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From: ydobyns@flagstaff.princeton.edu (York H. Dobyns)
Subject: Re: Review of Shadows of the Mind
Message-ID: <1995Apr4.145633.23317@Princeton.EDU>
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References: <1995Apr1.143159.4043@lugb.latrobe.edu.au>
Date: Tue, 4 Apr 1995 14:56:33 GMT
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In article <1995Apr1.143159.4043@lugb.latrobe.edu.au> Douglas Moore writes:
[...deletia; the "he" below refers to Penrose...]
> He then seems to become overwhelmed by the concept that any Turing machine
> can itself be  formalised in terms of the Generalised Turing Machine. 
> Any Turing machine together with it's "computation" or "program" can be itself
> represented as a single computation on the generalised Turing Machine.
>
> This wraps it all up. No need to delve into this subject any deeper. All
> computers are just a functionally equivalent subset of a generalised Turing
> Machine. Thus, any limitations of the Turing Machine must apply to any
> computer. Mustn't they?
>
>What rubbish!
>
>Can anyone who knows the slightest thing about computers, accept this argument
>for building the basic premise of practically everything he has to say about
>computers and AI?

Yes, quite easily. *Any* digital computer, no matter what bells and
whistles you put on it, no matter what kind of storage, I/O, or any
other system it incorporates, can be fully represented by a Turing
machine, and therefore by the universal Turing machine. (I don't quite
know what a "generalised" Turing machine might be; the universal Turing
machine is simply a Turing machine that can perform the action of any
other Turing machine if presented with the other machine's description
on its tape, and is therefore a quite straightforward analog to a
programmable general-purpose computer.) There is only one caveat to this
statement that even in principle possible, let alone established as a
fact; see below.

[...]
>The simple fact is that no Turing Machine, not even a Generalised Turing 
>machine
>could even do anything as rudimentary as allow me to make this posting on the 
>net.
>The reason being is that I am a part of my PCs environment and I have yet to
>see a Turing machine formulation which can express my intent and encapsulate it
>on its tape, everything I will be doing to my machine during the next minute 
>even,

And now we get to the caveat: The computer + environment system cannot
be represented by a Turing machine *only* if the environment performs 
non-Turing-computable actions. If the environment is Turing-computable,
then the whole system can be represented on a Turing machine, no matter
what capabilities have been built into the computer. 

But please note the irony that Moore's "refutation" of Penrose in the
paragraph quoted above actually consists of *granting* Penrose's entire
thesis! Penrose, the AI opponent, has built this entire logical edifice
to demonstrate the likelihood -- even he could not provide an absolute
proof -- that human behavior must contain noncomputable elements. Moore,
apparently an AI advocate, or at least an advocate of the powers of
digital computers, claims to refute Penrose's argument by simply
*declaring* that he is himself non-Turing-computable! Even Penrose
didn't have the chutzpah to think he could get away with making
noncomputable physics an axiom, and instead felt compelled to provide
arguments and justifications for it.

And, regardless of what you think of Penrose's argument, it's *really*
weird to see someone saying, in effect, "I know Penrose's argument is
hogwash, because it's obvious that he's completely right all along."

[...Subsequent argument, discussing the necessity for anything called a
"computer" to support interrupts, deleted...]

Again, even having an interrupt system does not rescue you from being
Turing-computable. An interrupt-driven system *in a Turing-computable
environment* remains Turing-computable; the only way out is to make the
environment non-computable. Making the environment non-computable grants
Penrose's whole argument.

-- 
York Dobyns		ydobyns@phoenix.princeton.edu
Honest skeptics must be willing to question *their own* beliefs, as
well as those of people with whom they disagree.
