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 nothing wrong with the situation.

Obviously, even though Achilles does have to keep moving, the time it takes him to do so after passing the first half is half the time it took to pass the previous half.

Let the total distance be 10m, and the speed be 1m/s.
Time taken = 5/1 + 2.5/1 + 1.25/1 + ... + 1/(1 * infinity)
Time taken = 10 seconds
If you were to say Achilles needed to run an infinite amount of evenly spaced segments, the time that he would take to run each segment would be (1/infinity)/speed = speed/infinity = a finite value.

Posted by Berry on 2003-05-10 02:53:10