><a href="https://en.wikipedia.org/wiki/RoboCup">RoboCup</a></li> <li><a href="https://en.wikipedia.org/wiki/International_Aerial_Robotics_Competition">IARC</a></li> <li><a href="https://en.wikipedia.org/wiki/UAV_Outback_Challenge">UAV Outback Challenge</a></li> <li><a href="https://en.wikipedia.org/wiki/Intelligent_Ground_Vehicle_Competition">IGVC challenges</a></li> <li><a href="https://en.wikipedia.org/wiki/DARPA_Grand_Challenge">DARPA Grand Challenge</a></li></ul> <ul><li>See also: <a href="https://en.wikipedia.org/wiki/Robot_competition">Robot competition</a></li></ul> </div></td></tr><tr><th>Other</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/X_Prize_Foundation#2021_Gigaton_Scale_Carbon_Removal">Gigaton Scale Carbon Removal X Prize</a></li> <li><a href="https://en.wikipedia.org/wiki/Foresight_Institute_Feynman_Prize_in_Nanotechnology">Feynman Grand Prize</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th>Mathematics</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Millennium_Prize_Problems">Millennium Prize</a></li> <li><a href="https://en.wikipedia.org/wiki/Erdős_problems">Erdős problems</a></li> <li><a href="https://en.wikipedia.org/wiki/Hutter_Prize">Hutter Prize</a></li></ul> </div></td></tr><tr><td colspan="2"><div><a href="https://en.wikipedia.org/wiki/List_of_challenge_awards">List of challenge awards</a></div></td></tr></tbody></table></div> </section> https://en.wikipedia.org/wiki/Grigori_Perelman Ti5JnpeK4CHJwFD2Ji-yx9ELcxulkPsc6dq3Sw== Tue, 15 Sep 2026 08:48:03 +0000 Russian mathematician (born 1966) <div>Russian mathematician (born 1966)</div><div>In this name that follows <a href="https://en.wikipedia.org/wiki/East_Slavic_naming_customs">East Slavic naming customs</a>, the <a href="https://en.wikipedia.org/wiki/Patronymic">patronymic</a> is <i> Yakovlevich</i> and the <a href="https://en.wikipedia.org/wiki/Surname">family name</a> is <i> Perelman</i>.</div><p> </p><table><tbody><tr><th colspan="2"><div>Grigori Perelman</div></th></tr><tr><td colspan="2"><div><span>Григорий Перельман</span></div></td></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Grigori_Perelman,_1993_(re-scanned)_(cropped).jpg"></a></span><div>Perelman in 1993</div></td></tr><tr><th>Born</th><td><div>Grigori Yakovlevich Perelman</div><br/><span> (<span>1966-06-13</span>) </span>13 June 1966<span> (age<span> </span>60)</span><br/><div><a href="https://en.wikipedia.org/wiki/Leningrad">Leningrad</a>, Russian SFSR, Soviet Union</div></td></tr><tr><th>Education</th><td><a href="https://en.wikipedia.org/wiki/Leningrad_State_University">Leningrad State University</a> (<a href="https://en.wikipedia.org/wiki/PhD">PhD</a>)</td></tr><tr><th>Known<span> </span>for</th><td>Proof of the <a href="https://en.wikipedia.org/wiki/Soul_conjecture">soul conjecture</a>, <a href="https://en.wikipedia.org/wiki/Poincaré_conjecture">Poincaré conjecture</a> and <a href="https://en.wikipedia.org/wiki/Geometrization_conjecture">geometrization</a> of 3-manifolds</td></tr><tr><th>Awards</th><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Saint_Petersburg_Mathematical_Society">Saint Petersburg Mathematical Society</a> Prize (1991)</li><li><a href="https://en.wikipedia.org/wiki/EMS_Prize">EMS Prize</a> (1996, declined)</li><li><a href="https://en.wikipedia.org/wiki/Fields_Medal">Fields Medal</a> (2006, declined)</li><li><a href="https://en.wikipedia.org/wiki/Millennium_Prize_Problems">Millennium Prize</a> (2010, declined)</li></ul></div></td></tr><tr><td colspan="2"><b>Scientific career</b></td></tr><tr><th>Fields</th><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Differential_geometry">Differential geometry</a></li><li><a href="https://en.wikipedia.org/wiki/Geometric_analysis">Geometric analysis</a></li><li><a href="https://en.wikipedia.org/wiki/Geometric_topology">Geometric topology</a></li></ul></div></td></tr><tr><th>Workplaces</th><td><div><ul><li><a href="https://en.wikipedia.org/wiki/St._Petersburg_Department_of_Steklov_Mathematical_Institute_of_the_Russian_Academy_of_Sciences">PDMI</a></li><li><a href="https://en.wikipedia.org/wiki/Courant_Institute_of_Mathematical_Sciences">New York University</a></li><li><a href="https://en.wikipedia.org/wiki/University_of_California,_Berkeley">University of California, Berkeley</a></li></ul></div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Thesis">Thesis</a></th><td><i><a href="https://www.mathgenealogy.org/id.php?id=84354">Saddle Surfaces in Euclidean Spaces</a></i><span> </span><span>(1990)</span></td></tr><tr><th><div><a href="https://en.wikipedia.org/wiki/Doctoral_advisor">Doctoral advisor</a></div></th><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Aleksandr_Danilovich_Aleksandrov">Aleksandr Aleksandrov</a></li><li><a href="https://en.wikipedia.org/wiki/Yuri_Burago">Yuri Burago</a></li></ul></div></td></tr><tr><td colspan="2"> </td></tr></tbody></table><p><b>Grigori Yakovlevich Perelman</b> (<a href="https://en.wikipedia.org/wiki/Russian_language">Russian</a><span>: </span><span>Григорий Яковлевич Перельман</span>, <span>pronounced</span> <span><a href="https://en.wikipedia.org/wiki/Help:IPA/Russian"><span>[</span>ɡrʲɪˈɡorʲɪj ˈjakəvlʲɪvʲɪtɕ pʲɪrʲɪlʲˈman<span>]</span></a></span> <span><span><a href="https://upload.wikimedia.org/wikipedia/commons/transcoded/e/ec/Ru-Grigori_Yakovlevich_Perelman.oga/Ru-Grigori_Yakovlevich_Perelman.oga.mp3"></a></span>^{<a href="https://en.wikipedia.org/wiki/File:Ru-Grigori_Yakovlevich_Perelman.oga">ⓘ</a>}</span>; born 13<span><span> </span></span>June 1966) is a Russian <a href="https://en.wikipedia.org/wiki/Mathematician">mathematician</a> and geometer who is known for his contributions to the fields of <a href="https://en.wikipedia.org/wiki/Geometric_analysis">geometric analysis</a>, <a href="https://en.wikipedia.org/wiki/Riemannian_geometry">Riemannian geometry</a>, and <a href="https://en.wikipedia.org/wiki/Geometric_topology">geometric topology</a>. In 2005, Perelman resigned from his research post in <a href="https://en.wikipedia.org/wiki/Steklov_Institute_of_Mathematics">Steklov Institute of Mathematics</a> and in 2006 stated that he had quit professional mathematics, owing to feeling disappointed over the ethical standards in the field. He lives in seclusion in <a href="https://en.wikipedia.org/wiki/Saint_Petersburg">Saint Petersburg</a> and has declined requests for interviews since 2006.</p><p>In the 1990s, partly in collaboration with <a href="https://en.wikipedia.org/wiki/Yuri_Burago">Yuri Burago</a>, <a href="https://en.wikipedia.org/wiki/Mikhail_Leonidovich_Gromov">Mikhael Gromov</a>, and Anton Petrunin, he made contributions to the study of <a href="https://en.wikipedia.org/wiki/Alexandrov_space">Alexandrov spaces</a>. In 1994, he proved the <a href="https://en.wikipedia.org/wiki/Soul_theorem">soul conjecture</a> in Riemannian geometry, which had been an open problem for the previous 20 years. In 2002 and 2003, he developed new techniques in the analysis of <a href="https://en.wikipedia.org/wiki/Ricci_flow">Ricci flow</a>, and proved the <a href="https://en.wikipedia.org/wiki/Poincaré_conjecture">Poincaré conjecture</a> and <a href="https://en.wikipedia.org/wiki/Geometrization_conjecture">Thurston&#39;s geometrization conjecture</a>, the former of which had been a famous <a href="https://en.wikipedia.org/wiki/Open_problem">open problem</a> in mathematics for the past century. The full details of Perelman&#39;s work were filled in and explained by various authors over the following several years.</p><p>In August 2006, Perelman was offered the <a href="https://en.wikipedia.org/wiki/Fields_Medal">Fields Medal</a>^{<span><span>[</span>1<span>]</span></span>} for &quot;his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow&quot;, but he declined the award, stating: &quot;I&#39;m not interested in money or fame; I don&#39;t want to be on display like an animal in a zoo.&quot;^{<span><span>[</span>2<span>]</span></span>} On 22 December 2006, the scientific journal <i><a href="https://en.wikipedia.org/wiki/Science_(journal)">Science</a></i> recognized Perelman&#39;s proof of the Poincaré conjecture as the scientific &quot;<a href="https://en.wikipedia.org/wiki/Breakthrough_of_the_Year">Breakthrough of the Year</a>&quot;, the first such recognition in the area of mathematics.^{<span><span>[</span>3<span>]</span></span>}</p><p>On 18 March 2010, it was announced that he had met the criteria to receive the first Clay <a href="https://en.wikipedia.org/wiki/Millennium_Prize_Problems">Millennium Prize</a>^{<span><span>[</span>4<span>]</span></span>} for resolution of the Poincaré conjecture. On 1 July 2010, he rejected the prize of one million dollars, saying that he considered the decision of the board of the Clay Institute to be unfair, in that his contribution to solving the Poincaré conjecture was no greater than that of <a href="https://en.wikipedia.org/wiki/Richard_S._Hamilton">Richard S. Hamilton</a>, the mathematician who pioneered the Ricci flow partly with the aim of attacking the conjecture.^{<span><span>[</span>5<span>]</span></span>}^{<span><span>[</span>6<span>]</span></span>} He had previously rejected the prestigious prize of the <a href="https://en.wikipedia.org/wiki/European_Mathematical_Society">European Mathematical Society</a> in 1996.^{<span><span>[</span>7<span>]</span></span>}</p> https://en.wikipedia.org/wiki/Shut_Up_%26_Write! kL4xkje4Y8e9RIt4--PrdnYmnHCGXjgDors0VA== Tue, 15 Sep 2026 08:26:17 +0000 Time management method for writing <section><div>Time management method for writing</div> <table><tbody><tr><td><div><span><a href="https://en.wikipedia.org/wiki/File:Wiki_letter_w.svg"></a></span></div></td><td><div>This article <b>is an <a href="https://en.wikipedia.org/wiki/Wikipedia:Orphan">orphan</a>, as no other articles <span><a href="https://en.wikipedia.org/w/index.php?title=Special:WhatLinksHere&amp;target=Shut_Up_%26_Write!&amp;namespace=0">link to it</a></span></b>. Please <a href="https://en.wikipedia.org/wiki/Help:Link">introduce links</a> to this page from <span><a href="https://en.wikipedia.org/w/index.php?title=Special%3ASearch&amp;redirs=1&amp;search=Shut+Up+%26%2338%3B+Write%21&amp;fulltext=Search&amp;ns0=1&amp;title=Special%3ASearch&amp;advanced=1&amp;fulltext=Shut+Up+%26%2338%3B+Write%21">related articles</a></span>. <span><i>(<span>June 2026</span>)</i></span></div></td></tr></tbody></table> <p><b>Shut Up &amp; Write!</b> creates communities of writing practice that encourage people to gather to write together, online or face to face. It was introduced by Rennie Saunders in 2007 at Crossroads Cafe, San Francisco. It has since been adopted by over 100,000 members in over 60 countries.^{<span><span>[</span>1<span>]</span></span>}</p> <p>At each session, writers are encouraged to set a clear goal, and then write in focused bursts with short intervals for conversation. At the end of the session, writers are invited to reflect on what they have achieved. Many sessions use the <a href="https://en.wikipedia.org/wiki/Pomodoro_Technique">Pomodoro Technique</a> to manage periods of writing and breaks. Shut Up and Write! provides writers with sessions focused on dedicated writing time and open conversation. It focuses on building community between writers and developing good writing habits.^{<span><span>[</span>2<span>]</span></span>}</p> <p>A hallmark of Shut Up and Write! is the absence of read-alouds, critiques, and feedback. There is no requirement for writers to share their work.^{<span><span>[</span>2<span>]</span></span>} That is, it focuses on increasing writing productivity rather than increasing writing quality.^{<span><span>[</span>3<span>]</span></span>} It also fosters inclusion and reduces isolation.^{<span><span>[</span>4<span>]</span></span>}</p> </section><section><div><h2>Effectiveness</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Shut_Up_%26_Write!&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div> <p>In 2023, Chelsea Proulx et al. demonstrated that writers showed significant gains in self-efficacy and self-regulation through attending Shut Up and Write!^{<span><span>[</span>5<span>]</span></span>} Megan von Isenburg et al. found that, while Shut Up and Write! was effective for those who attended, it was difficult for busy people to find time to attend sessions.^{<span><span>[</span>6<span>]</span></span>} Jennifer Stritch reported that participants felt that they had confidence, connectedness, and support, as well as a reduction in unproductive writing behaviors and an improvement in writing generativity and outputs.^{<span><span>[</span>7<span>]</span></span>}</p> </section><section><div><h2>Adoption by academia</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Shut_Up_%26_Write!&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div> <p>Although Shut Up and Write! was developed for writers outside of academia, it has been adopted by academia as an effective strategy. Many articles identify a blog post in 2011 by <a href="https://en.wikipedia.org/wiki/Inger_Mewburn">Inger Mewburn</a> as a trigger for adoption (e.g.^{<span><span>[</span>3<span>]</span></span>}^{<span><span>[</span>8<span>]</span></span>}). In 2016, <a href="https://en.wikipedia.org/wiki/Tara_Brabazon">Tara Brabazon</a> utilised a distinctive methodology from the Shut Up and Write! project to reduce isolation among graduate students as part of the Digital Doctorate project.^{<span><span>[</span>9<span>]</span></span>} This methodology was then transformed through Write Club, where all the sessions were recorded, and asynchronous participation was encouraged. A year of <a href="https://www.youtube.com/playlist?list=PLFnd097NntmbRBhrJVEPJ-yVHYUR1oEO4">Write Club Sessions</a> are available to share and use.^{<span><span>[</span>10<span>]</span></span>}</p> <p>In 2017, Michelle Reeve and Matthew Partridge argued that Shut Up and Write! could provide isolated researchers with support, and encourage discussion and sharing of problems.^{<span><span>[</span>8<span>]</span></span>} In 2018, Joe Thorogood et al. identified Shut Up and Write! as part of the <a href="https://en.wikipedia.org/wiki/Slow_movement_(culture)">Slow Movement</a>, and an effective way to reduce stress and overwork in academia.^{<span><span>[</span>11<span>]</span></span>} Fabian Cannizzo sees Shut Up and Write! as a way to expose academics and students to different rhythms, paces, senses of pressure and relief, social and technological infrastructures.^{<span><span>[</span>12<span>]</span></span>} In 2021, Thea Blackler argues that setting up a Shut Up and Write! session allowed her to support her colleagues while building the culture of research and writing, as well as meeting her own writing goals.^{<span><span>[</span>13<span>]</span></span>}</p><blockquote><p><i>The great advantage of SUAW for me is that it allows me to make a contribution to supporting my colleagues and building research and writing culture but does not take any extra time out of my day as I am writing too. And it forces me to write for around 1.5 hours each week, even if I get no other writing done that week.</i>^{<span><span>[</span>13<span>]</span></span>}</p></blockquote><p>In particular, Shut Up and Write! is seen as a useful practice for PhD students. In 2023, Cally Guerin and Claire Aitchison wrote that Shut Up and Write helps students to understand how long writing takes, as well as a sense of how others manage their writing time.^{<span><span>[</span>14<span>]</span></span>} In 2024, Catherine Déri argued that Shut Up and Write! allows for socialization into academia through peer exchange, the development of skills beyond writing, and a better understanding of the difficulties encountered during the PhD.^{<span><span>[</span>15<span>]</span></span>}</p> </section><section><div><h2>Variations</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Shut_Up_%26_Write!&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <p>Many groups have adapted the Shut Up and Write! model to focus on a particular group of writers, or to include some element of feedback.^{<span><span>[</span>16<span>]</span></span>} Some groups have adopted the model, but have changed the name. Examples include Sit Down &amp; Write!^{<span><span>[</span>16<span>]</span></span>} Just Write!^{<span><span>[</span>17<span>]</span></span>} WEWRITE!^{<span><span>[</span>7<span>]</span></span>} and the Write Bunch^{<span><span>[</span>18<span>]</span></span>}</p> </section><section><div><h2>Writing partners</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Shut_Up_%26_Write!&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <p>In 2018 Rennie Saunders established a US-based 501(c)(3) <a href="https://en.wikipedia.org/wiki/Not-for-profit_organization">not-for-profit</a>, Writing Partners, in California to support Shut Up and Write! globally.^{<span><span>[</span>19<span>]</span></span>} In 2024, Writing Partners organised a symposium on Community in Writing at ThinkLab, <a href="https://en.wikipedia.org/wiki/University_of_Cambridge">Cambridge University</a>, UK.^{<span><span>[</span>20<span>]</span></span>} In 2025, the Community in Writing symposium will take place in conjunction with <a href="https://en.wikipedia.org/wiki/Deakin_University">Deakin University</a>, Melbourne, Australia.^{<span><span>[</span>21<span>]</span></span>}</p> </section><section><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Shut_Up_%26_Write!&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <div> <div><ol><li><span><span>↑</span></span> <span><cite><a href="https://www.shutupwrite.com/about">&quot;Shut Up &amp; Write! About Shut Up &amp; Write!&quot;</a>. <i>Shut Up &amp; Write!</i><span>. Retrieved <span>2025-08-03</span></span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite><a href="https://www.shutupwrite.com/method">&quot;Shut Up &amp; Write! The Shut Up &amp; Write! Method&quot;</a>. <i>Shut Up &amp; Write!</i><span>. Retrieved <span>2025-08-03</span></span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Carter, Susan; Guerin, Cally; Aitchison, Claire (2020). <i>Doctoral Writing: Practices, Processes and Pleasures</i>. Singapore: Springer Singapore Pte. Limited. p.<span> </span>52. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-981-15-1808-9"><bdi>978-981-15-1808-9</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Fegan, Suzanne (2016-05-21). <a href="https://journal.aall.org.au/index.php/jall/article/view/404">&quot;When shutting up brings us together: Several affordances of a scholarly writing group&quot;</a>. <i>Journal of Academic Language and Learning</i>. <b>10</b> (2): <span>A20–</span>A31. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/1835-5196">1835-5196</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Proulx, Chelsea N.; Rubio, Doris M.; Norman, Marie K.; Mayowski, Colleen A. (2023). <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10308422">&quot;Shut Up &amp; Write!® builds writing self-efficacy and self-regulation in early-career researchers&quot;</a>. <i>Journal of Clinical and Translational Science</i>. <b>7</b> (1) e141. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1017%2Fcts.2023.568">10.1017/cts.2023.568</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/2059-8661">2059-8661</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a><span> </span><span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10308422">10308422</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a><span> </span><a href="https://pubmed.ncbi.nlm.nih.gov/37396813">37396813</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Von Isenburg, Megan; Lee, Linda S.; Oermann, Marilyn H. (2017-04-04). <a href="http://jmla.pitt.edu/ojs/jmla/article/view/222">&quot;Writing Together to Get AHEAD: an interprofessional boot camp to support scholarly writing in the health professions&quot;</a>. <i>Journal of the Medical Library Association</i>. <b>105</b> (2): <span>167–</span>172. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.5195%2Fjmla.2017.222">10.5195/jmla.2017.222</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/1558-9439">1558-9439</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a><span> </span><span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5370609">5370609</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a><span> </span><a href="https://pubmed.ncbi.nlm.nih.gov/28377681">28377681</a>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Stritch, Jennifer Moran (2025). <a href="https://doi.org/10.1016%2Fj.profnurs.2025.06.007">&quot;Enhancing academic writing confidence and productivity: The impact of TUS WEWRITE!&quot;</a>. <i>Journal of Professional Nursing</i>. <b>60</b>: <span>32–</span>35. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1016%2Fj.profnurs.2025.06.007">10.1016/j.profnurs.2025.06.007</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a><span> </span><a href="https://pubmed.ncbi.nlm.nih.gov/40915763">40915763</a>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Reeve, M. A.; Partridge, M. (2017-09-01). <a href="https://academic.oup.com/aesa/article/110/5/449/4103473">&quot;The Use of Social Media to Combat Research-Isolation&quot;</a>. <i>Annals of the Entomological Society of America</i>. <b>110</b> (5): <span>449–</span>456. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1093%2Faesa%2Fsax051">10.1093/aesa/sax051</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0013-8746">0013-8746</a>. <a href="https://en.wikipedia.org/wiki/PMC_(identifier)">PMC</a><span> </span><span><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5846695">5846695</a></span>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a><span> </span><a href="https://pubmed.ncbi.nlm.nih.gov/29563645">29563645</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Brabazon, Tara; Armstrong, Elisa; Baker, Nicky; Batchelor, Samantha; Brose, Julie; Charlton, Sue; Carpenter-Mew, Rebecca; Collett, Maive Jackson; Cooper, Amanda; Ganzer, Sharon; Hayden, Cheryl; Hammond, Libby; McLeod, Anne; Phillips, Jane; Thomas, Jessica (2021). <a href="https://ijsses.tiu.edu.iq/index.php/ijsses/article/view/185">&quot;Deeply Digital in Shallow Times: Writing Communities in the Shadow of the Pandemic&quot;</a>. <i>International Journal of Social Sciences &amp; Educational Studies</i>. <b>8</b> (4): <span>230–</span>253. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.23918%2Fijsses.v8i4p230">10.23918/ijsses.v8i4p230</a></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://brabazon.net/2023/05/07/join-write-club-and-doh-digital-office-hours/">&quot;Join Write Club and DoH (Digital Office Hours) – Tara Brabazon&quot;</a>. 2023-05-07<span>. Retrieved <span>2025-08-14</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Thorogood, Joe; Faulkner, Simon; Warner, Laura (2018-11-15). <a href="https://sehej.raise-network.com/raise/article/view/698">&quot;Slow strategies for student (and staff) engagement&quot;</a>. <i>Student Engagement in Higher Education Journal</i>. <b>2</b> (2): <span>105–</span>123. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/2399-1836">2399-1836</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Cannizzo, Fabian (2018-11-12). <a href="https://www.oneducation.net/no-03_december-2018/the-shifting-rhythms-of-academic-work/">&quot;the shifting rhythms of academic work&quot;</a>. <i>on_education</i><span>. Retrieved <span>2025-08-03</span></span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Blackler, Alethea (2021). &quot;Research Leadership&quot;. <i>How to Be a Design Academic</i>. CRC Press. pp.<span> </span><span>219–</span>220. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-429-35169-3"><bdi>978-0-429-35169-3</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Guerin, Cally; Aitchison, Claire (2023), <span><a href="https://link.springer.com/10.1007/978-3-031-42875-3_13">&quot;Finding Confidence in Writing: Doctoral Writing Groups&quot;</a></span>, in Elliot, Dely L.; Bengtsen, Søren S. E.; Guccione, Kay (eds.), <i>Developing Researcher Independence Through the Hidden Curriculum</i>, Cham: Springer International Publishing, pp.<span> </span><span>147–</span>156, <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2F978-3-031-42875-3_13">10.1007/978-3-031-42875-3_13</a>, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-3-031-42874-6"><bdi>978-3-031-42874-6</bdi></a><span>, retrieved <span>2025-08-03</span></span></cite></span></li> <li><span><span>↑</span></span> <span><cite>Déri, Catherine E. (2024). <a href="https://archivesoresquebec.ca/id/eprint/451/1/ORES_RELAIS_Numero9_Deri.pdf">&quot;How do Doctoral Students Socialize into the Profession of Researcher in Academic Writing Cafés?&quot;</a> <span>(PDF)</span>. <i>Relais</i>. <b>9</b>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Micsinszki, Samantha K.; Yeung, Lily (2021). <span><a href="https://journals.healio.com/doi/10.3928/00220124-20210611-05">&quot;Adapting &quot;Shut Up &amp; Write! ®&quot; to Foster Productive Scholarly Writing in Graduate Nursing Students&quot;</a></span>. <i>The Journal of Continuing Education in Nursing</i>. <b>52</b> (7): <span>313–</span>318. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.3928%2F00220124-20210611-05">10.3928/00220124-20210611-05</a>. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0022-0124">0022-0124</a>. <a href="https://en.wikipedia.org/wiki/PMID_(identifier)">PMID</a><span> </span><a href="https://pubmed.ncbi.nlm.nih.gov/34166156">34166156</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Mewburn, Inger (2022-07-05). <a href="https://researchwhisperer.org/2022/07/05/just-write/">&quot;How Shut Up and Write became &#39;Just Write!&#39;: An American Tale&quot;</a>. <i>The Research Whisperer</i><span>. Retrieved <span>2025-08-03</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Brabazon, Tara; Armstrong, Elisa; Baker, Nicky; Batchelor, Samantha; Brose, Julie; Charlton, Sue; Carpenter-Mew, Rebecca; Jackson Collett, Maive; Cooper, Amanda; Ganzer, Sharon; Hayden, Cheryl; Hammond, Libby; McLeod, Anne; Phillips, Jane; Thomas, Jessica; Witt, Susan (2021). <a href="https://ijsses.tiu.edu.iq/index.php/ijsses/article/view/185">&quot;Deeply Digital in Shallow Times: Writing Communities in the Shadow of the Pandemic&quot;</a>. <i>International Journal of Social Sciences &amp; Educational Studies</i>. <b>8</b> (4). <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.23918%2Fijsses.v8i4p230">10.23918/ijsses.v8i4p230</a></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.writingpartners.org/about">&quot;About&quot;</a>. <i>Writing Partners</i><span>. Retrieved <span>2025-08-03</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Shore, Tyler (4 December 2024). <a href="https://www.thinklab.strategic-partnerships.admin.cam.ac.uk/posts/2024/12/04/reflections-on-the-first-shut-up-write-community-in-writing-symposium/">&quot;Reflections on the First Shut Up &amp; Write! Community in Writing Symposium&quot;</a>. <i>Thinklab</i><span>. Retrieved <span>2025-08-10</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>&quot;Shut Up &amp; Write! Community in Writing 2025&quot;. <i>Writing Partners</i><span>. Retrieved <span>11 August</span> 2025</span>.</cite></span></li> </ol></div></div> </section> https://en.wikipedia.org/wiki/Uncanny_valley _ExTPoPpnWXrSNYJyqs1xywCEYt6E2zzE5YENw== Tue, 15 Sep 2026 07:42:42 +0000 Hypothesis that human replicas elicit revulsion <div>Hypothesis that human replicas elicit revulsion</div><div>This article is about the hypothesis. For other uses, see <a href="https://en.wikipedia.org/wiki/Uncanny_valley_(disambiguation)">Uncanny valley (disambiguation)</a>.</div><figure><a href="https://en.wikipedia.org/wiki/File:Mori_Uncanny_Valley.svg"></a><figcaption>Hypothesized emotional response of subjects is plotted against <a href="https://en.wikipedia.org/wiki/Anthropomorphism">anthropomorphism</a> of a robot, according to <a href="https://en.wikipedia.org/wiki/Masahiro_Mori_(roboticist)">Masahiro Mori</a>&#39;s statements. The uncanny valley is the region of negative emotional response towards robots that seem &quot;almost&quot; human. Movement amplifies the emotional response.