Monday, April 24, 2017

Achilles’ Torch

          Achilles’ Torch

This paradox combines the Paradox of Dichotomy with the Paradox of the Parity of Infinity.

Achilles, swiftest of mortals, opens the Olympic Games by bringing a torch to light the Olympic flame. Unfortunately he is too swift for his torch, and it flickers due to the speed of his passage. For the first 1/2 stadia of his run, his torch is lit; for the next 1/4 stadia of his run, it is out; ; for the next 1/6 stadia, it is lit; for the next 1/16, it is out; and so on indefinitely.

Achilles’ torch flickers infinitely many times by the time he reaches the Olympic flame. By that time, is his torch lit or out?

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