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
I used to have a lot of problems with Zeno's and related paradoxes, but there is an interesting point in Quantum Theory that makes it all easier to swallow.
Firstly, the statement above requires that every time interval and every distance interval is smaller than the one before it. Eventually at this rate, the distance interval drops to the order of the Planck scale (~10^-30 m), and Heisenberg's uncertainty takes over, telling us we no longer KNOW the exact position of each contestant, and there is therefore no validity to saying that one is ahead of the other, because they are actually both ahead and both behind at the same time! (Hey, nobody ever said quantum had to make sense!)
The same applies to any such problem related with distance or time: there actually IS a physical limit to how small something can be, or how short a time can be, and still be a definite value.
Just something to chew on...
Science to the rescue!
