(Reposting from G+ for posterity) I came across this 1907 book by Arthur Guiterman (who was previously encountered here), titled “Betel Nuts: or What They Say in Hindustan”, in which he claims to have collected proverbs and sayings “gleaned in Bengal, in the Punjab, in Rajputana, and even among the mountains of Kashmir and Afghanistan”. […]| The Lumber Room
[Needs cleanup… just dumping here for now.] Mark Jason Dominus tweeted and later blogged about this puzzle: From the four numbers [6, 6, 5, 2], using only the binary operations [+, -, *, /], form the number 17. When he tweeted the first time, I thought about it a little bit (while walking from my […]| The Lumber Room
In his wonderful On Proof and Progress in Mathematics, Thurston begins his second section “How do people understand mathematics?” as follows: This is a very hard question. Understanding is an individual and internal matter that is hard to be fully aware of, hard to understand and often hard to communicate. We can only touch on […]| The Lumber Room
The Pandit (काशीविद्यासुधानिधिः) A Monthly Journal, of the Benares College, devoted to Sanskrit Literature This was a journal that ran from 1866 to 1920, and some issues are available online. “The Benares College” in its title is what was the first college in the city (established 1791), later renamed the Government Sanskrit College, Varanasi, and […]| The Lumber Room
(TODO: Learn and elaborate more on their respective histories and goals.) The formula (reminded via this post), a special case at of was found by Leibniz in 1673, while he was trying to find the area (“quadrature”) of a circle, and he had as prior work the ideas of Pascal on infinitesimal triangles, and that […]| The Lumber Room
1. Alphabet Suppose we have an alphabet of size . Its generating function (using the variable to mark length) is simply , as contains elements of length each. 2. Words Let denote the class of all words over the alphabet . There are many ways to find the generating function for . 2.1. We have […]| The Lumber Room
This is trivial, but was awfully hard to find via Google Search. Eventually had to give up and actually think about it. :-) So, a data-URI looks something like the following: data:image/png;base64,[and a stream of base64 characters here] The part after the comma is literally the contents of the file (image or whatever), encoded in […]| The Lumber Room
(I don’t have a solution yet.) I just wanted to show what the sky looks like over the course of a week. On a Mac with Stellarium installed, I ran the following with the following stellarium.ssc: It took a while (some 10–15 minutes) and created those 336 images in ~/Pictures/Stellarium/uj*, occupying a total size of […]| The Lumber Room
Is hard. Just dumping some links here for now: Feynman on “cargo cult science”: http://www.lhup.edu/~DSIMANEK/cargocul.htm Feynman on “what is science”: http://www.fotuva.org/feynman/what_is_science.html Ioannidis, Why Most Published Research Findings Are False: http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0020124 On how subtle it is: http://slatestarcodex.com/2014/04/28/the-control-group-is-out-of-control/ Reinhart, http://www.statisticsdonewrong.com http://...| The Lumber Room
Bhavabhūti, the 8th-century author of the very moving play Uttara-rāma-carita, has in one of his other works these lines, any author’s consolation that even if your work receives not enough praise today, someday the right sort of reader will come along, who will derive great joy or meaning from it. ये नाम केचिदिह नः प्रथयन्त्यवज्ञां […]| The Lumber Room
Everyone knows that floating-point numbers, being discrete, cannot possibly exactly represent every real number. In particular, the usual binary (IEEE 754) floating point numbers cannot even exactly store all numbers exactly representable in decimal (e.g. 0.3 or 0.1, which are not dyadic rationals). But what about printing them? Just because the number stored internally is […]| The Lumber Room
(Another example of good vs bad translations from Sanskrit. Previously see here and here.) One of Kālidāsa’s famous similes is in the following verse from the Raghuvaṃśa, in the context of describing the svayaṃvara of Indumatī. The various hopeful suitors of the princess, all kings from different regions, are lined up as she passes them […]| The Lumber Room
A long time ago, Diophantus (sort of) discussed integer solutions to the equation (solutions to this equation are called Pythagorean triples). Centuries later, in 1637, Fermat made a conjecture (now called Fermat’s Last Theorem, not because he uttered it in his dying breath, but because it was the last one to be proved — in ~1995) […]| The Lumber Room
(Just digesting the first page of Google search results.) One of the lessons from functional programming is to encode as much information as possible into the types. Almost all programmers understand to some extent that types are helpful: they know not to store everything as void* (in C/C++) or as Object (in Java). They even […]| The Lumber Room
E.g. there is no such thing as a “method” in C++. As far as the C++ standard is concerned, functions inside classes are always called “member functions”. Here is a handout from this course (taught by, AFAICT, Jeffrey S. Leon) that helps me understand the Java people.| The Lumber Room
[incomplete: must add examples and more discussion] Most programming languages include a “remainder” or “modulo” function, and also an integer division (“quotient”) function. Given two integers and , let’s call the results of these functions and respectively. For positive and , it is clear what and should be: is the largest integer such that , […]| The Lumber Room
Viṣṇu, appearing before Bali as Vāmana, transformed into Trivikrama, filling the universe, covering all the earth and the heavens in two steps. The verse that opens the Pūrva-pīṭhikā of Daṇḍin’s Daśakumāracarita plays on this imagination, and on the word daṇda / daṇḍin. Here’s the verse (in Sragdharā metre of pattern GGGGLGG—LLLLLLG—GLGGLGG): May the leg of […]| The Lumber Room
[Originally posted to linguistics.stackexchange.com as an answer to a question by user Manishearth, who asked: “I’ve heard many times that learning German is easier for those who speak Sanskrit, and vice versa. Is there any linguistic basis for this? What similarities exist between the two languages that may be able to explain this?”] This is […]| The Lumber Room
Found via G+, a new physical experiment that approximates $latex \pi$, like Buffon’s needle problem: The Pi Machine. Roughly, the amazing discovery of Gregory Galperin is this: When a ball of…| The Lumber Room
Here is a program that fails with UnboundLocalError three out of four times: Note that line 15 uses the variables first and second, which are defined only if zero_or_one() returned 1 both times. (C…| The Lumber Room
