On Tue, Apr 12, 2005 at 01:26:46PM +1000, Stathis Papaioannou wrote: > >I think this situation is essentially hypothetical. No machine is > >completely deterministic - computers are designed to be as > >deterministic as possible, but still suffer bit errors through > >chance. Human brains, however, strongly appear to be tuned to amplify > >noise generated at the synaptic level to effect system level. (Fractal > >structures in brainwave patterns, and the like). > > I would like this important point clarified. There is a fundamental > difference between a classical, chaotic system and a truly random quantum > system. The classical system may look random and for practical purposes may > be taken as random, but if (a) we could measure the system's initial > conditions to an arbitrary level of precision, (b) we knew the equations > governing the behaviour of the system to an arbitrary level of precision, > and (c) we had an arbitrarily fast/precise computer (or an arbitrarily long > period in which to perform the calculation), we could calculate all future > states of the system. With even a relatively simple quantum system, > however, such as a single atom of a radioactive isotope, no amount of > computing power, precise measurement or knowledge of the laws of physics > can help us decide exactly when it will decay. > > Now, it seems to me that in the brain both types of "random" event would > combine to give a very complex and unpredictable picture indeed: quantum > events at the atomic or subatomic scale would be amplified by chaotic > interactions at the classical scale. However, I have seen it stated that > quantum events would in fact not be significant at the scale of neuronal > processes. Which is correct? And does it really make much difference, > whether we are talking truly random or intractably pseudo-random?

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Since we live in a quantum mechanical world, randomness is inherently quantum mechanical. Chaos, as a classical mechanism will amplify quantum randomness. However, from the point of view of extracting sufficient randomness to fool opponents in an evolutionary setting, classical chaos is good enough. No agent will have the computational power of Laplace's daemon I'm dealing with these questions in an artificial life system - Tierra to be precise. I have compared the original Tierra code, with one in which the random no. generator is replaced with a true random no. generator called HAVEGE, and another simulation in which the RNG is replaced with a cryptographically secure RNG called ISAAC. The results to date (and this _is_ work in progress) is that there is a distinct difference between the original Tierra PRNG, and the other two generators, but that there is little difference between HAVEGE and ISAAC. This seems to indicate that algorithmic randomness can be good enough to fool learning algorithms. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------

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