Super Glossary

Zenos Paradox

Entertainment / Literature / Zenos Paradox: The name comes from Zeno of Elea (born c. 495-480 BCE). Zeno proposed four paradoxes in order to challenge accepted notions of space and time as defined in various philosophical circles. The term 'Zeno's Paradox' is usually applied to the paradox of the arrow or the paradox of Hercules and the tortoise, but the other two paradoxes are often lumped under the same designation. To illustrate a sample paradox, Zeno asks the audience to imagine the great athlete Achilles engaged in a race with a tortoise. The tortoise is given a head start of twelve feet or so in front of Achilles, and the race-track is a hundred yards long. When the race begins, Achilles begins charging ahead with a speed much faster than the tortoise's crawl. However, to reach the half-way point between his starting position and the tortoise's position, Achilles must spend half of his time reaching the midway point before he has covered half the distance. Then again, before Achilles can ever travel a quarter of the distance to the tortoise (the half-way point to the half-way point), he must spend half of his time covering that distance. Then again, according to traditional definitions of space and time, he must spend half his time traveling to reach the half-way point to that half-way distance, and so on, ad infinitum. No matter how fast Achilles runs, by the normal definitions of spatial and temporal distance, Achilles will never be able to catch up with the turtle because an endless series of 'half-way' points must be crossed first. In fact, any movement at all should be impossible because Achilles must cross an endless number of 'halfway' points before any motion can take place at all, each movement taking an infinitely smaller slice of time to do. Zeno's paradoxes perplexed mathematicians and logicians for millennia. It wasn't until Cantor developed the theory of infinite sets that the paradoxes could be fully resolved--but that idea only came about in the 1860s and 1870s. In literature, postmodern writers such as Umberto Eco, Italo Calvino, and postmodern films like Run Lola Run all use allusions to Zeno's Paradox to convey ideas about the absurdity of time and distance.
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