The story goes that if Achilles ( the famous hero from The Iliad ) were to race a tortoise , but the tortoise were given a head start , Achilles could never catch the tortoise no matter how fast or how long Achilles ran . In the paradox of Achilles and the Tortoise , Achilles is in a footrace with the tortoise . Achilles allows the tortoise a head start of 100 metres .