“In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.”
—Aristotle, Physics VI:9, 239b15
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. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.
The Illiad is a Greek epic poem written in approximately the 8th century B.C, attributed to Homer and written in dactylic hexameter. The poem, also known as the Song of Illium of Illion, narrates the war between the Greeks of the city-state Sparta and the Trojans of Troy. Helen, the queen of Sparta, has eloped with the Trojan prince Paris. Menelaus, her husband, sends his brother Agammemnon to lead the expedition against Troy. The poem takes place during the final year of the war, covering the final battle scenes in which the Greek warrior Achilles argues with Agammemnon, kills the Trojan warrior Hector, and is later killed by Paris' arrow hitting his only weak point, his heel. The Greek's mock defeat, and infiltrate the Trojan city walls through an empty wooden horse. Greek soldiers were concealed in the empty horse, and once the city walls were breached they surprise attack Troy, and win the war.