Achilles And The Tortoise


Another striking paradox is the one called Achilles And The Tortoise, enunciated by the Greek philosopher Zeno of Elea (ca. 490–430 BC) to suggest, as an argument of absurdity or contradiction (reductio ad absurdum), that motion is nothing but an illusion.
The thought logic, as recorded by Aristotle is that “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.” In the paradox, Achilles is in a footrace with a tortoise. Achilles allows the tortoise a head start of 100 meters, for example. 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 meters, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. 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.

Zeno’s paradox has engaged the attention of mathematicians, philosophers, and logicians through the ages. Bertrand Russell offered his own version of the elusive solution. In 1979, Douglas Hofstadter, American cognitive scientist, wrote a book titled ‘Gödel, Escher, Bach’, which was based on an analogous logical paradox in Lewis Carroll’s ‘What the Tortoise Said to Achilles (1895).’ There, Hofstadter sought to develop a connection between Zeno’s paradox to Gödel’s Incompleteness Theorem, to show that Zeno’s conundrums represent a philosophy of human mind which gets incorporated into all application systems, including the ones of artificial intelligence.

@ Yeshwant Marathe


(Thanks to Prashant Naik for his inputs)

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Hemant Marathe

2 months ago


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