Zeno's Paradox

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
gut@sebank.se

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