Suppose that the swift Achilles is having a race with a tortoise. Since the tortoise is much slower, she gets a head start. When the tortoise has reached a given point a, Achilles starts. But by the time Achilles reaches a, the tortoise has already moved beyond point a, to point b. And by the time Achilles reaches b the tortoise has already moved a little bit farther along, to point c. Since this process goes on indefinitely, Achilles can never catch up with the tortoise.

How can this be?

Taken from - http://members.aol.com/kiekeben/zeno.html

Although the ancients considered this a paradox, it is really a matter of perception or of defining the problem

Just as the distances keep getting shorter, so too, do the times involved. Just as the sum of Achilles' advances always fall short (by ever decreasing amounts) of the sum of the tortoise's advances plus its head start, the sum of times of those advances always falls short of a certain figure (the time it takes for Achilles to overtake the tortoise calculated by a more conventional approach to the problem.

As long as the time-frame is confined to before that moment, it is true that Achilles cannot catch the tortoise.

Posted by TomM on 2002-11-22 21:22:04