</figcaption></figure><table><tbody><tr><td>Part of <a href="https://en.wikipedia.org/wiki/Category:Artificial_intelligence">a series</a> on</td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Artificial_intelligence">Artificial intelligence (AI)</a></th></tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Artificial_intelligence#Goals">Major goals</a></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Artificial_general_intelligence">Artificial general intelligence</a> <ul><li><a href="https://en.wikipedia.org/wiki/Artificial_superintelligence">superintelligence</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Intelligent_agent">Intelligent agent</a></li> <li><a href="https://en.wikipedia.org/wiki/Recursive_self-improvement">Recursive self-improvement</a></li> <li><a href="https://en.wikipedia.org/wiki/Automated_planning_and_scheduling">Planning</a></li> <li><a href="https://en.wikipedia.org/wiki/Computer_vision">Computer vision</a></li> <li><a href="https://en.wikipedia.org/wiki/General_game_playing">General game playing</a></li> <li><a href="https://en.wikipedia.org/wiki/Knowledge_representation_and_reasoning">Knowledge representation</a></li> <li><a href="https://en.wikipedia.org/wiki/Natural_language_processing">Natural language processing</a></li> <li><a href="https://en.wikipedia.org/wiki/Robotics">Robotics</a></li> <li><a href="https://en.wikipedia.org/wiki/AI_safety">AI safety</a></li></ul></div></div></td> </tr><tr><td> <div><div>Approaches</div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Machine_learning">Machine learning</a></li> <li><a href="https://en.wikipedia.org/wiki/Data_mining">Data mining</a></li> <li><a href="https://en.wikipedia.org/wiki/Symbolic_artificial_intelligence">Symbolic</a></li> <li><a href="https://en.wikipedia.org/wiki/Deep_learning">Deep learning</a></li> <li><a href="https://en.wikipedia.org/wiki/Bayesian_network">Bayesian networks</a></li> <li><a href="https://en.wikipedia.org/wiki/Evolutionary_algorithm">Evolutionary algorithms</a></li> <li><a href="https://en.wikipedia.org/wiki/Neuro-symbolic_AI">Neuro-symbolic AI</a></li> <li><a href="https://en.wikipedia.org/wiki/Artificial_intelligence_systems_integration">Systems integration</a></li> <li><a href="https://en.wikipedia.org/wiki/Open-source_artificial_intelligence">Open-source</a></li> <li><a href="https://en.wikipedia.org/wiki/Open_weights">Open weights</a></li> <li><a href="https://en.wikipedia.org/wiki/AI_data_center">AI data centers</a></li></ul></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Applications_of_artificial_intelligence">Applications</a></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/AI_art">Art</a> <ul><li><a href="https://en.wikipedia.org/wiki/Artificial_intelligence_in_music">Music</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Machine_learning_in_bioinformatics">Bioinformatics</a></li> <li><a href="https://en.wikipedia.org/wiki/Deepfake">Deepfake</a></li> <li><a href="https://en.wikipedia.org/wiki/Machine_learning_in_earth_sciences">Earth sciences</a></li> <li><a href="https://en.wikipedia.org/wiki/Applications_of_artificial_intelligence#Finance"> Finance </a></li> <li><a href="https://en.wikipedia.org/wiki/Generative_AI">Generative AI</a> <ul><li><a href="https://en.wikipedia.org/wiki/Generative_audio">Audio</a></li> <li><a href="https://en.wikipedia.org/wiki/AI_image">Images</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Artificial_intelligence_in_government">Government</a></li> <li><a href="https://en.wikipedia.org/wiki/Artificial_intelligence_in_healthcare">Healthcare</a></li> <li><a href="https://en.wikipedia.org/wiki/Artificial_intelligence_in_industry">Industry</a></li> <li><a href="https://en.wikipedia.org/wiki/AI-assisted_software_development">Software development</a></li> <li><a href="https://en.wikipedia.org/wiki/Machine_translation">Translation</a></li> <li><a href="https://en.wikipedia.org/wiki/Artificial_intelligence_arms_race"> Military </a></li> <li><a href="https://en.wikipedia.org/wiki/Machine_learning_in_physics">Physics</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_artificial_intelligence_projects">Projects</a></li></ul></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Philosophy_of_artificial_intelligence">Philosophy</a></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/AI_alignment">AI alignment</a></li> <li><a href="https://en.wikipedia.org/wiki/Artificial_consciousness">Artificial consciousness</a></li> <li><a href="https://en.wikipedia.org/wiki/Bitter_lesson">The bitter lesson</a></li> <li><a href="https://en.wikipedia.org/wiki/Chinese_room">Chinese room</a></li> <li><a href="https://en.wikipedia.org/wiki/Friendly_artificial_intelligence">Friendly AI</a></li> <li><a href="https://en.wikipedia.org/wiki/Ethics_of_artificial_intelligence">Ethics</a></li> <li><a href="https://en.wikipedia.org/wiki/Existential_risk_from_artificial_general_intelligence">Existential risk</a></li> <li><a href="https://en.wikipedia.org/wiki/Turing_test">Turing test</a></li> <li><a href="https://en.wikipedia.org/wiki/Uncanny_valley">Uncanny valley</a></li> <li><a href="https://en.wikipedia.org/wiki/Human–AI_interaction">Human–AI interaction</a></li></ul></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/History_of_artificial_intelligence">History</a></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Timeline_of_artificial_intelligence">Timeline</a></li> <li><a href="https://en.wikipedia.org/wiki/Progress_in_artificial_intelligence">Progress</a></li> <li><a href="https://en.wikipedia.org/wiki/AI_winter">AI winter</a></li> <li><a href="https://en.wikipedia.org/wiki/AI_boom">AI boom</a></li> <li><a href="https://en.wikipedia.org/wiki/AI_build-out_financing">AI build-out financing</a></li> <li><a href="https://en.wikipedia.org/wiki/AI_bubble">AI bubble</a></li></ul></div></div></td> </tr><tr><td> <div><div><a href="https://en.wikipedia.org/wiki/Artificial_intelligence_controversies">Controversies</a></div><div> <ul><li><a href="https://en.wikipedia.org/wiki/Deepfake_pornography">Deepfake pornography</a> <ul><li><a href="https://en.wikipedia.org/wiki/Taylor_Swift_deepfake_pornography_controversy">Taylor Swift deepfake pornography controversy</a></li> <li><a href="https://en.wikipedia.org/wiki/Grok_sexual_deepfake_scandal">Grok sexual deepfake scandal</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Google_Gemini_image_generation_controversy">Google Gemini image generation controversy</a></li> <li><i><a href="https://en.wikipedia.org/wiki/It&#39;s_the_Most_Terrible_Time_of_the_Year">It&#39;s the Most Terrible Time of the Year</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Navier–Stokes_priority_controversy">Navier–Stokes priority controversy</a></li> <li><a href="https://en.wikipedia.org/wiki/Pause_Giant_AI_Experiments:_An_Open_Letter">Pause Giant AI Experiments</a></li> <li><a href="https://en.wikipedia.org/wiki/Project_Panama">Project Panama</a></li> <li><a href="https://en.wikipedia.org/wiki/Removal_of_Sam_Altman_from_OpenAI">Removal of Sam Altman from OpenAI</a></li> <li><a href="https://en.wikipedia.org/wiki/Statement_on_AI_Risk">Statement on AI Risk</a></li> <li><a href="https://en.wikipedia.org/wiki/Tay_(chatbot)">Tay (chatbot)</a></li> <li><i><a href="https://en.wikipedia.org/wiki/Théâtre_D&#39;opéra_Spatial">Théâtre D&#39;opéra Spatial</a></i></li> <li><a href="https://en.wikipedia.org/wiki/Voiceverse_NFT_plagiarism_scandal">Voiceverse NFT plagiarism scandal</a></li></ul></div></div></td> </tr><tr><td> <a href="https://en.wikipedia.org/wiki/Glossary_of_artificial_intelligence">Glossary</a></td></tr><tr><td><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Artificial_intelligence"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Artificial_intelligence"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Artificial_intelligence"><abbr>e</abbr></a></li></ul></div></td></tr></tbody></table><p>The <b>uncanny valley</b> effect is a hypothesized psychological and aesthetic relation between an object&#39;s degree of resemblance to a human being and the emotional response to the object. The uncanny valley hypothesis predicts that an entity appearing <i>almost human</i> will elicit uncanny or eerie feelings in viewers. </p><p>Examples of the phenomenon exist among <a href="https://en.wikipedia.org/wiki/Robot">robots</a>, <a href="https://en.wikipedia.org/wiki/Animatronic">animatronics</a>, and lifelike <a href="https://en.wikipedia.org/wiki/Doll">dolls</a> as well as visuals produced by <a href="https://en.wikipedia.org/wiki/3D_computer_animation">3D computer animation</a> and predominantly by <a href="https://en.wikipedia.org/wiki/Artificial_intelligence">artificial intelligence</a>. The increasing prevalence of digital technologies (e.g., <a href="https://en.wikipedia.org/wiki/Virtual_reality">virtual reality</a>, <a href="https://en.wikipedia.org/wiki/Augmented_reality">augmented reality</a>, and <a href="https://en.wikipedia.org/wiki/Unbiased_rendering">photorealistic</a> computer animation) and their increasing <a href="https://en.wikipedia.org/wiki/Realism_(arts)">verisimilitude</a> have prompted debate about &quot;the valley&quot;.</p> https://en.wikipedia.org/wiki/Columnar_jointing kzMefeqbakeVWiIWT9V4XiA4fpuheCMXtRZiyA== Tue, 15 Sep 2026 07:42:42 +0000 Places <div><h2>Places</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div><div>Main article: <a href="https://en.wikipedia.org/wiki/List_of_places_with_columnar_jointed_volcanics">List of places with columnar jointed volcanics</a></div><p>Some famous locations in the United States where columnar jointing can be found are <a href="https://en.wikipedia.org/wiki/Devils_Tower">Devils Tower</a> in Wyoming, <a href="https://en.wikipedia.org/wiki/Devils_Postpile">Devils Postpile</a> in California and the <a href="https://en.wikipedia.org/wiki/Columbia_River">Columbia River</a> <a href="https://en.wikipedia.org/wiki/Flood_basalt">flood basalts</a> in <a href="https://en.wikipedia.org/wiki/Oregon">Oregon</a>, <a href="https://en.wikipedia.org/wiki/Washington_(state)">Washington</a> and <a href="https://en.wikipedia.org/wiki/Idaho">Idaho</a>. Other famous places include the <a href="https://en.wikipedia.org/wiki/Giant&#39;s_Causeway">Giant&#39;s Causeway</a> in <a href="https://en.wikipedia.org/wiki/Northern_Ireland">Northern Ireland</a>, <a href="https://en.wikipedia.org/wiki/Fingal&#39;s_Cave">Fingal&#39;s Cave</a> on the island of <a href="https://en.wikipedia.org/wiki/Staffa">Staffa</a>, <a href="https://en.wikipedia.org/wiki/Scotland">Scotland</a> and the <a href="https://en.wikipedia.org/wiki/Stuðlagil">Stuðlagil</a> Canyon, <a href="https://en.wikipedia.org/wiki/Iceland">Iceland</a>.^{<span><span>[</span>5<span>]</span></span>}</p><section><div><h3>Devils Tower</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Devils_Tower">Devils Tower</a></div> <figure><a href="https://en.wikipedia.org/wiki/File:&quot;This_means_something._This_is_important&quot;_(19967592275).jpg"></a><figcaption>Devils Tower is an eroded <a href="https://en.wikipedia.org/wiki/Laccolith">laccolith</a> in the <a href="https://en.wikipedia.org/wiki/Black_Hills_National_Forest">Black Hills National Forest</a>, <a href="https://en.wikipedia.org/wiki/Wyoming">Wyoming</a>.</figcaption></figure> <p>Devils Tower in Wyoming in the United States is about 40 million years old and <span>382 meters (1,253 feet)</span> high.^{<span><span>[</span>1<span>]</span></span>} Geologists agree that the rock forming Devils Tower solidified from an intrusion, but it has not been established whether the <a href="https://en.wikipedia.org/wiki/Magma">magma</a> from this intrusion ever reached the surface. Most columns are 6-sided, but 4, 5, and 7-sided ones can also be found.^{<span><span>[</span>6<span>]</span></span>}</p> </section><section><div><h3>Giant&#39;s Causeway</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Giant&#39;s_Causeway">Giant&#39;s Causeway</a></div> <p>The Giant&#39;s Causeway (<a href="https://en.wikipedia.org/wiki/Irish_language">Irish</a>: <i>Clochán An Aifir</i>) on the <a href="https://en.wikipedia.org/wiki/County_Antrim">north Antrim coast</a> of Northern Ireland was created by volcanic activity 60 million years ago, and consists of over 40,000 columns.^{<span><span>[</span>1<span>]</span></span>}^{<span><span>[</span>7<span>]</span></span>} According to a legend, the giant <a href="https://en.wikipedia.org/wiki/Finn_McCool">Finn McCool</a> created the Giant&#39;s Causeway, as a <a href="https://en.wikipedia.org/wiki/Causeway">causeway</a> to Scotland.^{<span><span>[</span>8<span>]</span></span>}</p> </section><section><div><h3>High Island Reservoir</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div> <p>Formed in Cretaceous, the columnar rocks are found around the reservoir and the islands nearby in <a href="https://en.wikipedia.org/wiki/Sai_Kung_Peninsula">Sai Kung</a>, <a href="https://en.wikipedia.org/wiki/Hong_Kong">Hong Kong</a>. It is special that the rocks are not mafic, but felsic <a href="https://en.wikipedia.org/wiki/Tuff">tuff</a> instead.</p> <figure><a href="https://en.wikipedia.org/wiki/File:Hexagonal_volcanic_tuffs_at_East_Dam_of_High_Island_Reservoir_1.jpg"></a><figcaption>Hexagonal volcanic tuffs at East Dam of High Island Reservoir</figcaption></figure> </section><section><div><h3>Cerro Kõi</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=10"><span>edit</span></a><span>]</span></span></div> <p>There are several examples of columnar jointed sandstones in the greater <a href="https://en.wikipedia.org/wiki/Asunción">Asunción</a> region of <a href="https://en.wikipedia.org/wiki/Paraguay">Paraguay</a>. The best known is Cerro Kõi in <a href="https://en.wikipedia.org/wiki/Areguá">Areguá</a>, but there are also several quarries in <a href="https://en.wikipedia.org/wiki/Luque">Luque</a>. </p> </section><section><div><h3>Mars</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Marte_Vallis">Marte Vallis</a></div> <p>Several exposures of columnar jointing have been discovered on the planet Mars by the High Resolution Imaging Science Experiment (<a href="https://en.wikipedia.org/wiki/HiRISE">HiRISE</a>) camera, which is carried by the <a href="https://en.wikipedia.org/wiki/Mars_Reconnaissance_Orbiter">Mars Reconnaissance Orbiter</a> (MRO).^{<span><span>[</span>10<span>]</span></span>}^{<span><span>[</span>11<span>]</span></span>}</p> <figure><a href="https://en.wikipedia.org/wiki/File:Martevallis_hir_2007304_lrgMod1.png"></a><figcaption>Columnar jointed rocks in unnamed crater wall, <a href="https://en.wikipedia.org/wiki/Marte_Vallis">Marte Vallis</a> region, Mars. Image courtesy of the <a href="https://en.wikipedia.org/wiki/High_Resolution_Imaging_Science_Experiment">High Resolution Imaging Science Experiment</a>, <a href="https://en.wikipedia.org/wiki/University_of_Arizona">University of Arizona</a>.</figcaption></figure> </section><section><div><h3>Columnar basalt of Tawau (Batu Bersusun)</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=14"><span>edit</span></a><span>]</span></span></div> <p>At Kampung Balung Cocos, <a href="https://en.wikipedia.org/wiki/Tawau">Tawau</a>, <a href="https://en.wikipedia.org/wiki/Malaysia">Malaysia</a>, the river flows through the area of columnar basalt. One section is seen vertically high on river bank. The rest lies on river bank. The water flows from the lowest area forming waterfall.</p> <figure><a href="https://en.wikipedia.org/wiki/File:Garni_Gorge_Armenia_axxp.JPG"></a><figcaption>Garni gorge</figcaption></figure> </section><section><div><h3>Gorge of Garni, Armenia</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=15"><span>edit</span></a><span>]</span></span></div> <p>The <a href="https://en.wikipedia.org/wiki/Garni_Gorge">Garni Gorge</a> is situated 23 km east of Yerevan, Armenia, just below the village of the same name. This portion of the Garni Gorge is typically referred to as the &quot;Symphony of the Stones.&quot; On a promontory above the gorge the first-century AD Temple of Garni may be seen.</p> </section><section><div><h3>Stuðlagil Canyon, Iceland</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=16"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Stuðlagil">Stuðlagil</a></div> <p>The Stuðlagil Canyon, situated 45 miles west of Egilsstaðir, showing a view of columnar joint basalts rock formations and the blue-green water that runs through it.</p> </section><section><div><h3>Black Point, Australia</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=17"><span>edit</span></a><span>]</span></span></div> <p>Black Point, situated in the D&#39;Entrecasteaux National Park, in Western Australia is an example of black columnar basalt.</p> </section><section><div><h3>Jusangjeolli, South Korea</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Columnar_jointing&amp;action=edit&amp;section=18"><span>edit</span></a><span>]</span></span></div> <p>The columnar jointing (<i><a href="https://en.wikipedia.org/wiki/Daepo_Jusangjeolli_Cliff">Jusangjeolli</a></i> in Korean) on the southern coast near <a href="https://en.wikipedia.org/wiki/Seogwipo">Seogwipo</a> on the island of <a href="https://en.wikipedia.org/wiki/Jeju_Province">Jeju</a> is a popular tourist destination.</p> </section> https://en.wikipedia.org/wiki/Acacia_paradoxa 726l2qQvwH2NIiOCTXDH-5fgcwPKQFfDu_iN5Q== Tue, 15 Sep 2026 07:42:42 +0000 Species of plant <section><div>Species of plant</div> <table> <tbody><tr> <th colspan="2"><i>Acacia paradoxa</i></th></tr> <tr> <td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Acacia_armata_C.jpg"></a></span></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/Acacia"></a></span></span></th></tr> <tr> <td>Kingdom:</td> <td><a href="https://en.wikipedia.org/wiki/Plant">Plantae</a></td></tr> <tr> <td><i>Clade</i>:</td> <td><a href="https://en.wikipedia.org/wiki/Vascular_plant">Tracheophytes</a></td></tr> <tr> <td><i>Clade</i>:</td> <td><a href="https://en.wikipedia.org/wiki/Flowering_plant">Angiosperms</a></td></tr> <tr> <td><i>Clade</i>:</td> <td><a href="https://en.wikipedia.org/wiki/Eudicots">Eudicots</a></td></tr> <tr> <td><i>Clade</i>:</td> <td><a href="https://en.wikipedia.org/wiki/Rosids">Rosids</a></td></tr> <tr> <td>Order:</td> <td><a href="https://en.wikipedia.org/wiki/Fabales">Fabales</a></td></tr> <tr> <td>Family:</td> <td><a href="https://en.wikipedia.org/wiki/Fabaceae">Fabaceae</a></td></tr> <tr> <td>Subfamily:</td> <td><a href="https://en.wikipedia.org/wiki/Caesalpinioideae">Caesalpinioideae</a></td></tr> <tr> <td><i>Clade</i>:</td> <td><a href="https://en.wikipedia.org/wiki/Mimosoideae">Mimosoid clade</a></td></tr> <tr> <td>Genus:</td> <td><a href="https://en.wikipedia.org/wiki/Acacia"><i>Acacia</i></a></td></tr> <tr> <td>Species:</td> <td><div><i><b>A.<span> </span>paradoxa</b></i></div></td></tr> <tr> <th colspan="2"><a href="https://en.wikipedia.org/wiki/Binomial_nomenclature">Binomial name</a></th></tr> <tr> <td colspan="2"><b><span><i>Acacia paradoxa</i></span></b><br/><div><a href="https://en.wikipedia.org/wiki/A._P._de_Candolle">DC.</a></div></td></tr> <tr> <td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:Acacia_paradoxaDistMap672.png"></a></span></td></tr> <tr> <td colspan="2">Occurrence data from <a href="https://en.wikipedia.org/wiki/Australasian_Virtual_Herbarium">AVH</a></td></tr> <tr> <th colspan="2"><a href="https://en.wikipedia.org/wiki/Synonym_(taxonomy)">Synonyms</a>^{<span><span>[</span>1<span>]</span></span>}</th></tr> <tr> <td colspan="2"> <div> <ul><li> <small><b>Homotypic Synonyms</b></small> <ul><li><i>Acacia armata <span>var.</span> angustifolia</i> <small> Benth. </small></li><li><i>Acacia armata <span>var.</span> paradoxa</i> <small> (DC.) Ser. </small></li><li><i>Acacia undulata</i> <small> Spin, Jard. St. Sebastien </small></li><li><i>Mimosa paradoxa</i> <small> (DC.) Dum.Cours. </small></li><li><i>Racosperma paradoxum</i> <small> (DC.) Pedley </small></li></ul> <p><small><b>Heterotypic Synonyms</b></small></p> <ul><li><i>Acacia armata</i> <small> R.Br. </small></li><li><i>Acacia armata <span>var.</span> longipedunculata</i> <small> Regel </small></li><li><i>Acacia armata <span>var.</span> microphylla</i> <small> Benth. </small></li><li><i>Acacia armata <span>f.</span> ornithophora</i> <small> (Sweet) Siebert &amp; Voss </small></li><li><i>Acacia armata <span>var.</span> ornithophora</i> <small> (Sweet) Benth. </small></li><li><i>Acacia armata <span>var.</span> pendula</i> <small> Seem. </small></li><li><i>Acacia armata <span>var.</span> typica</i> <small> Domin </small></li><li><i>Acacia armata <span>var.</span> undulata</i> <small> (Siebert &amp; Voss) Riebe </small></li><li><i>Acacia armata <span>f.</span> undulata</i> <small> (Link) Siebert &amp; Voss </small></li><li><i>Acacia armatoides</i> <small> Walp. </small></li><li><i>Acacia falcifolia</i> <small> Hoffmanns. </small></li><li><i>Acacia furcifera</i> <small> Lindl. </small></li><li><i>Acacia ornithophora</i> <small> Sweet </small></li><li><i>Acacia undulata</i> <small> Willd. ex Spreng. </small></li><li><i>Acacia undulata</i> <small> Willd. ex H.L.Wendl. </small></li><li><i>Acacia undulata <span>var.</span> elegans</i> <small> Jacques </small></li><li><i>Acacia undulata <span>var.</span> longispina</i> <small> Vis. </small></li><li><i>Phyllodoce armata</i> <small> (R.Br.) Link </small></li><li><i>Phyllodoce undulata</i> <small> Link </small></li><li><i>Racosperma armatum</i> <small> (R.Br.) Mart. </small></li><li><i>Racosperma undulatum</i> <small> Mart. </small></li></ul> </li></ul> </div></td></tr> </tbody></table> <figure><a href="https://en.wikipedia.org/wiki/File:Acacia_paradoxa_kz3.jpg"></a><figcaption>Habit</figcaption></figure> <figure><a href="https://en.wikipedia.org/wiki/File:Acacia_paradoxa_(Hedge_Wattle)_(24631313579).jpg"></a><figcaption>Foliage, stipules and flowers</figcaption></figure> <p><i><b>Acacia paradoxa</b></i>^{<span><span>[</span>2<span>]</span></span>} is a plant in the family <a href="https://en.wikipedia.org/wiki/Fabaceae">Fabaceae</a>. Its common names include <b>kangaroo acacia</b>,^{<span><span>[</span>3<span>]</span></span>} <b>kangaroo thorn</b>, <b>prickly wattle</b>, <b>hedge wattle</b>^{<span><span>[</span>4<span>]</span></span>} and <b>paradox acacia</b>.</p> </section><section><div><h2>Description</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Acacia_paradoxa&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div> <p>The large <a href="https://en.wikipedia.org/wiki/Shrub">shrub</a> or tree up to <span>2 to 4 metres (7 to 13</span><span> </span><span>ft)</span> tall^{<span><span>[</span>5<span>]</span></span>} and has a similar width,^{<span><span>[</span>4<span>]</span></span>} it has ribbed branchlets that are often arched downward. It is dense with foliage; the leaves are actually enlarged <a href="https://en.wikipedia.org/wiki/Petiole_(botany)">petioles</a> known as <a href="https://en.wikipedia.org/wiki/Phyllode">phyllodes</a>. They are crinkly and the new ones are covered in hairs. The erect phyllodes are asymmetric and have a <a href="https://en.wikipedia.org/wiki/Lanceolate">lanceolate</a> shape and are around <span>30 millimetres (1.18</span><span> </span><span>in)</span> in length and <span>7</span><span> </span><span>mm (0.276</span><span> </span><span>in)</span> wide.^{<span><span>[</span>5<span>]</span></span>} The bush is also full of long spines. It usually flowers between August and November^{<span><span>[</span>4<span>]</span></span>} producing an axillary flower-spike with small, bright yellow spherical flower heads and the fruits are brown pods <span>4 to 7 centimetres (1.6 to 2.8</span><span> </span><span>in)</span> long. The hard black seeds within have an oblong shape and are about <span>6</span><span> </span><span>mm (0.236</span><span> </span><span>in)</span> in length and half as wide.^{<span><span>[</span>5<span>]</span></span>}</p> <p>The spiny <a href="https://en.wikipedia.org/wiki/Stipule">stipules</a> that grow at the base of the phyllodes deter livestock from feeding on or too close to the plant.</p> </section><section><div><h2>Taxonomy</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Acacia_paradoxa&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div> <p>The species was first formally described by the botanist <a href="https://en.wikipedia.org/wiki/Augustin_Pyramus_de_Candolle">Augustin Pyramus de Candolle</a> in 1813 as part of the work <i>Catalogus Plantarum Horti Botanici Monspeliensis</i>.^{<span><span>[</span>3<span>]</span></span>} The species name is from the <a href="https://en.wikipedia.org/wiki/Greek_(language)">Greek</a> words <i>para</i> which means <i>near</i> and <i>doxa</i> meaning <i>glory</i>. This probably refers the unattractive and thorny shrub being quite showy when it is in bloom.^{<span><span>[</span>5<span>]</span></span>}</p> <p>Many synonyms are known for the plant including; <i>Acacia ornithophora</i>, <i>Acacia undulata</i>, <i>Mimosa paradoxa</i>, <i>Racosperma paradoxum</i>, <i>Acacia armata</i> and <i>Acacia hybrida</i>.^{<span><span>[</span>3<span>]</span></span>}</p> </section><section><div><h2>Distribution</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Acacia_paradoxa&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <p>Kangaroo thorn is widely spread across Australia, regenerating from seed after disturbances, such as bush fire. Small birds, including wrens, use this plant as shelter and dwelling, while it is relied upon as a food source for moths, butterflies and other insects, birds also feed on its seeds.</p> <p>It is <a href="https://en.wikipedia.org/wiki/Endemism">endemic</a> to south eastern parts of <a href="https://en.wikipedia.org/wiki/South_Australia">South Australia</a>, much of <a href="https://en.wikipedia.org/wiki/Victoria_(Australia)">Victoria</a>, eastern <a href="https://en.wikipedia.org/wiki/New_South_Wales">New South Wales</a> and south eastern parts of <a href="https://en.wikipedia.org/wiki/Queensland">Queensland</a>.^{<span><span>[</span>3<span>]</span></span>} It has become naturalised in parts of <a href="https://en.wikipedia.org/wiki/Western_Australia">Western Australia</a> and <a href="https://en.wikipedia.org/wiki/Tasmania">Tasmania</a>.^{<span><span>[</span>5<span>]</span></span>}</p> <p>The plant has also been introduced to other continents. In the United States, kangaroo thorn is a well-known <a href="https://en.wikipedia.org/wiki/Noxious_weed">noxious weed</a> in California.^{<span><span>[</span>6<span>]</span></span>}</p> </section><section><div><h2>Cultivation</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Acacia_paradoxa&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <p>The plant is used as an ornamental or as a dense screening plant. It make an excellent habitat and food source for birds. It grows well in full sun or in a partly shaded position. It can be planted in dry to moist well-drained areas.^{<span><span>[</span>4<span>]</span></span>} Seeds require pre-treatment such as scarification prior to planting.^{<span><span>[</span>5<span>]</span></span>}</p> <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 <a href="https://commons.wikimedia.org/wiki/Category:Acacia%20paradoxa"><span>Acacia paradoxa</span></a>.</div></div> </div> </section><section><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Acacia_paradoxa&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <div> <div><ol><li><span><span>↑</span></span> <span><cite><a href="https://powo.science.kew.org/taxon/471079-1">&quot;<i>Acacia paradoxa</i>&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Plants_of_the_World_Online">Plants of the World Online</a></i>. <a href="https://en.wikipedia.org/wiki/Royal_Botanic_Gardens,_Kew">Royal Botanic Gardens, Kew</a><span>. Retrieved <span>28 August</span> 2022</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://web.archive.org/web/20220928142050/https://www.anbg.gov.au/cgi-bin/apni?TAXON_NAME=ACACIA%20PARADOXA">&quot;<i>Acacia paradoxa</i>&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/Australian_Plant_Name_Index">Australian Plant Name Index</a> (APNI), IBIS database</i>. Centre for Plant Biodiversity Research, Australian Government, Canberra. Archived from <a href="http://www.anbg.gov.au/cgi-bin/apni?TAXON_NAME=ACACIA+PARADOXA">the original</a> on 2022-09-28<span>. Retrieved <span>2008-04-03</span></span>.</cite></span></li> <li><span><span>1</span> <span>2</span> <span>3</span> <span>4</span></span> <span><cite><a href="https://web.archive.org/web/20181126180852/https://bie.ala.org.au/species/http://id.biodiversity.org.au/node/apni/2920772#names">&quot;<i>Acacia paradoxa</i> DC. Kangaroo Acacia&quot;</a>. <i>Atals of Living Australia</i>. <a href="https://en.wikipedia.org/wiki/Global_Biodiversity_Information_Facility">Global Biodiversity Information Facility</a>. Archived from <a href="https://bie.ala.org.au/species/http://id.biodiversity.org.au/node/apni/2920772#names">the original</a> on 26 November 2018<span>. Retrieved <span>3 October</span> 2018</span>.</cite></span></li> <li><span><span>1</span> <span>2</span> <span>3</span> <span>4</span></span> <span><cite><a href="https://web.archive.org/web/20200301151409/http://fe.yarraranges.vic.gov.au/Residents/Trees_Vegetation/Yarra_Ranges_Plant_Directory/Yarra_Ranges_Local_Plant_Directory/Middle_Storey/Shrubs_1_12m_-10m/Acacia_paradoxa">&quot;<i>Acacia paradoxa</i>&quot;</a>. Yarra Ranges. Archived from <a href="http://fe.yarraranges.vic.gov.au/Residents/Trees_Vegetation/Yarra_Ranges_Plant_Directory/Yarra_Ranges_Local_Plant_Directory/Middle_Storey/Shrubs_1_12m_-10m/Acacia_paradoxa">the original</a> on 1 March 2020<span>. Retrieved <span>3 October</span> 2018</span>.</cite></span></li> <li><span><span>1</span> <span>2</span> <span>3</span> <span>4</span> <span>5</span> <span>6</span></span> <span><cite><a href="http://saseedbank.com.au/species_information.php?rid=196">&quot;<i>Acacia paradoxa</i> (Leguminosae) Kangaroo Thorn&quot;</a>. <i>Seeds of South Australia</i>. <a href="https://en.wikipedia.org/wiki/Government_of_South_Australia">Government of South Australia</a><span>. Retrieved <span>3 October</span> 2018</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://plants.usda.gov/java/profile?symbol=ACPA8">&quot;Acacia paradoxa&quot;</a>. <i>Plants Profile</i>. <a href="https://en.wikipedia.org/wiki/United_States_Department_of_Agriculture">United States Department of Agriculture</a><span>. Retrieved <span>2 April</span> 2012</span>.</cite></span></li> </ol></div></div> </section><section><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Acacia_paradoxa&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div> <ul><li><cite>Zenni, R. D.; Wilson, J. R. U.; Le Roux, J. J.; Richardson, D. M. (August 2009). <a href="https://doi.org/10.1016%2Fj.sajb.2009.04.001">&quot;Evaluating the invasiveness of Acacia paradoxa in South Africa&quot;</a>. <i>South African Journal of Botany</i>. <b>75</b> (3): <span>485–</span>496. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1016%2Fj.sajb.2009.04.001">10.1016/j.sajb.2009.04.001</a></span>.</cite></li> <li><cite>Correia, Marta; Castro, Silvia; Ferrero, Victoria (April 2014). <a href="https://doi.org/10.1111%2Fboj.12155">&quot;Reproductive biology and success of invasive Australian acacias in Portugal&quot;</a>. <i>Botanical Journal of the Linnean Society</i>. <b>174</b> (4): <span>574–</span>588. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<span><a href="https://doi.org/10.1111%2Fboj.12155">10.1111/boj.12155</a></span>.</cite></li> <li><cite>Castro-Diez, P.; Langendoen, T.; Poorter, L. (1 November 2011). &quot;Predicting Acacia invasive success in South Africa on the basis of functional traits, native climatic niche and human use&quot;. <i>Biodiversity and Conservation</i>. <b>20</b> (12): <span>2729–</span>2743. <a href="https://en.wikipedia.org/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2011BiCon..20.2729C">2011BiCon..20.2729C</a>. <a href="https://en.wikipedia.org/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2Fs10531-011-0101-5">10.1007/s10531-011-0101-5</a>. <a href="https://en.wikipedia.org/wiki/S2CID_(identifier)">S2CID</a><span> </span><a href="https://api.semanticscholar.org/CorpusID:41606801">41606801</a>.</cite></li></ul> </section><section><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Acacia_paradoxa&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://plants.usda.gov/java/profile?symbol=ACPA8">USDA Plants Profile</a></li> <li><a href="http://www.cdfa.ca.gov/phpps/ipc/weedinfo/acacia.htm">EncycloWeedia Profile</a></li> <li><a href="http://calphotos.berkeley.edu/cgi/img_query?query_src=photos_index&amp;where-taxon=Acacia+paradoxa">Photo gallery</a></li></ul> <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>Acacia paradoxa</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/Q1524950">Q1524950</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/Acacia%20paradoxa">Acacia paradoxa</a></span></span></span></li> <li><span>APDB: <span><a href="https://africanplantdatabase.ch/en/nomen/67508">67508</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Australian_Plant_Name_Index">APNI</a>: <span><a href="https://id.biodiversity.org.au/name/apni/68149">68149</a></span></span></li> <li><span>Calflora: <span><a href="https://www.calflora.org/cgi-bin/species_query.cgi?where-calrecnum=37">37</a></span></span></li> <li><span>Cal-IPC: <span><a href="https://www.cal-ipc.org/plants/profile/acacia-paradoxa-profile/">acacia-paradoxa</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/8PSR">8PSR</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/State_Herbarium_of_South_Australia">eFloraSA</a>: <span><a href="http://www.flora.sa.gov.au/cgi-bin/speciesfacts_display.cgi?form=speciesfacts&amp;name=Acacia_paradoxa">Acacia_paradoxa</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/648693">648693</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/ACAAR">ACAAR</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Flora_of_Australia">FoAO2</a>: <span><a href="https://profiles.ala.org.au/opus/foa/profile/Acacia%20paradoxa">Acacia paradoxa</a></span></span></li> <li><span>FoIO: <span><a href="https://flora.org.il/en/plants/ACAPAR">ACAPAR</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Global_Biodiversity_Information_Facility">GBIF</a> (old): <span><a href="https://www.gbif.org/species/2981159">2981159</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Germplasm_Resources_Information_Network">GRIN</a>: <span><a href="https://npgsweb.ars-grin.gov/gringlobal/taxonomydetail.aspx?id=313094">313094</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/INaturalist">iNaturalist</a>: <span><a href="https://inaturalist.org/taxa/75251">75251</a></span></span></li> <li><span>IPA: <span><a href="https://www.invasiveplantatlas.org/subject.html?sub=5031">5031</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/International_Plant_Names_Index">IPNI</a>: <span><a href="https://www.ipni.org/n/471080-1">471080-1</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=506811">506811</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/IUCN_Red_List">IUCN</a>: <span><a href="https://www.iucnredlist.org/details/198972253/0">198972253</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/datasets/taxonomy/139014/">139014</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/NSWFlora">NSWFlora</a>: <span><a href="https://plantnet.rbgsyd.nsw.gov.au/cgi-bin/NSWfl.pl?page=nswfl&amp;lvl=sp&amp;name=Acacia~paradoxa">Acacia~paradoxa</a></span></span></li> <li><span>NZOR: <span><a href="https://www.nzor.org.nz/names/9cca9631-615e-4469-9360-ab53adab3280">9cca9631-615e-4469-9360-ab53adab3280</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/New_Zealand_Plant_Conservation_Network">NZPCN</a>: <span><a href="https://web.archive.org/web/*/http://nzpcn.org.nz/flora_details.aspx?ID=2421">2421</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=343261">343261</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Plants_for_a_Future">PfaF</a>: <span><a href="https://pfaf.org/user/Plant.aspx?LatinName=Acacia+paradoxa">Acacia paradoxa</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/The_Plant_List">Plant List</a>: <span><a href="http://www.theplantlist.org/tpl1.1/record/ild-31551">ild-31551</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Natural_Resources_Conservation_Service#Plants">PLANTS</a>: <span><a href="https://plants.sc.egov.usda.gov/plant-profile/ACPA8">ACPA8</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Plants_of_the_World_Online">POWO</a>: <span><a href="https://powo.science.kew.org/taxon/urn%3Alsid%3Aipni.org%3Anames%3A471079-1">urn:lsid:ipni.org:names:471079-1</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Royal_Horticultural_Society">RHS</a>: <span><a href="https://www.rhs.org.uk/plants/84362/wd/details">84362</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/Tropicos">Tropicos</a>: <span><a href="https://www.tropicos.org/name/13024320">13024320</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/National_Herbarium_of_Victoria">VicFlora</a>: <span><a href="https://vicflora.rbg.vic.gov.au/flora/taxon/fc1c0e04-bf6f-4220-aac8-7a26a9eb36dc">fc1c0e04-bf6f-4220-aac8-7a26a9eb36dc</a></span></span></li> <li><span><a href="https://en.wikipedia.org/wiki/World_Flora_Online">WFO</a>: <span><a href="https://list.worldfloraonline.org/wfo-0000185340">wfo-0000185340</a></span></span></li></ul> </div></td></tr></tbody></table></div> </section> https://en.wikipedia.org/wiki/Windows_Recall CQazyKfNfL6MPdyo6Ey9iZ5cTW9aFk7ecn3tCQ== Tue, 15 Sep 2026 07:28:06 +0000 AI-powered feature of Windows 11 <section><div>AI-powered feature of Windows 11</div> <p><b>Windows Recall</b> is an AI-powered feature of <a href="https://en.wikipedia.org/wiki/Windows_11">Windows 11</a> intended to help users remember anything they do on their PC at any time and potentially resume or investigate it later. Users can query the AI through natural language. This feature has a rigid set of system requirements, including a 40-trillion-operations-per-second <a href="https://en.wikipedia.org/wiki/Neural_processing_unit">neural processing unit</a> (NPU), and device-level <a href="https://en.wikipedia.org/wiki/Cryptography">cryptography</a>. The feature has met significant backlash.