Saturday, March 13, 2010

Can you reach anywhere?

Today I was reading something and Zeno of Elea's paradox drew my attention. It is quite interesting, hold your breath and read on. Wikipedia says "Zeno's paradoxes have puzzled, challenged, influenced, inspired, infuriated, and amused philosophers, mathematicians, physicists and school children for over two millennia. The most famous are the so-called "arguments against motion" described by Aristotle in his Physics."

This arguments against motion can be descibed as:
"That which is in motion must arrive at the half-way stage before it arrives at the goal. "
-Aristotle, Physics VI:9, 239b10

What does it mean? Suppose my friend JD wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a fourth, he must travel one-eighth; before an eighth, one-sixteenth; and so on. As he must travel an infinite number of distances, he can never catch the bus. This argument is called the Dichotomy because it involves repeatedly splitting a distance into two parts. If this is not true than infinity is something that can practically yield "finitism". If this is true there is no point moving.

What do you think?