Mathematical History: Zeno’s Paradoxes
Toby Evans
Zeno was an Italian Mathematician, he was born in about 490 BC and died around 425 BC but during his brief life he made some great discoveries. Since he lived so long ago, we know little about him; however we do know that he was a philosopher. Many of his paradoxes are known to us today, and in this article, I will explain the paradox of Achilles and the Tortoise. Achilles was a legendary Greek hero; he was a terrific fighter and could run very quickly, whereas a tortoise is an animal known for being slow.
Zeno
Zeno stated that if the tortoise was given a small head start, then despite Achilles being so much faster, he could never catch up and overtake. The logic behind this was that Achilles would have to cover the distance the tortoise had already moved to catch up with it, however by this time the tortoise would have moved on. Hence Achilles would then have to cover that additional distance too, and, whilst doing this, the tortoise would move on even further. This cycle would continue endlessly, with the tortoise always moving further away. Whilst the gap might narrow, the tortoise would always win this race.
The conclusion is that anything, given a head start and no matter how slow it is going, will inevitably beat a faster object, for example a formula one car would lose to a snail if the snail starts the race
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