On 7/8/12, Warren Smith <warren.wds@gmail.com> wrote:
From: Ray Tayek <rtayek@ca.rr.com> Subject: [math-fun] ON "ITERATED PRISONER?S DILEMMA CONTAINS STRATEGIES THAT DOMINATE ANY EVOLUTIONARY OPPONENT" The highly technical paper, <http://www.pnas.org/content/early/2012/05/16/1206569109.abstract>" Prisoner?s Dilemma contains strategies that dominate any evolutionary opponent" by William H. Press and Freeman J. Dyson has now been published in PNAS (May 22, 2012), which was followed by a PNAS Commentary by Alexander Stewart and Joshua Plotkin of the Department of Biology, University of Pennsylvania
--WDS: based on trying to figure out what they are doing without actually reading it, it seems they are arguing that if the opponent in IPD generates his moves via a Markov chain... which presumably is necessarily true for any real opponent given the laws of physics since that opponent is bounded, i.e. has a finite bounded number of states, and has access to a source of randomness, and hence must be a Markov chain on those states... then you, where by "you" I mean a Turing machine, can outplay him asymptotically by learning his markov model and then predicting his play.
This is probably completely irrelevant to real life because the "number of states" of a human being containing 10^27 atoms is going to be around 2^(10^27) if each atom could store 1 bit, so the time it takes to learn your opponent's Markov chain in real life is going to far exceed the lifetime of that human, or for that matter of the universe.
--indeed, just to make this completely clear: suppose I play IPD by deciding my moves "defect" or "cooperate" by use of a pseudorandom number generator based on the AES (advanced encryption standard) using a secret key I selected once and for all by 256 coin tosses. How are Dyson and Press going to beat me? If they can it is equivalent to them breaking the AES cryptosystem. (Or put any other cryptosystem.) It is reasonable to suppose this is for practical purposes impossible in 1000 times the lifetime of this universe. This is true even though my strategy after the initial 256 coin tosses is completely deterministic, i.e. for Dyson and Press the simplest possible case. So this is all garbage: those evolutionary biologists writing the review acting like this all "matters" for biology, are completely confused. It should have no significance for biology at all. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)