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Article 5100 of comp.ai.philosophy:
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>From: erwin@trwacs.fp.trw.com (Harry Erwin)
Newsgroups: comp.ai.philosophy
Subject: Re: Robert Rosen & Physical form of Church's Thesis
Message-ID: <541@trwacs.fp.trw.com>
Date: 13 Apr 92 13:29:30 GMT
References: <TogZiB1w164w@cybernet.cse.fau.edu> <1992Apr10.165224.11963@organpipe.uug.arizona.edu> <539@trwacs.fp.trw.com> <1992Apr13.005357.154@organpipe.uug.arizona.edu>
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bill@NSMA.AriZonA.EdU (Bill Skaggs) writes:

>In article <539@trwacs.fp.trw.com> 
>erwin@trwacs.fp.trw.com (Harry Erwin) writes:
>>The question is asked--is a turbulent flow useful as an algorithm for
>>something?
>>
>  It was me who asked this question, but actually not quite
>this question.  Precisely, I asked whether there is any
>useful computation that can be made using a chaotic process
>(such as a turbulent flow) that cannot also be made by some
>Turing machine.

>  The answers you give are reasonable, but it is not obvious
>that the turbulent flow produces any useful information that cannot
>equally well be produced by a detailed digital simulation of
>the flow.

>  If you could identify such information, you would have a
>counterexample to the Church-Turing thesis.

>	-- Bill

OK, I see what you're driving at. I will try to address your issue by
_assuming_ the postulated equilavence between chaotic flows and turbulent
flows. We know that a detailed digital simulation of a chaotic flow will
diverge exponentially unless the machine has an infinite word length.
Grebogi and Yorke have shown that digital simulation of the flow will
track _a_ nearby true trajectory of the flow for a long time, but Huberman
and Hogg have shown that a simulation of a flow by a finite state machine
with finite word length will eventually fall into a terminal cycle. I'll
have to talk to my wife about this (she's a mathematical logician), but I
may be able to argue that no Church's Thesis is false for simulations of
chaotic processes. And chaotic processes do provide useful information...


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



