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From: ins_apmj@jhunix.UUCP (Patrick M Juola)
Newsgroups: net.philosophy,net.math,net.physics
Subject: Re: Mind as Turing Machine: a proof *and* a disproof!
Message-ID: <1096@jhunix.UUCP>
Date: Sun, 3-Nov-85 00:10:29 EST
Article-I.D.: jhunix.1096
Posted: Sun Nov  3 00:10:29 1985
Date-Received: Tue, 5-Nov-85 08:15:56 EST
References: <1996@umcp-cs.UUCP> <667@hwcs.UUCP> <2031@umcp-cs.UUCP> <509@klipper.UUCP>
Reply-To: ins_apmj@jhunix.ARPA (Patrick M Juola)
Organization: Johns Hopkins Univ. Computing Ctr.
Lines: 23
Keywords: minds, Turing machines
Xref: linus net.philosophy:2746 net.math:2110 net.physics:3235
Summary: I found a flaw in the disproof

In article <509@klipper.UUCP> biep@klipper.UUCP (J. A. "Biep" Durieux) 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
everything in the right sub-tree is > the root and the left is < the root.
Program the machine to start at some designated root (call it position 1) on
the tape.  If the item to be searched for is < position n, shift left (for 
example) to position n*2.  If the item is >, shift left to position n*2+1.
This, on the average, will find any item in memory in log(base 2)n comparisons,
and you've still got an infinite amount of tape to the right for storage of
other items.
	Any EE/CS majors out there, feel free to totally trash my program, but
I think a valid algorithm could be designed.  Any data structure that would let
you perform a binary search would work, and I would be *fascinated* by a proof
that no such structure exists.  (Yes, J.A., that was a challenge :-)
						Pat Juola
						Johns Hopkins Univ.
						Dept of Maths.