Re: zeno paradox.

porky_pig...@xxxxxxxxxxx" wrote (in part):

I've started searching the web and came across
at the following page:

http://www.mathpages.com/rr/s3-07/3-07.htm

which says, essentially, what I thought as well. There
are some things in the continuous model that go strictly
against the actual experiences. The best example on this
page, I think, is the light bouncing between the infinite
series of mirrors, with decreasing distances, 1/2, 1/4,
1/8, etc. Of course eventually the light should exit
(the series converges, right?) but the direction of
light is undefined since *there is no last mirror the
light bounced off right before the exiting*. So the
fact that the series of terms 1/2^n converges does
not resolve the paradox at all.

I agree, the "convergent infinite series" explanation
doesn't really resolve things. By the way, the Greeks
(well, Archimedes did, at least) certainly worked with
infinite series and such to some extent, although I
don't think they actually dealt with Zeno's paradox
in this way.

You might find it interesting to research "infinity machines":

http://scholar.google.com/scholar?q=infinity-machines

For what it's worth, here's something from a sci.math
post of mine a couple of years ago:

-------------------------------------------------

Although an enormous amount has been written about
Zeno's paradoxes, much of it is probably overly verbose
and mathematically naive for someone with a background
in mathematics. Below is what I'd recommend for someone
like this. Meyerstein's article is a bit weaker than
the others, but I'm including it because it's on-line.

Florian Cajori, "The history of Zeno's arguments
on motion" (in 9 parts), American Mathematical Monthly
22 (1915), 1-6, 39-47, 77-82, 109-115, 143-149, 179-186,
215-220, 253-258, 292-297.
[JFM 45.0095.07 & 45.1215.09]
http://www.emis.de/cgi-bin/JFM-item?45.0095.07
http://www.emis.de/cgi-bin/JFM-item?45.1215.09

Florian Cajori, "The purpose of Zeno's arguments
on motion", Isis 3 (1920), 7-20.

Clive W. Kilmister, "Zeno, Aristotle, Weyl and Shuard:
two-and-a-half millenia of worries over number",
Mathematical Gazette 64 #429 (October 1980),
149-158. [MR 82i:01075]

F. Walter Meyerstein, "Is movement an illusion?
Zeno's paradox: from a modern viewpoint", Complexity
4(4) (March/April 1999), 26-30. [MR 2000f:00007]
http://www.mindship.org/meyerst.htm
http://www3.interscience.wiley.com/cgi-bin/abstract/61005919

Wesley C. Salmon (editor), ZENO'S PARADOXES, Hackett
Publishing Company, 2001, 320 pages. [Reprint of the
1970 edition.]

-------------------------------------------------

Dave L. Renfro
.

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