</p> </section><section><div><h2>Overview</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Windows_Recall&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div> <p>Windows Recall takes a screenshot of a user&#39;s desktop every few seconds, then uses on-device <a href="https://en.wikipedia.org/wiki/Large_language_model">large language models</a> to allow a user to retrieve items and information that had previously been on their screen. It was announced by <a href="https://en.wikipedia.org/wiki/Microsoft">Microsoft</a>, alongside the integration of <a href="https://en.wikipedia.org/wiki/GPT-4o">GPT-4o</a> into <a href="https://en.wikipedia.org/wiki/Microsoft_Copilot">Microsoft Copilot</a> and an upgraded user interface in <a href="https://en.wikipedia.org/wiki/Windows_11">Windows 11</a>, in May 2024.^{<span><span>[</span>1<span>]</span></span>}</p> <p>Systems using Recall must meet the following requirements:^{<span><span>[</span>2<span>]</span></span>}</p> <ul><li>A <a href="https://en.wikipedia.org/wiki/Copilot+_PC">Copilot+</a> PC that meets the <a href="https://en.wikipedia.org/wiki/Secured-core_standard?action=edit&amp;redlink=1">Secured-core standard</a></li> <li>A <a href="https://en.wikipedia.org/wiki/Neural_processing_unit">neural processing unit</a> (NPU) capable of 40 TOPS</li> <li>16 GB <a href="https://en.wikipedia.org/wiki/RAM">RAM</a></li> <li>8 <a href="https://en.wikipedia.org/wiki/Logical_processor">logical processors</a></li> <li>256 GB storage capacity, with 50 GB of free space (saving snapshots automatically pauses if the device has less than 25 GB of free storage space)</li> <li><a href="https://en.wikipedia.org/wiki/BitLocker">BitLocker</a> Device Encryption enabled</li> <li><a href="https://en.wikipedia.org/wiki/Windows_Hello">Windows Hello</a> Enhanced Sign-in Security enabled, with at least one biometric sign-in option</li></ul> </section><section><div><h2>Reception</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Windows_Recall&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div> <p>Microsoft announced Recall during Build conference in May 2024 claiming that Recall stores all user (index) data locally and encrypted.^{<span><span>[</span>3<span>]</span></span>} Shortly after announcement, security experts criticized lack of an option to disable the feature. In early June, a simple script tool called <i>Total Recall</i> demonstrated a bypass of Windows Recall security stealing all local data (which was stored unencrypted).^{<span><span>[</span>4<span>]</span></span>} Shortly after, Microsoft pledged to rework Windows Recall to address demonstrated weaknesses.^{<span><span>[</span>5<span>]</span></span>} Originally Microsoft planned to sidestep testing Recall in Microsoft Insiders program to ship Recall on Copilot Plus PC program launch on June 18. On June 13, 2024, tech media reported that Microsoft engineers struggled to secure Recall by the original deadline,^{<span><span>[</span>6<span>]</span></span>} prompting Microsoft on June 14 to delay release and to do more testing in Windows Insiders release channel.^{<span><span>[</span>7<span>]</span></span>} In early September 2024, Recall appeared among optional Windows 11 features allowing users to uninstall it, but Microsoft promptly claimed that this ability is a bug.^{<span><span>[</span>8<span>]</span></span>} Later the same month, via a blog post Microsoft announced a &quot;more secure&quot; version of Recall with full database encryption and the ability to be uninstalled.^{<span><span>[</span>9<span>]</span></span>} Microsoft then changed the feature to opt-in and provided instructions for how to remove it.^{<span><span>[</span>2<span>]</span></span>}</p> <p>In May 2025, the <a href="https://en.wikipedia.org/wiki/Secure_messaging">secure messaging</a> app <a href="https://en.wikipedia.org/wiki/Signal_(software)">Signal</a> added a new &quot;screen security&quot; function to its Windows client, which uses <a href="https://en.wikipedia.org/wiki/Digital_rights_management">digital rights management</a> to prevent the program from being visible to Recall or any other screen capture tools; this feature is enabled by default for all Windows 11 users. Signal&#39;s developers explicitly cited Recall as an impetus for the feature, arguing that software developers &quot;shouldn&#39;t have to implement &#39;one weird trick&#39; in order to maintain the privacy and integrity of their services without proper developer tools. People who care about privacy shouldn&#39;t be forced to sacrifice accessibility upon the altar of AI aspirations either.&quot;^{<span><span>[</span>10<span>]</span></span>}^{<span><span>[</span>11<span>]</span></span>} <a href="https://en.wikipedia.org/wiki/Brave_browser">Brave</a> and <a href="https://en.wikipedia.org/wiki/AdGuard">AdGuard</a> added similar functionality in July 2025.^{<span><span>[</span>12<span>]</span></span>}</p> </section><section><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Windows_Recall&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <div> <div><ol><li><span><span>↑</span></span> <span><cite>Khan, Imad (May 20, 2024). <a href="https://www.cnet.com/tech/services-and-software/microsoft-copilot-embraces-the-power-of-openais-new-gpt-4-o/">&quot;Microsoft&#39;s Copilot Embraces the Power of OpenAI&#39;s New GPT-4o&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/CNET">CNET</a></i>. <a href="https://en.wikipedia.org/wiki/CBS_Interactive">CBS Interactive</a>. <a href="https://web.archive.org/web/20240523165249/https://www.cnet.com/tech/services-and-software/microsoft-copilot-embraces-the-power-of-openais-new-gpt-4-o/">Archived</a> from the original on May 23, 2024<span>. Retrieved <span>May 23,</span> 2024</span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite><a href="https://web.archive.org/web/20250408170949/https://support.microsoft.com/en-us/windows/retrace-your-steps-with-recall-aa03f8a0-a78b-4b3e-b0a1-2eb8ac48701c">&quot;Retrace your steps with Recall&quot;</a>. <i>Microsoft Support</i>. <a href="https://en.wikipedia.org/wiki/Microsoft">Microsoft</a>. Archived from <a href="https://support.microsoft.com/en-us/windows/retrace-your-steps-with-recall-aa03f8a0-a78b-4b3e-b0a1-2eb8ac48701c">the original</a> on April 8, 2025.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Edwards, Benj (2024-05-20). <a href="https://arstechnica.com/gadgets/2024/05/microsofts-new-recall-feature-will-record-everything-you-do-on-your-pc/">&quot;New Windows AI feature records everything you&#39;ve done on your PC&quot;</a>. <i>Ars Technica</i><span>. Retrieved <span>2026-05-18</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Cunningham, Andrew (2024-06-04). <a href="https://arstechnica.com/ai/2024/06/windows-recall-demands-an-extraordinary-level-of-trust-that-microsoft-hasnt-earned/">&quot;Windows Recall demands an extraordinary level of trust that Microsoft hasn&#39;t earned&quot;</a>. <i>Ars Technica</i><span>. Retrieved <span>2026-05-18</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Cunningham, Andrew (2024-06-07). <a href="https://arstechnica.com/gadgets/2024/06/microsoft-makes-recall-feature-off-by-default-after-security-and-privacy-backlash/">&quot;Microsoft is reworking Recall after researchers point out its security problems&quot;</a>. <i>Ars Technica</i><span>. Retrieved <span>2026-05-18</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Warren, Tom (2024-06-13). <a href="https://www.theverge.com/2024/6/13/24177703/microsoft-xbox-game-showcase-windows-recall">&quot;Xbox delivered and Windows scrambles to secure Recall&quot;</a>. <i>The Verge</i><span>. Retrieved <span>2026-05-18</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Warren, Tom (2024-06-13). <a href="https://www.theverge.com/2024/6/13/24178144/microsoft-windows-ai-recall-feature-delay">&quot;Microsoft&#39;s all-knowing Recall AI feature is being delayed&quot;</a>. <i>The Verge</i><span>. Retrieved <span>2026-05-18</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Warren, Tom (2024-09-02). <a href="https://www.theverge.com/2024/9/2/24233992/microsoft-recall-windows-11-uninstall-feature-bug">&quot;Microsoft says its Recall uninstall option in Windows 11 is just a bug&quot;</a>. <i>The Verge</i><span>. Retrieved <span>2026-05-18</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Warren, Tom (2024-09-27). <a href="https://www.theverge.com/2024/9/27/24255721/microsoft-windows-recall-ai-security-improvements-overhaul-uninstall">&quot;Microsoft&#39;s more secure Windows Recall feature can also be uninstalled by users&quot;</a>. <i>The Verge</i><span>. Retrieved <span>2026-05-18</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Lund, Joshua (May 21, 2025). <a href="https://signal.org/blog/signal-doesnt-recall/">&quot;By Default, Signal Doesn&#39;t Recall&quot;</a>. <i>Signal.org</i>. Signal.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Goodin, Dan (2025-05-21). <a href="https://arstechnica.com/security/2025/05/signal-resorts-to-weird-trick-to-block-windows-recall-in-desktop-app/">&quot;&quot;Microsoft has simply given us no other option,&quot; Signal says as it blocks Windows Recall&quot;</a>. <i>Ars Technica</i><span>. Retrieved <span>2026-05-18</span></span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Warren, Tom (2025-07-25). <a href="https://www.theverge.com/news/713676/brave-adguard-windows-recall-block-microsoft">&quot;Microsoft&#39;s controversial Recall feature is now blocked by Brave and AdGuard&quot;</a>. <i><a href="https://en.wikipedia.org/wiki/The_Verge">The Verge</a></i>. <a href="https://en.wikipedia.org/wiki/Vox_Media">Vox Media</a><span>. Retrieved <span>2025-07-28</span></span>.</cite></span></li> </ol></div></div> </section> https://en.wikipedia.org/wiki/Huffman_coding 4HaJk5M4mVPC9R2M5mu9ikKxKay5LpcQk7UVKA== Tue, 15 Sep 2026 06:49:51 +0000 Problem definition <div><h2>Problem definition</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Huffman_coding&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></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 <a href="https://en.wikipedia.org/wiki/Wikipedia:Verifiability">more citations</a></b>.<span> Please help <a href="https://en.wikipedia.org/wiki/Special:EditPage/Huffman_coding">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 <a href="https://en.wikipedia.org/wiki/Wikipedia:Verifiability#Burden_of_evidence">removed</a>.<br/><small><span><i>Find sources:</i><span> </span><a href="https://www.google.com/search?as_eq=wikipedia&amp;q=%22Huffman+coding%22">&quot;Huffman coding&quot;</a><span> </span>–<span> </span><a href="https://www.google.com/search?tbm=nws&amp;q=%22Huffman+coding%22+-wikipedia&amp;tbs=ar:1">news</a> <b>·</b> <a href="https://www.google.com/search?&amp;q=%22Huffman+coding%22&amp;tbs=bkt:s&amp;tbm=bks">newspapers</a> <b>·</b> <a href="https://www.google.com/search?tbs=bks:1&amp;q=%22Huffman+coding%22+-wikipedia">books</a> <b>·</b> <a href="https://scholar.google.com/scholar?q=%22Huffman+coding%22">scholar</a> <b>·</b> <a href="https://www.jstor.org/action/doBasicSearch?Query=%22Huffman+coding%22&amp;acc=on&amp;wc=on">JSTOR</a></span></small></span> <span><i>(<span>December 2021</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:HuffmanCodeAlg.png"></a><figcaption>Constructing a Huffman tree</figcaption></figure><section><div><h3>Informal description</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Huffman_coding&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <dl><dt>Given</dt><dd>A set of symbols <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> and for each symbol <span><span><math> <semantics> <mrow> <mstyle> <mi>x</mi> <mo>∈</mo> <mi>S</mi> </mstyle> </mrow> <annotation>{\displaystyle x\in S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51186ba8afb2067573a9082d55dd383df1ea9214" alt="{\displaystyle x\in S}" title=""/></span>, the frequency <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>f</mi> <mrow> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle f_{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb36605624ab2287dc5ec558513c625b88acfee3" alt="{\displaystyle f_{x}}" title=""/></span> representing the fraction of symbols in the text that are equal 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>.^{<span><span>[</span>5<span>]</span></span>}</dd> <dt>Find</dt><dd>A <a href="https://en.wikipedia.org/wiki/Prefix_code">prefix-free binary code</a> (a set of codewords) with minimum <a href="https://en.wikipedia.org/wiki/Expected_value">expected</a> codeword length (equivalently, a tree with minimum <a href="https://en.wikipedia.org/wiki/Glossary_of_graph_theory#W">weighted path length from the root</a>).</dd></dl> </section><section><div><h3>Formalized description</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Huffman_coding&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <p><b>Input</b>.<br/> Alphabet <span><span><math> <semantics> <mrow> <mstyle> <mi>A</mi> <mo>=</mo> <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> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle A=(a_{1},a_{2},\dots ,a_{n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd7971cd308b54a9afb4b897a990d32c3c5174f4" alt="{\displaystyle A=(a_{1},a_{2},\dots ,a_{n})}" title=""/></span>, which is the symbol alphabet of size <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>. <br/> Tuple <span><span><math> <semantics> <mrow> <mstyle> <mi>W</mi> <mo>=</mo> <mo>(</mo> <msub> <mi>w</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>w</mi> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>w</mi> <mrow> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle W=(w_{1},w_{2},\dots ,w_{n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eea6a64cad1424b3d68c8ac38a360c5383486ce4" alt="{\displaystyle W=(w_{1},w_{2},\dots ,w_{n})}" title=""/></span>, which is the tuple of the (positive) symbol weights (usually proportional to probabilities), i.e. <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mi>weight</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>∈</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo>}</mo> </mstyle> </mrow> <annotation>{\displaystyle w_{i}=\operatorname {weight} \left(a_{i}\right),\,i\in \{1,2,\dots ,n\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d928718b91ee67e2ffe43864cdd8a4e9e815007" alt="{\displaystyle w_{i}=\operatorname {weight} \left(a_{i}\right),\,i\in \{1,2,\dots ,n\}}" title=""/></span>. <br/> <br/> <b>Output</b>.<br/> Code <span><span><math> <semantics> <mrow> <mstyle> <mi>C</mi> <mrow> <mo>(</mo> <mi>W</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>(</mo> <msub> <mi>c</mi> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>c</mi> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>c</mi> <mrow> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle C\left(W\right)=(c_{1},c_{2},\dots ,c_{n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea3b6a7da9769c2d5f87be6ea75b14ea4ee97621" alt="{\displaystyle C\left(W\right)=(c_{1},c_{2},\dots ,c_{n})}" title=""/></span>, which is the tuple of (binary) codewords, where <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>c</mi> <mrow> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation>{\displaystyle c_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01acb7953ba52c2aa44264b5d0f8fd223aa178a2" alt="{\displaystyle c_{i}}" title=""/></span> is the codeword for <span><span><math> <semantics> <mrow> <mstyle> <msub> <mi>a</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>∈</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo>}</mo> </mstyle> </mrow> <annotation>{\displaystyle a_{i},\,i\in \{1,2,\dots ,n\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/447bbca06d834d18d87bd270b4eadede332990bb" alt="{\displaystyle a_{i},\,i\in \{1,2,\dots ,n\}}" title=""/></span>.<br/> <br/> <b>Goal</b>.<br/> Let <span><span><math> <semantics> <mrow> <mstyle> <mi>L</mi> <mo>(</mo> <mi>C</mi> <mo>(</mo> <mi>W</mi> <mo>)</mo> <mo>)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> </mrow> </munderover> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> <mi>length</mi> <mo>⁡</mo> <mo>(</mo> <msub> <mi>c</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mstyle> </mrow> <annotation>{\textstyle L(C(W))=\sum _{i=1}^{n}w_{i}\operatorname {length} (c_{i})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c450f9a883d163b16ded56056d9b0c5f720874f6" alt="{\textstyle L(C(W))=\sum _{i=1}^{n}w_{i}\operatorname {length} (c_{i})}" title=""/></span> be the weighted path length of code <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/4fc55753007cd3c18576f7933f6f089196732029" alt="{\displaystyle C}" title=""/></span>. Condition: <span><span><math> <semantics> <mrow> <mstyle> <mi>L</mi> <mo>(</mo> <mi>C</mi> <mo>(</mo> <mi>W</mi> <mo>)</mo> <mo>)</mo> <mo>≤</mo> <mi>L</mi> <mo>(</mo> <mi>T</mi> <mo>(</mo> <mi>W</mi> <mo>)</mo> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle L(C(W))\leq L(T(W))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/495b97b04a92245e7a8b3fc3eeda5b3b6fff6ef8" alt="{\displaystyle L(C(W))\leq L(T(W))}" title=""/></span> for any code <span><span><math> <semantics> <mrow> <mstyle> <mi>T</mi> <mo>(</mo> <mi>W</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle T(W)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12bbad443fb07fbf7882a2a4af08d919952cb4c9" alt="{\displaystyle T(W)}" title=""/></span>.</p> </section><section><div><h3>Example</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Huffman_coding&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div> <p>We give an example of the result of Huffman coding for a code with five characters and given weights. We will not verify that it minimizes <i>L</i> over all codes, but we will compute <i>L</i> and compare it to the <a href="https://en.wikipedia.org/wiki/Shannon_entropy">Shannon entropy</a> <i>H</i> of the given set of weights; the result is nearly optimal.</p> <table> <tbody><tr><th rowspan="2">Input (<i>A</i>, <i>W</i>)</th> <th>Symbol (<span><i>a</i>_<i>i</i></span>)</th> <td>a</td> <td>b</td> <td>c</td> <td>d</td> <td>e</td> <th>Sum</th></tr> <tr> <th>Weights (<span><i>w</i>_<i>i</i></span>)</th> <td>0.10</td> <td>0.15</td> <td>0.30</td> <td>0.16</td> <td>0.29</td> <td>= 1</td></tr> <tr> <th rowspan="3">Output <i>C</i></th> <th>Codewords (<span><i>c</i>_<i>i</i></span>)</th> <td><code>010</code></td> <td><code>011</code></td> <td><code>11</code></td> <td><code>00</code></td> <td><code>10</code></td> <td rowspan="2"><span> </span></td></tr> <tr> <th>Codeword length (in bits)<br/>(<span><i>ℓ</i>_<i>i</i></span>)</th> <td>3</td> <td>3</td> <td>2</td> <td>2</td> <td>2</td></tr> <tr> <th>Contribution to weighted path length<br/>(<span><i>ℓ</i>_<i>i</i></span> <span><i>w</i>_<i>i</i></span> )</th> <td>0.30</td> <td>0.45</td> <td>0.60</td> <td>0.32</td> <td>0.58</td> <td><i>L</i>(<i>C</i>) = 2.25</td></tr> <tr> <th rowspan="3">Optimality</th> <th>Probability budget<br/>(<span>2^{−<i>ℓ</i>_<i>i</i>}</span>)</th> <td>1/8</td> <td>1/8</td> <td>1/4</td> <td>1/4</td> <td>1/4</td> <td>= 1.00</td></tr> <tr> <th>Information content (in bits)<br/>(<span>−log₂ <i>w</i>_<i>i</i></span>) ≈</th> <td>3.32</td> <td>2.74</td> <td>1.74</td> <td>2.64</td> <td>1.79</td> <td><span> </span></td></tr> <tr> <th>Contribution to entropy<br/>(<span>−<i>w</i>_<i>i</i> log₂ <i>w</i>_<i>i</i></span>)</th> <td>0.332</td> <td>0.411</td> <td>0.521</td> <td>0.423</td> <td>0.518</td> <td><i>H</i>(<i>A</i>) = 2.205</td></tr> </tbody></table> <p>For any code that is <i>biunique</i>, meaning that the code is <a href="https://en.wikipedia.org/wiki/Variable-length_code#Uniquely_decodable_codes"><i>uniquely decodeable</i></a>, the sum of the probability budgets across all symbols is always less than or equal to one. In this example, the sum is strictly equal to one; as a result, the code is termed a <i>complete</i> code. If this is not the case, one can always derive an equivalent code by adding extra symbols (with associated null probabilities), to make the code complete while keeping it <i>biunique</i>.</p> <p>As defined by <a href="https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication">Shannon (1948)</a>, the information content <i>h</i> (in bits) of each symbol <i>a</i>_i with non-null probability is</p> <dl><dd><span><span><math> <semantics> <mrow> <mstyle> <mi>h</mi> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>)</mo> <mo>=</mo> <msub> <mi>log</mi> <mrow> <mn>2</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mfrac> <mn>1</mn> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation>{\displaystyle h(a_{i})=\log _{2}{1 \over w_{i}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2799f589d23a9f11345131ef8cef9937c5e7c456" alt="{\displaystyle h(a_{i})=\log _{2}{1 \over w_{i}}.}" title=""/></span></dd></dl> <p>The <a href="https://en.wikipedia.org/wiki/Information_entropy">entropy</a> <i>H</i> (in bits) is the weighted sum, across all symbols <span><i>a</i>_<i>i</i></span> with non-zero probability <span><i>w</i>_<i>i</i></span>, of the information content of each symbol:</p> <dl><dd><span><span><math> <semantics> <mrow> <mstyle> <mi>H</mi> <mo>(</mo> <mi>A</mi> <mo>)</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </munder> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> <mi>h</mi> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>)</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </munder> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> <msub> <mi>log</mi> <mrow> <mn>2</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mfrac> <mn>1</mn> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <munder> <mo>∑</mo> <mrow> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </munder> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> <msub> <mi>log</mi> <mrow> <mn>2</mn> </mrow> </msub> <mo>⁡</mo> <msub> <mi>w</mi> <mrow> <mi>i</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation>{\displaystyle H(A)=\sum _{w_{i}&gt;0}w_{i}h(a_{i})=\sum _{w_{i}&gt;0}w_{i}\log _{2}{1 \over w_{i}}=-\sum _{w_{i}&gt;0}w_{i}\log _{2}w_{i}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9bcff36f9acd0c27a57e42c99cc8fda6410934a" alt="{\displaystyle H(A)=\sum _{w_{i}&gt;0}w_{i}h(a_{i})=\sum _{w_{i}&gt;0}w_{i}\log _{2}{1 \over w_{i}}=-\sum _{w_{i}&gt;0}w_{i}\log _{2}w_{i}.}" title=""/></span></dd></dl> <p>(Note: A symbol with zero probability has zero contribution to the entropy, since <span><span><math> <semantics> <mrow> <mstyle> <munder> <mo>lim</mo> <mrow> <mi>w</mi> <mo>→</mo> <msup> <mn>0</mn> <mrow> <mo>+</mo> </mrow> </msup> </mrow> </munder> <mi>w</mi> <msub> <mi>log</mi> <mrow> <mn>2</mn> </mrow> </msub> <mo>⁡</mo> <mi>w</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation>{\displaystyle \lim _{w\to 0^{+}}w\log _{2}w=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a25181e71e7e86ccfe31ba981214e6b31f57e7c8" alt="{\displaystyle \lim _{w\to 0^{+}}w\log _{2}w=0}" title=""/></span>. So for simplicity, symbols with zero probability can be left out of the formula above.)</p> <p>As a consequence of <a href="https://en.wikipedia.org/wiki/Shannon&#39;s_source_coding_theorem">Shannon&#39;s source coding theorem</a>, the entropy is a measure of the smallest codeword length that is theoretically possible for the given alphabet with associated weights. In this example, the weighted average codeword length is 2.25 bits per symbol, only slightly larger than the calculated entropy of 2.205 bits per symbol. So not only is this code optimal in the sense that no other feasible code performs better, but it is very close to the theoretical limit established by Shannon.</p> <p>In general, a Huffman code need not be unique. Thus the set of Huffman codes for a given probability distribution is a non-empty subset of the codes minimizing <span><span><math> <semantics> <mrow> <mstyle> <mi>L</mi> <mo>(</mo> <mi>C</mi> <mo>)</mo> </mstyle> </mrow> <annotation>{\displaystyle L(C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f31c05759c645f617ea0ef5952ea24ccef557716" alt="{\displaystyle L(C)}" title=""/></span> for that probability distribution. (However, for each minimizing codeword length assignment, there exists at least one Huffman code with those lengths.)</p> </section> https://en.wikipedia.org/wiki/Canton_(flag) I7d_V-0-pmJtm5dNLwUZuNoUygq8THoYdwcLzw== Tue, 15 Sep 2026 06:49:51 +0000 Territories, regions, states, and provinces <div><h4>Territories, regions, states, and provinces</h4><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Canton_(flag)&amp;action=edit&amp;section=4"><span>edit source</span></a><span>]</span></span></div><section><div><h5>Provinces of Canada</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Canton_(flag)&amp;action=edit&amp;section=6"><span>edit source</span></a><span>]</span></span></div> <p>Two of Canada&#39;s ten provinces use flags with cantons, both the UK national flag.</p> <ul> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Manitoba.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Manitoba">Manitoba</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Ontario.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Ontario">Ontario</a></div></li> </ul> </section><section><div><h5>Counties of Liberia</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Canton_(flag)&amp;action=edit&amp;section=7"><span>edit source</span></a><span>]</span></span></div> <p>Every county flag of Liberia contains the Liberian national flag in its canton.</p> <ul> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Bomi_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Bomi_County">Bomi County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Bong_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Bong_County">Bong County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Gbarpolu_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Gbarpolu_County">Gbarpolu County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Grand_Bassa_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Grand_Bassa_County">Grand Bassa County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Grand_Cape_Mount_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Grand_Cape_Mount_County">Grand Cape Mount County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Grand_Gedeh_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Grand_Gedeh_County">Grand Gedeh County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Grand_Kru_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Grand_Kru_County">Grand Kru County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Lofa_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Lofa_County">Lofa County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Margibi_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Margibi_County">Margibi County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Maryland_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Maryland_County">Maryland County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Montserrado_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Montserrado_County">Montserrado County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Nimba_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Nimba_County">Nimba County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Rivercess_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Rivercess_County">Rivercess County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_River_Gee_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/River_Gee_County">River Gee County</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Sinoe_County.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Sinoe_County">Sinoe County</a></div></li> </ul> </section><section><div><h5>Overseas Territories of the United Kingdom</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Canton_(flag)&amp;action=edit&amp;section=8"><span>edit source</span></a><span>]</span></span></div> <ul> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Anguilla.svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_Anguilla">flag of Anguilla</a> features a blue Ensign with the coat of arms of Anguilla in the fly.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Bermuda.svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_Bermuda">flag of Bermuda</a> features a red Ensign with the coat of arms of Bermuda in the fly.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_the_British_Indian_Ocean_Territory.svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_the_British_Indian_Ocean_Territory">flag of the British Indian Ocean Territory</a> features a Blue Ensign with 7 wavy white stripes, with a palm tree on the hoist side and a crown over it.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_the_British_Virgin_Islands.svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_the_British_Virgin_Islands">flag of the British Virgin Islands</a> features a blue ensign with the Union flag in the top left hand corner and the coat of arms centre-right.