X-Message-Number: 15376
Date: Wed, 17 Jan 2001 23:43:55 -0500
From: Thomas Donaldson <>
Subject: more re computers and brains

Hi everyone!

I guess I must repeat.

The fact that the connections of some given individual will never become
exponential is irrelevant to the arguments I have made. At any given
time the POSSIBLE connections are factorial. It is this possibility that
makes the use of Turing machines difficult (as I said before, even if
we forget the importance of TIME in studying just how we work and whether
or not Turing machines are important). 

The same issue that Mike Perry raises (that the number of connections 
will go up polynomially) shows up in ordinary computers. No one would
assess the ability of a computer by looking at its lifespan from 
its original owner to its disposal as junk by simply adding up the
calculations and programs which it ran during that period. Certainly
that figure will be way below the POSSIBLE programs it might have 
run, but it also says nothing at all about applicability of Turing's
ideas to computers of that kind. You want to get a bound on what ANY
computer of that design might achieve; the way to do so is to work
out the limits of their possible computations, not those of any 
particular instance. And it is in looking at those limits that we
can reasonably think about Turing machines at all. (Yes, I would agree
that Turing's computer serves as a model for a single sequential
computer, if we also limit the memory available to it, but I am
not discussing single sequential computers!).

I hope that my point is clearer now.

		Best wishes and long long life for all,

			Thomas Donaldson

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