Remember the busy Bee? The one that kept flying from the bicyclist to his home and back as he approached it?

Well, at the instant when the person finally got to his house, which way was the Bee facing? (Assume that the Bee's turns are instantaneous - that it can go from facing the house to facing the cyclist in no time.)

Surely the assumption that the bee makes an infinite number of turns, is faulty? It's equivalent to the paradox that says that in undertaking a journey, one covers half the distance, then half the remaining distance, then half the distance remaining after that, and so on, and that since the series 1/2, 1/4/, 1/8, 1/16... is infinite, motion is impossible. The bee will NOT make an infinite number of turns because motion does not work like that. After ten minutes the bee will be facing one way or the other. Or will be dead from exhaustion.

There is also a confusion arising from the use of a bee. Since the bee has a finite but non-zero length, it doesn't fit the mathematical abstraction.  The puzzle as stated attempts to pass off the bee as a point object, which (1) is simply false, and (2) if it were true, would render the puzzle meaningless as a point object doesn't "face" in any direction at all.

Posted by Jenny Turner on 2004-06-05 04:39:36