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Re: tortoise algorithms



At 10:08 AM -0400 8/31/03, John S. Denker wrote:

Does this mean to imply that Zeno _was_ "seriously
concerned with the fundamentals of the infinte /
infinitesimal"?

Zeno was totally unaware of the Constructivist school of
mathematics but WAS interested in getting people to think (logically)
in a variety of ways.
I find it difficult to believe that you folks don't think that Zeno
could SEE Achilles winning the race. He was trying to stretch peoples
minds, as _*I*_ am by questioning our blind faith in the continuum of
infinitesimals. The more people who become FAMILIAR with the
Banach-Tarski 'paradox', the more intelligent questioning minds we
will have.

I believe quite sincerely that much learning comes from being faced
with two incompatible results. Non-Euclidian geometry is an EXCELLENT
example of using non-traditional reasoning.


Also note that people can seem "serious" and still
be quite wrong.

As I see it, we can somewhat charitably summarize
Zeno's position as a syllogism:

I see it more as goad for disputation. (and quite effective it seems)


--
I never teach my pupils; I only attempt to provide the conditions in
which they can learn.
- Albert Einstein