X-Message-Number: 8663
From: Thomas Donaldson <>
Subject: Re: CryoNet #8652 - #8656
Date: Wed, 8 Oct 1997 22:47:06 -0700 (PDT)

Hi again!

It seems someone else doesn't like the idea of nonTuring Machine computers.

As I understand the model set up by the two guys who proposed it, it's not
necessary to work in infinite precision. Just work in arbitrarily large
precision. So you work with long sequences of integers. 

In a real device you can do even more. The claim of the paper was that if
the weights were incommensurate ie. they were not all rational and therefore
could not all be reduced simultaneously to a set of integer weights, then
the neural net could not be imitated by a Turing machine. Well, we do have
lengths which are incommensurable: the diagonal of a square and the 
circumference of a circle might be used as such lengths. We can apply 
rational operations to them, of course, like taking the midpoint. Nor is
there any issue of quantum physics which forces space to be digital. Sure,
the number of electrons is digital, but space isn't (not that I'm really
going to stick on this point --- the reconciliation of general relativity
and quantum mechanics still waits to be done, and just what notions we 
will get out of that I hardly know --- but find it very interesting). For the
neural net described in the paper, just one incommensurable weight makes it
non Turing. So, if we forget issues of speed, we implement our neural net
so that weight is given by (say) the total length of a set of strings kept
at each node. And we start with some of these strings given by the length
of a diagonal of a square formed by four (other) equal lengths of string.

One advantage of neural nets, as parallel machines, is of course that with
enough of them you can go fast enough to match any given machine speed.
If you don't like the neural net I've suggested because it's too slow,
then multiply the number of nodes by 1000 --- or however many.

Moreover, since mass == energy/c^2, and energy also need not be digital,
then we might even make much better neural nets using a similar idea. Sure,
the levels of energy of an electron (say) belonging to an atom are
(or might be considered) digital, but then other atoms have other levels,
and the energy levels can be affected by nearby atoms too.

None of this really affects the abstract theory. I'm just coming up with
ideas about how a real device could be a "computer" (whatever a computer
is) and still not be a Turing machine. If you want to know my real problem
with both Turing machines and the Turing test, it is that I find them both
poor models, a poor model for brains and how they work and a poor model 
for a human being. I've explained in other messages why, and pointed out
also that to me this did NOT mean that we could not make a device which
would fulfil all our tests for being a human being, at least intellectually.
Yes, Searle's ideas did influence me, but then I am not Searle nor do I
agree with everything he's said. 

Welcome to a world in which computers need not be mappable into Turing
machines.

			Best and long long life,

				Thomas Donaldson

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