Ever since I read Douglas Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid, I’ve had the paradox postulated by Zeno of Elea (c. 450 B.C.) bouncing around in my head. To summarize the paradox:
Zeno’s Paradox may be rephrased as follows. Suppose I wish to cross the room. First, of course, I must cover half the distance. Then, I must cover half the remaining distance. Then, I must cover half the remaining distance. Then I must cover half the remaining distance…and so on forever. The consequence is that I can never get to the other side of the room.
What this actually does is to make all motion impossible, for before I can cover half the distance I must cover half of half the distance, and before I can do that I must cover half of half of half of the distance, and so on, so that in reality I can never move any distance at all, because doing so involves moving an infinite number of small intermediate distances first.
I knew there must be a solution, as we all do manage to move around quite handily, I just never knew what it was. Luckily enough, I managed to stumble across an explanation of the paradox and its solution today. Nifty!
(Via Jason Kottke)