Thursday, January 5, 2012

New Scientist TV

Math in a Minute: How a tortoise can win a race

Move over Achilles, a tortoise could outrun the Greek hero given a head start. This animation from The Open University explores the paradox proposed by the Greek philosopher Zeno of Elea.
Suppose Achilles and the tortoise run at a constant speed with the slow tortoise given a slight advantage. While Achilles can cover the lead quickly, by the time he reaches his competitor's starting line the tortoise has lumbered forward a short distance. While this advantage narrows as the race goes on, Achilles will always have further to go at any point the tortoise has passed.
Considered further, the puzzle even discredits movement itself. The gap between the contenders is divided an infinite number of intervals, which Zeno argued is impossible to overtake. The puzzle perplexed mathematicians for centauries until Georg Cantor's work on infinite series helped unravel it.
If you enjoyed this video, explore other paradoxes in our animated series including the hotel infinity paradox.

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