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# There is a legendary paradox that involves a Greek warrior and a tortoise. Who is this mathematical paradox attributed to, and how can it be alternatively described using a lamp switch?

Question #58216. Asked by peasypod. (Jul 07 05 6:15 PM)

lanfranco

I think you're talking about one of Zeno's Paradoxes, which involves Achilles and a tortoise:

"The slower when running will never be overtaken by the quicker; for that which is pursuing must first reach the point from which that which is fleeing started, so that the slower is always some distance ahead ... "

I never have figured this one out:

http://plus.maths.org/issue17/xfile/

 Jul 07 05, 6:37 PM
peasypod

Nice One, yes, based on the indivisibility of time.

Interestingly Zeno was born in Elea, later called Velia by the Romans, in southern Italy. (What was Magna Graecia, of course.)

 Jul 07 05, 6:55 PM
someothername

Thompson's Lamp is controlled by a being with supernatural powers who likes to play with this lamp as follows. First, he turns it on. At the end of one minute, he turns it off. At the end of half a minute, he turns it on again. At the end of a quarter of a minute, he turns it off. In one eighth of a minute, he turns it on again. And so on, hitting the switch each time after waiting exactly one-half the time he waited before hitting it the last time. Applying the above discussion, it is easy to see that all these infinitely many time intervals add up to exactly two minutes. So given an infinite series, at the end of two minutes is the lamp on or off?

 Jul 07 05, 7:18 PM
BillyWhiz

A similar paradox "proves" that you cannot be hit by an arrow shot at you.

Any volunteers?

 Jul 09 05, 2:38 PM
lanfranco

You mean the reasons why the arrow must always be at rest?

Here's the whole collection:

 Jul 09 05, 3:22 PM

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