Date: 10/19/95 at 7:42:10 From: Gut, Thomas Please help me with an answer to the following problem. At eleven o'clock I put ten balls numbered 1,2, ...10 in a box and immediately take out the ball numbered 1. At eleven thirty I put balls numbered 11 through 20 into the box and take out the ball numbered 2. At eleven forty-five I put balls numbered 21 through 30 into the box and take out the ball numbered 3. This continues at time intervals that are half of the preceding one. How many balls are in the box at twelve o'clock? Kindest regards, Thomas Gut firstname.lastname@example.org
Date: 11/5/95 at 16:41:45 From: Doctor Josh Subject: Re: (no subject) This is Zeno's Paradox. Zeno is a dead guy who once argued with Aristotle (another dead guy) about whether motion is continuous or discrete. Zeno argued that it was discrete because of the fact that to get anywhere, you have to go half that distance first. Then you have to go half that distance,and half that distance, and so on. Accepting this as the case, he argued that you would never get there. It turns out that the series, 1/2 + 1/4 + 1/8 + 1/16 + ... converges to 1. Anyway, to answer your question... Your problem basically boils down to adding 9 balls to your box at every half point. After a while, you would have a lot of balls, but you would never reach twelve o'clock (a clever ploy often implemented by the numbered ball industry). This question touches on the basic fabric of time - is it discrete or continuous? Let us know what your answer is. -Doctor Josh, The Geometry Forum
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