A Race you Cannot Win

Monday, 12 July 2010   |   Creative Thinking

Zeno of Elea proposes a paradox in which it is impossible to finish a race.  But how can this be?

Let's say you have to run 1km.  What we do is divide this distance in half.  It will take you a period of time to run 500m.  Now we will half this again.  It will take you another period of time to run the next 250m.  And so we continue.  It will take you another period of time to complete the next 125m.  The thing is,  we can keep doing this.  For whatever distance is left we can divide it in half and add the period of time it takes to cover this to your total time thus far.  We can keep dividing however so we keep adding time but you never reach the finish line as we are always dividing the distance left in half.

You will never reach the finish line.  How can this be?

Can you think of any way you can prove or disprove this situation?