X-Message-Number: 9306
Subject: misunderstood models
Date: Tue, 17 Mar 1998 15:25:25 -0500
From: "Perry E. Metzger" <>

> From: Thomas Donaldson <>
> Date: Tue, 17 Mar 1998 00:17:42 -0800 (PST)
> 
> I will add, though, that since real Turing machines are impossible (because
> they have an infinite tape) it seems odd to argue that a machine able to
> mark down real numbers (ie. infinite decimal numbers) or have components
> a real number distance apart (such as pi or sqrt(2)) should be dismissed
> merely because infinite decimal numbers are impossible.

Turing machines don't actually possess infinite tapes.

Permit me to explain what I mean by that.

When we say a Turing machine has an infinite tape, we are really
saying that it can use a tape of arbitrary length. A Turing Machine
computation that is in any way bounded in time will of necessity use
only a finite amount of tape -- the "Infinite" constraint is there to
permit it to use a arbitrary amount of storage, as no program could
actually access infinite storage in finite time.

The human brain or your desktop computer do not actually possess
infinite storage -- they are in fact a weaker construction than a
Turing machine called a Finite State Automaton, because they are
bounded. We us the "Turing Machine" as a model of computation because
it is convenient and not because anyone actually would want to build
one. It is a maximal model in the sense that it is believed that no
real physical system could compute anything that a Turing Machine
could not compute. Any real machine or construction is necessarily
more constrained.

Let us not forget the point of this discussion: we are debating a very 
narrow topic, which is "can a digital computer simulate a human
mind". To argue against that successfully, Mr. Donaldson and
Mr. Ettinger are going to have to show that the neural networks making 
up the brain are somehow capable of producing non-Turing computable
results.

It appears that real neurons operating in real brains do not use
magical powers but in fact are based on electrochemical reactions, and 
are thus in principle straightforward to simulate. Given the practical 
engineering knowledge we have gained over the last 50 years of working 
with stored program digital computers, there does not appear to be
evidence that, in the long run, computers will not possess adequite
power to simulate even systems as complex as human brains.

Perry

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