Achilles and the Tortoise

David Cowles

Aug 23, 2021

You’ve no doubt heard about the race between Achilles and the Tortoise. My 8 year old grandson has so I assume you have too. It took place 2,500 years ago. The tortoise challenged Achilles (an anachronism in itself) but asked Achilles to give him a head start (1/2 the distance to the goal line). Supremely confident , Achilles agreed.

You’ve no doubt heard about the race between Achilles and the Tortoise. My 8 year old grandson has so I assume you have too. It took place 2,500 years ago. The tortoise challenged Achilles (an anachronism in itself) but asked Achilles to give him a head start (1/2 the distance to the goal line). Supremely confident , Achilles agreed.


While the bookies were taking bets, a philosopher named Zeno proved, using just the universally accepted assumptions of ordinary math and logic, that Achilles not only would not win the race but could not win it. I won’t repeat the proof here…maybe another time.


Where the betting had overwhelmingly favored Achilles, now it swung over to the tortoise. The race began and ended in seconds: Achilles 1, Tortoise 0. You can imagine that Zeno’s neighbors were none too pleased.


Was Zeno’s argument flawed? In my opinion, it was not! So, what went wrong? Zeno hadn’t proved that Achilles would lose the race; what he had proved was that there is something terribly wrong with our logical and mathematical assumptions.


More on Zeno in later posts.

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