Zeno’s paradoxes

Episode #3 of the course “Brain-twisting paradoxes”

Zeno’s paradoxes are a collection of philosophical problems believed to have been created by Greek philosopher Zeno of Elea in the 5th century BC. The paradoxes illustrate Parmenides’ doctrine that the belief in plurality and change is mistaken. In other words, contrary to the evidence of one’s senses, motion is nothing but an illusion. The most famous paradox is that of Achilles and the tortoise.

The paradox starts by posing a simple yet seemingly impossible question: How could a tortoise beat the legendary Greek hero Achilles in a race? Zeno first provides the assumption that the tortoise would be given a head start. Once the race starts, Achilles would have to gain back the ground he lost by the head start. This wouldn’t take very long, but even in that short amount of time, the tortoise would have moved up even more, thus creating more ground for Achilles to cover. Then, in the time Achilles took to make up this new ground, the tortoise moves ahead even more. Zeno proposes that this goes on and on forever, never allowing Achilles to overtake the tortoise.

Taken to an extreme, this paradox shows that movement is impossible, simply because while you “move,” so does everyone and everything else, thus creating no net change in your position. Even if this point is dismissed (i.e. movement is possible), what Zeno’s paradox showed was how something finite can be divided an infinite number of times. This concept is still used today in the finance world to work out payments such as mortgages and other loans.

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