Achilles and the Tortoise(s)

The inestimable Dorothy Lamb has yet again been doing her bit for our outreach effort here in the School of Mathematical and Physical Sciences at the University of Sussex. Charged with the task of coming up with some props to explain Zeno’s Paradox to schoolchildren. One famous version of this paradox features in the form of a story about Achilles and the Tortoise:

Achilles, the fleet-footed hero of the Trojan War, is engaged in a race with a lowly tortoise, which has been granted a head start. Achilles’ task initially seems easy, but he has a problem. Before he can overtake the tortoise, he must first catch up with it. While Achilles is covering the gap between himself and the tortoise that existed at the start of the race, however, the tortoise creates a new gap. The new gap is smaller than the first, but it is still a finite distance that Achilles must cover to catch up with the animal. Achilles then races across the new gap. To Achilles’ frustration, while he was scampering across the second gap, the tortoise was establishing a third. The upshot is that Achilles can never overtake the tortoise. No matter how quickly Achilles closes each gap, the slow-but-steady tortoise will always open new, smaller ones and remain just ahead of the Greek hero.

Anyway, we now have a splendid knitted Achilles along with not one but three lovely tortoises…DSC_0035

Achilles is a bit short in the leg, although I suppose that doesn’t necessarily mean that he can’t be fleet of foot, and we had to prop him up against the wall lest he should heel over, but nevertheless I think these are great. Could this be the next big thing in toys for mathematically inclined students?

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