Waiting for Achilles

Visual Revelations

There is a famous paradox, attributed to the Greek mathematician Zeno, in which there is a race between the great hero Achilles and a lowly tortoise. In view of their vastly different speeds, the tortoise was granted a substantial head start. The race began, and in a short time Achilles had reached t­­­he tortoise’s starting spot. But in that short time, the tortoise had moved slightly ahead. In the second stage of the race Achilles quickly covered that short distance, but the tortoise was not stationary and he moved a little further onward. And so it was that this continued—Achilles would reach where the tortoise had been, but the tortoise would always inch ahead, just out of his reach. From this example, the great Aristotle, concluded that, “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.”

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