Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site mmintl.UUCP Path: utzoo!linus!philabs!pwa-b!mmintl!franka From: franka@mmintl.UUCP (Frank Adams) Newsgroups: net.philosophy,net.math,net.physics Subject: Re: Mind as Turing Machine: a proof *and* a disproof! Message-ID: <774@mmintl.UUCP> Date: Tue, 5-Nov-85 11:16:19 EST Article-I.D.: mmintl.774 Posted: Tue Nov 5 11:16:19 1985 Date-Received: Fri, 8-Nov-85 08:24:50 EST References: <1996@umcp-cs.UUCP> <667@hwcs.UUCP> <2031@umcp-cs.UUCP> <509@klipper.UUCP> <1096@jhunix.UUCP> Reply-To: franka@mmintl.UUCP (Frank Adams) Organization: Multimate International, E. Hartford, CT Lines: 40 Keywords: minds, Turing machines Xref: linus net.philosophy:2779 net.math:2120 net.physics:3253 Summary: Fallacies refuted In article <1096@jhunix.UUCP> ins_apmj@jhunix.ARPA (Patrick M Juola) writes: >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. A human mind has a finite limit on the amount of information it can store. If you put an upper limit on the amount of information, searching only takes a finite amount of time. The behavior of algorithms with small amounts of data does not necessarily resemble their limiting behavior. > 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. By definition, a Turing machine can only move left or right one frame at a time. You can't find the data in less than O(t) time because you can't get to it any faster than that. (To be a little more formal, the total information potentially available in time t is O(t). A binary search requires potential access to O(2**t) information.) >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 :-) Is that proof fascinating? I thought not. Frank Adams ihpn4!philabs!pwa-b!mmintl!franka Multimate International 52 Oakland Ave North E. Hartford, CT 06108