gross@spp2.UUCP (Howard E. Gross) (03/27/86)
I would appreciate any information on the following question:
Since any calculations can perfomed by a turing machine,
and since the language accepted by the turing machine can be
generated by an unrestricted
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gross (Howard Gross) {decvax,hplabs,ihnp4,sdcrdcf}!trwrb!trwspp!spp2gross@spp2.UUCP (Howard E. Gross) (03/27/86)
Since any calculation can be performed by a turing machine,
and since the language accepted by a turing manchine can
be generated by an unrestricted grammar, what is the grammar
that describes nature? More specifically is there a grammar
for quantum mechanics?
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gross (Howard Gross) {decvax,hplabs,ihnp4,sdcrdcf}!trwrb!trwspp!spp2gwyn@brl-smoke.UUCP (03/29/86)
In article <898@spp2.UUCP> gross@spp2.UUCP (Howard E. Gross) writes: >Since any calculation can be performed by a turing machine, >and since the language accepted by a turing manchine can >be generated by an unrestricted grammar, what is the grammar >that describes nature? More specifically is there a grammar >for quantum mechanics? There are several things wrong with this idea, not the least of which is: Nature does not have to perform calculations.
breuel@h-sc1.UUCP (03/30/86)
||Since any calculation can be performed by a turing machine, ||and since the language accepted by a turing manchine can ||be generated by an unrestricted grammar, what is the grammar ||that describes nature? More specifically is there a grammar ||for quantum mechanics? | |There are several things wrong with this idea, not the least |of which is: Nature does not have to perform calculations. Yes, there are several things wrong with this idea, but it is not that 'nature does not have to perform calculations' (see below). It is indeed interesting to look at physical laws and principles from a computational point of view. 'Grammars' and 'Turing machines' are, however, relatively inconvenient devices of doing so. More appropriate models of physical reality based on computational devices are 'cellular automata'. Cellular automata are large (infinite) arrays of simple computing elements capable of local communication. Cellular automata can be the discrete counterparts of differential equations, and, in fact, are used to model and compute approximations to field equations, boundary value problems, &c. Cellular automata also display dynamical properties that are not found in their smooth counterparts. One of the most fundamental differences is, of course, by definition, that they have finite resolution in space, time, and, often, paramter space. From the computational point of view, cellular automata can be Turing equivalent. Common examples of cellular automata are Life and video feedback. The connection machine developed at M.I.T., and several computer prototypes used for vision research have architectures reminiscent of cellular automata. After my thesis is done, I might post references and a more comprehensive and detailed survey of cellular automata and their relationship to physics, if interest warrants it. Finally, there is (Doug, we do seem to have quite differing views of physical reality) absolutely no reason why we couldn't or shouldn't use physical models based on computation rather than on differential equations for modelling nature. Since all the verification of our current theories involves computation, I would argue that, in a weird sort of way, our models of nature are in fact already purely computational. Thomas. PS: let me stress again: I object to the statement 'Nature does not have to perform calculations'. The reason is that it contains a semantic confusion: 'calculations' are a human model of nature, just like 'differential equations', 'groups', &c. Obviously (or perhaps not so obviously), nature does not operate through the models that we make of it. I might therefore with equal right say: 'Nature does not obey physics', but clearly this statement is either tautological (namely if you interpret it to mean that the existence of our physical models of nature is not a prerequisite to the operation of nature), or it is a malformed version of the sentence 'physics is probably not an accurate model of nature'. Anyhow, as I have argued above, *computation may be as accurate a model of nature as modern physics is*.