A Story about John von Neumann |
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The following problem can be solved either the easy way or the hard way. Two trains 200 miles apart are moving toward each other;each one is going at a speed of 50 miles per hour. A fly starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown?
The fly actually hits each train an infinite number of times before it gets crushed,
and one could solve the problem the hard way with pencil and paper by summing an infinite
series of distances. When this problem was posed to John von Neumann, he immediately replied, "150 miles." "It is very strange," said the poser, "but nearly everyone tries to sum the infinite series." "What do you mean, strange?" asked Von Neumann. "That's how I did it!" |