Interview with Dr.Abrahamson

The Tortoise and Achilles

Zeno of Elea (c. 450 BCE) is credited with creating several famous paradoxes, and perhaps the best known is the paradox of the Tortoise and Achilles. 

This paradox ca be only applied in the branch of mathematics, because its complexity cannot be understood in other ones, for instance, physics.

The paradox consist on a race between Achilles and a tortoise. At the beginning, the Tortoise asks Achilles to give her a small head start. Achilles, laughing, answers 10 meters, knowing for sure he will win even though the tortoise begins "x" meters ahead, in this case, 10. 

Once the race was going to start, Achilles, annoyed by the tortoise´s laugh, asked her: "How can you be so happy when you will lose for sure?" "Because I won´t, and I´m sure about it" answered the tortoise. "How come?" replied Achilles "Well look, if I start, for instance 10 meters ahead, How long will take you to catch me?" asked smoothly the tortoise." One or two seconds, I mean, almost nothing" answered in a brave way Achilles."but... think about it, in these 2 seconds, I will not be there anymore, I´ll be ahead again." "Well, then I will catch you again in less than a second""but again... I will not be there, maybe 1 or less than one steps from you, but still ahead; therefore, I´m sorry Achilles, but you will never catch me" Achilles, surprised, answer"Yeah... but... but... oh no, you are right, as always" replied in a sad way.

This paradox obviously cannot happen in real life, but demonstrates that mathematics rules applied in non-mathematical situations can give us strange results; in this case, it give us one of the principals of an infinity limit.