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From: hes@ecsvax.UUCP (Henry Schaffer)
Newsgroups: net.math
Subject: Re: Mind as Turing Machine: a proof *and* a disproof!
Message-ID: <702@ecsvax.UUCP>
Date: Tue, 5-Nov-85 22:41:56 EST
Article-I.D.: ecsvax.702
Posted: Tue Nov  5 22:41:56 1985
Date-Received: Thu, 7-Nov-85 05:25:45 EST
References: <509@klipper.UUCP> <1096@jhunix.UUCP> <2081@umcp-cs.UUCP>
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Organization: NC State Univ.
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> In article <1096@jhunix.UUCP> ins_apmj@jhunix.ARPA (Patrick M Juola) writes:
> 
> >>	                                        Psycholinguistics has
> >>	found that humans can search their memory in < log n time, n
> >>	being the number of items. Turing machines clearly can not do
> >>	better than order n time. Proof that humans are not Turing machines.
> 
> >  I'm sure that a Turing machine can search its memory faster than order n
> 
> Unfortunately, this fails to work because in Turing machines, it is the
> number of *steps* which costs you; each step from one cell to the next costs
> at least on step.
> 
> Nevertheless, the original "proof" is still flawed.  The brain is quite
> obviously not a turing machine; on the other hand, neither are current
> computers.  The important question is whether or not it can be modelled by a
> turing machine.  Considering performance, this little "proof" tends one to
> believe that it can't; but ignoring performance, this "proof" gets us
> nowhere.
> 
> Charley Wingate

The usual concept is the "modelled" aspect, with performance speed quite
specifically excepted.  Let me quote from a handy reference (Encyclopedia
of Computer Science and Engineering 2/e Ralston & Reilly, eds, p. 1542)
"... one can show that any computer can be simulated (albeit rather slowly)
by a Turing machine." and "Since a Turing machine can simulate any computing
device, it follows that anything that cannot be computed on a Turing
machine cannot by computer at all.  The fact that there are such unsolvable
problems motivated Turing to devise his abstract machine."

Following this path, the rephrased question is "Can the mind be modelled
by a Turing machine?", and it can't be answered by showing speed 
differences -- but it could by showing that the mind can "compute" 
something that a Turing machine can't.  (Vice-versa isn't possible, because
it is evident that the mind can simulate a Turing machine.)
--henry schaffer  n c state univ