From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.ecf!utgpu!cs.utexas.edu!uunet!trwacs!erwin Thu Apr 16 11:33:45 EDT 1992
Article 5019 of comp.ai.philosophy:
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>From: erwin@trwacs.fp.trw.com (Harry Erwin)
Newsgroups: comp.ai.philosophy
Subject: Re: on Turing-Church hypothesis
Message-ID: <533@trwacs.fp.trw.com>
Date: 9 Apr 92 17:43:54 GMT
References: <1992Apr7.050118.25536@hellgate.utah.edu>
Organization: TRW Systems Division, Fairfax VA
Lines: 43

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.
The amplification will be exponential, but may not be of great magnitude.
In essence what happens is that the probability distribution of system
states at some future time (in a Bayesian sense) is smeared out over the
space of possible states. If the chaotic process is ergodic, this smearing
out will be independent of the time selected; if non-ergodic or
dissipative, this smearing out will be non-stationary.

>Assuming that space and time are continuous, then, due to its
>finiteness, a Turing machine cannot exactly represent an arbitrary
>dynamical system. 
This is correct, and Bob Rosen has made a similar argument. In particular,
constructable dynamical systems are countable. Yorke and Grebogi have
shown that constructable dynamic trajectories will approximate true
trajectories for arbitrarily long times.

>It follows that most chaotic processes cannot be simulated by 
>a Turing machine.
Most dynamic processes cannot be simulated by a Turing machine. Not just
most chaotic processes. Broewer and Bishop addressed these issues.

>The strong interpretation of the Turing-Church hypothesis is that 
>any physically realizable dynamical system can be simulated by a 
>Turing machine.
Far too strong a statement. 

>The hypothesis seems to be false for chaotic processes.

>Where is an error? 
Physically realizable is not computable.

>Thanks a lot

>Rok

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



