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From: breuel@h-sc1.UUCP (thomas breuel)
Newsgroups: net.philosophy,net.math,net.physics
Subject: Re: Mind as Turing Machine: a proof *and* a disproof!
Message-ID: <718@h-sc1.UUCP>
Date: Tue, 5-Nov-85 16:59:55 EST
Article-I.D.: h-sc1.718
Posted: Tue Nov  5 16:59:55 1985
Date-Received: Thu, 7-Nov-85 06:28:48 EST
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Organization: Harvard Univ. Science Center
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Xref: watmath net.philosophy:3047 net.math:2483 net.physics:3504

>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 : all it would have to do is store the stuff in its memory in some sort of 
>>order.  I'm thinking specifically of the structure called a binary tree, where
> While your premise is true for simple data forms, it breaks done as
> the complexity goes up. Namely semantic concepts vs a simple binary
> number search.

This discussion is non-sense. Whether the time complexity of a problem
on a Turing machine is equal to the time complexity of a problem on any
other (abstract) machine is utterly irrelevant to whether the mind 'is
a Turing machine' or not. The comparison of time complexities breaks
down even between different kinds of Turing machines (single- vs
multitape, although they are polynomially related).

What you really want to know is whether the human brain is 'Turing
equivalent'.  I think with fair certainty it can be said that it is
not, in the same sense that a general purpose computer is *not*
Turing equivalent: both don't have infinite memory. Both are much
more accurately captured by the notion of a finite state machine.
(This is, of course, not to say that the use of Turing machines
tells us nothing about computation in computers or the brain, just
that one has to be careful as to how far the similarities go).

					Thomas.