Thursday, June 14, 2012



At times, people have accused me of being a smart guy.  I always demur, and point out MY idea of a smart guy: the Hungarian-American polymath John von Neumann (1903 -1957).

Von Neumann made important contributions to dozens of mathematical fields.  He is considered one of the founders of game theory, continuous geometry, operator theory, and computer science.  He could do computations in his head at lightning speed, and his photographic memory allowed him to quote from any book he ever read (in multiple languages)!

He was one of the first professors at the Institute for Advanced Studies in Princeton, New Jersey.  He worked on the Manhattan Project and was credited with coming up (and naming) the Cold War theory of Mutually Assured Destruction (MAD).

On the other hand, he was a terrible driver (he liked to read books while driving) and enjoyed dirty jokes in Yiddish.  Nobody's perfect. 

Here's the usual story about just how smart von Neumann was.  It's a famous problem called "the fly puzzle" and there are two ways to solve it - a quick easy way and a longer hard one.  Here's the version that's on Wikipedia:

Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 mph. At the same time a fly that travels at a steady 15 mph starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover? The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann, "All I did was sum the infinite series."
I've also heard that von Neumann took a minute or two to solve this puzzle - which is quite natural, since he was computing the sum of the infinite series.  The person who posed the puzzle to him assumed that he had figured out the easy way, since no normal mathemetician could have done the long way in such a short time, without pencil and paper.  But von Neumann could, and did.

Even when I was in college and studying calculus, it would have taken me a whole blackboard and the better part of an hour to solve this via summing the infinite series.  (Nowadays I couldn't do it with a gun to my head!)

You want to accuse someone of being smart?  John von Neumann was a smart guy!

The above photo may be subject to copyright. 

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