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_the_Cayman_Islands.svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_the_Cayman_Islands">flag of the Cayman Islands</a> features a British blue ensign with the coat of arms of the Cayman Islands in the fly.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_the_Falkland_Islands.svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_the_Falkland_Islands">flag of the Falkland Islands</a> features a Blue Ensign with the coat-of-arms of the Falkland Islands in the fly.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Saint_Helena.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Flag_of_Saint_Helena">Flag of Saint Helena</a> in the <a href="https://en.wikipedia.org/wiki/United_Kingdom">United Kingdom</a>, has the <a href="https://en.wikipedia.org/wiki/UK">UK</a>&#39;s flag in its canton.</div></li> </ul> </section><section><div><h5>Other</h5><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Canton_(flag)&amp;action=edit&amp;section=9"><span>edit source</span></a><span>]</span></span></div> <ul> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Abkhazia.svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_Abkhazia">flag of Abkhazia</a> features a red canton with a white right hand and seven white stars on it.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Adjara.svg"></a></span></div><div>The flag of the autonomous province of <a href="https://en.wikipedia.org/wiki/Adjara">Adjara</a> contains the Georgian flag in the canton.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Bandeira_do_Amazonas.svg"></a></span></div><div>The flag of <a href="https://en.wikipedia.org/wiki/Amazonas_(Brazilian_state)">Amazonas</a> in Brazil</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Azad_Kashmir.svg"></a></span></div><div>The flag of <a href="https://en.wikipedia.org/wiki/Azad_Kashmir">Azad Kashmir</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Bandeira_da_Bahia.svg"></a></span></div><div>The flag of <a href="https://en.wikipedia.org/wiki/Bahia">Bahia</a> in Brazil</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_the_Balearic_Islands.svg"></a></span></div><div>Flag of <a href="https://en.wikipedia.org/wiki/The_Balearic_Islands">The Balearic Islands</a>, an autonomous community within the <a href="https://en.wikipedia.org/wiki/Spain">Kingdom of Spain</a>. </div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Brittany_(Gwenn_ha_du).svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Flag_of_Brittany">Flag of Brittany</a> in France, inspired by the American and Greek flags</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_the_French_Southern_and_Antarctic_Lands.svg"></a></span></div><div>Flag of the <a href="https://en.wikipedia.org/wiki/French_Southern_and_Antarctic_Lands">French Southern and Antarctic Lands</a> has a rare use of the <a href="https://en.wikipedia.org/wiki/Flag_of_France">flag of France</a> as its canton.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Georgia_(U.S._state).svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_Georgia_(U.S._state)">flag of Georgia</a> has the state coat of arms in the canton, surrounded by 13 stars which, like the stripes on the US flag, represent the original 13 colonies.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Goiás.svg"></a></span></div><div><a href="https://en.wikipedia.org/wiki/Goiás">Goiás</a> in Brazil</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_the_Guatemala_Department.svg"></a></span></div><div>Flag of <a href="https://en.wikipedia.org/wiki/Guatemala_Department">Guatemala Department</a> of Guatemala contains its <a href="https://en.wikipedia.org/wiki/Coat_of_arms">coat of arms</a>.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Hawaii.svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_Hawaii">flag of Hawaii</a> has the UK&#39;s flag in its canton.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Johor.svg"></a></span></div><div>Flag of <a href="https://en.wikipedia.org/wiki/Johor">Johor</a> in Malaysia, which contains the Islamic <a href="https://en.wikipedia.org/wiki/Star_and_crescent">star and crescent</a> in the canton, as does the national flag</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Bandeira_do_Maranhão.svg"></a></span></div><div>The flag of <a href="https://en.wikipedia.org/wiki/Maranhão">Maranhão</a> in Brazil</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Malacca.svg"></a></span></div><div>The <a href="https://en.wikipedia.org/wiki/Flag_of_Melaka">flag of Melaka</a> in Malaysia has a charge, of the Islamic <a href="https://en.wikipedia.org/wiki/Star_and_crescent">star and crescent</a>.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Negeri_Sembilan.svg"></a></span></div><div>Flag of <a href="https://en.wikipedia.org/wiki/Negeri_Sembilan">Negeri Sembilan</a> in Malaysia, the canton of which resembles the flag of <a href="https://en.wikipedia.org/wiki/Papua_New_Guinea">Papua New Guinea</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Bandeira_do_Piauí.svg"></a></span></div><div>The flag of <a href="https://en.wikipedia.org/wiki/Piauí">Piauí</a> in Brazil</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_the_United_Tribes_of_New_Zealand.svg"></a></span></div><div>Flag of the United Tribes of <a href="https://en.wikipedia.org/wiki/New_Zealand">New Zealand</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Sabah.svg"></a></span></div><div>The flag of <a href="https://en.wikipedia.org/wiki/Sabah">Sabah</a> in Malaysia contains a profile of local <a href="https://en.wikipedia.org/wiki/Mount_Kinabalu">Mount Kinabalu</a>.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:San_Salvador_Flag.png"></a></span></div><div>Flag of <a href="https://en.wikipedia.org/wiki/San_Salvador_Department">San Salvador Department</a> in El Salvador</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Santa_Ana_(El_Salvador)_flag.jpg"></a></span></div><div>Flag of <a href="https://en.wikipedia.org/wiki/Santa_Ana_Department">Santa Ana Department</a> in El Salvador</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Bandeira_do_estado_de_São_Paulo.svg"></a></span></div><div>The flag of <a href="https://en.wikipedia.org/wiki/São_Paulo_(state)">São Paulo</a> in Brazil</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Selangor.svg"></a></span></div><div>Flag and coat of arms of <a href="https://en.wikipedia.org/wiki/Selangor">Selangor</a> in Malaysia is not a true canton, although the standard of the <a href="https://en.wikipedia.org/wiki/Sultan_of_Selangor">Sultan of Selangor</a>, which derives from it, retains the upper hoist as a distinct canton.</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Bandeira_de_Sergipe.svg"></a></span></div><div>The flag of <a href="https://en.wikipedia.org/wiki/Sergipe">Sergipe</a> in Brazil</div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Wallis_and_Futuna.svg"></a></span></div><div>Unofficial flag of <a href="https://en.wikipedia.org/wiki/Wallis_and_Futuna">Wallis and Futuna</a> in <a href="https://en.wikipedia.org/wiki/France">France</a></div></li> <li><div><span><a href="https://en.wikipedia.org/wiki/File:Flag_of_Zanzibar.svg"></a></span></div><div>Flag of <a href="https://en.wikipedia.org/wiki/Zanzibar">Zanzibar</a> in <a href="https://en.wikipedia.org/wiki/Tanzania">Tanzania</a> with the <a href="https://en.wikipedia.org/wiki/Flag_of_Tanzania">flag of Tanzania</a> in it.</div></li> </ul> </section> https://en.wikipedia.org/wiki/Mulberry_harbours dvCX4D-OQkpXSJGldhsaFzm_oPnZf2lg0nyX_w== Tue, 15 Sep 2026 06:25:34 +0000 British Second World War portable temporary harbours <div>British Second World War portable temporary harbours</div><p> </p><table><tbody><tr><th colspan="2">Mulberry harbour</th></tr><tr><td colspan="2"><span><a href="https://en.wikipedia.org/wiki/File:The_Mulberry_artificial_harbour_off_Arromanches_in_Normandy,_September_1944._BU1024.jpg"></a></span><div>View of the Mulberry B harbour &quot;Port Winston&quot; at <a href="https://en.wikipedia.org/wiki/Arromanches">Arromanches</a> in September 1944. Centre and left are &quot;spud&quot; pierheads with floating piers of &quot;whales&quot; and &quot;beetles&quot;. At right is 2,000<span> </span>ft (610<span> </span>m) of &quot;Swiss roll&quot;.^{<span><span>[</span>1<span>]</span></span>}</div></td></tr><tr><th colspan="2">Location</th></tr><tr><th>Location</th><td><a href="https://en.wikipedia.org/wiki/Arromanches">Arromanches</a> and <a href="https://en.wikipedia.org/wiki/Omaha_Beach">Omaha Beach</a>, Normandy, France</td></tr><tr><th>Coordinates</th><td><span><span><a href="https://geohack.toolforge.org/geohack.php?pagename=Mulberry_harbours&amp;params=49.3475_N_0.634_W_type:landmark_region:FR"><span><span><span>49°20′51″N</span> <span>0°38′02″W</span></span></span><span><span></span> / <span></span></span><span><span>49.3475°N 0.6340°W</span><span><span></span> / <span>49.3475; -0.6340</span></span></span></a></span></span></td></tr><tr><th colspan="2">Details</th></tr><tr><th>Opened</th><td>June 1944</td></tr><tr><th>Closed</th><td>March 1945</td></tr><tr><th>Type</th><td>Temporary portable harbour</td></tr><tr><th>Purpose</th><td>Military equipment, stores and personnel</td></tr><tr><th>Joins</th><td>Beach</td></tr></tbody></table><div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Campaignbox_Normandy"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Campaignbox_Normandy"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Campaignbox_Normandy"><abbr>e</abbr></a></li></ul></div><div><span><a href="https://en.wikipedia.org/wiki/Operation_Overlord"><span>Operation Overlord</span></a><br/>(Battle of Normandy)</span></div></th></tr><tr><td colspan="2"><div><b>Prelude</b> <ul><li><a href="https://en.wikipedia.org/wiki/Atlantic_Wall">Atlantic Wall</a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Bodyguard"><i>Bodyguard</i></a> <ul><li><a href="https://en.wikipedia.org/wiki/Operation_Fortitude"><i>Fortitude</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Zeppelin_(deception_plan)"><i>Zeppelin</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Titanic"><i>Titanic</i></a></li> <li><a href="https://en.wikipedia.org/wiki/D-Day_naval_deceptions">Taxable, Glimmer &amp; Big Drum</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Combined_Bomber_Offensive">Combined Bomber Offensive</a></li> <li><a href="https://en.wikipedia.org/wiki/Pointblank_directive">Pointblank</a></li> <li><a href="https://en.wikipedia.org/wiki/Transport_Plan">Transport Plan</a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Postage_Able"><i>Postage Able</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Tarbrush"><i>Tarbrush</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Exercise_Tiger">Tiger</a></li> <li><a href="https://en.wikipedia.org/wiki/Exercise_Fabius">Fabius</a></li></ul> <p><b>Airborne assault</b><br/>British Sector</p> <ul><li><a href="https://en.wikipedia.org/wiki/Operation_Tonga"><i>Tonga</i></a> <ul><li><a href="https://en.wikipedia.org/wiki/Capture_of_the_Caen_Canal_and_Orne_River_bridges">Caen Canal and Orne River bridges</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Merville_Gun_Battery">Merville Battery</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Mallard"><i>Mallard</i></a></li></ul> <p><i><a href="https://en.wikipedia.org/wiki/American_airborne_landings_in_Normandy">American Sector</a></i></p> <ul><li><a href="https://en.wikipedia.org/wiki/Mission_Albany">Albany</a></li> <li><a href="https://en.wikipedia.org/wiki/Mission_Boston">Boston</a></li> <li><a href="https://en.wikipedia.org/wiki/Mission_Chicago">Chicago</a></li> <li><a href="https://en.wikipedia.org/wiki/Mission_Detroit">Detroit</a></li> <li><a href="https://en.wikipedia.org/wiki/Mission_Elmira">Elmira</a></li></ul> <p><b><a href="https://en.wikipedia.org/wiki/Normandy_landings">Normandy landings</a></b><br/>American Sector</p> <ul><li><a href="https://en.wikipedia.org/wiki/Omaha_Beach">Omaha</a></li> <li><a href="https://en.wikipedia.org/wiki/Utah_Beach">Utah</a></li> <li><a href="https://en.wikipedia.org/wiki/Pointe_du_Hoc">Pointe du Hoc</a></li></ul> <p>Anglo-Canadian Sector</p> <ul><li><a href="https://en.wikipedia.org/wiki/Operation_Gambit"><i>Gambit</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Sword_Beach">Sword</a></li> <li><a href="https://en.wikipedia.org/wiki/Juno_Beach">Juno</a></li> <li><a href="https://en.wikipedia.org/wiki/Gold_Beach">Gold</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Port-en-Bessin">Port-en-Bessin</a></li></ul> <p><b>Logistics</b></p> <ul><li><a href="https://en.wikipedia.org/wiki/American_logistics_in_the_Normandy_campaign">American</a> <ul><li><a href="https://en.wikipedia.org/wiki/Operation_Chastity"><i>Chastity</i></a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/British_logistics_in_the_Normandy_campaign">British</a> <ul><li><a href="https://en.wikipedia.org/wiki/Mulberry_harbour">Mulberry</a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Pluto"><i>Pluto</i></a></li></ul></li></ul> <p><b>Ground campaign</b><br/>American Sector</p> <ul><li><a href="https://en.wikipedia.org/wiki/Brécourt_Manor_Assault">Brécourt Manor</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Graignes">Graignes</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_La_Haye-du-Puits">La Haye-du-Puits</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Saint-Lô">Saint-Lô</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Carentan">Carentan</a> <ul><li><a href="https://en.wikipedia.org/wiki/Battle_of_Bloody_Gulch">Hill 30</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Cherbourg">Cherbourg</a> <ul><li><a href="https://en.wikipedia.org/wiki/Bombardment_of_Cherbourg">Naval</a></li></ul></li></ul> <p>Anglo-Canadian Sector</p> <ul><li><a href="https://en.wikipedia.org/wiki/Battle_for_Caen">Caen</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Bréville">Bréville</a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Perch"><i>Perch</i></a> <ul><li><a href="https://en.wikipedia.org/wiki/Battle_of_Villers-Bocage">Villers-Bocage</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Le_Mesnil-Patry">Le Mesnil-Patry</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Normandy_massacres">Normandy massacres</a> <ul><li><a href="https://en.wikipedia.org/wiki/Ardenne_Abbey_massacre">Ardenne Abbey</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Douvres_Radar_Station">Douvres</a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Martlet"><i>Martlet</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Epsom"><i>Epsom</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Windsor"><i>Windsor</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Charnwood"><i>Charnwood</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Jupiter_(1944)"><i>Jupiter</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Second_Battle_of_the_Odon">2nd Odon</a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Atlantic"><i>Atlantic</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Goodwood"><i>Goodwood</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Verrières_Ridge">Verrières Ridge</a></li></ul> <p><b>Breakout</b></p> <ul><li><a href="https://en.wikipedia.org/wiki/Operation_Cobra"><i>Cobra</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Spring"><i>Spring</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Bluecoat"><i>Bluecoat</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Totalize"><i>Totalize</i></a> <ul><li><a href="https://en.wikipedia.org/wiki/Battle_for_Hill_140">Hill 140</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Lüttich"><i>Lüttich</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Tractable"><i>Tractable</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Hill_262">Hill 262</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Chambois">Chambois</a></li> <li><a href="https://en.wikipedia.org/wiki/Falaise_Pocket">Falaise</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_for_Brittany">Brittany</a> <ul><li><a href="https://en.wikipedia.org/wiki/Liberation_of_Rennes">Rennes</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Saint-Malo">Saint-Malo</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_for_Brest">Brest</a></li> <li><a href="https://en.wikipedia.org/wiki/Saint-Nazaire_pocket">Saint-Nazaire</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Seine_River_Crossing_at_Mantes-Gassicourt">Mantes-Gassicourt</a></li> <li><a href="https://en.wikipedia.org/wiki/Liberation_of_Paris">Paris</a></li></ul> <p><b>Air and Sea operations</b></p> <ul><li><a href="https://en.wikipedia.org/wiki/Battle_of_Ushant_(1944)">Ushant</a></li> <li><a href="https://en.wikipedia.org/wiki/RAF_raid_on_La_Caine_HQ">La Caine</a></li> <li><a href="https://en.wikipedia.org/wiki/Bombardment_of_Cherbourg">Cherbourg</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Pierres_Noires">Pierres Noires</a></li> <li><a href="https://en.wikipedia.org/wiki/Battle_of_Audierne_Bay">Audierne Bay</a></li></ul> <p><b>Supporting operations</b></p> <ul><li><a href="https://en.wikipedia.org/wiki/Operation_Jedburgh"><i>Jedburgh</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Dingson"><i>Dingson</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Samwest"><i>Samwest</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Titanic"><i>Titanic</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Cooney"><i>Cooney</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Bulbasket"><i>Bulbasket</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Houndsworth"><i>Houndsworth</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Haft"><i>Haft</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Loyton"><i>Loyton</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Kipling"><i>Kipling</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operation_Dragoon"><i>Dragoon</i></a></li> <li><a href="https://en.wikipedia.org/wiki/Operations_Wallace_and_Hardy"><i>Wallace</i> &amp; <i>Hardy</i></a></li></ul> <hr/> <p><b>Aftermath</b></p> <ul><li><a href="https://en.wikipedia.org/wiki/List_of_military_cemeteries_in_Normandy">Cemeteries</a></li></ul></div></td></tr></tbody></table></div><p>The <b>Mulberry harbours</b> were two temporary portable <a href="https://en.wikipedia.org/wiki/Harbour">harbours</a> developed by the <a href="https://en.wikipedia.org/wiki/Admiralty_(United_Kingdom)">British Admiralty</a> and <a href="https://en.wikipedia.org/wiki/War_Office">War Office</a> during the <a href="https://en.wikipedia.org/wiki/Second_World_War">Second World War</a> to facilitate the rapid offloading of cargo onto beaches during the <a href="https://en.wikipedia.org/wiki/Allies_of_World_War_II">Allied</a> <a href="https://en.wikipedia.org/wiki/Invasion_of_Normandy">invasion of Normandy</a> in June 1944. They were designed in 1942, then built in under a year in great secrecy; within hours of the Allies creating beachheads after <a href="https://en.wikipedia.org/wiki/D-Day">D-Day</a>, sections of the two prefabricated harbours were towed across the <a href="https://en.wikipedia.org/wiki/English_Channel">English Channel</a> from southern England and placed in position off <a href="https://en.wikipedia.org/wiki/Omaha_Beach">Omaha Beach</a> (Mulberry &quot;A&quot;) and <a href="https://en.wikipedia.org/wiki/Gold_Beach">Gold Beach</a> (Mulberry &quot;B&quot;), along with old ships to be sunk as <a href="https://en.wikipedia.org/wiki/Breakwater_(structure)">breakwaters</a>.</p><p>The Mulberry harbours solved the problem of needing deepwater jetties and a harbour to provide the invasion force with the necessary reinforcements and supplies, and were to be used until major French ports could be captured and brought back into use after repair of the inevitable sabotage by German defenders. Composed of floating but sinkable breakwaters, floating pontoons, piers and floating roadways, this innovative and technically difficult system was being used for the first time.</p><p>The Mulberry B harbour at Gold Beach was used for ten months after D-Day, while over two million men, four million tons of supplies and half a million vehicles were landed before it was fully decommissioned. The partially completed Mulberry A harbour at Omaha Beach was damaged on 19 June by a violent storm that arrived from the northeast before the pontoons were securely anchored. After three days, the storm finally abated; the damage was found to be so severe that the harbour was abandoned and the Americans resorted to landing men and material over the open beaches.</p> https://en.wikipedia.org/wiki/Metropolitan 1KxB5moGb6r2hQP3WoFVKYmd6ZVHu2NbLghJ9A== Tue, 15 Sep 2026 06:22:41 +0000 Areas and governance (secular and ecclesiastical) <section><div><h2>Areas and governance (secular and ecclesiastical)</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Metropolitan&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/Metropolitan_archdiocese">Metropolitan archdiocese</a>, the jurisdiction of a metropolitan archbishop <ul><li><a href="https://en.wikipedia.org/wiki/Metropolitan_bishop">Metropolitan bishop</a> or archbishop, leader of an ecclesiastical &quot;mother see&quot;</li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_area">Metropolitan area</a>, a region consisting of a densely populated urban core and its surrounding territories</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_borough">Metropolitan borough</a>, a form of local government district in England, United Kingdom</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_county">Metropolitan county</a>, a type of county-level administrative division of England, United Kingdom</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Corporation_(Pakistan)">Metropolitan Corporation (Pakistan)</a>, a local government authority in Pakistan</li></ul> </section><section><div><h2>Colleges and universities</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Metropolitan&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/Metropolitan_University,_Sylhet">Metropolitan University, Sylhet</a>, Bangladesh</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_University_Prague">Metropolitan University Prague</a>, Czech Republic</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_University_College">Metropolitan University College</a>, Denmark</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_University_(Puerto_Rico)">Metropolitan University (Puerto Rico)</a></li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_University_(Belgrade)">Metropolitan University (Belgrade)</a>, Serbia</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Community_College_(Omaha)">Metropolitan Community College (Omaha)</a>, United States</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_State_University_of_Denver">Metropolitan State University of Denver</a>, United States <ul><li><a href="https://en.wikipedia.org/wiki/Metro_State_Roadrunners">Metro State Roadrunners</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_State_University">Metropolitan State University</a>, Saint Paul, Minnesota, United States</li></ul> <div>See also: <a href="https://en.wikipedia.org/wiki/Metropolitan_University_(disambiguation)">Metropolitan University (disambiguation)</a></div> </section><section><div><h2>Literature</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Metropolitan&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/The_Metropolitan_(newspaper)"><i>The Metropolitan</i> (newspaper)</a>, the college newspaper of Metropolitan State University of Denver</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_(novel)"><i>Metropolitan</i> (novel)</a>, a fantasy novel by Walter Jon Williams</li> <li><i><a href="https://en.wikipedia.org/wiki/The_Metropolitan_Magazine">The Metropolitan Magazine</a></i>, a publication from London</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Magazine_(New_York_City)"><i>Metropolitan Magazine</i> (New York City)</a>, a literary magazine</li> <li><i><a href="https://en.wikipedia.org/wiki/Seattle_Metropolitan">Seattle Metropolitan</a></i>, a local-interest magazine published in Seattle, Washington</li></ul> </section><section><div><h2>Music</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Metropolitan&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/Metropolitan_(band)">Metropolitan (band)</a>, an indie rock group from Washington, D.C.</li> <li>&quot;Metropolitan&quot;, a song by <a href="https://en.wikipedia.org/wiki/Nemo_(American_band)">Nemo</a></li></ul> </section><section><div><h2>Transport</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Metropolitan&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div> <section><div><h3>Transit systems</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Metropolitan&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/Metropolitan_(train)">Metropolitan (train)</a>, a discontinued German train service between Cologne and Hamburg</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_line">Metropolitan line</a>, a London Underground route</li></ul> </section><section><div><h3>Vehicles</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Metropolitan&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/Convair_Metropolitan">Convair Metropolitan</a>, an airliner</li> <li><i>Metropolitan</i>, a named train of the <a href="https://en.wikipedia.org/wiki/Pennsylvania_Railroad">Pennsylvania Railroad</a>, from New York City to St. Louis</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Special">Metropolitan Special</a>, a named train of the Baltimore and Ohio Railroad, from Jersey City to St. Louis</li> <li><a href="https://en.wikipedia.org/wiki/Nash_Metropolitan">Nash Metropolitan</a>, an automobile</li> <li><a href="https://en.wikipedia.org/wiki/Scania_Metropolitan">Scania Metropolitan</a>, a double-decker bus</li></ul> </section></section><section><div><h2>Other uses</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Metropolitan&amp;action=edit&amp;section=11"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/Metropolitan_(cocktail)">Metropolitan (cocktail)</a>, a variation of the Brandy Manhattan</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_area_network">Metropolitan area network</a>, a city-spanning computer network</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Division">Metropolitan Division</a>, a division in the National Hockey League</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Police_Service">Metropolitan Police Service</a>, the police force of Greater London, England</li> <li><a href="https://en.wikipedia.org/wiki/New_York_Metropolitans">New York Metropolitans</a>, 19th century baseball team</li></ul> </section><section><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Metropolitan&amp;action=edit&amp;section=12"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/Met_(disambiguation)">Met (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Metro_(disambiguation)">Metro (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Metropol_(disambiguation)">Metropol (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Metropole">Metropole</a>, &quot;mother country&quot;, or central part of a colonizing state</li> <li><a href="https://en.wikipedia.org/wiki/Metropolis">Metropolis</a>, a large city or conurbation</li> <li><a href="https://en.wikipedia.org/wiki/Metropolis_(disambiguation)">Metropolis (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/The_Metropolitan_(disambiguation)">The Metropolitan (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Bank_(disambiguation)">Metropolitan Bank (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Building_(disambiguation)">Metropolitan Building (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_France">Metropolitan France</a>, the part of France in Europe</li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Magazine_(disambiguation)">Metropolitan Magazine (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Opera_House_(disambiguation)">Metropolitan Opera House (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Metropolitan_Police_(disambiguation)">Metropolitan Police (disambiguation)</a></li> <li><a href="https://en.wikipedia.org/wiki/Moscow_Metro">Moscow Metro</a> (<a href="https://en.wikipedia.org/wiki/Russian_language">Russian</a><span>: </span><span>Московский метрополитен</span>), a rapid transit system in Moscow, Russia</li> <li><a href="https://en.wikipedia.org/wiki/Paris_Metro">Paris Metro</a> (<a href="https://en.wikipedia.org/wiki/French_language">French</a><span>: </span><i>Métropolitain</i>), a rapid transit system in Paris, France</li> <li><a href="https://en.wikipedia.org/wiki/Rapid_transit">Rapid transit</a> system, in an urban area</li> <li><i><a href="https://en.wikipedia.org/wiki/Transmetropolitan">Transmetropolitan</a></i>, a comic book series</li></ul> <div>Topics referred to by the same term</div><div><span><a href="https://en.wikipedia.org/wiki/File:Disambig_gray.svg"></a></span><div>This <a href="https://en.wikipedia.org/wiki/Help:Disambiguation">disambiguation</a> page lists articles associated with the title <b>Metropolitan</b>.<br/><small>If an <a href="https://en.wikipedia.org/w/index.php?title=Special:WhatLinksHere/Metropolitan&amp;namespace=0">internal link</a> incorrectly led you here, you may wish to change the link to point directly to the intended article.</small></div> </div></section> https://en.wikipedia.org/wiki/Application_binary_interface E4zEAE9U552w_ONz3ivQkIkD1PUb9KVrMQc4FA== Tue, 15 Sep 2026 05:19:41 +0000 Interface to software defined in terms of in-process, machine code access <section><div>Interface to software defined in terms of in-process, machine code access</div> <figure><a href="https://en.wikipedia.org/wiki/File:Linux_kernel_interfaces.svg"></a><figcaption>A high-level comparison of in-kernel and kernel-to-userspace APIs and ABIs</figcaption></figure> <figure><a href="https://en.wikipedia.org/wiki/File:Linux_API_and_Linux_ABI.svg"></a><figcaption>The <a href="https://en.wikipedia.org/wiki/Linux_kernel">Linux kernel</a> and <a href="https://en.wikipedia.org/wiki/GNU_C_Library">GNU C Library</a> define the <a href="https://en.wikipedia.org/wiki/Linux_kernel_interfaces#Kernel–user_space_API">Linux API</a>. After compilation, the binaries offer an ABI. Keeping this ABI stable over a long time is important for <a href="https://en.wikipedia.org/wiki/Independent_software_vendor">ISVs</a>.</figcaption></figure> <p>An <b>application binary interface</b> (<b>ABI</b>) is an <a href="https://en.wikipedia.org/wiki/Interface_(computing)">interface</a> exposed by <a href="https://en.wikipedia.org/wiki/Software">software</a> that is defined for in-<a href="https://en.wikipedia.org/wiki/Process_(computing)">process</a> <a href="https://en.wikipedia.org/wiki/Machine_code">machine code</a> access. Often, the exposing software is a <a href="https://en.wikipedia.org/wiki/Library_(computing)">library</a>, and the consumer is a <a href="https://en.wikipedia.org/wiki/Computer_program">program</a>.</p> <p>An ABI is at a relatively low level of <a href="https://en.wikipedia.org/wiki/Abstraction_(computer_science)">abstraction</a>. Interface compatibility depends on the target <a href="https://en.wikipedia.org/wiki/Computer_hardware">hardware</a> and the <a href="https://en.wikipedia.org/wiki/Software_build">software build</a> <a href="https://en.wikipedia.org/wiki/Toolchain">toolchain</a>. In contrast, an <a href="https://en.wikipedia.org/wiki/Application_programming_interface">application programming interface</a> (API) defines access in <a href="https://en.wikipedia.org/wiki/Source_code">source code</a>, which is a relatively high-level, hardware-independent, and <a href="https://en.wikipedia.org/wiki/Human-readable">human-readable</a> format. An API defines an interface at the source code level, before compilation, whereas an ABI defines an interface to compiled code.