From: philbo@soda.berkeley.edu (Philip Gross (philbo))
Newsgroups: comp.ai.philosophy
Subject: Re: on Turing-Church hypothesis
Date: 8 Apr 1992 05:19:07 GMT
Organization: Philosophy and Computers and System Science, Binghamton Univ.
NNTP-Posting-Host: soda.berkeley.edu
Summary: bing, bing, bing!

In article <1992Apr7.050118.25536@hellgate.utah.edu> sosic%asylum.utah.edu@cs.utah.edu (Rok Sosic) writes:
>Taking a chaotic process, arbitrary small deviation at the
>beginning will be amplified to great proportions.
>
>Assuming that space and time are continuous, then, due to its
>finiteness, a Turing machine cannot exactly represent an arbitrary
>dynamical system. 
>
>It follows that most chaotic processes cannot be simulated by 
>a Turing machine.
>
>The strong interpretation of the Turing-Church hypothesis is that 
>any physically realizable dynamical system can be simulated by a 
>Turing machine.

(actually this is more in the line of the Physical Symbol System
Hypothesis. All the Church-Turing thesis states is that any computable
function can be done with Univ Turing machines, the Lambda calculus,
et al., but this is minor, as your interpretation is canon for strong
AI)

>The hypothesis seems to be false for chaotic processes.
>
>Where is an error? 
>Thanks a lot
>
>Rok
 
Heh. This is a good question.

OK. The problem with a chaotic system is that 'arbitrarially small
changes in beginning states can cause an arbitrarially large change
in end states.'  This would be a problem if what computers were trying
to do was to model any system with perfect accuracy. This is not what
is going on. In the case of the weather, we can model a dynamical
system which extreme accuracy; our models behave as phenomena in the
real world do. The problem is the next step, making predictions. Like
the 3 body problem in physics, we can understand what is going on at
any point, but we can't predict where bodies will end up.  (This by
the way is one of the best refutations of Hempel's D-N model, which
maintains, among other things, that prediction and explanation are the
same thing)  

So, in the case of neurobiology, it would be difficult, if not impossible, to
model any specific brain (if it's a chaotic process, which, at first
blush, I would guess that it was, although normally in equilibrium),
it would not be impossible to model brain-like behavior, or even model
a brain, just not a specific one.

A couple of minor points;
A UTM has an infinite tape, so theoretically it might be able to
simulate continuous processes, I'm really not sure. I believe that a
Von Neuman machine is less powerful in this way, and has only a finite
tape. (Don't hold me to this, I'm not taking Computability and Logic
'till next year)

Also, another response to your query is that since energy is
quantized, there is a built in level more than which you don't need to
know information. This is a cheap answer, although probably true.  It
is impractical to find values to quantum positions, and theoretically
impossible to both know positions and momentum (for photons at least),
so you still wouldn't have enough information to model a system.  I'm
not sure if the Q Mech response can be made stronger, and I really
don't care much, because, as I said, it's a cheap answer.

Hope this helps, and if I've made any errors in thinking, I'm sure
people would be happy to jump all over me (and please do).

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