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Math Science

The Game Theory of Life 85

Posted by samzenpus
from the life-and-math dept.
An anonymous reader writes In what appears to be the first study of its kind, computer scientists report that an algorithm discovered more than 50 years ago in game theory and now widely used in machine learning is mathematically identical to the equations used to describe the distribution of genes within a population of organisms. Researchers may be able to use the algorithm, which is surprisingly simple and powerful, to better understand how natural selection works and how populations maintain their genetic diversity.
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The Game Theory of Life

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  • Two things (Score:5, Interesting)

    by kruach aum (1934852) on Thursday June 19, 2014 @03:24AM (#47269917)

    1. If the machine learning algorithm has been found to be mathematically identical to the genetic spread algorithm, how would biologists be able to use it to better understand natural selection and genetic diversity? What can they learn from the first algorithm that they couldn't learn from the one they already had? If the two algorithms are mathematically identical, aren't they both just different names for the same mathematical structure? Learning a cat is called neko in Japanese doesn't tell you anything about cats you didn't already know -- it just tells you something about the Japanese language.

    2. Are algorithms discovered, or created? If anything is discovered, the underlying mathematical structure more than one algorithm can point to seems to be a better candidate than the algorithms themselves. Fossils are discovered; algorithms are made up.

    • It seems the process is there, and the algorithm merely describes it. Cats abound; one language calls them 'neko'.
    • Re:Two things (Score:4, Interesting)

      by lfourrier (209630) on Thursday June 19, 2014 @03:55AM (#47269983)
      "algorithms are made up"

      succint unproven "fact" for a question that can give work to philosophers for a few years.

      are mathematics (of which algorythms are a small part) discovered or created ? No one has a clear answer to that question.
      • Re:Two things (Score:5, Insightful)

        by Tom (822) on Thursday June 19, 2014 @05:01AM (#47270137) Homepage Journal

        are mathematics (of which algorythms are a small part) discovered or created ? No one has a clear answer to that question.

        Really? Maybe it's because the answer is so simple, no one serious has bothered tackling it.

        Mathematics is a language. As such, it is created.

        The things that mathematics describes are where it gets interesting. Much like in other languages, you have tangible things (easily verified as existing independent of the language), intangible things (dreams, emotions, forces) that are generally accepted as existing independent of language. And then you have two classes of things that are not entirely independent.

        You have categories or groups. "Animal" is not an intangible thing, because it doesn't describe anything that actually exists, it is a term for a collection of things that exist. The term itself is semantics, but most categories have an objective component that exists independent of language.

        The final category is pure language constructs. Rhymes, sentences, grammar, poems, etc. - while you can argue that they are linked to some biological or neurological element of human nature, a rhyme or a poem is very much a language construct and does neither describe a thing nor a group of things, it's a self-referential language construct.

        And if you look closely, you find the same in mathematics.

        • by lfourrier (209630)
          Begin with https://en.wikipedia.org/wiki/Philosophy_of_mathematics. Then find from which position you stand whith your "simple answer". Then study the diversity of points of view and arguments, and see if you can prove their errors. If you can do that really well, publish. You will be famous.

          But saying mathematics is a language and the things described are not part of mathematics, or perhaps they are, and a poem cannot describe something... I feel you have some work to do before being able to convince every
          • by Tom (822)

            Begin with https://en.wikipedia.org/wiki/... [wikipedia.org]

            From that page:
            Although most mathematicians and physicists (and many philosophers) would accept the statement "mathematics is a language", [...bla bla... it's not as simple, but the more we think about it... ] that the distinction between mathematical language and natural language may not be as great as it seems.

            There's actually a more specific article [wikipedia.org] right on WP, but as always, never believe anything you read on WP without checking it against other sources.

            • by lfourrier (209630)
              one can discuss, at length, and some will. The initial question I asked was : " are algorithms discovered or created? ". The only sure thing I can say (and I think any honest person would say) is : It seems an easy question, but there is no easy universal answer (even without going to theories where consciousness and self are emergent illusions)
              • by Tom (822)

                I do not agree that the question is difficult.

                I do agree that a lot of people consider it difficult, because they are trapped in category mistakes and cannot properly seperate their levels of abstraction.

                Once you get that right, it isn't all that hard anymore. You just need to go beyond the word, into meaning. What is it, exactly, that you mean by the word "algorithm"? Is it

                a) the particular formula in particular mathematical notation?
                b) the operations described by that formula?
                c) the process described by t

                • by Xest (935314)

                  I think it's still hard because you could equally have:

                  1) Person A who thinks up the algorithm in his head and writes it down hence creating it

                  2) Person B who independently spots the algorithm executing in a natural process and writes it down, hence discovering it.

