The dichotomy paradox leads to the following mathematical joke. 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
apart at time 0, they are
at
,
at
,
at
, 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.
From the source.
The dichotomy paradox is:
“That which is in locomotion must arrive at the half-way stage before it arrives at the goal.”
—Aristotle, Physics VI:9, 239b10
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