THE RACE COURSE PARADOX

Greek Philosopher Zeno

The ancient Greek philosopher Zeno proposed a set of philosophical problems he called paradoxes. One of the most famous is the Race Course Paradox.  It was posited as follows:

“Suppose Atalanta wants to walk to the end of a path. Before she can get to the end, she must get half-way to the end. And before she can get to the end from the half-way point, she must first get half-way to the end from there. And so on, infinitely. According to this reasoning, Zeno said, it would be impossible for Atalanta to ever get to the end of the path. No matter how close she got to the end, she would still have to first go half-way.”

Democritus proposed that the universe was composed of tiny indivisible particles called atoms and reasoned that when Atalanta reached only one atom from the end of the path, the distance could no longer be divided in half so, the paradox was solved!  Although this solution was challenged, it remains relevant because it corresponds more to modern science than any such theory of the ancient world.

Since I’ve earned degrees in both mathematics and Industrial Engineering, I recognized the paradox from a different perspective.  It seems there was a young mathematician and a young engineer who were both vying for the hand of a beautiful maiden that couldn’t chose between them.  After much bickering, they solicited her father to settle the issue.  The father liked both of the suitors so, he proposed drawing a line in front of his young daughter and challenged the two of them with the Race Course Paradox. 

The mathematician immediately threw up his hands and announced that “I know of this paradox and I give up as it cannot be resolved!”  The engineer thought about it for a few minutes and began walking towards his future wife.  When the other young man questioned his strategy, the engineer announced that “I may not get to the very end, but I’ll get close enough for all practical purposes.”

The young woman’s father welcomed him into the family!

P.S.

I’ve learned over the years that it takes significantly more energy, cost and effort to attempt perfection when good enough will do quite nicely, thank you.