Date: Mon, 17 Apr 1995 17:21:02 -0500 (CDT)
From: jlelson-AT-utdallas.edu
Subject: RE: re: more e.r.


On Mon, 17 Apr 1995 WIDDER-AT-vax.lse.ac.uk wrote:

> Finally, there's the problem that things simply do not necessarily return.
> About a year ago, Martin Hogan posted a mathematical problem on the list.
> I don't remember it very well, but it had to do with three circles lined up
> and sent rotating around their axes.  The point was (and, as I say, I really
> don't remember the example that well) that the three circles would never line
> up as they had at the beginning.  The point was that a rather simple problem
> of geometry would prove the eternal return as a return of the same to be
> wrong (which is not to say that Nietzsche didn't advance it, but that such a
> doctrine is rather easy to disprove).

I am familiar with that argument, however it is based upon a rather
questionable assumption.  The key to the argument is that it invovles
pi which is a transcendental number.  Thus, for that argument to be valid,
space must be infinitely divisible.   Although this is possible, our 
current 'scientific' understanding of space indicates that this is not the
case for after a certain point, about 10^-31 cm, the Planck distance, the
notion of space completely breaks down.  Of course, this analysis of that
"disproof" of the "e.r. of the same" only demonstrates that that "disproof"
assumes a premise which is not supported by the best available data. Perhaps
the "e.r. of the same" may be 'disproved' in other ways.  

--Jim
===========================================================================James L Elson:              |<o  When you stare into the abyss too long  o>|
School of Arts & Humanities |<o       the abyss stares back into you.    o>|
University of Texas-Dallas  |                  --Nietzsche--               |




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