Zeno's paradox

Zeno of Elea was a philosopher with a wicked imagination, and he made up a puzzle which can be simply described like this. Suppose you have a hundred-metre race between a man called Achilles and a tortoise. Assume that Achilles runs ten times as fast as the tortoise, and that he gives the tortoise a ten-metre ‘start’.

Zeno said that Achilles can never catch the tortoise for while the man runs the first hundred metres, the tortoise waddles ten metres, and is still ahead. The man runs the extra ten metres, but the tortoise gains an extra metre.

As the man sprints desperately across that metre, the tortoise sneaks a further tenth of a metre, and while Achilles is lunging across that tenth of a metre, the tortoise drifts another centimetre, and so the human can never catch the tortoise. The same argument can be used to show that a thrown spear can never reach its target!

Zeno’s aim was to prove that something we can see happening is impossible, from which it follows that since we can see the impossible happening, our senses must be faulty. In other words, his paradoxes were designed to make people think. Later, Aristotle would argue against Zeno’s ideas, and Zeno’s assumption that space and time were infinitely divisible would make Democritus try to resolve the problem by suggesting that matter was not infinitely divisible, finally coming up with the idea of atoms—and all because Zeno believed the senses could not be trusted —because even though Zeno had proved that Achilles could never catch the tortoise, we know that in real life, he can!

Other paradoxes can be more fun...

That is to say: to be continued