                  An algorithm is a set of instructions, but how you come to getting into your mind and writing down those instructions results in a dividing line between whether it was created or discovered and even that's not simple when there's a debate about wh

                  • by Tom (822)

                    Again, I think you are mixing different levels of abstraction here.

                    Let's, for simplicity sake, take an extremely simple algorithm as an example: 1+1=2

                    Person A writes it down as a purely mathematical description, finds out he can draw nice conclusions from it and generally enjoys it in the sphere of pure math. It was created, no doubt.

                    Person B does not ever spot "1+1=2" anywhere in nature. What person A spots is that if he has one stone in his hand, and he adds a second one, he now has two stones in his hand

                    • by Xest (935314)

                      But I don't think anyone talks about creating a description when they're referring to description vs. discovery of an algorithm. Everyone knows that language, which is ultimately what math is, is a creation of the human mind (or is it discovered inside the human mind? I'll let you figure that one out).

                      What you're referring to as the creation of an algorithm is simply the creation of the description of the algorithm which is a different thing to the creation/discovery of the algorithm. Fundamentally the poin

                    • by Tom (822)

                      (or is it discovered inside the human mind? I'll let you figure that one out).

                      There's not even an argument there. Current scientific knowledge indicates strongly that our brains are wired for language processes, but not for a specific language.

                      What you're referring to as the creation of an algorithm is simply the creation of the description of the algorithm which is a different thing to the creation/discovery of the algorithm.

                      No. You are trying to introduce some kind of strange sideways category. Or maybe it is the word "algorithm" that's causing the confusion here. I've described my view, how about you describe yours?

        • by radtea (464814)

          Mathematics is a language. As such, it is created.

          The interesting thing about math is that it is a language that reveals underlying isomorophisms, like the one described in TFA. This feature is one of the things that leads to naive people thinking that the math somehow "precedes" the things it describes.

          But we see similar isomorphisms in all languages. Consider the "ballad" form of poem. It occurs in incredibly diverse contexts, but the underlying structure is always the same, which means you can sing "Amazing Grace" to the tune of the theme from "Gilligan

      • by Bongo (13261)

        Phenomena manifest in many ways, many perspectives.

        The colour "red" is a human phenomena, and the notion of "wavelengths" and "energy" are also something humans see/have/experience as phenomena. You can then use signifiers, signified, words, sounds, etc. to say "red" for what you see in your vision as "red" whilst noting on some instrument the "wavelength".

        There is no really real reality beyond your experience of sights, sounds, concepts, etc. -- reality which we can speak of, IF we can't observe it. In thi

      • by Anonymous Coward

        I have a clear answer to that. Mathematics are discovered. If they were invented, they would work exactly as we wanted them to. But they don't. For example, the pythagoreans were convinced that all numbers could be represented as a ratio of integers. But they were proven wrong.

      • > are mathematics discovered or created?

        Uh, you do realize the question is not mutually exclusive, right?

        The answer is: Both

        Stop thinking linear, and start thinking multidimensionally.

      • "are mathematics (of which algorythms are a small part) discovered or created ? No one has a clear answer to that question."

        I thought it was pretty clear that stuff is discovered. To me this kind of question reads like "Well, does it stop being right at any time once it is discovered?" and the answer is generally no. (A, you sometimes get stuff that was discovered and not properly reported, at which point the original discovery is not at fault and it is just a reporting problem, or B, you get stuff that was

    • When you have two distinct things, which you understand to different extents, proving that they're identical allows you to learn about one thing from the knowledge of the other thing.

      To use your example:

      Prior to today, we knew that cats lapped up milk with their tongues, and also preen their fur with their tongues. Also prior to today, we knew that a Japanese animal called neko coughs up balls of stuff.

      Today we found out that cats are identical to neko.

      We now know that cats cough up balls of stuff, and that

    • Just call it "Intelligent Design". Lots of people are going to be claiming they were right all along, although most of them won't have any chance of actually understanding the maths.

    • "equations used to describe the distribution of genes", meaning the algorithm (mechanism) was probably unknown while the equations just described the end result. Also, the behavior of an algorithm that sees lots of use has probably been studied a lot so there's a treasure trove of material for researchers to dig through to find stuff relevant for genetics.
  • by SigmundFloyd (994648) on Thursday June 19, 2014 @03:46AM (#47269953)

    ...has the "simulated universe" hypotesis just got a slight boost from this finding?

    • by rusty0101 (565565)

      I think that kid of depends on whether you think that an algorithm that makes something work requires that the universe within which that algorithm appears to be at work, has to be a simulated universe. Is it possible as an alternative that there are several possible processes where these results, or results statistically insignificantly different, might obtain, and it happens that this process wins because it simply uses less energy and produces results that provide better survivability than the other proc

    • by drinkypoo (153816)

      ...has the "simulated universe" hypotesis just got a slight boost from this finding?

