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Article 2427 of comp.ai.philosophy:
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>From: jbaez@nevanlinna.mit.edu (John C. Baez)
Newsgroups: sci.philosophy.tech,sci.logic,sci.math,comp.ai.philosophy
Subject: Re: Penrose on Man vs. Machine
Keywords: the limits of human understanding: no such thing
Message-ID: <1991Dec28.194855.16543@galois.mit.edu>
Date: 28 Dec 91 19:48:55 GMT
Article-I.D.: galois.1991Dec28.194855.16543
References: <1991Dec23.135321.6894@husc3.harvard.edu> <1991Dec27.051804.6985@cambridge.oracorp.com> <1991Dec27.184248.6939@husc3.harvard.edu>
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In article <1991Dec27.184248.6939@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:
>Why shouldn't a neuron be capable of infinitely many distinguishable states?

Well, having a neuron whose functioning made essential use of infinitely
many distinguishable states in order to repeatably compute unrecursive 
functions goes against what we know about physics.  See for example my paper
"Recursivity in Quantum Mechanics," Trans. A.M.S. 280, p. 339, or
Pour-El and Richards' book on computability in physics.  Unless the
normal functioning of a neuron makes use of laws of physics other than
the ones we know about, it seems most likely that its *expected*
behavior is recursive.  I emphasize *expected* because quantum mechanics
is nondeterministic, so that if you want to "compute a nonrecursive
function" it appears that all you have to do is keep track of the ticks
of a Geiger counter, or any other quantum process.  One can't find a
quantum system following laws of the sort we know that *repeatedly,* or
even "on average" computes a fixed nonrecursive function.  (My paper
considers the Schroedinger equation with Coulomb forces, which is
oversimplified, but it's clear, especially with what Pour-El and
Richards (and others) have done, that there's nothing special about this
case.)

If anyone believes that somehow quantum mechanics, or the fact that
biological systems are continuous rather than discrete, gives the brain
powers over and above that of a universal Turing machine with a random
number generator oracle, then they have some explaining to do concerning
HOW this is supposed to work.  

Interested people may seek the work of Deutsch on quantum computation.
Sorry, I don't have a more precise reference.  He and others consider
whether quantum computation could help solve NP problems.


