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

There is a mathematical explanation to this seemingly unexplainable paradox. The paradox arises if we think that an infinite set of space fragments must be infinite (that is, the movement of the tortoise when Achilles has reached a certain point). But that is not true, since there is a limit for that, since the amount of space that the tortoise walks tends to zero as time increases. It is interesting to note that this paradox has puzzled scientists for centuries and it was only solved relatively recently.

Posted by Gustavo on 2004-06-15 11:11:33