Path: utzoo!utgpu!watmath!att!tut.cis.ohio-state.edu!gem.mps.ohio-state.edu!ginosko!ctrsol!IDA.ORG!rwex From: rwex@IDA.ORG (Richard Wexelblat) Newsgroups: comp.ai Subject: Re: intelligence and the initial conditions of the universe (BANG!!!) Message-ID: <1989Aug15.193003.3348@IDA.ORG> Date: 15 Aug 89 19:30:03 GMT References: <2182@hub.UUCP> <1490@l.cc.purdue.edu> <1989Aug11.114022.481@IDA.ORG> <0YtCI7a00V4G40XHNL@andrew.cmu.edu> Reply-To: rwex@csed-42.UUCP (Richard Wexelblat) Organization: IDA, Alexandria, VA Lines: 45 In article <0YtCI7a00V4G40XHNL@andrew.cmu.edu> jk3k+@andrew.cmu.edu (Joe Keane) writes: >In article 1989Aug11.114022.481@IDA.ORG> rwex@IDA.ORG (Richard Wexelblat) >writes: >>In article <1490@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: >>> The mathematics is independent >>>of the universe. >> >>You beg the question. How do you know this is so? > >Because we state in advance what assumptions (axioms) we're using. Everything >else can be derived from them. If you prove 2+2=3 (in your universe) either >you're using different axioms or you're using the same ones and have found a >contradiction in them. In either case, Herman's statement is still true. Sorry, I don't see what the assumptions have to do with the universe. If you mean that the axioms are ASSUMED to be independent of the universe, then that confirms my statement that the original poster is begging the question. If you mean that the axioms can be PROVEN independent of the universe that I'd like to see the proof. Classical math is just the opposite. Your example comes from that trivial(:-) part of mathematics* wherein one can prove things by demonstration. Let's go on to geometry. Does the same argument hold for the law of parallels? Going back to Riemann's dissertation (in translation, of course) Space is only a special-case of of a three-fold extensive magnitude. From this, however, it follows of necessity that the propositions of geometry cannot be deduced from magnitude-ideas but that these peculiarities through which space distinguishes itself from other thinkable three-fold extended magnitudes can only be gotten from experience. I.e. the mathematics is conditioned by experience or observation. Look at Lobachevski's Theory of Parallels. I think the excellent 1914 translation by G. B. Halstead is still in print. *Here is my argument that number theory is trivial: Computers are very good at number theory (Lenat, etc.) Anything a computer can do is only a step or so away from trivial Ergo, number theory is next to trivial. -- --Dick Wexelblat |I must create a System or be enslav'd by another Man's; | (rwex@ida.org) |I will not Reason and Compare: my business is to Create.| 703 824 5511 | -Blake, Jerusalem |