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What is the explanation of the apparent randomness of high-level phenomena in nature? For example the distribution of females vs. males in a population (I am referring to randomness in terms of the unpredictability and not in the sense of it necessarily having to be evenly distributed). 1. Is it accepted that these phenomena are not really random, meaning that given enough information one could predict it? If so isn't that the case for all random phenomena? 2. If there is true randomness and the outcome cannot be predicted - what is the origin of that randomness? (is it a result of the randomness in the micro world - quantum phenomena etc...)

where can i find resources about the subject?

Gil Kalai
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liza
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    This question seems overly broad and speculative to me, with no possibility of a clear mathematical answer. It's not a bad question at all, but I'm not sure it is appropiate for MO. – Alicia Garcia-Raboso Dec 19 '09 at 15:26
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    It is certainly not a typical MO question (and should not be), but I think this type of question should be welcomed in MO (and by mathematicians, in general). – Gil Kalai Dec 19 '09 at 17:03
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    Closed per Alberto's comment. It's a good question, and I agree that it's one that mathematicians should think about and attempt to answer --- but not here. – Scott Morrison Dec 19 '09 at 18:04
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    Too bad. Greg could give a beautiful and useful answer. – Gil Kalai Dec 19 '09 at 18:56
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    More answers, some discussion, are welcome here: http://gilkalai.wordpress.com/2009/12/27/randomness-in-nature/ – Gil Kalai Dec 27 '09 at 08:47
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    I think that, with some rewriting, this question could and should be reopened. Although there some risk of getting too far into philosophy and philosophical debates and so forth, I think that there are probably many interesting answers to this question that are purely mathematical. If someone had instead asked for explanations of, say, Benford's law (certainly a "natural phenomenon"), well, there are definitely interesting mathematical aspects and it would be worth keeping open on MO. I think this is (or can be) a similar kind of question. – Kevin H. Lin Dec 27 '09 at 16:19

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This is, of course, a very important problem. One (extreme) point of view is that any form of classical (=commutative) randomness reflects "only" human uncertainty and does not have an "objective" physical meaning.

(Further answers to this question and more discussion are welcome on the posting entitled "Randomness in nature" on my blog "Combinatorics and More". Here is a link to a subsequent post with further discussion.) Some related material can be found in the site of the conference "The Probable and the Improbable: The Meaning and Role of Probability in Physics".

Gil Kalai
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  • +1 for opening a discussion on your blog, but -1 for philosophizing on MO ;-) – Kevin H. Lin Dec 27 '09 at 16:20
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    Hi Kevin, I regard the question about the foundations of probability as important in mathematics as the question of the foundations of quantum mechanics is important in physics (and mathematics). It is true that there are various offered answers, and that there are philosophical aspects to the questions.

    Liza's question about randomness is similar in spirit but is more to my taste than say the question on Poincare conjecure and the shape of the universe (which nevertheless produced good answers). http://mathoverflow.net/questions/9708/poincare-conjecture-and-the-shape-of-the-universe

     – Gil Kalai Dec 28 '09 at 06:26
  • I think philosophical issues are important and interesting as well. I think mathematical aspects of philosophy (e.g. mathematical arguments for or against some philosophical point of view) are OK for MO. But there are also many non-mathematical aspects of philosophy (and philosophy of math/physics/science), and I don't think that belongs here. Nothing wrong with such things, but I just think they'd be too discussion-y for this site. – Kevin H. Lin Dec 28 '09 at 12:26
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The field of statistical physics exists for this question. Basically when you have a nonequilibrium state that is complicated (e.g., has high entropy, Kolmogorov complexity, or whatever you like) and some kind of hyperbolic dynamics, the process of averaging leads to effective parabolicity. Thus you have things like the heat equation emerging from the effectively deterministic but complex Newtonian (quantum effects really aren't responsible for anything but perhaps the averaging scale, which is extremely small) microdynamics of particle collisions.

Steve Huntsman
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  • PS. The best place to learn about this stuff is Sklar's book Physics and Chance: http://www.amazon.com/Physics-Chance-Philosophical-Foundations-Statistical/dp/0521558816 – Steve Huntsman Dec 19 '09 at 16:18
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You might be interested in Poincare's method of arbitrary functions for establishing probability distributions on "random" mechanical events. A quick search turned up this article by Jan van Plato: http://bjps.oxfordjournals.org/cgi/pdf_extract/34/1/37

jrshipley
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