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.)
This puzzle is the same as Thomson's lamp, where he turns it on at one second, off half a second later, on a quater of a second later, and so on. Is it on or off at two seconds.
The answer is that the question is meaningless in the bounds of the question, because the instructions for what he, or the bee, does are given up to the very end, but not at the very end. The sequence 1 + 0.5 + 0.25 *tends* to 2, and in calculus is equal to 2, but you cannot say what happens *at* 2.
This paradox is basically similar to asking if the "last" integer is even or odd  the question doesn't make sense.

Posted by sam
on 20030906 15:54:13 