Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83 (MC840302); site klipper.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!philabs!cmcl2!seismo!mcvax!vu44!botter!klipper!biep 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: <509@klipper.UUCP> Date: Fri, 1-Nov-85 07:09:46 EST Article-I.D.: klipper.509 Posted: Fri Nov 1 07:09:46 1985 Date-Received: Sun, 3-Nov-85 09:36:59 EST References: <1996@umcp-cs.UUCP> <667@hwcs.UUCP> <2031@umcp-cs.UUCP> Reply-To: biep@klipper.UUCP (J. A. "Biep" Durieux) Organization: VU Informatica, Amsterdam Lines: 47 Xref: watmath net.philosophy:2993 net.math:2460 net.physics:3469 Summary: Be sure to realise which equivalence relation you use! [] The problem in the discussion in that nobody has stated clearly which equivalence relation he is using. 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. (Note I took an equivalence relation which did look at time.) Now take the equivalence relation "true(x, y)", and it is equally clear that anything is equivalent to a Turing machine. The reason math has done so well for the last so many years is, that they have provided us with a set of equivalence relations which left out anything math couldn't deal with. So, using those (normally only implicitly used) relations, any real world pheno- menon turned out to be equivalent to some mathematical model. There are many aspects of reality which are not easily modelled mathematically, and the result has not been that mathematical models have been abandoned, but often that the existence of those aspects has been denied. For those who look at the reality from a mathematical point of view, there will be a mathematical model for the human mind for every equivalence relation they can think of; for those who look at mathematics from reality, there will never be such a model for any equivalence relation *they* can think of. Notes: 1) Before you flame me: yes, I have a masters of mathematics. 2) At the moment a human says he is equivalent to a model he has thought out, he is like a correctness proving program that is saying it has proven itself correct 3) Now first start discussing the form of your equivalence relation, that is much more productive. Mathematicians, don't get angry if the other guy's relation is not mathematizable! Success in learning to understand each other's point of view! -- 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?