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From: bpvanstr@yoho.uwaterloo.ca (Brian Van Straalen)
Subject: Re: Can neural nets think
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References: <3t2fmh$7cn@kaleka.seanet.com> <1995Jul1.173245.17879@news.cs.indiana.edu>
Date: Wed, 5 Jul 1995 20:20:28 GMT
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In article <1995Jul1.173245.17879@news.cs.indiana.edu>,
>
>Bottom line: you could simulate a human brain-sized neural network on
>a Turing Machine if you had a realllllly long tape and you were
>realllllly patient.
>
>
>Mark Meiss (mmeiss@indiana.edu)
>Indiana University CS Dept. Student
>

hmmmm, I'm not positive of that one.  To make that statement you would
need to be able to prove that an arbitrary parallel computation can
be performed serially, given careful control of sequence and
information flow.  Now, we do this all the time when we parallelize
our computer codes (serial -> parallel, test on parallel simulator sitting
on our inexpensive serial workstation ),
but I don't think the conjecture can be proven. (I'm not up on current
`theory of computation' anymore).  

As for the digital/analog comparison:  Yes, it is true, a digital
signal will be `dense' in the analog function space (I mean the 
strict mathematical meaning of `dense') if your using a supprenum
or L2 norm (typical Banach spaces), but is ion diffusion governed
by such a norm ? 

In fact, an analog signal flowing through a massively parallel network
(a neural net) is about the complete opposite of a digital signal
flowing through a very long Turing program.  I could envision very
different behaviour. That's not to say they wouldn't have similar
complexity.

   You can see this from early chaos experiments.  analytically solve
the path of particles in some force field, then digitally simulate
the process.  For Lyaptov exponent greater than 1, given sufficient
time, the digital simulation ALWAYS gives different results, and may times
markedly different behaviour (stable/unstable, missing fixed points...).

   It's time for the Revolution in Analog Computing to begin !!!

	Brian Van Straalen  :)

