Friday, December 3, 2010

Zeno's Paradox of Motion

Consider a runner on a track who will run 400 meters.  Before he can run 400 meters, he must pass a halfway point (200 meters).  From there, he must again pass another halfway point (100 meters).  In the final hundred meters, he must again halve the difference.  In fact, from any point on the track, he must necessarily halve the distance between that point and the finish line.  However, if he has infinitely many points he must pass before getting to the 400 meter mark, he can never get there.

Note that the 400 meters originally selected is arbitrary, and this would be true of any distance no matter how large or small.  The more interesting case comes when you consider shrinking this distance down to a centimeter, a millimeter, and smaller.  The result is that motion is itself completely impossible.

Can that be?