</p> <p>API compatibility is generally the concern for <a href="https://en.wikipedia.org/wiki/System_design">system design</a> and of the toolchain. However, a <a href="https://en.wikipedia.org/wiki/Programmer">programmer</a> may have to deal with an ABI directly when writing a program in multiple <a href="https://en.wikipedia.org/wiki/Programming_language">languages</a> or when using multiple <a href="https://en.wikipedia.org/wiki/Compiler">compilers</a> for the same language.</p> <p>A complete ABI enables a program that supports an ABI to run without modification on multiple operating systems that provide the ABI. The target system must provide any required libraries (that implement the ABI), and there may be other prerequisites.</p> </section><section><div><h2>Description</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Application_binary_interface&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div> <p>Interface aspects covered by an ABI include:</p> <ul><li><a href="https://en.wikipedia.org/wiki/Processor_(computing)">Processor</a> <a href="https://en.wikipedia.org/wiki/Instruction_set">instruction set</a>, with details like register file structure, <a href="https://en.wikipedia.org/wiki/Computer_memory">memory</a> access types, etc.</li> <li>Size, layout, and <a href="https://en.wikipedia.org/wiki/Data_structure_alignment">alignment</a> of basic <a href="https://en.wikipedia.org/wiki/Data_type">data types</a> that the processor can directly access</li> <li><a href="https://en.wikipedia.org/wiki/Calling_convention">Calling convention</a>, which controls how the arguments of <a href="https://en.wikipedia.org/wiki/Function_(programming)">functions</a> are passed, and return values retrieved; for example, it controls the following: <ul><li>How the <a href="https://en.wikipedia.org/wiki/Call_stack">call stack</a> is organized</li> <li>Whether all parameters are passed on the call stack, or some are passed in registers</li> <li>Which registers are used for which function parameters</li> <li>Which registers should be preserved by the callee (restore its value if changed)</li> <li>Whether the first function parameter passed on the call stack is pushed first or last</li> <li>Whether the caller or callee is responsible for cleaning up the call stack after the function call</li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Stack_unwinding">Stack unwinding</a> (<code>setjmp</code>/<code>longjmp</code>)</li> <li><a href="https://en.wikipedia.org/wiki/Name_mangling">Name mangling</a>, or how an API entity is named in the resulting <a href="https://en.wikipedia.org/wiki/Object_file">object file</a> (not in C)^{<span><span>[</span>1<span>]</span></span>}</li> <li><a href="https://en.wikipedia.org/wiki/Exception_handling">Exception</a> propagation (not in C)^{<span><span>[</span>2<span>]</span></span>}</li> <li>How an application should make <a href="https://en.wikipedia.org/wiki/System_call">system calls</a> to the operating system, and if the ABI specifies direct system calls rather than procedure calls to system call <a href="https://en.wikipedia.org/wiki/Method_stub">stubs</a>, the system call numbers</li> <li>In the case of a complete operating system ABI, the binary format of <a href="https://en.wikipedia.org/wiki/Object_file">object files</a>, program libraries, etc.</li></ul> <p>Example ABIs include the obsolete <a href="https://en.wikipedia.org/wiki/Intel_Binary_Compatibility_Standard">Intel Binary Compatibility Standard</a> (iBCS),^{<span><span>[</span>3<span>]</span></span>}, the <a href="https://en.wikipedia.org/wiki/System_V_Release_4">System V Release 4</a> ABIs for various instruction set architectures (ISAs) used by many Unix-like systems, and the Microsoft Windows ABIs for various ISAs.^{<span><span>[</span>4<span>]</span></span>}</p> </section><section><div><h2>Embedded ABI</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Application_binary_interface&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div> <p>An <b>embedded ABI</b> (<b>EABI</b>), used on an <a href="https://en.wikipedia.org/wiki/Embedded_operating_system">embedded operating system</a>, specifies aspects such as <a href="https://en.wikipedia.org/wiki/File_format">file formats</a>, data types, register usage, <a href="https://en.wikipedia.org/wiki/Stack_frame">stack frame</a> organization, and function parameter passing of an <a href="https://en.wikipedia.org/wiki/Embedded_system">embedded</a> software program.</p> <p>Each compiler and <a href="https://en.wikipedia.org/wiki/Assembly_language">assembler</a> that supports an EABI creates <a href="https://en.wikipedia.org/wiki/Object_code">object code</a> that is compatible with code generated by other such compilers and assemblers. This allows developers to link libraries generated by one compiler with object code generated by another.</p> <p>Typically, an EABI is optimized for performance for the limited resources of the target embedded system. Therefore, an EABI may omit abstractions between <a href="https://en.wikipedia.org/wiki/User_space_and_kernel_space">kernel and user space</a> typically found in <a href="https://en.wikipedia.org/wiki/Desktop_computer">desktop</a> operating systems. For example, <a href="https://en.wikipedia.org/wiki/Dynamic_linking">dynamic linking</a> may be avoided to allow smaller executables and faster loading, fixed register usage allows more compact stacks and kernel calls, and running the application in privileged mode allows direct access to custom hardware operation without the indirection of calling a device driver.^{<span><span>[</span>5<span>]</span></span>} The choice of EABI can affect performance.^{<span><span>[</span>6<span>]</span></span>}^{<span><span>[</span>7<span>]</span></span>}</p> <p>Widely used EABIs include the <a href="https://en.wikipedia.org/wiki/PowerPC">PowerPC</a>,^{<span><span>[</span>5<span>]</span></span>} <a href="https://en.wikipedia.org/wiki/Arm_architecture">Arm</a>,^{<span><span>[</span>8<span>]</span></span>} and <a href="https://en.wikipedia.org/wiki/MIPS_architecture">MIPS</a> EABIs.^{<span><span>[</span>9<span>]</span></span>} Specific software implementations like the C library may impose additional limitations to form more concrete ABIs; one example is the GNU OABI and EABI for ARM, both of which are subsets of the ARM EABI.^{<span><span>[</span>10<span>]</span></span>} Another point of distinction is whether optional features such as hardware floating-point is present. For example, in GCC and LLVM, <code>armv7-unknown-linux-musleabi</code>, <code>armv7-unknown-linux-musleabihf</code> both refer to GNU EABI with the <a href="https://en.wikipedia.org/wiki/Musl">musl</a> C library, except the latter uses hardware floating-point and therefore has a slightly different call convention.^{<span><span>[</span>11<span>]</span></span>}</p> </section><section><div><h2>Language ABIs</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Application_binary_interface&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <p>Each <a href="https://en.wikipedia.org/wiki/Programming_language">programming language</a> may use a different set of features and data types. If there is no existing ABI for a feature, the language often needs to define its own ABI as an extension of the existing ABI.</p> <section><div><h3>C</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Application_binary_interface&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <p>The official website of the <a href="https://en.wikipedia.org/wiki/C_(programming_language)">C programming language</a> describes C as a <a href="https://en.wikipedia.org/wiki/Lingua_franca">lingua franca</a> in <a href="https://en.wikipedia.org/wiki/Foreign_function_interface">foreign function interfaces</a> (FFIs: function calls between different programming languages).^{<span><span>[</span>12<span>]</span></span>} Many languages define their FFIs around the C ABI, for example the <code>extern &quot;C&quot;</code> of Rust and C++.^{<span><span>[</span>13<span>]</span></span>} This is because almost every current operating system, both Unix-like and Windows, provides an agreed-upon C ABI. These systems themselves mainly provide a C API, which depends upon a C ABI for functioning, hence the ubiquity of a C ABI.^{<span><span>[</span>14<span>]</span></span>} (Furthermore, C is relatively limited in what it requires of the ABI rules compared to other languages, only requiring definition of data structure layout and calling convention.)^{<span><span>[</span>15<span>]</span></span>}</p> <p>Nevertheless, C was not originally designed to serve in this role, and the ABI has been criticized for many of its perceived deficiencies as an FFI:</p> <ul><li>C ABIs are defined by C APIs, which are defined in C header files. However, C header files are very hard to parse and most FFI implementations resort to calling the compiler.^{<span><span>[</span>11<span>]</span></span>}</li> <li>C ABIs define interpretations for C-specific types such as <code>long long</code>, <code>time_t</code>, <code>intmax_t</code>. These choices of types are set in stone by the ABI, but there exist valid reasons to change them, which ends up breaking the ABI.^{<span><span>[</span>16<span>]</span></span>}</li> <li>C ABIs do not have parts required to support features in other languages, e.g. <a href="https://en.wikipedia.org/wiki/Type_safety">type safety</a> and <a href="https://en.wikipedia.org/wiki/Memory_safety">memory safety</a>.^{<span><span>[</span>13<span>]</span></span>}</li></ul> </section><section><div><h3>C++</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Application_binary_interface&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <p>There is no portable C++ ABI: even on the same operating system, different compilers (or combination of compiler and standard library implementations) may use different ABIs.^{<span><span>[</span>13<span>]</span></span>} Most C++ ABIs are extensions on top of the C ABI, filling in the missing <a href="https://en.wikipedia.org/wiki/Name_mangling">name mangling</a> (required for <a href="https://en.wikipedia.org/wiki/Function_overloading">function overloading</a>) and <a href="https://en.wikipedia.org/wiki/Exception_handling">exception handling</a> details. In modern systems two main schemes are encountered: Microsoft&#39;s Visual C++ scheme and the Itanium scheme.^{<span><span>[</span>1<span>]</span></span>}</p> <p>Although the ABI documents define the rules for transforming identifiers into names, they do not define the whole ABI surface of the standard library, leaving it to the specific standard library implementation (see section &quot;Library ABI&quot; below). As a result, each implementation has its own ABI; even on the same architecture and operating system, two object files end up having different ABIs if linked to standard libraries with incompatible ABIs.^{<span><span>[</span>13<span>]</span></span>} In 2015, GCC/libstdc++ revised its implementation of <code>std::string</code>, leading to an ABI change. Even though the new library supports both ABIs, users still had to make a choice between the old ABI and the new ABI, as this determines what precompiled libraries their programs can be linked to.^{<span><span>[</span>17<span>]</span></span>} Similarly, <a href="https://en.wikipedia.org/wiki/Visual_C++">Visual C++</a> does not guarantee compatibility when code produced by different versions of the compiler (intended for different versions of the runtime library) are linked together.^{<span><span>[</span>18<span>]</span></span>}</p> </section></section><section><div><h2>Library ABI</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Application_binary_interface&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div> <p>As defined above the &quot;ABI&quot; documents describe how an API is transformed into a concrete form at the <a href="https://en.wikipedia.org/wiki/Assembly_language">assembly language</a> level. In the case of <a href="https://en.wikipedia.org/wiki/Library_(computing)">libraries</a>, the term &quot;ABI&quot; instead refers to the concrete interface resulting from the transformation of ABI.^{<span><span>[</span>19<span>]</span></span>} For example, changing the <a href="https://en.wikipedia.org/wiki/Type_signature">type signature</a> of a function, either directly or indirectly (e.g. by changing the definition of a <a href="https://en.wikipedia.org/wiki/Struct">struct</a> used by the function), often changes the ABI to the point of incompatibility, an &quot;ABI break&quot;.^{<span><span>[</span>20<span>]</span></span>}^{<span><span>[</span>21<span>]</span></span>}</p> <p>Because operating systems include a number of libraries for use by the programmer, their ABIs also include the library ABIs. The <a href="https://en.wikipedia.org/wiki/Linux_Standard_Base">Linux Standard Base</a> specifications, for example, includes details about what the <a href="https://en.wikipedia.org/wiki/Symbol_table">symbol tables</a> of certain libraries should contain, what API they correspond to, and that SysV ABI should be used.^{<span><span>[</span>22<span>]</span></span>} This kind of distinctions matter for compilers and other kinds of code generators; in the case of GCC and LLVM, each option is given a name called a <i>target triple</i>. (The choice of a standard library implementation also affects the ABI: for example, musl and <a href="https://en.wikipedia.org/wiki/UClibc">uClibc</a> for ARMv7 GNU EABI as well as libstdc++ and <a href="https://en.wikipedia.org/wiki/Microsoft_Visual_C++">Microsoft Visual C++</a> for x64 Windows each have different triples.)^{<span><span>[</span>11<span>]</span></span>}</p> </section><section><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Application_binary_interface&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div> <ul> <li><span><span><a href="https://en.wikipedia.org/wiki/File:Octicons-terminal.svg"></a></span></span><span><a href="https://en.wikipedia.org/wiki/Portal:Computer_programming">Computer programming portal</a></span></li></ul> <ul><li><a href="https://en.wikipedia.org/wiki/Binary-code_compatibility">Binary-code compatibility</a><span> </span><span>– Ability of computer system to run code for a different system</span></li> <li><a href="https://en.wikipedia.org/wiki/Bytecode">Bytecode</a><span> </span><span>– Instruction set designed to be run by a software interpreter</span></li> <li><a href="https://en.wikipedia.org/wiki/Comparison_of_application_virtualization_software">Comparison of application virtualization software</a></li> <li><a href="https://en.wikipedia.org/wiki/Debug_symbol">Debug symbol</a><span> </span><span>– Information to facilitate code debugging</span><span>Pages displaying short descriptions of redirect targets</span></li> <li><a href="https://en.wikipedia.org/wiki/Foreign_function_interface">Foreign function interface</a><span> </span><span>– Interface to call functions from other programming languages</span></li> <li><a href="https://en.wikipedia.org/wiki/Language_binding">Language binding</a><span> </span><span>– Interface allowing one programming language to use a library written in another</span></li> <li><a href="https://en.wikipedia.org/wiki/Native_(computing)">Native (computing)</a><span> </span><span>– Software that operates directly in a given context</span></li> <li><a href="https://en.wikipedia.org/wiki/Opaque_pointer">Opaque pointer</a><span> </span><span>– Opaque data type which stores a memory address</span></li> <li><a href="https://en.wikipedia.org/wiki/PowerOpen_Environment">PowerOpen Environment</a><span> </span><span>– Open standard by AIM alliance</span></li> <li><a href="https://en.wikipedia.org/wiki/Symbol_table">Symbol table</a><span> </span><span>– Data structure used by a language translator such as a compiler or interpreter</span></li> <li><a href="https://en.wikipedia.org/wiki/SWIG">SWIG</a><span> </span><span>– Open-source programming tool</span></li> <li><a href="https://en.wikipedia.org/wiki/Microsoft_Visual_C++">Microsoft Visual C++</a><span> </span><span>– Integrated development environment product</span></li></ul> </section><section><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Application_binary_interface&amp;action=edit&amp;section=8"><span>edit</span></a><span>]</span></span></div> <div><ol><li><span><span>1</span> <span>2</span></span> <span><cite><a href="https://itanium-cxx-abi.github.io/cxx-abi/">&quot;Itanium C++ ABI&quot;</a>.</cite> (compatible with multiple architectures)</span></li> <li><span><span>↑</span></span> <span><cite><a href="https://itanium-cxx-abi.github.io/cxx-abi/abi-eh.html">&quot;Itanium C++ ABI: Exception Handling&quot;</a>.</cite> (compatible with multiple architectures)</span></li> <li><span><span>↑</span></span> <span><cite><a href="http://www.everything2.com/index.pl?node=iBCS">&quot;Intel Binary Compatibility Standard (iBCS)&quot;</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://learn.microsoft.com/en-us/cpp/build/x64-calling-convention?view=msvc-170">&quot;x64 Calling Convention&quot;</a>. <i>learn.microsoft.com</i>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>&quot;EABI Summary&quot;. <a href="https://www.nxp.com/docs/en/application-note/PPCEABI.pdf"><i>PowerPC Embedded Application Binary Interface: 32-Bit Implementation</i></a> <span>(PDF)</span> (Version 1.0<span> </span>ed.). Freescale Semiconductor, Inc. 1 October 1995. pp.<span> </span><span>28–</span>30.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://web.archive.org/web/20070121183413/http://www.linuxdevices.com/news/NS9048137234.html">&quot;Debian ARM accelerates via EABI port&quot;</a>. Linuxdevices.com. 16 October 2016. Archived from <a href="http://linuxdevices.com/news/NS9048137234.html">the original</a> on 21 January 2007<span>. Retrieved <span>11 October</span> 2007</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Andrés Calderón and Nelson Castillo (14 March 2007). <a href="https://web.archive.org/web/20070331193917/http://www.linuxdevices.com/articles/AT5920399313.html">&quot;Why ARM&#39;s EABI matters&quot;</a>. Linuxdevices.com. Archived from <a href="http://linuxdevices.com/articles/AT5920399313.html">the original</a> on 31 March 2007<span>. Retrieved <span>11 October</span> 2007</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://developer.arm.com/architectures/system-architectures/software-standards/abi">&quot;ABI for the Arm Architecture&quot;</a>. Developer.arm.com<span>. Retrieved <span>4 February</span> 2020</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Eric Christopher (11 June 2003). <a href="https://sourceware.org/legacy-ml/binutils/2003-06/msg00436.html">&quot;mips eabi documentation&quot;</a>. <i>binutils@sources.redhat.com</i> (Mailing list)<span>. Retrieved <span>19 June</span> 2020</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://wiki.debian.org/ArmEabiPort">&quot;ArmEabiPort&quot;</a>. <i>Debian Wiki</i>. <q>Strictly speaking, both the old and new ARM ABIs are subsets of the ARM EABI specification, but in everyday usage the term &quot;EABI&quot; is used to mean the new one described here and &quot;OABI&quot; or &quot;old-ABI&quot; to mean the old one.</q></cite></span></li> <li><span><span>1</span> <span>2</span> <span>3</span></span> <span><cite>Desires, Aria (16 March 2022). <a href="https://faultlore.com/blah/c-isnt-a-language/">&quot;C Isn&#39;t A Programming Language Anymore - Faultlore&quot;</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.c-language.org/faq">&quot;C language: FAQ&quot;</a>. <i>www.c-language.org</i>.</cite></span></li> <li><span><span>1</span> <span>2</span> <span>3</span> <span>4</span></span> <span><cite>Sutter, Herb (2014). <a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2014/n4028.pdf">&quot;Defining a Portable C++ ABI&quot;</a> <span>(PDF)</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://dev.to/dimension-ai/why-c-is-still-the-most-important-programming-language-2n9j">&quot;Why C is still the most important programming language&quot;</a>. <i>DEV Community</i>. 7 January 2026.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://github.com/WebAssembly/tool-conventions/blob/main/BasicCABI.md">&quot;tool-conventions/BasicCABI.md at main · WebAssembly/tool-conventions&quot;</a>. <i>GitHub</i>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://thephd.dev/to-save-c-we-must-save-abi-fixing-c-function-abi">&quot;To Save C, We Must Save ABI&quot;</a>. <i>The Pasture</i>. 13 March 2022.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://gcc.gnu.org/onlinedocs/libstdc++/manual/using_dual_abi.html">&quot;Dual ABI&quot;</a>. <i>gcc.gnu.org</i>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://learn.microsoft.com/en-us/cpp/porting/binary-compat-2015-2017?view=msvc-170">&quot;C++ binary compatibility 2015-2026&quot;</a>. <i>learn.microsoft.com</i>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://curl.se/libcurl/abi.html">&quot;libcurl - ABI&quot;</a>. <i>curl.se</i>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://pypackaging-native.github.io/background/binary_interface/">&quot;Application Binary Interface (ABI) - pypackaging-native&quot;</a>. <i>pypackaging-native.github.io</i>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Winters, T (2020). <a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p2028r0.pdf">&quot;What is ABI, and What Should WG21 Do About It?&quot;</a> <span>(PDF)</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://refspecs.linuxfoundation.org/LSB_5.0.0/LSB-Core-PPC64/LSB-Core-PPC64/libc.html">&quot;Interfaces for libc (LSB 5.0 PPC64)&quot;</a>. <i>refspecs.linuxfoundation.org</i>.</cite></span></li> </ol></div> </section><section><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Application_binary_interface&amp;action=edit&amp;section=9"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://community.kde.org/Policies/Binary_Compatibility_Issues_With_C%2B%2B">Policies/Binary Compatibility Issues With C++</a><span> </span><span>–</span> a compendium of development rules of thumb for not breaking binary compatibility between library releases</li> <li><a href="https://developer.apple.com/library/content/documentation/DeveloperTools/Conceptual/LowLevelABI/000-Introduction/introduction.html">OS X ABI Function Call Guide</a></li> <li><a href="https://wiki.debian.org/ArmEabiPort">Debian ARM EABI port</a></li> <li>μClib: Motorola 8/16-bit embedded ABI</li> <li><a href="https://web.archive.org/web/20080528070803/http://www.x86-64.org/documentation.html">AMD64 (x86-64) Application Binary Interface</a><span> at the </span><a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a> <span>(archived 2008-05-28)</span></li> <li><a href="http://infocenter.arm.com/help/index.jsp?topic=/com.arm.doc.ihi0036b/index.html">Application Binary Interface (ABI) for the ARM Architecture</a></li> <li><a href="https://sourceware.org/legacy-ml/binutils/2003-06/msg00436.html">MIPS EABI documentation</a></li> <li><a href="https://web.archive.org/web/20150114065444/http://www.oracle.com/technetwork/server-storage/solaris10/about-amd64-abi-141142.html">Sun Studio 10 Compilers and the AMD64 ABI</a><span> at the </span><a href="https://en.wikipedia.org/wiki/Wayback_Machine">Wayback Machine</a> <span>(archived 2015-01-14)</span><span> </span><span>–</span> a summary and comparison of some popular ABIs</li> <li><a href="https://www.nxp.com/docs/en/reference-manual/MCOREABISM.pdf">M•CORE Applications Binary Interface Standards Manual</a> for the Freescale <a href="https://en.wikipedia.org/wiki/M·CORE">M·CORE</a> processors</li></ul> <div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Application_binary_interface"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Application_binary_interface"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Application_binary_interface"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Application_binary_interface">Application binary interface</a> (ABI)</div></th></tr><tr><th>Parts,<br/>conventions</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Data_structure_alignment">Alignment</a></li> <li><a href="https://en.wikipedia.org/wiki/Calling_convention">Calling convention</a></li> <li><a href="https://en.wikipedia.org/wiki/Call_stack">Call stack</a></li> <li><a href="https://en.wikipedia.org/wiki/Library_(computing)">Library</a> <ul><li><a href="https://en.wikipedia.org/wiki/Static_library">static</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Machine_code">Machine code</a></li> <li><a href="https://en.wikipedia.org/wiki/Memory_segmentation">Memory segmentation</a></li> <li><a href="https://en.wikipedia.org/wiki/Name_mangling">Name mangling</a></li> <li><a href="https://en.wikipedia.org/wiki/Object_code">Object code</a></li> <li><a href="https://en.wikipedia.org/wiki/Opaque_pointer">Opaque pointer</a></li> <li><a href="https://en.wikipedia.org/wiki/Position-independent_code">Position-independent code</a></li> <li><a href="https://en.wikipedia.org/wiki/Relocation_(computing)">Relocation</a></li> <li><a href="https://en.wikipedia.org/wiki/System_call">System call</a></li> <li><a href="https://en.wikipedia.org/wiki/Virtual_method_table">Virtual method table</a></li></ul> </div></td></tr><tr><th>Related topics</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Binary-code_compatibility">Binary-code compatibility</a></li> <li><a href="https://en.wikipedia.org/wiki/Foreign_function_interface">Foreign function interface</a></li> <li><a href="https://en.wikipedia.org/wiki/Language_binding">Language binding</a></li> <li><a href="https://en.wikipedia.org/wiki/Linker_(computing)">Linker</a> <ul><li><a href="https://en.wikipedia.org/wiki/Dynamic_linker">dynamic</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Loader_(computing)">Loader</a></li></ul> </div></td></tr></tbody></table></div> </section> https://en.wikipedia.org/wiki/Hipparchus IrHhAsEU5dvIRQmUzJKzFQ_oaN-LZVPWgXQi5A== Mon, 14 Sep 2026 23:58:33 +0000 Motion of the Moon <div><h3>Motion of the Moon</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Hipparchus&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div><div>Further information: <a href="https://en.wikipedia.org/wiki/Lunar_theory">Lunar theory</a> and <a href="https://en.wikipedia.org/wiki/Orbit_of_the_Moon">Orbit of the Moon</a></div><p>Hipparchus also studied the motion of the <a href="https://en.wikipedia.org/wiki/Moon">Moon</a> and confirmed the accurate values for two periods of its motion that Chaldean astronomers are widely presumed to have possessed before him. The traditional value (from Babylonian System B) for the mean <a href="https://en.wikipedia.org/wiki/Synodic_month">synodic month</a> is 29<span> </span>days; 31,50,8,20 (sexagesimal) = 29.5305941... days. Expressed as 29<span> </span>days + 12<span> </span>hours + <span><span>⁠</span><span><span>793</span><span>/</span><span>1080</span></span><span>⁠</span></span><span> </span>hours this value has been used later in the <a href="https://en.wikipedia.org/wiki/Hebrew_calendar">Hebrew calendar</a>. The Chaldeans also knew that 251 <a href="https://en.wikipedia.org/wiki/Synodic_month">synodic months</a> ≈ 269 <a href="https://en.wikipedia.org/wiki/Anomalistic_month">anomalistic months</a>. Hipparchus used the multiple of this period by a factor of 17, because that interval is also an eclipse period, and is also close to an integer number of years (4,267 moons<span> </span>: 4,573 anomalistic periods<span> </span>: 4,630.53 nodal periods<span> </span>: 4,611.98 lunar orbits<span> </span>: 344.996 years<span> </span>: 344.982 solar orbits<span> </span>: 126,007.003 days<span> </span>: 126,351.985 rotations).^{<span><span>[</span>b<span>]</span></span>} What was so exceptional and useful about the cycle was that all 345-year-interval eclipse pairs occur slightly more than 126,007 days apart within a tight range of only approximately ±<span><span>1</span><span>⁄</span><span>2</span></span> hour, guaranteeing (after division by 4,267) an estimate of the synodic month correct to one part in order of magnitude 10 million.</p><p>Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141<span> </span>BC and 26 November 139<span> </span>BC according to Toomer^{<span><span>[</span>24<span>]</span></span>}) with eclipses from Babylonian records 345 years earlier (<i>Almagest</i> IV.2^{<span><span>[</span>12<span>]</span></span>}).</p><p>Later <a href="https://en.wikipedia.org/wiki/Al-Biruni">al-Biruni</a> (<i>Qanun</i> VII.2.II) and <a href="https://en.wikipedia.org/wiki/Nicolaus_Copernicus">Copernicus</a> (<i>de revolutionibus</i> IV.4) noted that the period of 4,267 moons is approximately five minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the timing methods of the Babylonians had an error of no fewer than eight minutes.^{<span><span>[</span>25<span>]</span></span>}^{<span><span>[</span>26<span>]</span></span>} Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than to try to derive an improved value from his own observations. From modern ephemerides^{<span><span>[</span>27<span>]</span></span>} and taking account of the change in the length of the day (see <a href="https://en.wikipedia.org/wiki/ΔT_(timekeeping)">ΔT</a>) we ^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions"><span>who?</span></a></i><span>]</span>} estimate that the error in the assumed length of the synodic month was less than 0.2 second in the fourth century<span> </span>BC and less than 0.1 second in Hipparchus&#39;s time.</p> https://en.wikipedia.org/wiki/Qubit heTm0xIj0QWwXcgdsZwRPA-rb7WevqmIgjdNKw== Mon, 14 Sep 2026 23:58:23 +0000 Qubit states <div><h2>Qubit states</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Qubit&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div><figure><a href="https://en.wikipedia.org/wiki/File:Qubit_represented_by_linear_polarization_of_light.png"></a><figcaption><a href="https://en.wikipedia.org/wiki/Polarization_(waves)">Polarization of light</a> offers a straightforward way to present orthogonal states. With a typical mapping <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mo>|</mo> </mrow> <mi>H</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mrow> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {|H\rangle }={|0\rangle }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf518794fbab183eea3a3f91ec6a4f573680bd14" alt="{\displaystyle {|H\rangle }={|0\rangle }}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mo>|</mo> </mrow> <mi>V</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mrow> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {|V\rangle }={|1\rangle }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb42f19942bf9429d64d0d18a106d23b94d16ed0" alt="{\displaystyle {|V\rangle }={|1\rangle }}" title=""/></span>, quantum states <span><span><math> <semantics> <mrow> <mstyle> <mo>(</mo> <mrow> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> </mrow> <mo>±</mo> <mrow> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mrow> <mo>)</mo> <mrow> <mo>/</mo> </mrow> <mrow> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation>{\displaystyle ({|0\rangle }\pm {|1\rangle })/{\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cdb0f31603a83d6e9d47f519defa5d5fb9d9d81" alt="{\displaystyle ({|0\rangle }\pm {|1\rangle })/{\sqrt {2}}}" title=""/></span> have a direct physical representation, both easily demonstrable experimentally in a class with <a href="https://en.wikipedia.org/wiki/Polarizer">linear polarizers</a> and, for real <span><span><math> <semantics> <mrow> <mstyle> <mi>α</mi> </mstyle> </mrow> <annotation>{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" alt="{\displaystyle \alpha }" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>β</mi> </mstyle> </mrow> <annotation>{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" alt="{\displaystyle \beta }" title=""/></span>, matching the high-school definition of <a href="https://en.wikipedia.org/wiki/Orthogonality">orthogonality</a>.