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From: biep@klipper.UUCP (J. A. "Biep" Durieux)
Newsgroups: net.philosophy,net.math,net.physics
Subject: Re: Mind as Turing Machine: a proof *and* a disproof!
Message-ID: <516@klipper.UUCP>
Date: Thu, 7-Nov-85 11:11:22 EST
Article-I.D.: klipper.516
Posted: Thu Nov  7 11:11:22 1985
Date-Received: Sun, 10-Nov-85 10:11:51 EST
References: <1996@umcp-cs.UUCP> <718@h-sc1.UUCP>
Reply-To: biep@klipper.UUCP (J. A. "Biep" Durieux)
Organization: VU Informatica, Amsterdam
Lines: 55
Xref: watmath net.philosophy:3073 net.math:2498 net.physics:3526

I wrote (in a context which subsequent respondents left out):
>>>>	                                        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.

[some people commented on this, which they shouldn't have done because it
	was very much besides the point I was making (see below) ]

In article <718@h-sc1.UUCP> breuel@h-sc1.UUCP (thomas breuel) writes:

>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.

What I was pointing out was, that it is nonsense to talk about equivalence
without defining the equivalence relation. So, to give an example, I took
an equivalence relation which took time complexity into account. Please 
don't say that is a wrong equivalence relation, please tell me which one
is the *right* one. Then we can start to decide whether the two are or are
not equivalent.

>What you really want to know is whether the human brain is 'Turing
>equivalent'.

Can you define that? 

>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.

Can you define "memory"; some people have pointed out that people can write
things down, and then you should start to look at the question whether the
universe contains infinite mass (to write things down upon) or not...
[Just an extreme example again! Please don't pick on me for that!]

>(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.

Isn't that exactly what I am asking for all the time: Please give your
equivalence relation!! [And look at it yourself, whether you are not
leaving out of account anything which would make a mind different/equal
to a TM, depending on your point of view.]

May I suggest to reread my original article, in which I also proved equality?
-- 
							  Biep.
	{seismo|decvax|philabs|garfield|okstate}!mcvax!vu44!biep

Is the difference between a difference of degree and a differ-
ence of sorts a difference of degree or a difference of sorts?