Date: Thu, 03 Dec 2009 22:18:51 -0800 Subject: Re: [math-fun] Solving polynomial equations with roots, etc. From: "Stephen B. Gray" <stevebg@roadrunner.com> Dan Asimov wrote:

As interesting as this discussion could be, for the record I assert that anything said about this issue is total B.S. unless there is a precise definition made of the term "God" and of the term "knowing".

--Dan

<< Date: Mon, 30 Nov 2009 19:44:17 -0800 Subject: Re: [math-fun] Solving polynomial equations with roots, etc. From: "Stephen B. Gray" <stevebg@roadrunner.com>

On a different subject, for anyone to comment on.

Everyone knows that sqrt(2), pi, and all irrational numbers have no decimal strings that repeat an infinite number of times. That's not necessarily the same as the decimal expansion being totally without any pattern. That is, is there any way to predict the next digits of say sqrt(2) or pi without doing one of the usual computations? In other words, is it possible to "know" the entire decimal expansion of any "ordinary" irrational? Is anything known about patterns in "regular" irrational expansions?

I'm excluding numbers invented for the sole purpose of being irrational or transcendental and with an obvious pattern like .101001000100001.... or .123456789101112..... ), etc.) I know about the question of "normal" expansions but that has little to do with my question. Any info will be appreciated.

_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

Dan - By "God" I mean the traditional Christian Omnigod, which is omnipotent, omniscient, omnibenevolent, omnipresent, infinite, eternal, personal, etc., etc., (all of which properties need to be defined and proved separately because they are independent of each other). By "knowing," I'm not currently able to define it because among other things I'm not sure what part of the common meaning you're not satisfied with. Steve Gray