^{<span><span>[</span>6<span>]</span></span>}</figcaption></figure><p>where <span><i>α</i></span> and <span><i>β</i></span> are the <a href="https://en.wikipedia.org/wiki/Probability_amplitude">probability amplitudes</a>, and are both <a href="https://en.wikipedia.org/wiki/Complex_number">complex numbers</a>. When we measure this qubit in the standard basis, according to the <a href="https://en.wikipedia.org/wiki/Born_rule">Born rule</a>, the probability of outcome <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {|0\rangle }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1f21e28a6c668b8e81b44f0146ad7ce75b36b42" alt="{\displaystyle {|0\rangle }}" title=""/></span> with value &quot;0&quot; is <span><span><math> <semantics> <mrow> <mstyle> <msup> <mrow> <mrow> <mo>|</mo> </mrow> <mi>α</mi> <mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle {|\alpha |}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8903f892f93544d73470689e47c78febd5c395d" alt="{\displaystyle {|\alpha |}^{2}}" title=""/></span> and the probability of outcome <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {|1\rangle }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6bd17e289ebd071d9460c567dae090b52b563d1" alt="{\displaystyle {|1\rangle }}" title=""/></span> with value &quot;1&quot; is <span><span><math> <semantics> <mrow> <mstyle> <msup> <mrow> <mrow> <mo>|</mo> </mrow> <mi>β</mi> <mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle {|\beta |}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d630ea5754141a602a2695b69766b74792edccd" alt="{\displaystyle {|\beta |}^{2}}" title=""/></span>. Because the absolute squares of the amplitudes equate to probabilities, it follows that <span><span><math> <semantics> <mrow> <mstyle> <mi>α</mi> </mstyle> </mrow> <annotation>{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" alt="{\displaystyle \alpha }" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>β</mi> </mstyle> </mrow> <annotation>{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" alt="{\displaystyle \beta }" title=""/></span> must be constrained according to the <a href="https://en.wikipedia.org/wiki/Probability_axioms#Second_axiom">second axiom of probability theory</a> by the equation^{<span><span>[</span>4<span>]</span></span>}</p><p>The probability amplitudes, <span><span><math> <semantics> <mrow> <mstyle> <mi>α</mi> </mstyle> </mrow> <annotation>{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" alt="{\displaystyle \alpha }" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>β</mi> </mstyle> </mrow> <annotation>{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" alt="{\displaystyle \beta }" title=""/></span>, encode more than just the probabilities of the outcomes of a measurement; the <i>relative phase</i> between <span><span><math> <semantics> <mrow> <mstyle> <mi>α</mi> </mstyle> </mrow> <annotation>{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" alt="{\displaystyle \alpha }" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>β</mi> </mstyle> </mrow> <annotation>{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" alt="{\displaystyle \beta }" title=""/></span> is, for example, responsible for <a href="https://en.wikipedia.org/wiki/Wave_interference">quantum interference</a>, as seen in the <a href="https://en.wikipedia.org/wiki/Double-slit_experiment">double-slit experiment</a>.</p><section><div><h3>Bloch sphere representation</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Qubit&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <figure><a href="https://en.wikipedia.org/wiki/File:Bloch_Sphere_representation.svg"></a><figcaption>Bloch Sphere representation of a qubit.</figcaption></figure><p> The <a href="https://en.wikipedia.org/wiki/Probability_amplitude">probability amplitudes</a> for the superposition state, <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mo>|</mo> </mrow> <mi>ψ</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mi>α</mi> <mrow> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> </mrow> <mo>+</mo> <mi>β</mi> <mrow> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle {|\psi \rangle }=\alpha {|0\rangle }+\beta {|1\rangle },\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c01801d4b188cfb58e6d97e978e598c2cc919a4" alt="{\displaystyle {|\psi \rangle }=\alpha {|0\rangle }+\beta {|1\rangle },\,}" title=""/></span> are given by <span><span><math> <semantics> <mrow> <mstyle> <mi>α</mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle \alpha =\cos \left({\frac {\theta }{2}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae3ed18da7e0970ca3c0704c6ee98070ea5cde16" alt="{\displaystyle \alpha =\cos \left({\frac {\theta }{2}}\right)}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>β</mi> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>i</mi> <mi>φ</mi> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle \beta =e^{i\varphi }\sin \left({\frac {\theta }{2}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37406b735c7c755eff6fa3bc8e44c04c4107478a" alt="{\displaystyle \beta =e^{i\varphi }\sin \left({\frac {\theta }{2}}\right)}" title=""/></span></p> <p>It might, at first sight, seem that there should be four <a href="https://en.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry)">degrees of freedom</a> in <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mo>|</mo> </mrow> <mi>ψ</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mi>α</mi> <mrow> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> </mrow> <mo>+</mo> <mi>β</mi> <mrow> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {|\psi \rangle }=\alpha {|0\rangle }+\beta {|1\rangle }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39e944ccf3603fca40f6aedf2c7ebc4374fb36c1" alt="{\displaystyle {|\psi \rangle }=\alpha {|0\rangle }+\beta {|1\rangle }\,}" title=""/></span>, as <span><span><math> <semantics> <mrow> <mstyle> <mi>α</mi> </mstyle> </mrow> <annotation>{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" alt="{\displaystyle \alpha }" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>β</mi> </mstyle> </mrow> <annotation>{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" alt="{\displaystyle \beta }" title=""/></span> are <a href="https://en.wikipedia.org/wiki/Complex_number">complex numbers</a> with two degrees of freedom each. However, one degree of freedom is removed by the normalization constraint <span>|<i>α</i>|² + |<i>β</i>|² = 1</span>. This means, with a suitable change of coordinates, one can eliminate one of the degrees of freedom. One possible choice is that of <a href="https://en.wikipedia.org/wiki/Hopf_coordinates">Hopf coordinates</a>:</p> <dl><dd><span><span><math> <semantics> <mrow> <mstyle> <mrow> <mtable> <mtr> <mtd> <mi>α</mi> </mtd> <mtd> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>i</mi> <mi>δ</mi> </mrow> </msup> <mi>cos</mi> <mo>⁡</mo> <mrow> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>β</mi> </mtd> <mtd> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>i</mi> <mo>(</mo> <mi>δ</mi> <mo>+</mo> <mi>φ</mi> <mo>)</mo> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mrow> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\begin{aligned}\alpha &amp;=e^{i\delta }\cos {\frac {\theta }{2}},\\\beta &amp;=e^{i(\delta +\varphi )}\sin {\frac {\theta }{2}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a04caa23ec5de0352d284f5c4f67c3bf63941240" alt="{\displaystyle {\begin{aligned}\alpha &amp;=e^{i\delta }\cos {\frac {\theta }{2}},\\\beta &amp;=e^{i(\delta +\varphi )}\sin {\frac {\theta }{2}}.\end{aligned}}}" title=""/></span></dd></dl> <p>Additionally, for a single qubit, the <i>global <a href="https://en.wikipedia.org/wiki/Phase_factor">phase</a></i> of the state <span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>e</mi> <mrow> <mi>i</mi> <mi>δ</mi> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle e^{i\delta }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10e0d05e18919dd554d63a1786a0731d87bbd59c" alt="{\displaystyle e^{i\delta }}" title=""/></span> has no physically observable consequences,^{<span><span>[</span>a<span>]</span></span>} so we can arbitrarily choose <span><i>α</i></span> to be real (or <span><i>β</i></span> in the case that <span><i>α</i></span> is zero), leaving just two degrees of freedom:</p> <dl><dd><span><span><math> <semantics> <mrow> <mstyle> <mrow> <mtable> <mtr> <mtd> <mi>α</mi> </mtd> <mtd> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>β</mi> </mtd> <mtd> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>i</mi> <mi>φ</mi> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mrow> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {\begin{aligned}\alpha &amp;=\cos {\frac {\theta }{2}},\\\beta &amp;=e^{i\varphi }\sin {\frac {\theta }{2}},\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/331611b25e84100e5855cab579e572ac3ae1c52a" alt="{\displaystyle {\begin{aligned}\alpha &amp;=\cos {\frac {\theta }{2}},\\\beta &amp;=e^{i\varphi }\sin {\frac {\theta }{2}},\end{aligned}}}" title=""/></span></dd></dl> <p>where <span><span><math> <semantics> <mrow> <mstyle> <msup> <mi>e</mi> <mrow> <mi>i</mi> <mi>φ</mi> </mrow> </msup> </mstyle> </mrow> <annotation>{\displaystyle e^{i\varphi }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/342db58722ad42021edbdf5725582a840c7af7b1" alt="{\displaystyle e^{i\varphi }}" title=""/></span> is the physically significant <i>relative phase</i>.^{<span><span>[</span>7<span>]</span></span>}^{<span><span>[</span>b<span>]</span></span>}</p> <p>The possible quantum states for a single qubit can be visualised using a <a href="https://en.wikipedia.org/wiki/Bloch_sphere">Bloch sphere</a> (see picture). Represented on such a <a href="https://en.wikipedia.org/wiki/2-sphere">2-sphere</a>, a classical bit could only be at the &quot;North Pole&quot; or the &quot;South Pole&quot;, in the locations where <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {|0\rangle }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1f21e28a6c668b8e81b44f0146ad7ce75b36b42" alt="{\displaystyle {|0\rangle }}" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation>{\displaystyle {|1\rangle }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6bd17e289ebd071d9460c567dae090b52b563d1" alt="{\displaystyle {|1\rangle }}" title=""/></span> are respectively. This particular choice of the polar axis is arbitrary, however. The rest of the surface of the Bloch sphere is inaccessible to a classical bit, but a pure qubit state can be represented by any point on the surface. For example, the pure qubit state <span><span><math> <semantics> <mrow> <mstyle> <mo>(</mo> <mrow> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> </mrow> <mo>+</mo> <mrow> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mrow> <mo>)</mo> <mrow> <mo>/</mo> </mrow> <mrow> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation>{\displaystyle ({|0\rangle }+{|1\rangle })/{\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0df4c1e9e36d758c71d40f1ab11f73fd4d0362fc" alt="{\displaystyle ({|0\rangle }+{|1\rangle })/{\sqrt {2}}}" title=""/></span> would lie on the equator of the sphere at the positive X-axis. In the <a href="https://en.wikipedia.org/wiki/Classical_limit">classical limit</a>, a qubit, which can have quantum states anywhere on the Bloch sphere, reduces to the classical bit, which can be found only at either poles.</p> <p>The surface of the Bloch sphere is a <a href="https://en.wikipedia.org/wiki/Plane_(mathematics)">two-dimensional space</a>, which represents the observable <a href="https://en.wikipedia.org/wiki/State_space_(physics)">state space</a> of the pure qubit states. This state space has two local degrees of freedom, which can be represented by the two angles <span><span><math> <semantics> <mrow> <mstyle> <mi>φ</mi> </mstyle> </mrow> <annotation>{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" alt="{\displaystyle \varphi }" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>θ</mi> </mstyle> </mrow> <annotation>{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" alt="{\displaystyle \theta }" title=""/></span>.</p> </section><section><div><h3>Mixed state</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Qubit&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div> <div>Main article: <a href="https://en.wikipedia.org/wiki/Density_matrix">Density matrix</a></div> <p>A pure state is fully specified by a single ket, <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mrow> <mo>|</mo> </mrow> <mi>ψ</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mi>α</mi> <mrow> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> </mrow> <mo>+</mo> <mi>β</mi> <mrow> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation>{\displaystyle {|\psi \rangle }=\alpha {|0\rangle }+\beta {|1\rangle },\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c01801d4b188cfb58e6d97e978e598c2cc919a4" alt="{\displaystyle {|\psi \rangle }=\alpha {|0\rangle }+\beta {|1\rangle },\,}" title=""/></span> a coherent superposition, represented by a point on the surface of the Bloch sphere as described above. Coherence is essential for a qubit to be in a superposition state. With interactions, <a href="https://en.wikipedia.org/wiki/Quantum_noise">quantum noise</a> and <a href="https://en.wikipedia.org/wiki/Decoherence">decoherence</a>, it is possible to put the qubit in a <a href="https://en.wikipedia.org/wiki/Mixed_state_(physics)">mixed state</a>, a statistical combination or &quot;incoherent mixture&quot; of different pure states. Mixed states can be represented by points <i>inside</i> the Bloch sphere (or in the Bloch ball). A mixed qubit state has three degrees of freedom: the angles <span><span><math> <semantics> <mrow> <mstyle> <mi>φ</mi> </mstyle> </mrow> <annotation>{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" alt="{\displaystyle \varphi }" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mi>θ</mi> </mstyle> </mrow> <annotation>{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" alt="{\displaystyle \theta }" title=""/></span>, as well as the length <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/0d1ecb613aa2984f0576f70f86650b7c2a132538" alt="{\displaystyle r}" title=""/></span> of the vector that represents the mixed state.</p> <p><a href="https://en.wikipedia.org/wiki/Quantum_error_correction">Quantum error correction</a> can be used to maintain the purity of qubits.</p> </section> https://en.wikipedia.org/wiki/Quantum_computing e6itXO0NUIKQOHzdIt50Us4uI5plD7ZeQAs6EA== Mon, 14 Sep 2026 23:58:23 +0000 Computer hardware technology that uses quantum mechanics <div>Computer hardware technology that uses quantum mechanics</div><p> </p><figure><a href="https://en.wikipedia.org/wiki/File:IBM_Quantum_Computer_Demo_at_ITUWTSA_2024,_Delhi_2.jpg"></a><figcaption><a href="https://en.wikipedia.org/wiki/IBM">IBM</a> quantum computer demo at <a href="https://en.wikipedia.org/wiki/International_Telecommunication_Union">ITU</a> <a href="https://en.wikipedia.org/wiki/World_Telecommunication_Standardization_Assembly">WTSA</a> 2024 in <a href="https://en.wikipedia.org/wiki/Delhi">Delhi</a></figcaption></figure><figure><a href="https://en.wikipedia.org/wiki/File:Bloch_sphere.svg"></a><figcaption><a href="https://en.wikipedia.org/wiki/Bloch_sphere">Bloch sphere</a> representation of a qubit. The state <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mo>|</mo> </mrow> <mi>ψ</mi> <mo>⟩</mo> <mo>=</mo> <mi>α</mi> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> <mo>+</mo> <mi>β</mi> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mstyle> </mrow> <annotation>{\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/259aaac5393082d769c30b0b58fd0fafe4032d8d" alt="{\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle }" title=""/></span> is a point on the surface of the sphere, partway between the poles, <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mo>|</mo> </mrow> <mn>0</mn> <mo>⟩</mo> </mstyle> </mrow> <annotation>{\displaystyle |0\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed066a3ad158da0ad6d6a421a606b1c8a35eb95b" alt="{\displaystyle |0\rangle }" title=""/></span> and <span><span><math> <semantics> <mrow> <mstyle> <mrow> <mo>|</mo> </mrow> <mn>1</mn> <mo>⟩</mo> </mstyle> </mrow> <annotation>{\displaystyle |1\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f53021ca18e77477ee5bd3c1523e5830189ec5c" alt="{\displaystyle |1\rangle }" title=""/></span>.</figcaption></figure><p>A <b>quantum computer</b> is a <a href="https://en.wikipedia.org/wiki/Computer">computer</a> that represents and processes information using <a href="https://en.wikipedia.org/wiki/Quantum_state">quantum states</a>. Quantum computations exploit phenomena such as <a href="https://en.wikipedia.org/wiki/Quantum_superposition">superposition</a>, <a href="https://en.wikipedia.org/wiki/Wave_interference">interference</a>, and <a href="https://en.wikipedia.org/wiki/Quantum_entanglement">entanglement</a>. Quantum computers have the potential to complete some calculations exponentially faster than classical computers. For example, a large-scale quantum computer could <a href="https://en.wikipedia.org/wiki/Post-quantum_cryptography">break widely used encryption schemes</a> and aid physicists in performing <a href="https://en.wikipedia.org/wiki/Quantum_simulator">physical simulations</a>. However, current hardware implementations of quantum computation are largely experimental and suitable for only certain specialized tasks.</p><p>The basic <a href="https://en.wikipedia.org/wiki/Unit_of_information">unit of information</a> in quantum computing, the <a href="https://en.wikipedia.org/wiki/Qubit">qubit</a> (quantum bit), serves a similar function as the <a href="https://en.wikipedia.org/wiki/Bit">bit</a> in ordinary or &quot;classical&quot; computing.^{<span><span>[</span>1<span>]</span></span>} Unlike a classical bit, which can be in one of two states (a <a href="https://en.wikipedia.org/wiki/Binary_number">binary</a>), a qubit can exist in a <a href="https://en.wikipedia.org/wiki/Linear_combination">linear combination</a> of states known as a <a href="https://en.wikipedia.org/wiki/Quantum_superposition">quantum superposition</a>. The result of <a href="https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics">measuring</a> a qubit is one of the two states, given by a <a href="https://en.wikipedia.org/wiki/Born_rule">probabilistic rule</a>. If a quantum computer manipulates the qubit in a particular way, <a href="https://en.wikipedia.org/wiki/Wave_interference">wave interference</a> effects amplify the probability of the desired measurement result. <a href="https://en.wikipedia.org/wiki/Quantum_algorithms">Quantum algorithm</a> design involves creating procedures that allow a quantum computer to perform this amplification.</p><p>Quantum computers are not yet practical for real-world applications. If a physical qubit is not sufficiently <a href="https://en.wikipedia.org/wiki/Isolated_system">isolated</a> from its environment, it suffers from <a href="https://en.wikipedia.org/wiki/Quantum_decoherence">quantum decoherence</a>, introducing <a href="https://en.wikipedia.org/wiki/Noise_(signal_processing)">noise</a> (error) into calculations. Governments have invested in research aimed at developing qubits with longer coherence times and lower error rates. Example implementations include <a href="https://en.wikipedia.org/wiki/Superconducting_quantum_computing">superconductors</a> (which isolate an <a href="https://en.wikipedia.org/wiki/Electrical_current">electrical current</a> by eliminating <a href="https://en.wikipedia.org/wiki/Electrical_resistance">electrical resistance</a>) and <a href="https://en.wikipedia.org/wiki/Trapped_ion_quantum_computer">ion traps</a> (which confine a single <a href="https://en.wikipedia.org/wiki/Atom">atomic particle</a> using <a href="https://en.wikipedia.org/wiki/Electromagnetic_fields">electromagnetic fields</a>). Researchers have claimed that quantum devices can outperform classical computers on specific tasks, a metric referred to as quantum advantage or <a href="https://en.wikipedia.org/wiki/Quantum_supremacy">quantum supremacy</a>. Such tasks are not necessarily useful for real-world applications. As a result, as of 2026 demonstrations are best understood as scientific milestones rather than evidence for near-term deployment. Global government investment in quantum computing reached $10 billion by April 2025.^{<span><span>[</span>2<span>]</span></span>}</p> https://en.wikipedia.org/wiki/Pharmaceutical_industry ynzrSoWlh73cFpkJvJw7SAK6onwv1SVMSPvUpw== Mon, 14 Sep 2026 23:58:17 +0000 Industry involved with discovery, development, production and marketing of drugs <div>Industry involved with discovery, development, production and marketing of drugs</div><figure><a href="https://en.wikipedia.org/wiki/File:Inspecting_a_Drug_Manufacturer_(FDA034)_(6982162417).jpg"></a><figcaption>A drug manufacturer inspection by the US <a href="https://en.wikipedia.org/wiki/Food_and_Drug_Administration">Food and Drug Administration</a></figcaption></figure><p>The <b>pharmaceutical industry</b> is a <a href="https://en.wikipedia.org/wiki/Medicine">medical</a> industry that discovers, develops, produces, and markets pharmaceutical <a href="https://en.wikipedia.org/wiki/Goods">goods</a> such as <a href="https://en.wikipedia.org/wiki/Medication">medications</a>. Medications are then administered to (or <a href="https://en.wikipedia.org/wiki/Self-medicate">self-administered</a> by) patients for curing or preventing disease or for alleviating symptoms of illness or injury.^{<span><span>[</span>1<span>]</span></span>}^{<span><span>[</span>2<span>]</span></span>}</p><p>Generic drugs are typically not protected by patents, whereas branded drugs are covered by <a href="https://en.wikipedia.org/wiki/Chemical_patent">patents</a>. The industry&#39;s various subdivisions include distinct areas, such as manufacturing <a href="https://en.wikipedia.org/wiki/Biopharmaceutical">biologics</a> and <a href="https://en.wikipedia.org/wiki/Total_synthesis">total synthesis</a>. The industry is subject to a <a href="https://en.wikipedia.org/wiki/Legal_drug_trade">variety of laws and regulations</a> that govern the <a href="https://en.wikipedia.org/wiki/Patent">patenting</a>, efficacy testing, <a href="https://en.wikipedia.org/wiki/Drug_safety">safety evaluation</a>, and marketing of these drugs.</p><p>The global pharmaceutical market was valued at approximately US$1.48 trillion in 2022, reflecting steady growth from 2020 and continuing expansion despite the impacts of the COVID-19 pandemic.^{<span><span>[</span>3<span>]</span></span>} The sector showed a <a href="https://en.wikipedia.org/wiki/Compound_annual_growth_rate">compound annual growth rate</a> (CAGR) of 1.8% in 2021, including the effects of the <a href="https://en.wikipedia.org/wiki/COVID-19_pandemic">COVID-19 pandemic</a>.^{<span><span>[</span>4<span>]</span></span>}</p><p>In historical terms, the pharmaceutical industry, as an intellectual <a href="https://en.wikipedia.org/wiki/Concept">concept</a>, arose in the middle to late 1800s in nation-states with developed economies such as Germany, Switzerland, and the United States. Some businesses engaging in synthetic <a href="https://en.wikipedia.org/wiki/Organic_chemistry">organic chemistry</a>, such as several firms generating <a href="https://en.wikipedia.org/wiki/Dye">dyestuffs</a> derived from <a href="https://en.wikipedia.org/wiki/Coal_tar">coal tar</a> on a large scale, were seeking out new applications for their artificial materials in terms of human health. This trend of increased <a href="https://en.wikipedia.org/wiki/Capital_(economics)">capital investment</a> occurred in <a href="https://en.wikipedia.org/wiki/Tandem">tandem</a> with the scholarly study of <a href="https://en.wikipedia.org/wiki/Pathology">pathology</a> as a field advancing significantly, and a variety of businesses set up cooperative relationships with academic laboratories evaluating human injury and disease. Examples of industrial companies with a pharmaceutical focus that have endured to this day after such distant beginnings include <a href="https://en.wikipedia.org/wiki/Bayer">Bayer</a> (based in Germany) and <a href="https://en.wikipedia.org/wiki/Pfizer">Pfizer</a> (based in the U.S.).^{<span><span>[</span>5<span>]</span></span>}</p><p>The pharmaceutical industry has faced extensive criticism for its <a href="https://en.wikipedia.org/wiki/Marketing">marketing</a> practices, including undue influence on <a href="https://en.wikipedia.org/wiki/Physician">physicians</a> through <a href="https://en.wikipedia.org/wiki/Pharmaceutical_sales_representative">pharmaceutical sales representatives</a>, biased <a href="https://en.wikipedia.org/wiki/Continuing_medical_education">continuing medical education</a>, and <a href="https://en.wikipedia.org/wiki/Disease_mongering">disease mongering</a> to expand markets. Pharmaceutical <a href="https://en.wikipedia.org/wiki/Lobbying">lobbying</a> has made it one of the most powerful influences on <a href="https://en.wikipedia.org/wiki/Health_policy">health policy</a>, particularly in the <a href="https://en.wikipedia.org/wiki/United_States">United States</a>. There are documented cases of <a href="https://en.wikipedia.org/wiki/Pharmaceutical_fraud">pharmaceutical fraud</a>, including off-label promotion and <a href="https://en.wikipedia.org/wiki/Kickbacks">kickbacks</a>, resulting in multi-billion dollar settlements. <a href="https://en.wikipedia.org/wiki/Drug_pricing">Drug pricing</a> continues to be a major issue, with many unable to afford essential <a href="https://en.wikipedia.org/wiki/Prescription_drugs">prescription drugs</a>. Regulatory agencies like the <a href="https://en.wikipedia.org/wiki/FDA">FDA</a> have been accused of being too lenient due to <a href="https://en.wikipedia.org/wiki/Revolving_door_(politics)">revolving doors</a> with industry. During the <a href="https://en.wikipedia.org/wiki/COVID-19_pandemic">COVID-19 pandemic</a>, major pharmaceutical companies received public funding while retaining <a href="https://en.wikipedia.org/wiki/Intellectual_property">intellectual property</a> rights, prompting calls for greater transparency and access.</p> https://en.wikipedia.org/wiki/Quality_control zvOoQtwV_n6I7yTaGbt12Xo04BCOPIZXLE3Qiw== Mon, 14 Sep 2026 23:58:12 +0000 This article is about the project management process. For the record label, see Quality Control Music. <section><div>This article is about the project management process. For the record label, see <a href="https://en.wikipedia.org/wiki/Quality_Control_Music">Quality Control Music</a>.</div> <div>&quot;TQC&quot; redirects here. For other uses, see <a href="https://en.wikipedia.org/wiki/TQC_(disambiguation)">TQC (disambiguation)</a>.</div> <div>Processes that maintain quality at a constant level</div> <figure><a href="https://en.wikipedia.org/wiki/File:Fotothek_df_n-04_0000019.jpg"></a><figcaption>Quality inspector in a <a href="https://en.wikipedia.org/wiki/Volkseigener_Betrieb">Volkseigener Betrieb</a> sewing machine parts factory in Dresden, <a href="https://en.wikipedia.org/wiki/East_Germany">East Germany</a>, 1977</figcaption></figure> <figure><a href="https://en.wikipedia.org/wiki/File:Women_workers_checking_25-pounder_artillery_shells_at_the_small_arms_factory_of_J_&amp;_F_Pool_Ltd_in_Hayle,_Cornwall,_1943._TR660.jpg"></a><figcaption>Munitions workers inspecting <a href="https://en.wikipedia.org/wiki/ML_3-inch_mortar">3-inch mortar</a> bombs, 1943</figcaption></figure> <p><b>Quality control</b> (<b>QC</b>) is a process by which entities review the quality of all factors involved in <a href="https://en.wikipedia.org/wiki/Production_(economics)">production</a>. <a href="https://en.wikipedia.org/wiki/ISO_9000">ISO 9000</a> defines quality control as &quot;a part of <a href="https://en.wikipedia.org/wiki/Quality_management">quality management</a> focused on fulfilling quality requirements&quot;.^{<span><span>[</span>1<span>]</span></span>}</p> <p>This approach places emphasis on three aspects (enshrined in standards such as ISO 9001):^{<span><span>[</span>2<span>]</span></span>}^{<span><span>[</span>3<span>]</span></span>}</p> <ol><li>Elements such as controls, job management, defined and well managed processes,^{<span><span>[</span>4<span>]</span></span>}^{<span><span>[</span>5<span>]</span></span>} performance and integrity criteria, and identification of records</li> <li>Competence, such as knowledge, skills, experience, and qualifications</li> <li>Soft elements, such as personnel, <a href="https://en.wikipedia.org/wiki/Integrity">integrity</a>, <a href="https://en.wikipedia.org/wiki/Confidence">confidence</a>, <a href="https://en.wikipedia.org/wiki/Organizational_culture">organizational culture</a>, <a href="https://en.wikipedia.org/wiki/Motivation">motivation</a>, <a href="https://en.wikipedia.org/wiki/Team_spirit">team spirit</a>, and quality relationships.</li></ol> <p><a href="https://en.wikipedia.org/wiki/Inspection">Inspection</a> is a major component of quality control, where physical product is examined visually (or the end results of a service are analyzed). Product inspectors will be provided with lists and descriptions of unacceptable <a href="https://en.wikipedia.org/wiki/Product_defect">product defects</a> such as <a href="https://en.wikipedia.org/wiki/Fracture">cracks</a> or surface <a href="https://en.wiktionary.org/wiki/blemish">blemishes</a> for example.^{<span><span>[</span>3<span>]</span></span>}</p> </section><section><div><h2>History and introduction</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Quality_control&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div> <div>See also: <a href="https://en.wikipedia.org/wiki/History_of_technology">History of technology</a></div> <p>Early <a href="https://en.wikipedia.org/wiki/Stone_tools">stone tools</a> such as <a href="https://en.wikipedia.org/wiki/Anvil">anvils</a> had no holes and were not designed as <a href="https://en.wikipedia.org/wiki/Interchangeable_parts">interchangeable parts</a>. <a href="https://en.wikipedia.org/wiki/Mass_production">Mass production</a> established processes for the creation of parts and system with identical dimensions and design, but these processes are not uniform and hence some customers were unsatisfied with the result. Quality control separates the act of <a href="https://en.wikipedia.org/wiki/Test_method">testing</a> <a href="https://en.wikipedia.org/wiki/Product_(business)">products</a> to uncover defects from the decision to allow or deny product release, which may be determined by fiscal constraints.^{<span><span>[</span>6<span>]</span></span>} For contract work, particularly work awarded by government agencies, quality control issues are among the top reasons for not renewing a contract.^{<span><span>[</span>7<span>]</span></span>}</p> <p>The simplest form of quality control was a sketch of the desired item. If the item did not match the sketch, the item was rejected, in a simple <a href="https://en.wikipedia.org/wiki/Go/no_go">Go/no go</a> procedure. However, manufacturers soon found it was difficult and costly to make parts be exactly like their depiction; hence around 1840 tolerance limits were introduced, wherein a design would function if its parts were measured to be within the limits. Quality was thus precisely defined using devices such as <a href="https://en.wikipedia.org/wiki/Plug_gauge">plug gauges</a> and <a href="https://en.wikipedia.org/wiki/Ring_gauge">ring gauges</a>. However, this did not address the problem of defective items; recycling or disposing of the <a href="https://en.wikipedia.org/wiki/Waste">waste</a> adds to the cost of production, as does trying to reduce the defect rate. Various methods have been proposed to prioritize quality control issues and determine whether to leave them unaddressed or use <a href="https://en.wikipedia.org/wiki/Quality_assurance">quality assurance</a> techniques to improve and stabilize production.