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Re: TIME - Achilles and the tortoise.



I read some of the things I was able to find about Lynds' assertions,
and it doesn't make sense to me. However, I do not have access to the
original stuff, so I had to read summarized versions.

I am mostly writing about the Achilles/Tortoise puzzle to see if others
see this the same way I see it.

I have periodically argued with local math professors that we do not
need an infinite series to "solve the puzzle" because there isn't any
puzzle in the first place. Early in general physics we routinely solve
this type of problem by finding the equations of motion for Achilles and
the tortoise, and simple algebraic analysis or graphical analysis of
these equations of motion show us who reaches the finish line first
(depending on their respective velocities, the overall distance of the
race, and the amount of head start given the tortoise).

The puzzle is simply a play on words. When the tortoise is pointing out
where he will be when Achilles gets to where the tortoise was, the
tortoise is simply pointing out the obvious fact that the tortoise will
be ahead of Achilles for all those times Achilles is behind. The way
the tortoise words the argument ends up analyzing only those portions of
the race that the tortoise is ahead, and excludes those portions of the
race that occur when and after Achilles passes the tortoise.

I would say the tortoise won by distraction. He caused Achilles to
focus only on the portion of the race when the tortoise was ahead (which
must occur if the tortoise gets a head start) and distracted Achilles
from seeing the portions of the race when Achilles is ahead (which must
occur if Achilles moves faster and the race distance is long enough).

Therefore it amazes me there are many web sites that claim the
Achilles/Tortoise puzzle continues to baffle scientists and
mathematicians. And it bugs me that math professors are teaching
students that an infinite series is the way to solve the puzzle, when
simple algebra and the equations of motion clearly describe the race and
the results. Am I missing something here?

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu