From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.ecf!utgpu!cs.utexas.edu!sun-barr!olivea!uunet!trwacs!erwin Thu Apr 16 11:34:33 EDT 1992
Article 5099 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: <544@trwacs.fp.trw.com>
Date: 14 Apr 92 12:37:53 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> <541@trwacs.fp.trw.com> <542@trwacs.fp.trw.com>
Organization: TRW Systems Division, Fairfax VA
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I consulted with an expert last night (my wife) and a number of points
were made.

1. Church's Thesis is that the standard characterizations (Turing, etc.)
are equivalent to the informal concept of function computable by
algorithm. The algorithm proposed earlier in this sequence of messages
(Initialize an analog computer, run it, and take measurements) is not an
algorithm in the sense recognized by mathematical logicians.

2. It is not clear that an analog computation of a chaotic or turbulent
process avoids the problems that the digital computation encounters. If
the process is chaotic, errors in initial conditions should grow
exponentially. In addition, if the process is dissipative, it should be
non-stationary, implying that even the statistics will vary over time.

On the other hand, if there is chaos in the brain (as Paul Rapp claims),
and if it is useful (if only as a starting point for pattern recognition),
the implication is that the brain is not equivalent to a Turing Machine...

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


