From: paul cockshott (clyder@GN.APC.ORG)
Date: Fri Jan 23 2004 - 08:09:04 EST
Andrew: 5. Logic: formal or dialectical, and the finite/infinite distinction It seems that we are all agreed on Godel and Chaitlin. Of course a computer can run several things at a time so is not tied to just one formal system. Nevertheless, however much info content you stuff in a computer, and whatever the additional variety brought in by consideration of initial conditions, the problem is that the universe has a lot more 'info content' stuffed into it, than any computer. There remains a fundamental distinction between the infinite universe and the finite computer. ------------------------------------------ It is questionable whether the universe is strictly speaking infinite. But your general point is valid even if we remove infinities. The number of possible micro-configurations of systems being computed will be greater than the number of possible configurations of the computing system. This means that any simulation is only approximate. The extended form of the Church Turing thesis given by Deutsch states that any physical system can be simulated to an arbitrary degree of accuracy by a universal computer, see: Quantum theory, the Church-Turing principle and the universal quantum computer (1985) ( David Deutsch Proceedings of the Royal Society of London Ser. download from http://citeseer.ist.psu.edu/deutsch85quantum.html Andrew: Ian I would be greatful if you could give me a good reference to explain what you mean by 'computation theory' (or whatever the correct term is). It does seem, from my perspective, that you have a more reductionist notion in mind than what I take from dialectics. ------------------- A good summary of writings in this spirit is in 'The Universal Turing Machine a Half Century Survey', Oxford University Press. Wolframs book 'A new Kind of Science', is also very much in this tradition.
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