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Article 5052 of comp.ai.philosophy:
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>From: tomh.bbs@cybernet.cse.fau.edu
Newsgroups: comp.ai.philosophy
Subject: Re: Robert Rosen & Physical form of Church's Thesis
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Date: 10 Apr 92 22:24:35 GMT
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In article <538@trwacs.fp.trw.com> erwin@trwacs.fp.trw.com (Harry Erwin) 
writes:

>tomh.bbs@cybernet.cse.fau.edu writes:

>>Rosen claims that the physical form of Church's Thesis is false.
>>This means there are physically realizable processes that are
>>not effectively calculable.
>
>Rosen is correct in this claim. The effectively calculable models are
>countable, and the physically realizable processes are uncountable.
>...
>>3) What happens if we use an analog computer instead of a digital one?
>>   The analog computer still has the 'initial condition' problem.
>>
>I'm not sure what problem you're aluding to here. Do you mean the 
problem
>of calibration?

Well, the idea is to use an analog computer to 'compute' one of those
non-effectively computable physical processes.  The difficulty is that
an analog computer cannot be started with a specified exact initial
condition, due to limitations of finite precision.

Wolfram [1] has talked about "computationally irreducible" physical
processes.  He maintains that the physical form of Church's thesis
holds - "one expects in fact that universal computers are as powerful
in their computational capabilities as any physically realizable
system can be, so they can simulate any physical system."
But there are processes that can only be 'computed' by the process
itself; such processes are irreducible.

Church's thesis holds because physical laws (or as Rosen would say,
contemporary physical formalisms) are all computable.  Rosen also
points out that this places severe restrictions on natural systems
(the real world), and that this justifies throwing out all those
formalisms as being too restrictive.

Perhaps this doesn't matter though.  Rosen doesn't say much about
self-organization in _Life Itself_, but he does say qualitative is
more than just quantitative: "mathematics has more to offer besides
numbers and ... perceptual qualities may be expressed in terms of
them," i.e. that measurement is not simply quantization.  He argues
in a different direction from there, but to me (knowing what I know
about open systems and self-organization), that the qualitative
properties of a system are more important than its precise physical
state.

[1] S. Wolfram, "Undecidability and Intractability in Theoretical
Physics," Phys. Rev. Lett. 54:735-738 (1985)

>Harry Erwin
>Internet: erwin@trwacs.fp.trw.com

Tom Holroyd
Center for Complex Systems and Brain Sciences
Florida Atlantic University, Boca Raton, FL
tomh@bambi.ccs.fau.edu


