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

Assume that Achilles gives the tortise a 1m head start (measure from the front of Achilles and the back of the tortise) and moves at 1m/s. Assume the torise moves at .5m/s. In 1 second the two bodies are .5m apart. (1/2 the original distance). In another .5 seconds, the two bodies are .25m apart (1/2 the new distance). Certainly time can be sliced infinitely small such that the distances keep decreasing by a factor of 1/2. But notice under these conditions, the summation of time this takes approaches 2s, never at or above. Logic allows us then to consider what happens at the instant of 2s (as does the simple calculation of the veolcity and distance). The distance between the 2 is 0m and thus Achilles wins (horray!)

--Graatz

Posted by Jeff on 2003-12-23 21:00:42