All entries for Monday 30 July 2007

July 30, 2007

The dichotomy paradox

A mathematician, a physicist and an engineer were asked to answer the following question. A group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are then instructed to advance toward each other by one quarter the distance separating them, every ten seconds (i.e., if they are distance d apart at time 0, they are d/2 at t=10, d/4 at t=20, d/8 at t=30, and so on.) When do they meet at the center of the dance hall? The mathematician said they would never actually meet because the series is infinite. The physicist said they would meet when time equals infinity. The engineer said that within one minute they would be close enough for all practical purposes.


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