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Dennis Lendrem
Dennis Lendrem
Making Data Make Sense
Posted in Business / Industries / Pharmaceuticals

The Paradox of Achilles and the Tortoise

Mar. 22, 2012 3:40 pm
Categories: R&D, Science
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
Aristotle, Physics VI:9, 239b15

There's an old joke about a mathematician and a statistician.

The joke is based on the Paradox of Achilles and the Tortoise.

In this paradox, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 yards, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 yards, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 yards. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.

And the joke?

It's a joke about approximation and pragmatism; a joke about theoretical and applied approaches.

In the family version of the joke the two are chasing a runner holding a $100 prize to the first person to catch them.

The mathematician explains to the statistician that they cannot overtake the runner with the prize and that the chase is futile.

Ignoring this explanation, the statistician continues with the chase calling back to the mathematician "Don't worry, I can get close enough."


This joke only works with certain groups each with different outcomes:

Mathematical Conferences: Never attempt this joke at a mathematical conference. They will understand it and you will be alienated for the rest of the conference. Mathematical conferences can turn ugly.

Logicians and Philosphers: They will understand the joke and spend the rest of the conference arguing about its fundamental premise.

Statisticians: This joke works well at statistical conferences and will render your listeners helpless with laughter.

This joke is not known to work with any other groups for it breaks the Third Law of Humour which states "Any joke must be shorter than the explanation."

(Or is it the other way round? I can never remember.)

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