^{<span><span>[</span>6<span>]</span></span>}</p> </section><section><div><h2>Notable approaches</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Quality_control&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div> <p>There is a tendency for individual consultants and organizations to name their own unique approaches to quality control—a few of these have ended up in widespread use:</p> <table> <tbody><tr> <th>Terminology</th><th>Approximate year of first use</th><th>Description</th></tr> <tr> <td>Statistical quality control (SQC)</td><td>1930s</td><td>The application of statistical methods (specifically <a href="https://en.wikipedia.org/wiki/Control_chart">control charts</a> and <a href="https://en.wikipedia.org/wiki/Acceptance_sampling">acceptance sampling</a>) to quality control^{<span><span>[</span>8<span>]</span></span>}^{<span><span>:</span><span> </span>556<span> </span></span>}</td></tr> <tr> <td>Total quality control (TQC)</td><td>1956</td><td>Popularized by <a href="https://en.wikipedia.org/wiki/Armand_V._Feigenbaum">Armand V. Feigenbaum</a> in a <a href="https://en.wikipedia.org/wiki/Harvard_Business_Review">Harvard Business Review</a> article^{<span><span>[</span>9<span>]</span></span>} and book of the same name;^{<span><span>[</span>10<span>]</span></span>} stresses involvement of departments in addition to production (e.g., accounting, design, finance, human resources, marketing, purchasing, sales)</td></tr> <tr> <td><a href="https://en.wikipedia.org/wiki/Statistical_process_control">Statistical process control</a> (SPC)</td><td>1960s</td><td>The use of <a href="https://en.wikipedia.org/wiki/Control_chart">control charts</a> to monitor an individual industrial process and feed back performance to the operators responsible for that process; inspired by <a href="https://en.wikipedia.org/wiki/Control_system">control systems</a></td></tr> <tr> <td>Company-wide quality control (CWQC)</td><td>1968</td><td>Japanese-style total quality control.^{<span><span>[</span>11<span>]</span></span>}</td></tr> <tr> <td><a href="https://en.wikipedia.org/wiki/Total_quality_management">Total quality management</a> (TQM)</td><td>1985</td><td>Quality movement originating in the <a href="https://en.wikipedia.org/wiki/United_States_Department_of_Defense">United States Department of Defense</a> that uses (in part) the techniques of statistical quality control to drive continuous organizational improvement^{<span><span>[</span>12<span>]</span></span>}</td></tr> <tr> <td><a href="https://en.wikipedia.org/wiki/Six_Sigma">Six Sigma</a> (6σ)</td><td>1986</td><td>Statistical quality control applied to business strategy;^{<span><span>[</span>13<span>]</span></span>} originated by <a href="https://en.wikipedia.org/wiki/Motorola">Motorola</a></td></tr> <tr> <td><a href="https://en.wikipedia.org/wiki/Lean_Six_Sigma">Lean Six Sigma</a> (L6σ)</td><td>2001</td><td>Six Sigma applied with the principles of <a href="https://en.wikipedia.org/wiki/Lean_manufacturing">lean manufacturing</a> and/or <a href="https://en.wikipedia.org/wiki/Lean_enterprise">lean enterprise</a>; originated by Wheat <i>et al.</i>^{<span><span>[</span>14<span>]</span></span>}</td></tr> </tbody></table> </section><section><div><h2>In project management</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Quality_control&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <p>In <a href="https://en.wikipedia.org/wiki/Project_management">project management</a>, quality control requires the project manager and/or the project team to inspect the accomplished work to ensure its alignment with the project scope.^{<span><span>[</span>15<span>]</span></span>} In practice, projects typically have a dedicated quality control team which focuses on this area.^{<span><span>[</span>16<span>]</span></span>}</p> </section><section><div><h2>See also</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Quality_control&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="https://en.wikipedia.org/wiki/Analytical_quality_control">Analytical quality control</a></li> <li><a href="https://en.wikipedia.org/wiki/Corrective_and_preventative_action">Corrective and preventative action</a> (CAPA)</li> <li><a href="https://en.wikipedia.org/wiki/Eight_dimensions_of_quality">Eight dimensions of quality</a></li> <li><a href="https://en.wikipedia.org/wiki/First_article_inspection">First article inspection</a> (FAI)</li> <li><a href="https://en.wikipedia.org/wiki/Good_Automated_Manufacturing_Practice">Good automated manufacturing practice</a> (GAMP)</li> <li><a href="https://en.wikipedia.org/wiki/Good_manufacturing_practice">Good manufacturing practice</a></li> <li><a href="https://en.wikipedia.org/wiki/Quality_assurance">Quality assurance</a></li> <li><a href="https://en.wikipedia.org/wiki/Quality_management_framework">Quality management framework</a></li> <li><a href="https://en.wikipedia.org/wiki/Standard_operating_procedure">Standard operating procedure</a> (SOP)</li> <li><a href="https://en.wikipedia.org/wiki/QA/QC">QA/QC</a></li></ul> </section><section><div><h2>References</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Quality_control&amp;action=edit&amp;section=5"><span>edit</span></a><span>]</span></span></div> <div> <div><ol><li><span><span>↑</span></span> <span>ISO 9000:2005, Clause 3.2.10</span></li> <li><span><span>↑</span></span> <span><cite>Praxiom Research Group Limited (16 August 2017). <a href="https://web.archive.org/web/20171202150849/http://www.praxiom.com/iso-9001.htm">&quot;ISO 9001 Translated Into Plain English&quot;</a>. Praxiom Research Group Limited. Archived from <a href="http://www.praxiom.com/iso-9001.htm">the original</a> on 2 December 2017<span>. Retrieved <span>29 November</span> 2017</span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Aft, L.S. (1997). &quot;Chapter 1: Introduction&quot;. <i>Fundamentals of Industrial Quality Control</i>. CRC Press. pp.<span> </span><span>1–</span>17.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Dennis Adsit (9 November 2007). <a href="https://web.archive.org/web/20170704064643/http://www.nationalcallcenters.org/images/stories/InQueue/vol2no21.pdf">&quot;What the Call Center Industry Can Learn from Manufacturing: Part I&quot;</a> <span>(PDF)</span>. National Association of Call Centers. Archived from the original on 4 July 2017<span>. Retrieved <span>21 December</span> 2012</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Dennis Adsit (23 November 2007). <a href="https://web.archive.org/web/20170704063943/http://www.nationalcallcenters.org/images/stories/InQueue/Vol2No22.pdf">&quot;What the Call Center Industry Can Learn from Manufacturing: Part II&quot;</a> <span>(PDF)</span>. National Association of Call Centers. Archived from the original on 4 July 2017<span>. Retrieved <span>21 December</span> 2012</span>.</cite></span></li> <li><span><span>1</span> <span>2</span></span> <span><cite>Shewhart, Walter A. (Walter Andrew); Deming, W. Edwards (William Edwards) (1939). <a href="https://archive.org/stream/CAT10502416#page/2/mode/2up"><i>Statistical method from the viewpoint of quality control</i></a>. Washington: The Graduate School, The Department of Agriculture. pp.<span> </span><span>1–</span>5.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://www.opm.gov/fedclass/gs1910.pdf">&quot;Position Classification Standard for Quality Assurance Series, GS-1910&quot;</a> <span>(PDF)</span>. US Office of Personnel Management. March 1983. <a href="https://ghostarchive.org/archive/20221009/http://www.opm.gov/fedclass/gs1910.pdf">Archived</a> <span>(PDF)</span> from the original on 9 October 2022<span>. Retrieved <span>21 December</span> 2012</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Joseph_M._Juran">Juran, Joseph M.</a>, ed. (1995), <span><a href="https://archive.org/details/historyofmanagin0000unse"><i>A History of Managing for Quality: The Evolution, Trends, and Future Directions of Managing for Quality</i></a></span>, <a href="https://en.wikipedia.org/wiki/Milwaukee">Milwaukee, Wisconsin</a>: The <a href="https://en.wikipedia.org/wiki/American_Society_for_Quality">American Society for Quality Control</a>, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/9780873893411"><bdi>9780873893411</bdi></a>, <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/32394752">32394752</a></cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Armand_V._Feigenbaum">Feigenbaum, Armand V.</a> (1956). &quot;Total Quality Control&quot;. <i><a href="https://en.wikipedia.org/wiki/Harvard_Business_Review">Harvard Business Review</a></i>. <b>34</b> (6). <a href="https://en.wikipedia.org/wiki/Cambridge,_Massachusetts">Cambridge, Massachusetts</a>: <a href="https://en.wikipedia.org/wiki/Harvard_University_Press">Harvard University Press</a>: <span>93–</span>101. <a href="https://en.wikipedia.org/wiki/ISSN_(identifier)">ISSN</a><span> </span><a href="https://search.worldcat.org/issn/0017-8012">0017-8012</a>. <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/1751795">1751795</a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Feigenbaum, Armand Vallin (1961), <i>Total Quality Control</i>, New York, McGraw-Hill, <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/250573852">250573852</a></cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://en.wikipedia.org/wiki/Kaoru_Ishikawa">Ishikawa, Kaoru</a> (1985), <span><a href="https://archive.org/details/whatistotalquali00ishi/page/90"><i>What Is Total Quality Control? The Japanese Way</i></a></span> (1<span> </span>ed.), <a href="https://en.wikipedia.org/wiki/Englewood_Cliffs,_New_Jersey">Englewood Cliffs, New Jersey</a>: <a href="https://en.wikipedia.org/wiki/Prentice-Hall">Prentice-Hall</a>, pp.<span> </span><a href="https://archive.org/details/whatistotalquali00ishi/page/90">90–91</a>, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/978-0-13-952433-2"><bdi>978-0-13-952433-2</bdi></a>, <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/11467749">11467749</a></cite></span></li> <li><span><span>↑</span></span> <span><cite>Evans, James R.; Lindsay, William M. (1999), <a href="https://archive.org/details/managementcontro0004evan/page/118"><i>The Management and Control of Quality</i></a> (4<span> </span>ed.), <a href="https://en.wikipedia.org/wiki/Cincinnati">Cincinnati, Ohio</a>: South-Western College Publications, p.<span> </span><a href="https://archive.org/details/managementcontro0004evan/page/118">118</a>, <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/9780538882422"><bdi>9780538882422</bdi></a>, <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/38475486">38475486</a>, <q>The term <b>total quality management</b>, or <b>TQM</b>, has been commonly used to denote the system of managing for total quality. (The term TQM was actually developed within the Department of Defense. It has since been renamed Total Quality Leadership, since leadership outranks management in military thought.)</q></cite></span></li> <li><span><span>↑</span></span> <span><cite><a href="https://web.archive.org/web/20131203031507/http://www.motorolasolutions.com/web/Business/_Moto_University/_Documents/_Static_Files/What_is_SixSigma.pdf">&quot;What Is Six Sigma?&quot;</a> <span>(PDF)</span>. <a href="https://en.wikipedia.org/wiki/Schaumburg,_Illinois">Schaumburg, Illinois</a>: Motorola University. 19 February 2010. p.<span> </span>2. Archived from <a href="http://www.motorolasolutions.com/web/Business/_Moto_University/_Documents/_Static_Files/What_is_SixSigma.pdf">the original</a> <span>(PDF)</span> on 3 December 2013<span>. Retrieved <span>24 November</span> 2013</span>. <q>When practiced as a management system, Six Sigma is a high performance system for executing business strategy.</q></cite></span></li> <li><span><span>↑</span></span> <span><cite>Wheat, B.; Mills, C.; Carnell, M. (2001). <i>Leaning into Six Sigma: The Path to integration of Lean Enterprise and Six Sigma</i>. Publishing Partners. p.<span> </span>100. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/9780971249103"><bdi>9780971249103</bdi></a>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Phillips, Joseph (November 2008). <a href="http://www.pmhut.com/quality-control-in-project-management">&quot;Quality Control in Project Management&quot;</a>. The Project Management Hut<span>. Retrieved <span>21 December</span> 2012</span>.</cite></span></li> <li><span><span>↑</span></span> <span><cite>Rose, K.H. (2014). <i>Project Quality Management: Why, What and How</i>. J. Ross Publishing. p.<span> </span>224. <a href="https://en.wikipedia.org/wiki/ISBN_(identifier)">ISBN</a><span> </span><a href="https://en.wikipedia.org/wiki/Special:BookSources/9781604271027"><bdi>9781604271027</bdi></a>.</cite></span></li> </ol></div></div> <ul><li><span><span> </span>This article incorporates <a href="https://en.wikipedia.org/wiki/Copyright_status_of_works_by_the_federal_government_of_the_United_States">public domain material</a> from <cite><a href="https://web.archive.org/web/20220122224547/https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm"><i>Federal Standard 1037C</i></a>. <a href="https://en.wikipedia.org/wiki/General_Services_Administration">General Services Administration</a>. Archived from <a href="https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm">the original</a> on 22 January 2022.</cite><span> </span>(in support of <a href="https://en.wikipedia.org/wiki/MIL-STD-188">MIL-STD-188</a>). </span></li></ul> </section><section><div><h2>Further reading</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Quality_control&amp;action=edit&amp;section=6"><span>edit</span></a><span>]</span></span></div> <ul><li><cite>Radford, George S. (1922), <a href="https://archive.org/details/controlofquality00radf"><i>The Control of Quality in Manufacturing</i></a>, <a href="https://en.wikipedia.org/wiki/New_York_City">New York</a>: Ronald Press Co., <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/1701274">1701274</a><span>, retrieved <span>16 November</span> 2013</span></cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/Walter_A._Shewhart">Shewhart, Walter A.</a> (1931), <i>Economic Control of Quality of Manufactured Product</i>, <a href="https://en.wikipedia.org/wiki/New_York_City">New York</a>: D. Van Nostrand Co., Inc., <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/1045408">1045408</a></cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/Joseph_M._Juran">Juran, Joseph M.</a> (1951), <i>Quality-Control Handbook</i>, <a href="https://en.wikipedia.org/wiki/New_York_City">New York</a>: <a href="https://en.wikipedia.org/wiki/McGraw-Hill">McGraw-Hill</a>, <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/1220529">1220529</a></cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/Western_Electric_Company">Western Electric Company</a> (1956), <a href="https://en.wikipedia.org/wiki/Statistical_Quality_Control"><i>Statistical Quality Control Handbook</i></a> (1<span> </span>ed.), <a href="https://en.wikipedia.org/wiki/Indianapolis,_Indiana">Indianapolis, Indiana</a>: Western Electric Co., <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/33858387">33858387</a></cite></li> <li><cite><a href="https://en.wikipedia.org/wiki/Armand_V._Feigenbaum">Feigenbaum, Armand V.</a> (1961), <i>Total Quality Control</i>, <a href="https://en.wikipedia.org/wiki/New_York_City">New York</a>: <a href="https://en.wikipedia.org/wiki/McGraw-Hill">McGraw-Hill</a>, <a href="https://en.wikipedia.org/wiki/OCLC_(identifier)">OCLC</a><span> </span><a href="https://search.worldcat.org/oclc/567344">567344</a></cite></li></ul> </section><section><div><h2>External links</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Quality_control&amp;action=edit&amp;section=7"><span>edit</span></a><span>]</span></span></div> <ul><li><a href="http://www.astm.org/Standards/quality-control-standards.html">ASTM quality control standards</a></li></ul> <div><table><tbody><tr><th colspan="2"><div><ul><li><a href="https://en.wikipedia.org/wiki/Template:Statistics"><abbr>v</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Template_talk:Statistics"><abbr>t</abbr></a></li><li><a href="https://en.wikipedia.org/wiki/Special:EditPage/Template:Statistics"><abbr>e</abbr></a></li></ul></div><div><a href="https://en.wikipedia.org/wiki/Statistics">Statistics</a></div></th></tr><tr><td colspan="2"><div> <ul><li><a href="https://en.wikipedia.org/wiki/Outline_of_statistics">Outline</a></li> <li><a href="https://en.wikipedia.org/wiki/List_of_statistics_articles">Index</a></li></ul> </div></td></tr><tr><td colspan="2"><table><tbody><tr><th colspan="2"><div><a href="https://en.wikipedia.org/wiki/Descriptive_statistics">Descriptive statistics</a></div></th></tr><tr><td colspan="2"><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Continuous_probability_distribution">Continuous data</a></th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Central_tendency">Center</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Mean">Mean</a> <ul><li><a href="https://en.wikipedia.org/wiki/Arithmetic_mean">Arithmetic</a></li> <li><a href="https://en.wikipedia.org/wiki/Arithmetic–geometric_mean">Arithmetic-Geometric</a></li> <li><a href="https://en.wikipedia.org/wiki/Contraharmonic_mean">Contraharmonic</a></li> <li><a href="https://en.wikipedia.org/wiki/Cubic_mean">Cubic</a></li> <li><a href="https://en.wikipedia.org/wiki/Generalized_mean">Generalized/power</a></li> <li><a href="https://en.wikipedia.org/wiki/Geometric_mean">Geometric</a></li> <li><a href="https://en.wikipedia.org/wiki/Harmonic_mean">Harmonic</a></li> <li><a href="https://en.wikipedia.org/wiki/Heronian_mean">Heronian</a></li> <li><a href="https://en.wikipedia.org/wiki/Heinz_mean">Heinz</a></li> <li><a href="https://en.wikipedia.org/wiki/Lehmer_mean">Lehmer</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Median">Median</a></li> <li><a href="https://en.wikipedia.org/wiki/Mode_(statistics)">Mode</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Statistical_dispersion">Dispersion</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Average_absolute_deviation">Average absolute deviation</a></li> <li><a href="https://en.wikipedia.org/wiki/Coefficient_of_variation">Coefficient of variation</a></li> <li><a href="https://en.wikipedia.org/wiki/Interquartile_range">Interquartile range</a></li> <li><a href="https://en.wikipedia.org/wiki/Percentile">Percentile</a></li> <li><a href="https://en.wikipedia.org/wiki/Range_(statistics)">Range</a></li> <li><a href="https://en.wikipedia.org/wiki/Standard_deviation">Standard deviation</a></li> <li><a href="https://en.wikipedia.org/wiki/Variance#Sample_variance">Variance</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Shape_of_the_distribution">Shape</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Central_limit_theorem">Central limit theorem</a></li> <li><a href="https://en.wikipedia.org/wiki/Moment_(mathematics)">Moments</a> <ul><li><a href="https://en.wikipedia.org/wiki/Kurtosis">Kurtosis</a></li> <li><a href="https://en.wikipedia.org/wiki/L-moment">L-moments</a></li> <li><a href="https://en.wikipedia.org/wiki/Skewness">Skewness</a></li></ul></li></ul> </div></td></tr></tbody></table></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Count_data">Count data</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Index_of_dispersion">Index of dispersion</a></li></ul> </div></td></tr><tr><th>Summary tables</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Contingency_table">Contingency table</a></li> <li><a href="https://en.wikipedia.org/wiki/Frequency_distribution">Frequency distribution</a></li> <li><a href="https://en.wikipedia.org/wiki/Grouped_data">Grouped data</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Correlation_and_dependence">Dependence</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Partial_correlation">Partial correlation</a></li> <li><a href="https://en.wikipedia.org/wiki/Pearson_correlation_coefficient">Pearson product-moment correlation</a></li> <li><a href="https://en.wikipedia.org/wiki/Rank_correlation">Rank correlation</a> <ul><li><a href="https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient">Kendall&#39;s τ</a></li> <li><a href="https://en.wikipedia.org/wiki/Spearman&#39;s_rank_correlation_coefficient">Spearman&#39;s ρ</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Scatter_plot">Scatter plot</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Statistical_graphics">Graphics</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Bar_chart">Bar chart</a></li> <li><a href="https://en.wikipedia.org/wiki/Biplot">Biplot</a></li> <li><a href="https://en.wikipedia.org/wiki/Box_plot">Box plot</a></li> <li><a href="https://en.wikipedia.org/wiki/Control_chart">Control chart</a></li> <li><a href="https://en.wikipedia.org/wiki/Correlogram">Correlogram</a></li> <li><a href="https://en.wikipedia.org/wiki/Fan_chart_(statistics)">Fan chart</a></li> <li><a href="https://en.wikipedia.org/wiki/Forest_plot">Forest plot</a></li> <li><a href="https://en.wikipedia.org/wiki/Histogram">Histogram</a></li> <li><a href="https://en.wikipedia.org/wiki/Pie_chart">Pie chart</a></li> <li><a href="https://en.wikipedia.org/wiki/Q–Q_plot">Q–Q plot</a></li> <li><a href="https://en.wikipedia.org/wiki/Radar_chart">Radar chart</a></li> <li><a href="https://en.wikipedia.org/wiki/Run_chart">Run chart</a></li> <li><a href="https://en.wikipedia.org/wiki/Scatter_plot">Scatter plot</a></li> <li><a href="https://en.wikipedia.org/wiki/Stem-and-leaf_display">Stem-and-leaf display</a></li> <li><a href="https://en.wikipedia.org/wiki/Violin_plot">Violin plot</a></li> <li><a href="https://en.wikipedia.org/wiki/Heatmap">Heatmap</a></li> <li><a href="https://en.wikipedia.org/wiki/Scatter_plot">Scatter Plot Matrix</a></li> <li><a href="https://en.wikipedia.org/wiki/Empirical_distribution_function"> ECDF plot</a></li> <li><a href="https://en.wikipedia.org/wiki/Line_chart">Line chart</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><a href="https://en.wikipedia.org/wiki/Data_preprocessing">Statistical data processing</a></div></th></tr><tr><td colspan="2"><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Data_transformation_(statistics)">Transformations</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Data_transformation_(statistics)">Data transformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Log_transformation?action=edit&amp;redlink=1">Log transformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Power_transform">Power transform</a> <ul><li><a href="https://en.wikipedia.org/wiki/Box–Cox_transformation">Box–Cox transformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Yeo–Johnson_transformation">Yeo–Johnson transformation</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Variance-stabilizing_transformation">Variance-stabilizing transformation</a></li> <li><a href="https://en.wikipedia.org/wiki/Anscombe_transform">Anscombe transform</a></li> <li><a href="https://en.wikipedia.org/wiki/Fisher_transformation">Fisher transformation</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Feature_scaling">Scaling and normalization</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Feature_scaling">Feature scaling</a></li> <li><a href="https://en.wikipedia.org/wiki/Normalization_(statistics)">Normalization</a></li> <li><a href="https://en.wikipedia.org/wiki/Standard_score">Standardization (z-score)</a></li> <li><a href="https://en.wikipedia.org/wiki/Min–max_normalization?action=edit&amp;redlink=1">Min–max normalization</a></li> <li><a href="https://en.wikipedia.org/wiki/Unit_vector_normalization?action=edit&amp;redlink=1">Unit vector normalization</a></li></ul> </div></td></tr><tr><th>Data cleaning</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Data_cleaning">Data cleaning</a></li> <li><a href="https://en.wikipedia.org/wiki/Outlier">Outlier</a></li> <li><a href="https://en.wikipedia.org/wiki/Winsorizing">Winsorizing</a></li> <li><a href="https://en.wikipedia.org/wiki/Truncation_(statistics)">Truncation</a></li> <li><a href="https://en.wikipedia.org/wiki/Missing_data">Missing data</a></li></ul> </div></td></tr><tr><th>Data reduction</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Dimensionality_reduction">Dimensionality reduction</a></li> <li><a href="https://en.wikipedia.org/wiki/Principal_component_analysis">Principal component analysis</a></li> <li><a href="https://en.wikipedia.org/wiki/Factor_analysis">Factor analysis</a></li></ul> </div></td></tr><tr><th>Time-series preprocessing</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Differencing">Differencing</a></li> <li><a href="https://en.wikipedia.org/wiki/Detrending">Detrending</a></li> <li><a href="https://en.wikipedia.org/wiki/Seasonal_adjustment">Seasonal adjustment</a></li> <li><a href="https://en.wikipedia.org/wiki/Stationary_process">Stationarity transformation</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><a href="https://en.wikipedia.org/wiki/Data_collection">Data collection</a></div></th></tr><tr><td colspan="2"><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Design_of_experiments">Study design</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Effect_size">Effect size</a></li> <li><a href="https://en.wikipedia.org/wiki/Missing_data">Missing data</a></li> <li><a href="https://en.wikipedia.org/wiki/Optimal_design">Optimal design</a></li> <li><a href="https://en.wikipedia.org/wiki/Statistical_population">Population</a></li> <li><a href="https://en.wikipedia.org/wiki/Replication_(statistics)">Replication</a></li> <li><a href="https://en.wikipedia.org/wiki/Sample_size_determination">Sample size determination</a></li> <li><a href="https://en.wikipedia.org/wiki/Statistic">Statistic</a></li> <li><a href="https://en.wikipedia.org/wiki/Statistical_power">Statistical power</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Survey_methodology">Survey methodology</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Sampling_(statistics)">Sampling</a> <ul><li><a href="https://en.wikipedia.org/wiki/Cluster_sampling">Cluster</a></li> <li><a href="https://en.wikipedia.org/wiki/Stratified_sampling">Stratified</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Opinion_poll">Opinion poll</a></li> <li><a href="https://en.wikipedia.org/wiki/Questionnaire">Questionnaire</a></li> <li><a href="https://en.wikipedia.org/wiki/Standard_error">Standard error</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Experiment">Controlled experiments</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Blocking_(statistics)">Blocking</a></li> <li><a href="https://en.wikipedia.org/wiki/Factorial_experiment">Factorial experiment</a></li> <li><a href="https://en.wikipedia.org/wiki/Interaction_(statistics)">Interaction</a></li> <li><a href="https://en.wikipedia.org/wiki/Random_assignment">Random assignment</a></li> <li><a href="https://en.wikipedia.org/wiki/Randomized_controlled_trial">Randomized controlled trial</a></li> <li><a href="https://en.wikipedia.org/wiki/Randomized_experiment">Randomized experiment</a></li> <li><a href="https://en.wikipedia.org/wiki/Scientific_control">Scientific control</a></li></ul> </div></td></tr><tr><th>Adaptive designs</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Adaptive_clinical_trial">Adaptive clinical trial</a></li> <li><a href="https://en.wikipedia.org/wiki/Stochastic_approximation">Stochastic approximation</a></li> <li><a href="https://en.wikipedia.org/wiki/Up-and-Down_Designs">Up-and-down designs</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Observational_study">Observational studies</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Cohort_study">Cohort study</a></li> <li><a href="https://en.wikipedia.org/wiki/Cross-sectional_study">Cross-sectional study</a></li> <li><a href="https://en.wikipedia.org/wiki/Natural_experiment">Natural experiment</a></li> <li><a href="https://en.wikipedia.org/wiki/Quasi-experiment">Quasi-experiment</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><a href="https://en.wikipedia.org/wiki/Statistical_inference">Statistical inference</a></div></th></tr><tr><td colspan="2"><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Statistical_theory">Statistical theory</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Population_(statistics)">Population</a></li> <li><a href="https://en.wikipedia.org/wiki/Statistic">Statistic</a></li> <li><a href="https://en.wikipedia.org/wiki/Probability_distribution">Probability distribution</a></li> <li><a href="https://en.wikipedia.org/wiki/Sampling_distribution">Sampling distribution</a> <ul><li><a href="https://en.wikipedia.org/wiki/Order_statistic">Order statistic</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Empirical_distribution_function">Empirical distribution</a> <ul><li><a href="https://en.wikipedia.org/wiki/Density_estimation">Density estimation</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Statistical_model">Statistical model</a> <ul><li><a href="https://en.wikipedia.org/wiki/Model_specification">Model specification</a></li> <li><a href="https://en.wikipedia.org/wiki/Lp_space">L^<i>p</i> space</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Statistical_parameter">Parameter</a> <ul><li><a href="https://en.wikipedia.org/wiki/Location_parameter">location</a></li> <li><a href="https://en.wikipedia.org/wiki/Scale_parameter">scale</a></li> <li><a href="https://en.wikipedia.org/wiki/Shape_parameter">shape</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Parametric_statistics">Parametric family</a> <ul><li><a href="https://en.wikipedia.org/wiki/Likelihood_function">Likelihood</a><span> </span><a href="https://en.wikipedia.org/wiki/Monotone_likelihood_ratio"><span>(monotone)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Location–scale_family">Location–scale family</a></li> <li><a href="https://en.wikipedia.org/wiki/Exponential_family">Exponential family</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Completeness_(statistics)">Completeness</a></li> <li><a href="https://en.wikipedia.org/wiki/Sufficient_statistic">Sufficiency</a></li> <li><a href="https://en.wikipedia.org/wiki/Plug-in_principle">Statistical functional</a> <ul><li><a href="https://en.wikipedia.org/wiki/Bootstrapping_(statistics)">Bootstrap</a></li> <li><a href="https://en.wikipedia.org/wiki/U-statistic">U</a></li> <li><a href="https://en.wikipedia.org/wiki/V-statistic">V</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Optimal_decision">Optimal decision</a> <ul><li><a href="https://en.wikipedia.org/wiki/Loss_function">loss function</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Efficiency_(statistics)">Efficiency</a></li> <li><a href="https://en.wikipedia.org/wiki/Statistical_distance">Statistical distance</a> <ul><li><a href="https://en.wikipedia.org/wiki/Divergence_(statistics)">divergence</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Asymptotic_theory_(statistics)">Asymptotics</a></li> <li><a href="https://en.wikipedia.org/wiki/Robust_statistics">Robustness</a> (<a href="https://en.wikipedia.org/wiki/Sensitivity_analysis">Sensitivity analysis</a>)</li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Frequentist_inference">Frequentist inference</a></th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Point_estimation">Point estimation</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Estimating_equations">Estimating equations</a> <ul><li><a href="https://en.wikipedia.org/wiki/Maximum_likelihood">Maximum likelihood</a></li> <li><a href="https://en.wikipedia.org/wiki/Method_of_moments_(statistics)">Method of moments</a></li> <li><a href="https://en.wikipedia.org/wiki/M-estimator">M-estimator</a></li> <li><a