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                                   |