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From: firth@sei.cmu.edu (Robert Firth)
Newsgroups: talk.religion.misc,comp.ai
Subject: Re: The Ignorant assumption
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Date: 29 Sep 88 14:51:41 GMT
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Somehow, I get the feeling that our machines are better at forward
chaining than we are.  Please let me run this Turing machine stuff
by you once again.  (Translation: this post says nothing new, merely
recapitulates.)
----

The question that originally prompted me to speak was this one

[ <388@quintus.UUCP> ok@quintus.UUCP (Richard A. O'Keefe)]
>But is there any reason to suppose that the universe _is_ a Turing machine?

As I understood it, the question referred to the physical world, as
imperfectly revealed to us by science, and so I replied

[ <7059@aw.sei.cmu.edu> firth@bd.sei.cmu.edu (Robert Firth) ]
>None whatever.  The conjecture is almost instantly disprovable: no Turing
>machine can output a true random number, but a physical system can.

To elaborate:  I can build a box, whose main constituents are a supply
of photons and a half-silvered mirrir, that, when triggered, will emit
at random either the value "0" or the value "1".  This can be thought
of as a mapping

	{0,1} => 0|1

where I introduce "|" to designate the operator that arbitrarily selects
one of its operands.  The obvious generalisation of this - the function
that selects an arbitrary member of an input set - is surely not unfamiliar.

Nobody has denied that a Turing machine can't do this.  The assertion that
a physical system can do it rests on the quantum theory; in particular on
the proposition that the indeterminacy this theory ascribes to the
physical world is irreducible.  Since every attempt to build an alternative
deterministic theory has foundered, and no prediction of the quantum theory
has yet been falsified, this rests on pretty strong ground.

Now, it is not my job to supply an "algorithm" for this function: as the
physicist I have given you a specification and a model implementation; as
the computer scientist it is your job to give me an equivelent program.
However, being a kind-hearted soul, I shall point you to an algorithm;
it is given as equation (3.1) in the paper

[Deutsch: Proc Roy Soc A vol 400 pp 97-117]

Naturally, it uses primitive operations that you won't find in a
classical computing engine, which is why the title reads "Quantum theory,
the Church-Turing principle, and the universal quantum computer".

Turning now to that "principle":  The formulation I learned was, briefly,
that any function that would naturally be regarded as computible can be
computed by a universal Turing machine.  Once again, I made my opinion
on this absolutely clear [art. cit.]:

   Since a function is surely "computable" if a physical
   system can be constructed that computes it, ...

from which, I submit, the conclusion follows:

   ... the existence of true random-number generators directly
   disproves the Church-Turing conjecture.

Granted, one can readily evade this conclusion.  It is necessary merely
to redefine "natural", "computable", "function", or some other key
term.  For example, one could stipulate

   A function is to be regarded as computable only if it can be
   described by an algorithm written in a programming language
   implementable on a universal Turing machine.

In which case, the conjecture becomes vacuously true, and the discipline
of AI becomes vacuously futile.  For the point of "artificial intelligence",
surely, is accurately to reproduce, in some computing engine, the
behaviour of certain physical systems, especially those that show goal-
directed behaviour, judgement, creativity, or whatever else one means
by "intelligence".

If this is to be remotely feasible, then the model of the computation
process must be at least general enough to embrace the known basic
operational features of physical systems.  After all, if your programming
tools cannot reproduce so simple a physical system as my random Boolean
generator, the chance of their being able to reproduce a complicated
physical system - the brain of a flatworm, for instance - must be very
close to zero.

Robert Firth