href="https://en.wikipedia.org/wiki/Minimum_distance_estimation">Minimum distance</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Bias_of_an_estimator">Unbiased estimators</a> <ul><li><a href="https://en.wikipedia.org/wiki/Minimum-variance_unbiased_estimator">Mean-unbiased minimum-variance</a> <ul><li><a href="https://en.wikipedia.org/wiki/Rao–Blackwell_theorem">Rao–Blackwellization</a></li> <li><a href="https://en.wikipedia.org/wiki/Lehmann–Scheffé_theorem">Lehmann–Scheffé theorem</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Median-unbiased_estimator">Median unbiased</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Plug-in_principle">Plug-in</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Interval_estimation">Interval estimation</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Confidence_interval">Confidence interval</a></li> <li><a href="https://en.wikipedia.org/wiki/Pivotal_quantity">Pivot</a></li> <li><a href="https://en.wikipedia.org/wiki/Likelihood_interval">Likelihood interval</a></li> <li><a href="https://en.wikipedia.org/wiki/Prediction_interval">Prediction interval</a></li> <li><a href="https://en.wikipedia.org/wiki/Tolerance_interval">Tolerance interval</a></li> <li><a href="https://en.wikipedia.org/wiki/Resampling_(statistics)">Resampling</a> <ul><li><a href="https://en.wikipedia.org/wiki/Bootstrapping_(statistics)">Bootstrap</a></li> <li><a href="https://en.wikipedia.org/wiki/Jackknife_resampling">Jackknife</a></li></ul></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Statistical_hypothesis_test">Testing hypotheses</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/One-_and_two-tailed_tests">1- &amp; 2-tails</a></li> <li><a href="https://en.wikipedia.org/wiki/Power_(statistics)">Power</a> <ul><li><a href="https://en.wikipedia.org/wiki/Uniformly_most_powerful_test">Uniformly most powerful test</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Permutation_test">Permutation test</a> <ul><li><a href="https://en.wikipedia.org/wiki/Randomization_test">Randomization test</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Multiple_comparisons">Multiple comparisons</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Parametric_statistics">Parametric tests</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Likelihood-ratio_test">Likelihood-ratio</a> <ul><li><a href="https://en.wikipedia.org/wiki/G-test"><i>G</i>-test</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Score_test">Score/Lagrange multiplier</a></li> <li><a href="https://en.wikipedia.org/wiki/Wald_test">Wald</a> <ul><li><a href="https://en.wikipedia.org/wiki/Z-test"><i>Z</i>-test <span>(normal)</span></a></li></ul></li></ul> </div></td></tr></tbody></table></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/List_of_statistical_tests">Specific tests</a></th><td><table><tbody><tr><th>Parametric</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Student&#39;s_t-test">Student&#39;s <i>t</i>-test</a></li> <li><a href="https://en.wikipedia.org/wiki/F-test"><i>F</i>-test</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Goodness_of_fit">Goodness of fit</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Chi-squared_test">Chi-squared</a></li> <li><a href="https://en.wikipedia.org/wiki/Kolmogorov–Smirnov_test">Kolmogorov–Smirnov</a></li> <li><a href="https://en.wikipedia.org/wiki/Anderson–Darling_test">Anderson–Darling</a></li> <li><a href="https://en.wikipedia.org/wiki/Lilliefors_test">Lilliefors</a></li> <li><a href="https://en.wikipedia.org/wiki/Jarque–Bera_test">Jarque–Bera</a></li> <li><a href="https://en.wikipedia.org/wiki/Shapiro–Wilk_test">Normality <span>(Shapiro–Wilk)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Model_selection">Model selection</a> <ul><li><a href="https://en.wikipedia.org/wiki/Cross-validation_(statistics)">Cross validation</a></li> <li><a href="https://en.wikipedia.org/wiki/Akaike_information_criterion">AIC</a></li> <li><a href="https://en.wikipedia.org/wiki/Bayesian_information_criterion">BIC</a></li></ul></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Ranking_(statistics)">Rank statistics</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Sign_test">Sign</a> <ul><li><a href="https://en.wikipedia.org/wiki/Sample_median">Sample median</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test">Signed rank <span>(Wilcoxon)</span></a> <ul><li><a href="https://en.wikipedia.org/wiki/Hodges–Lehmann_estimator">Hodges–Lehmann estimator</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Mann–Whitney_U_test">Rank sum <span>(Mann–Whitney)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Nonparametric_statistics">Nonparametric</a> <a href="https://en.wikipedia.org/wiki/Analysis_of_variance">anova</a> <ul><li><a href="https://en.wikipedia.org/wiki/Kruskal–Wallis_test">1-way <span>(Kruskal–Wallis)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Friedman_test">2-way <span>(Friedman)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Jonckheere&#39;s_trend_test">Ordered alternative <span>(Jonckheere–Terpstra)</span></a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Van_der_Waerden_test">Van der Waerden test</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Bayesian_inference">Bayesian inference</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Bayesian_probability">Bayesian probability</a> <ul><li><a href="https://en.wikipedia.org/wiki/Prior_probability">prior</a></li> <li><a href="https://en.wikipedia.org/wiki/Posterior_probability">posterior</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Credible_interval">Credible interval</a></li> <li><a href="https://en.wikipedia.org/wiki/Bayes_factor">Bayes factor</a></li> <li><a href="https://en.wikipedia.org/wiki/Bayes_estimator">Bayesian estimator</a> <ul><li><a href="https://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation">Maximum posterior estimator</a></li></ul></li></ul> </div></td></tr></tbody></table></td></tr></tbody></table></td></tr><tr><td colspan="2"><table><tbody><tr><th colspan="2"><div><div><ul><li><a href="https://en.wikipedia.org/wiki/Correlation_and_dependence">Correlation</a></li><li><a href="https://en.wikipedia.org/wiki/Regression_analysis">Regression analysis</a></li></ul></div></div></th></tr><tr><td colspan="2"><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Correlation_and_dependence">Correlation</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient">Pearson product-moment</a></li> <li><a href="https://en.wikipedia.org/wiki/Partial_correlation">Partial correlation</a></li> <li><a href="https://en.wikipedia.org/wiki/Confounding">Confounding variable</a></li> <li><a href="https://en.wikipedia.org/wiki/Coefficient_of_determination">Coefficient of determination</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Regression_analysis">Regression analysis</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Errors_and_residuals">Errors and residuals</a></li> <li><a href="https://en.wikipedia.org/wiki/Regression_validation">Regression validation</a></li> <li><a href="https://en.wikipedia.org/wiki/Mixed_model">Mixed effects models</a></li> <li><a href="https://en.wikipedia.org/wiki/Simultaneous_equations_model">Simultaneous equations models</a></li> <li><a href="https://en.wikipedia.org/wiki/Multivariate_adaptive_regression_splines">Multivariate adaptive regression splines (MARS)</a></li> <li> <a href="https://en.wikipedia.org/wiki/Template:Least_squares_and_regression_analysis">Template:Least squares and regression analysis</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Linear_regression">Linear regression</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Simple_linear_regression">Simple linear regression</a></li> <li><a href="https://en.wikipedia.org/wiki/Ordinary_least_squares">Ordinary least squares</a></li> <li><a href="https://en.wikipedia.org/wiki/General_linear_model">General linear model</a></li> <li><a href="https://en.wikipedia.org/wiki/Bayesian_linear_regression">Bayesian regression</a></li></ul> </div></td></tr><tr><th>Non-standard predictors</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Nonlinear_regression">Nonlinear regression</a></li> <li><a href="https://en.wikipedia.org/wiki/Nonparametric_regression">Nonparametric</a></li> <li><a href="https://en.wikipedia.org/wiki/Semiparametric_regression">Semiparametric</a></li> <li><a href="https://en.wikipedia.org/wiki/Isotonic_regression">Isotonic</a></li> <li><a href="https://en.wikipedia.org/wiki/Robust_regression">Robust</a></li> <li><a href="https://en.wikipedia.org/wiki/Homoscedasticity_and_heteroscedasticity">Homoscedasticity and Heteroscedasticity</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Generalized_linear_model">Generalized linear model</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Exponential_family">Exponential families</a></li> <li><a href="https://en.wikipedia.org/wiki/Logistic_regression">Logistic <span>(Bernoulli)</span></a><span> </span>/ <a href="https://en.wikipedia.org/wiki/Binomial_regression">Binomial</a><span> </span>/ <a href="https://en.wikipedia.org/wiki/Poisson_regression">Poisson regressions</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Partition_of_sums_of_squares">Partition of variance</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Analysis_of_variance">Analysis of variance (ANOVA, anova)</a></li> <li><a href="https://en.wikipedia.org/wiki/Analysis_of_covariance">Analysis of covariance</a></li> <li><a href="https://en.wikipedia.org/wiki/Multivariate_analysis_of_variance">Multivariate ANOVA</a></li> <li><a href="https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)">Degrees of freedom</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><a href="https://en.wikipedia.org/wiki/Categorical_variable">Categorical</a><span> </span>/ <a href="https://en.wikipedia.org/wiki/Multivariate_statistics">multivariate</a><span> </span>/ <a href="https://en.wikipedia.org/wiki/Time_series">time-series</a><span> </span>/ <a href="https://en.wikipedia.org/wiki/Survival_analysis">survival analysis</a></div></th></tr><tr><td colspan="2"><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Categorical_variable">Categorical</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Cohen&#39;s_kappa">Cohen&#39;s kappa</a></li> <li><a href="https://en.wikipedia.org/wiki/Contingency_table">Contingency table</a></li> <li><a href="https://en.wikipedia.org/wiki/Graphical_model">Graphical model</a></li> <li><a href="https://en.wikipedia.org/wiki/Poisson_regression">Log-linear model</a></li> <li><a href="https://en.wikipedia.org/wiki/McNemar&#39;s_test">McNemar&#39;s test</a></li> <li><a href="https://en.wikipedia.org/wiki/Cochran–Mantel–Haenszel_statistics">Cochran–Mantel–Haenszel statistics</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Multivariate_statistics">Multivariate</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/General_linear_model">Regression</a></li> <li><a href="https://en.wikipedia.org/wiki/Multivariate_analysis_of_variance">Manova</a></li> <li><a href="https://en.wikipedia.org/wiki/Principal_component_analysis">Principal components</a></li> <li><a href="https://en.wikipedia.org/wiki/Canonical_correlation">Canonical correlation</a></li> <li><a href="https://en.wikipedia.org/wiki/Linear_discriminant_analysis">Discriminant analysis</a></li> <li><a href="https://en.wikipedia.org/wiki/Cluster_analysis">Cluster analysis</a></li> <li><a href="https://en.wikipedia.org/wiki/Statistical_classification">Classification</a></li> <li><a href="https://en.wikipedia.org/wiki/Structural_equation_modeling">Structural equation model</a> <ul><li><a href="https://en.wikipedia.org/wiki/Factor_analysis">Factor analysis</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Multivariate_distribution">Multivariate distributions</a> <ul><li><a href="https://en.wikipedia.org/wiki/Elliptical_distribution">Elliptical distributions</a> <ul><li><a href="https://en.wikipedia.org/wiki/Multivariate_normal_distribution">Normal</a></li></ul></li></ul></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Time_series">Time-series</a></th><td><table><tbody><tr><th>General</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Decomposition_of_time_series">Decomposition</a></li> <li><a href="https://en.wikipedia.org/wiki/Trend_estimation">Trend</a></li> <li><a href="https://en.wikipedia.org/wiki/Stationary_process">Stationarity</a></li> <li><a href="https://en.wikipedia.org/wiki/Seasonal_adjustment">Seasonal adjustment</a></li> <li><a href="https://en.wikipedia.org/wiki/Exponential_smoothing">Exponential smoothing</a></li> <li><a href="https://en.wikipedia.org/wiki/Cointegration">Cointegration</a></li> <li><a href="https://en.wikipedia.org/wiki/Structural_break">Structural break</a></li> <li><a href="https://en.wikipedia.org/wiki/Granger_causality">Granger causality</a></li></ul> </div></td></tr><tr><th>Specific tests</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Dickey–Fuller_test">Dickey–Fuller</a></li> <li><a href="https://en.wikipedia.org/wiki/Johansen_test">Johansen</a></li> <li><a href="https://en.wikipedia.org/wiki/Ljung–Box_test">Q-statistic <span>(Ljung–Box)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Durbin–Watson_statistic">Durbin–Watson</a></li> <li><a href="https://en.wikipedia.org/wiki/Breusch–Godfrey_test">Breusch–Godfrey</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Time_domain">Time domain</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Autocorrelation">Autocorrelation (ACF)</a> <ul><li><a href="https://en.wikipedia.org/wiki/Partial_autocorrelation_function">partial (PACF)</a></li></ul></li> <li><a href="https://en.wikipedia.org/wiki/Cross-correlation">Cross-correlation (XCF)</a></li> <li><a href="https://en.wikipedia.org/wiki/Autoregressive–moving-average_model">ARMA model</a></li> <li><a href="https://en.wikipedia.org/wiki/Box–Jenkins_method">ARIMA model <span>(Box–Jenkins)</span></a></li> <li><a href="https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity">Autoregressive conditional heteroskedasticity (ARCH)</a></li> <li><a href="https://en.wikipedia.org/wiki/Vector_autoregression">Vector autoregression (VAR)</a> (<a href="https://en.wikipedia.org/wiki/Autoregressive_model">Autoregressive model (AR)</a>)</li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Frequency_domain">Frequency domain</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Spectral_density_estimation">Spectral density estimation</a></li> <li><a href="https://en.wikipedia.org/wiki/Fourier_analysis">Fourier analysis</a></li> <li><a href="https://en.wikipedia.org/wiki/Least-squares_spectral_analysis">Least-squares spectral analysis</a></li> <li><a href="https://en.wikipedia.org/wiki/Wavelet">Wavelet</a></li> <li><a href="https://en.wikipedia.org/wiki/Whittle_likelihood">Whittle likelihood</a></li></ul> </div></td></tr></tbody></table></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Survival_analysis">Survival</a></th><td><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Survival_function">Survival function</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Kaplan–Meier_estimator">Kaplan–Meier estimator (product limit)</a></li> <li><a href="https://en.wikipedia.org/wiki/Proportional_hazards_model">Proportional hazards models</a></li> <li><a href="https://en.wikipedia.org/wiki/Accelerated_failure_time_model">Accelerated failure time (AFT) model</a></li> <li><a href="https://en.wikipedia.org/wiki/First-hitting-time_model">First hitting time</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Failure_rate">Hazard function</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Nelson–Aalen_estimator">Nelson–Aalen estimator</a></li></ul> </div></td></tr><tr><th>Test</th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Log-rank_test">Log-rank test</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 colspan="2"><div><a href="https://en.wikipedia.org/wiki/List_of_fields_of_application_of_statistics">Applications</a></div></th></tr><tr><td colspan="2"><table><tbody><tr><th><a href="https://en.wikipedia.org/wiki/Biostatistics">Biostatistics</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Bioinformatics">Bioinformatics</a></li> <li><a href="https://en.wikipedia.org/wiki/Clinical_trial">Clinical trials</a><span> </span>/ <a href="https://en.wikipedia.org/wiki/Clinical_study_design">studies</a></li> <li><a href="https://en.wikipedia.org/wiki/Epidemiology">Epidemiology</a></li> <li><a href="https://en.wikipedia.org/wiki/Medical_statistics">Medical statistics</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Engineering_statistics">Engineering statistics</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Chemometrics">Chemometrics</a></li> <li><a href="https://en.wikipedia.org/wiki/Methods_engineering">Methods engineering</a></li> <li><a href="https://en.wikipedia.org/wiki/Probabilistic_design">Probabilistic design</a></li> <li><a href="https://en.wikipedia.org/wiki/Statistical_process_control">Process</a><span> </span>/ <a href="https://en.wikipedia.org/wiki/Quality_control">quality control</a></li> <li><a href="https://en.wikipedia.org/wiki/Reliability_engineering">Reliability</a></li> <li><a href="https://en.wikipedia.org/wiki/System_identification">System identification</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Social_statistics">Social statistics</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Actuarial_science">Actuarial science</a></li> <li><a href="https://en.wikipedia.org/wiki/Census">Census</a></li> <li><a href="https://en.wikipedia.org/wiki/Crime_statistics">Crime statistics</a></li> <li><a href="https://en.wikipedia.org/wiki/Demographic_statistics">Demography</a></li> <li><a href="https://en.wikipedia.org/wiki/Econometrics">Econometrics</a></li> <li><a href="https://en.wikipedia.org/wiki/Jurimetrics">Jurimetrics</a></li> <li><a href="https://en.wikipedia.org/wiki/National_accounts">National accounts</a></li> <li><a href="https://en.wikipedia.org/wiki/Official_statistics">Official statistics</a></li> <li><a href="https://en.wikipedia.org/wiki/Population_statistics">Population statistics</a></li> <li><a href="https://en.wikipedia.org/wiki/Psychometrics">Psychometrics</a></li></ul> </div></td></tr><tr><th><a href="https://en.wikipedia.org/wiki/Spatial_analysis">Spatial statistics</a></th><td><div> <ul><li><a href="https://en.wikipedia.org/wiki/Cartography">Cartography</a></li> <li><a href="https://en.wikipedia.org/wiki/Environmental_statistics">Environmental statistics</a></li> <li><a href="https://en.wikipedia.org/wiki/Geographic_information_system">Geographic information system</a></li> <li><a href="https://en.wikipedia.org/wiki/Geostatistics">Geostatistics</a></li> <li><a href="https://en.wikipedia.org/wiki/Kriging">Kriging</a></li></ul> </div></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:Statistics">Category</a></b></li> <li><b><span><span><a href="https://en.wikipedia.org/wiki/File:Square_root_of_x.svg"></a></span> </span><a href="https://en.wikipedia.org/wiki/Portal:Mathematics">Mathematics portal</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:Statistics">Commons</a></b></li> <li> <b><a href="https://en.wikipedia.org/wiki/Wikipedia:WikiProject_Statistics">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:Authority_control">Authority control databases</a> <span><a href="https://www.wikidata.org/wiki/Q827792#identifiers"></a></span></div></th></tr><tr><th>National</th><td><div><ul><li><span><span><a href="https://id.loc.gov/authorities/sh85109440">United States</a></span></span></li><li><span><span><a href="https://catalogue.bnf.fr/ark:/12148/cb11932687h">France</a></span></span></li><li><span><span><a href="https://data.bnf.fr/ark:/12148/cb11932687h">BnF data</a></span></span></li><li><span><span><a href="https://id.ndl.go.jp/auth/ndlna/00563228">Japan</a></span></span></li><li><span><span><a href="https://datos.bne.es/resource/XX526624">Spain</a></span></span></li><li><span><a href="https://www.nli.org.il/en/authorities/987007550897905171">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/76d88833-8b5a-496b-a97d-e70e72996d6f">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div> </section> https://en.wikipedia.org/wiki/Occam%27s_razor dIVHX4x7qD4r-zDE1xo4M1amqNkNzU4rX0dyQQ== Mon, 14 Sep 2026 17:32:50 +0000 History <div><h2>History</h2><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Occam%27s_razor&amp;action=edit&amp;section=1"><span>edit</span></a><span>]</span></span></div><p>The phrase <i>Occam&#39;s razor</i> did not appear until a few centuries after William of Ockham&#39;s death in 1347. <a href="https://en.wikipedia.org/wiki/Libert_Froidmont">Libert Froidmont</a>, in his 1649 <i>Philosophia Christiana de Anima</i> (<i>On Christian Philosophy of the Soul</i>) claimed to have coined the phrase <i>novacula occami</i> when he described <a href="https://en.wikipedia.org/wiki/Gregory_of_Rimini">Gregory of Rimini</a>, one of Ockham&#39;s critics.^{<span><span>[</span>7<span>]</span></span>} Ockham did not invent this principle, but its fame – and its association with him – may be due to the frequency and effectiveness with which he used it.^{<span><span>[</span>8<span>]</span></span>} Ockham stated the principle in various ways, but the most popular version – &quot;Entities are not to be multiplied without necessity&quot; (<span><i>Non sunt multiplicanda entia sine necessitate</i></span>) – was formulated by the Irish <a href="https://en.wikipedia.org/wiki/Franciscan">Franciscan</a> philosopher <a href="https://en.wikipedia.org/wiki/John_Punch_(theologian)">John Punch</a> in his 1639 commentary on the works of <a href="https://en.wikipedia.org/wiki/Duns_Scotus">Duns Scotus</a>.^{<span><span>[</span>9<span>]</span></span>}</p><section><div><h3>Formulations before William of Ockham</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Occam%27s_razor&amp;action=edit&amp;section=2"><span>edit</span></a><span>]</span></span></div> <figure><a href="https://en.wikipedia.org/wiki/File:Pluralitas.jpg"></a><figcaption>Part of a page from <a href="https://en.wikipedia.org/wiki/John_Duns_Scotus">John Duns Scotus</a>&#39;s book <i>Commentaria oxoniensia ad IV libros magistri Sententiarum</i>, showing the words: &quot;<span><i>Pluralitas non est ponenda sine necessitate</i></span>&quot;, i.e., &quot;Plurality is not to be posited without necessity&quot;</figcaption></figure> <p>The origins of what has come to be known as Occam&#39;s razor are traceable to the works of earlier philosophers such as <a href="https://en.wikipedia.org/wiki/John_Duns_Scotus">John Duns Scotus</a> (1265–1308), <a href="https://en.wikipedia.org/wiki/Robert_Grosseteste">Robert Grosseteste</a> (1175–1253), <a href="https://en.wikipedia.org/wiki/Maimonides">Maimonides</a> (Moses ben-Maimon, 1138–1204), and even <a href="https://en.wikipedia.org/wiki/Aristotle">Aristotle</a> (384–322<span> </span>BC).^{<span><span>[</span>10<span>]</span></span>}^{<span><span>[</span>11<span>]</span></span>} Aristotle writes in his <i><a href="https://en.wikipedia.org/wiki/Posterior_Analytics">Posterior Analytics</a></i>, &quot;We may assume the superiority <span><i>ceteris paribus</i></span> [all other things being equal] of the demonstration which derives from fewer postulates or hypotheses.&quot; <a href="https://en.wikipedia.org/wiki/Ptolemy">Ptolemy</a> (<span><abbr>c.</abbr><span><span> </span>AD 90</span><span> </span>– c.<span><span> </span>168</span></span>) stated, &quot;We consider it a good principle to explain the phenomena by the simplest hypothesis possible.&quot;^{<span><span>[</span>12<span>]</span></span>}</p><p> Phrases such as &quot;It is vain to do with more what can be done with fewer&quot; and &quot;A plurality is not to be posited without necessity&quot; were commonplace in 13th-century <a href="https://en.wikipedia.org/wiki/Scholasticism">scholastic</a> writing.^{<span><span>[</span>12<span>]</span></span>} Robert Grosseteste, in <i>Commentary on</i> [Aristotle&#39;s] <i>the Posterior Analytics Books</i> (<i>Commentarius in Posteriorum Analyticorum Libros</i>) (<abbr>c.</abbr><span><span> </span>1217–1220</span>), declares: </p><blockquote><p>&quot;That is better and more valuable which requires fewer, other circumstances being equal ... For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because it makes us know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises. Similarly in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal.&quot;^{<span><span>[</span>13<span>]</span></span>}</p></blockquote><p>The <i><a href="https://en.wikipedia.org/wiki/Summa_Theologica">Summa Theologica</a></i> of <a href="https://en.wikipedia.org/wiki/Thomas_Aquinas">Thomas Aquinas</a> (1225–1274) states that &quot;it is superfluous to suppose that what can be accounted for by a few principles has been produced by many&quot;. Aquinas uses this principle to construct an objection to <a href="https://en.wikipedia.org/wiki/God&#39;s_existence">God&#39;s existence</a>, an objection that he in turn answers and refutes generally (cf. <i><a href="https://en.wikipedia.org/wiki/Quinque_viae">quinque viae</a></i>), and specifically, through an argument based on <a href="https://en.wikipedia.org/wiki/Causality">causality</a>.^{<span><span>[</span>14<span>]</span></span>} Hence, Aquinas acknowledges the principle that today is known as Occam&#39;s razor, but prefers causal explanations to other simple explanations (cf. also <a href="https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation">Correlation does not imply causation</a>).</p> </section><section><div><h3>William of Ockham</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Occam%27s_razor&amp;action=edit&amp;section=3"><span>edit</span></a><span>]</span></span></div> <figure><a href="https://en.wikipedia.org/wiki/File:William_of_Ockham_-_Logica_1341.jpg"></a><figcaption><a href="https://en.wikipedia.org/wiki/Manuscript">Manuscript</a> illustration of William of Ockham</figcaption></figure> <p><a href="https://en.wikipedia.org/wiki/William_of_Ockham">William of Ockham</a> (<abbr>c.</abbr><span><span> </span>1287–1347</span>) was an English Franciscan friar and <a href="https://en.wikipedia.org/wiki/Theologian">theologian</a>, an influential medieval philosopher and a <a href="https://en.wikipedia.org/wiki/Nominalist">nominalist</a>. His popular fame as a great logician rests chiefly on the maxim attributed to him and known as Occam&#39;s razor. The term <i>razor</i> refers to distinguishing between two hypotheses either by &quot;shaving away&quot; unnecessary assumptions or cutting apart two similar conclusions.</p> <p>While it has been claimed that Occam&#39;s razor is not found in any of William&#39;s writings,^{<span><span>[</span>15<span>]</span></span>} one can cite statements such as <span><i>Numquam ponenda est pluralitas sine necessitate</i></span> (&quot;Plurality must never be posited without necessity&quot;), which occurs in his theological work on the <a href="https://en.wikipedia.org/wiki/The_Four_Books_of_Sentences"><i>Sentences of Peter Lombard</i></a> (<i>Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi</i>; ed. Lugd., 1495, i, dist. 27, qu. 2, K).</p> <p>Nevertheless, the precise words sometimes attributed to William of Ockham, <span><i>Entia non sunt multiplicanda praeter necessitatem</i></span> (Entities must not be multiplied beyond necessity),^{<span><span>[</span>16<span>]</span></span>} are absent in his extant works;^{<span><span>[</span>17<span>]</span></span>} this particular phrasing comes from <a href="https://en.wikipedia.org/wiki/John_Punch_(theologian)">John Punch</a>,^{<span><span>[</span>18<span>]</span></span>} who described the principle as a &quot;common axiom&quot; (<i>axioma vulgare</i>) of the Scholastics.^{<span><span>[</span>9<span>]</span></span>} William of Ockham himself seems to restrict the operation of this principle in matters pertaining to miracles and God&#39;s power, considering a plurality of miracles possible in the <a href="https://en.wikipedia.org/wiki/Eucharist">Eucharist</a>^{<span>[</span><i><a href="https://en.wikipedia.org/wiki/Wikipedia:Please_clarify"><span>further explanation needed</span></a></i><span>]</span>} simply because it pleases God.^{<span><span>[</span>12<span>]</span></span>}</p> <p>This principle is sometimes phrased as <span><i>Pluralitas non est ponenda sine necessitate</i></span> (&quot;Plurality should not be posited without necessity&quot;).^{<span><span>[</span>19<span>]</span></span>} In his <i>Summa Totius Logicae</i>, i. 12, William of Ockham cites the principle of economy, <span><i>Frustra fit per plura quod potest fieri per pauciora</i></span> (&quot;It is futile to do with more things that which can be done with fewer&quot;; Thorburn, 1918, pp.<span> </span>352–53; <a href="https://en.wikipedia.org/wiki/William_Kneale_(logician)">Kneale</a> and Kneale, 1962, p.<span> </span>243.)</p> </section><section><div><h3>Later formulations</h3><span><span>[</span><a href="https://en.wikipedia.org/w/index.php?title=Occam%27s_razor&amp;action=edit&amp;section=4"><span>edit</span></a><span>]</span></span></div> <p>To quote <a href="https://en.wikipedia.org/wiki/Isaac_Newton">Isaac Newton</a>, &quot;We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the same natural effects we must, as far as possible, assign the same causes.&quot;^{<span><span>[</span>20<span>]</span></span>}^{<span><span>[</span>21<span>]</span></span>} In the sentence <a href="https://en.wikipedia.org/wiki/Hypotheses_non_fingo">hypotheses non fingo (&quot;I contrive no hypotheses&quot;)</a>, Newton affirms the success of this approach.</p> <p><a href="https://en.wikipedia.org/wiki/Bertrand_Russell">Bertrand Russell</a> offers a particular version of Occam&#39;s razor: &quot;Whenever possible, substitute constructions out of known entities for inferences to unknown entities.&quot;^{<span><span>[</span>22<span>]</span></span>}</p> <p>Around 1960, <a href="https://en.wikipedia.org/wiki/Ray_Solomonoff">Ray Solomonoff</a> founded the <a href="https://en.wikipedia.org/wiki/Solomonoff&#39;s_theory_of_inductive_inference">theory of universal inductive inference</a>, the theory of prediction based on observations<span> </span><span>–</span> for example, predicting the next symbol based upon a given series of symbols. The only assumption is that the environment follows some unknown but computable probability distribution. This theory is a mathematical formalization of Occam&#39;s razor.^{<span><span>[</span>23<span>]</span></span>}^{<span><span>[</span>24<span>]</span></span>}^{<span><span>[</span>25<span>]</span></span>}</p> <p>Another technical approach to Occam&#39;s razor is <a href="https://en.wikipedia.org/wiki/Ontological_commitment#Ontological_parsimony">ontological parsimony</a>.^{<span><span>[</span>26<span>]</span></span>} Parsimony means spareness and is also referred to as the Rule of Simplicity. This is considered a strong version of Occam&#39;s razor.^{<span><span>[</span>27<span>]</span></span>}^{<span><span>[</span>28<span>]</span></span>} A variation used in medicine is called the &quot;<a href="https://en.wikipedia.org/wiki/Zebra_(medicine)">Zebra</a>&quot;: a physician should reject an exotic medical diagnosis when a more commonplace explanation is more likely, derived from <a href="https://en.wikipedia.org/wiki/Theodore_Woodward">Theodore Woodward</a>&#39;s dictum &quot;When you hear hoofbeats, think of horses not zebras&quot;.^{<span><span>[</span>29<span>]</span></span>}</p> <p><a href="https://en.wikipedia.org/wiki/Ernst_Mach">Ernst Mach</a> formulated the stronger version of Occam&#39;s razor into <a href="https://en.wikipedia.org/wiki/Physics">physics</a>, which he called the Principle of Economy stating: &quot;Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses.&quot;^{<span><span>[</span>30<span>]</span></span>}</p> </section>