You, you of all people, should have known that Zeno* proposed a number of paradoxes about the impossibility of motion, a subject that greatly occupied philosophers of his day.

His most famous paradox tells how Achilles, champion among athletes, had a race with a tortoise. Racing a tortoise was, perhaps, better than being killed by one, as happened to poor Aeschylus (an eagle dropped it on his head). Achilles, confident of winning magnanimously gave the tortoise a hundred yards start, but by the time he got to the place where the tortoise had started, it had crawled forwards three yards.

By the time Achilles reached this point, the tortoise had covered three inches. While Achilles did three inches, the tortoise had moved on three thirty-seconds of an inch. And so on. In this way Zeno showed that however hard he ran Achilles could never quite overtake the tortoise, because it would always be slightly ahead of him. His mistake was to have given the tortoise a head start in the first place.

Anyone can tell you that Achilles would actually have outstripped the tortoise and won the race easily. Perhaps Zeno’s paradox really illustrates the impossibility of philosophers. Yet, you sit at your door in the cool of a summer’s evening and dream about the philosophy of the ancients.

*Zeno of Elea, fl. 5th century BC.

George Learmonth