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Xenon Turtle and Achilles



allright guys and girls, maybe it's already on this forum somewhere?

this one is copyright by Zenon (or Zeno) roughly 400 B.C.

I use description from http://www.saliu.com/aporia.html since it's one of the shortest explanations.

Zenon made an extremely attractive art to prove that motion was not possible. He came up with a riddle that used Achilles as the main character. We know that the legendary hero was also known as the Quick-Foot Achilles, or Speedy Achilles. Really? Zeno questioned the speed of Achilles. I, Zeno, will prove that your speedy Achilles will never beat a tortoise in a running race!

Okay, your Achilles is faster than a tortoise, admitted Zeno. Therefore we must necessarily give the tortoise a long start. But here is the kicker, puzzled Zeno his audience. Achilles does reach the starting point of the tortoise. But when Achilles reaches that space, the tortoise would reach a farther position in space. Let's name it position 2. When Achilles reaches position 2, the tortoise would have reached a new position; let's name it position 3. When Achilles reaches position 3, the tortoise would have reached a new position; let's name it position 4. When Achilles reaches position 4, the tortoise would have reached a new position; let's name it position 5. And so on ad infinitum. Achilles can never pass the tortoise…

Here's the trick for you fellas. Zeno's riddle is as old as time, and I know you'll be discussing it here.

But the real question is, "What did Zeno prove?"

Have fun =)

oh, almost forgot. I've seen tons of explanations around the net, involving all science we know.

you do understand, though, that if question is easily comprehended even by small kids, the true answer is just as simple?

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Zeno proved that if you give the turtle a head start, even if it's only a nanosecond, achillies could never beat the turtle in any distance race. Achillies could never pass the turtle, because by the time that achillies would catch up to where the turtle was, the turtle would have moved on.

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