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From: pindor@gpu.utcc.utoronto.ca (Andrzej Pindor)
Subject: Re: Chaos in Turing Machines
Message-ID: <DMsEw8.GKp@gpu.utcc.utoronto.ca>
Organization: UTCC Public Access
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Date: Wed, 14 Feb 1996 22:38:31 GMT
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Xref: glinda.oz.cs.cmu.edu sci.nonlinear:4926 sci.logic:17002 comp.ai:37045 comp.ai.philosophy:37775

In article <4fquni$8it@newsbf02.news.aol.com>,
Storgodar <storgodar@aol.com> wrote:
...............
>Now, the operative question is whether non-terminating reals are at least
>as "real,"  philosophically speaking, as integers. I'd be interested in
>hearing from anyone claiming they are not. In any event, I also lean
>heavily toward the position that the role non-terminating reals play in
>real physical phenomena are at least as "true" as that of integers. In
>that case, when a "law of physics" can be said to "calculate" something,
>it should be utilizing the non-terminating real as a whole package, acting
>in one fell swoop. (At least, I have never seen any physical object hung
>in stasis as it infinitely computes some non-terminating real). 
>
I think that a lot of the problems you are pointing out to disappear if
you accept that "laws of physics" are elements of our model of reality,
and not the reality itself, which we know nothing about. Our models are
always approximate, and what we can see (observe) about the nature is 
always approximate too. Hence the problem is rather if a Turing machine (of 
any sort) can give us (calculate) models of reality which we can observe.
Since what we can observe is always finite, it clearly can. Non-terminating 
reals are needed to describe a certain feature of the reality namely, that 
there are situations that however we increase the accuracy of observations
we will always get more digits (and we cannot represent this train of digits 
by a ratio of two integers). However we never actually observe an infinite 
sequence of digits of such nonterminating real, do we?

>This is what I mean by a Turing machine's problems with iteration. Thus,
>physical phenomena can never perform a SINGLE computation that is beyond
>the in-principle capacity of a Turing machine,  but an iterative SET of
>computations easily would be beyond the capacity of any Turing machine.
>
I am not sure I appreciate your distinction between SINGLE computations and
iterative SET of computations. Descriptions of many physical phenomena require
iterative computations, but again always for a given accuracy of observations
a finite number of iterations is enough.

Andrzej


-- 
Andrzej Pindor                        The foolish reject what they see and 
University of Toronto                 not what they think; the wise reject
Information Commons                   what they think and not what they see.
pindor@breeze.hprc.utoronto.ca                      Huang Po