      No, it hasn't. You would expect things to be governed by simple, predictable principles. Otherwise they'd happen wildly differently every time, and we wouldn't have life at all.

    • by Theovon (109752)

      The simulated universe hypothesis is based on the seeming odd coincidence that our universe’s operation looks identical to information theory.

      The problem with that hypothesis is that people seem to forget that our concept of information theory is a function of the universe it was developed in. Thus, it’s no coincidence, and the congruence of physics and information theory is not evidence of simulation.

      • our concept of information theory is a function of the universe it was developed in.

        I don't think it needs to look similar to the universe's inner mechanisms just because of that.

  • by tree_frog (113005) on Thursday June 19, 2014 @04:34AM (#47270087)

    Only having read the abstract, and the linked article, I don't really see how this is different from the "2 Armed Bandit" theory which John Holland Laid out 40 years ago in "Evolution in Natural and Artificial Systems". Holland laid out how the combination of sexual reproduction with mutation within a population otpimises search across the space by combining exploitation of good areas of the search space with exploration to find better areas.

    Can someone more up to date enlighten me?

    kind regards

    tree frog

    • by sweetenham (78025)

      It's worth reading the paper: http://www.pnas.org/content/ea... [pnas.org]

      The point is that the well known properties of the game theory algorithm explain why sex has the effective properties which have been observed but not explained. I haven't read John Holland's paper. Does it refer to the details of the multiplicative weight updates algorithm?

    • I haven't read that specific work but I have read "Hidden Order: How Adaptation Builds Complexity", so I am generally familiar with his conceptual framework. I agree, they are all offering the same explanation. I think the difference may be that Holland did not lay it out mathematically in a game theory framework. For another perspective, check out Stuart Kauffman's "Origins of Order", which also provides an analytical (though not equation-based) treatment.
  • by Alsee (515537) on Thursday June 19, 2014 @05:47AM (#47270233) Homepage

    It has been known for years, probably decades, that gene frequencies follow this mathematical rule, and that it has been mathematically proven optimal for solving Multi-armed bandit [wikipedia.org] type problems. Each generation genes are tested by natural selection, and increase or decrease in frequency according to multiplicative increase or decrease. This is a mathematically optimal strategy for exploring and optimizing payoff in a complex unknown environment. Mutation creates random stuff to try, and this mathematically selection algorithm optimally crafts it into useful new information.

    -

    • by Anonymous Coward

      And each generation rediscovers for itself that they can publish a paper with this "exciting result!" that is decades old.

      This happens a lot when the professor, and the grad students, have never really studied the history of related fields.

  • Why does Slashdot seem to buy in so often to spinning the recurrence of mathematical tools across various fields as some kind of scientific breakthrough? Correlation is not causation, not all structural similarities imply some kind of necessary physical theoretical account. We as empirical agents use logical tools for the formation, quantification and application of theories - so of course some functions will occur in several different settings, because we're bringing the same resources to the table each t

  • The Earth was created 7000 years ago by some unknown but benign power, evolution doesn't exist - how can some equation possibly describe it using mathematics? Mathematics itself is obviously a made up tool anyway, so you can make it say whatever you want. They'll be using Empirical Science next to debunk what is clearly the One Truth. :)

  • ... I imagined that someone discovered a mechanism in genes that favored survival if there were exactly two or three neighboring genes, and non-survival if there were fewer or greater numbers. Oh, and something about a new gene being 'created' when there are exactly 3 neighboring ones.

  • Novel, it is not (Score:4, Interesting)

    by jw3 (99683) on Thursday June 19, 2014 @10:24AM (#47271895) Homepage

    John Maynard Smith introduced the game theory to evolutionary biology in the early 70's. It was a breakthrough at that time, however today it is scarcely news. Evolutionary biology, and in especially population genetics has been a highly mathematized discipline ever since before WWII, when it was developed by Fisher, Wright and Haldane. Later you had Hamilton and Maynard Smith. It is nice that computer scientists noticed that something exciting is going on here, but don't fall for press releases and insubstantiated claims.

  • "We demonstrate that in the regime of weak selection, the standard equations of population genetics describing natural selection in the presence of sex become identical to those of a repeated game between genes played according to multiplicative weight updates (MWUA)..."
  • There's a preprint of what seems to be a more complete paper on the work hosted on arxiv. There's a bit more math in it, but it's still somewhat understandable: http://arxiv.org/pdf/1208.3160.pdf [arxiv.org].

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