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The Man Who Invented Modern Probability
- te_platt 13y agoAn interesting take the Kolmogorov system can be found here: http://www-biba.inrialpes.fr/Jaynes/cappal.pdf http://www-biba.inrialpes.fr/Jaynes/cappal.pdf In it E. T. Jaynes compares Bayesian statistics Kolmogorov probabilities and finds them essentially identical in result even after working from very different first principles.
- wamatt 13y agoFor anyone interested, the above appendix comes from ET Jaynes's[1] magnum opus, "Probability Theory: The Logic of Science" [2]. Which, IMHO is deserving of it's grand title and provides an excellent framework for using Bayes in the real world. [1] http://en.wikipedia.org/wiki/Edwin_Thompson_Jaynes http://en.wikipedia.org/wiki/Edwin_Thompson_Jaynes [2] http://shawnslayton.com/open/Probability%20book/book.pdf http://shawnslayton.com/open/Probability%20book/book.pdf
- consz 13y agoMy father was the grand-grad student of Kolmogorov. He (Kolmogorov) is a very impressive mathematician. My father's advisor, Yakov Sinai, is equally impressive and arguably one of the founders of Dynamical Systems, a very interesting subfield of mathematics (and, in some ways, probability theory) in its own right.
- dev1n 13y agoDo you mean Kolmogorov-Sinai entropy? I just read about this in Chaos Theory Tamed by Garnett P. Williams. Really interesting stuff with respect to information theory in dynamical systems.
- tikhonj 13y ago> Kolmogorov armed a group of researchers with electromechanical calculators and charged them with the task of calculating the rhythmical structures of Russian poetry And this is what "big data" and NLP were like before computers :). One can only imagine what he could have done with a modern computer. (Which is particular hard to imagine because he's responsible for advances which ultimately led to these same modern computers...) Also, as an aside, I'm very impressed by the quality of nautil.us articles. I've come a across a few randomly, and they've been uniformly high in quality, interesting and insightful. Moreover, unlike much popular science/math reporting, the articles are not ridden with obvious errors and yet are easily followed by somebody not in the field. An impressive combination. (Not surprising for this particular article, I suppose: it was written by a professor teaching the history of mathematics at MIT.)
- dxbydt 13y ago>And this is what "big data" and NLP were like before computers :) aside, I recently interviewed a candidate for a "Big Data" position. He got quite chatty about Kolmogorov & Measure Theory, so I quickly cooked up an interesting problem to relax his nerves. I opened the interview with "If the side of a cube comes from a uniform distribution between 1 and 5 inches, what's the expected volume of the cube ?" I thought he'll give me the answer in 10 seconds & we'll move on but instead he was completely stumped & just stared blankly. I asked him to use the whiteboard but he simply drew a cube and wrote a^3, a~[1,5], and then went back to staring at it. Finally after 10 minutes of pin-drop silence, my partner, a non-math guy, took over the interview & asked him some Hadoop related technology questions & he started speaking again.
- Chris2048 13y agoWhat's the answer?
- relaia 13y ago27?
- lsconjugate 13y ago39
- solve 13y agofrom random import random sum([(random()*4+1)**3 for x in xrange(1000000)])/1000000 => ~39 Weird.
- bluetech 13y agosum(random.uniform(1, 5)**3 for i in range(10000)) / 10000 Many people don't know that the random module allows to sample from many distributions directly without having to construct your own.
- sampo 13y agoThe treatment of the Paradox of the Great Circle in the article is not very good. If you're left wondering, Wikipedia helps: http://en.wikipedia.org/wiki/Borel%E2%80%93Kolmogorov_paradox#A_great_circle_puzzle http://en.wikipedia.org/wiki/Borel%E2%80%93Kolmogorov_parado...
- lmkg 13y agotl;dr Because Great Circles have measure 0, any treatment of probability on them must instead use limits that asymptotically approach Great Circles. Also because they have measure 0, such limits don't converge in a consistent fashion. As it turns out, the two most common limit constructions give different results for that particular problem. The closest analogy I can think of is trying to assign a value to the expression 0/0. It doesn't have a value, but you can construct limits that appear to converge to it. One such limit is lim{x/x} as x approaches 0, which tends to 1. Another limit is lim{x log(x)} as x approaches 0, which tends towards 0. Both of these constructions have claim to being the value of 0/0, and they don't reconcile with each other.
- nawitus 13y ago>For example, irrational numbers—those that cannot be written as fractions— almost surely have no pattern in the numbers that appear after the decimal point. Therefore, most irrational numbers are complex objects, because they can be reproduced only by writing out the actual sequence. That's false. Pi is irrational, but there's many short algorithms to calculate it's digits.
- micro_cam 13y agoIt reads to be like the write heard someone say almost all and didn't realize that that has special mathematical meaning: http://en.wikipedia.org/wiki/Almost_all http://en.wikipedia.org/wiki/Almost_all
- mag487 13y agoThe key phrases there are "almost surely" and "most irrational numbers." There are irrational numbers like pi which can be defined algorithmically, but taken together as a set they have zero Lebesgue measure. (In fact, they're countable.)
- nawitus 13y agoI didn't know that. Any link to a proof?
- nwhitehead 13y agoConsider the set P of programs that take no input and generate an infinite stream of digits. Each program in P has a finite length and is written out of a finite set of symbols, so there must only be a finite number of programs of any given length. That makes P countable. Let Q be the set of numbers described by programs in P. Each program from P describes exactly one number, so Q must also be countable. The set of irrational numbers is uncountable, so there must be an uncountable set of "complex" irrational numbers remaining after you take away all the "non complex" ones in Q.
- nawitus 13y ago
- pessimizer 13y agoWhy haven't I heard of this journal? Looks great.
- japaget 13y agoIt's a startup! They started publishing about a month ago.
- saosebastiao 13y agoThey haven't been around too long, but for the two months I have seen, I have been delighted at the quality of their articles.
- tlarkworthy 13y agoDiscovered, not invented.
- lutusp 13y ago> Discovered, not invented. This refers to a philosophical debate that asks whether mathematics is part of nature or an artificial invention of man. I think the debate has begun to lean toward mathematics being part of nature, in which case yes, the proper term is discovered.
- bachback 13y agoInterestingly enough this notion, that there is only this one type of probability was debated before Kolmogorov by people like Ramsey and Keynes. Now the subjective interpretation of probability is called Bayesian statistics, which is not a helpful term. http://plato.stanford.edu/entries/probability-interpret/ http://plato.stanford.edu/entries/probability-interpret/
- kenko 13y agoHow is this not about Francis Galton?!
- anifow 13y agoFor those not in the know, Galton invented the simplest way of understanding normal distribution. Here's a copy you ca ceck on your phone. www.intromath.ca/aakkozzll A quote from Galton: http://www.aakkozzll.com/docs/order/galton.htm http://www.aakkozzll.com/docs/order/galton.htm
- ceautery 13y agoI am not a statistician, but if I found myself in an infinite forest, I would probably get drunk, too.
- richardjordan 13y agoI have no reason to particularly disbelieve the research that went into this article. But I'm just naturally skeptical when he reels off a list of puns that depend on the english language used by a group of Russian researchers. This seems unlikely to me. It seems like unnecessary color of dubious provenance.
- buro9 13y agoI thought this was going to be about Pierre Simon Marquis de Laplace who wrote A Philosophical Essay on Probabilities in 1814. http://neuroself.com/2012/01/21/pierre-simon-laplace-1814-a-philosophical-essay-on-probabilities/ http://neuroself.com/2012/01/21/pierre-simon-laplace-1814-a-...