CREDOS: Zeno’s paradox — I

According to Hindu beliefs, a second for Lord Brahma is a hundred thousand years for us mortals. On the other side of the spectrum, Austrian scientists claim to have measured the shortest span of time yet, one hundred attoseconds or 10-18 seconds. If 100 attoseconds is stretched to last one second, one second would last 300 million years on the same scale. From metaphysical to mechanical dimensions, the measure and understanding of time occupies a vast range. Around the 5th century BC, the Greek philosopher Zeno of Elea brought this property to light in a number of paradoxes that have puzzled, challenged and influenced many.

Zeno presents a scenario in which Achilles races against a pondourous tortoise. Achilles being the swiftest of all Greeks gives the tortoise a head start of a hundred meters. Zeno claims that Achilles has to run to where the tortoise started before he catches up with him. However, during this time interval the tortoise will move a short distance ahead say one meter. It will take Achilles some more time to reach this new position, but during this time interval, the tortoise will have moved further ahead say ten centimeters. This mathematical halving of distance can be continued infinitely. Thus, whenever Achilles reaches the point where the tortoise was, he still has a bit more to go before catching up. Thus, contrary to common sense Zeno claims that Achilles can never catch the tortoise. This is the paradox.