Zeno’s Paradox Solution

Achilles and the Tortoise.

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Achilles will overtake the tortoise at time= 1.111(repeating)

Achilles gives the tortoise a ten mile head start. Achilles travels at 10 mph. The turtle travels at 1 mph. After one hour Achilles has caught up to the original starting point of the tortoise. The tortoise has travelled a further mile from his starting point. It will then take a further time to reach that distance; afterwards of which the tortoise has travelled yet further and so on.

If the speed of Achilles is 10 mph and the speed of the tortoise is 1 mph, Achilles will catch up to the tortoise slightly after one hour and six minutes. (1.111 hours)

Looking at the wrong parameters (in this case, discrete distance and segmented time) results in the experience of paradox. By examining only a single parameter (time), the solution is elementary.

Achilles =10T

Tortoise = 1T+10

10T=1T+10

9T=10

T=10/9

T=1.111~