Saturday, February 23, 2008

Great Unknown Scientists #1

John Von Neumann was an influential mathematician and physicist in a wide variety of fields, basically all the ones I'm interested. To quote Wikipedia, he
made major contributions to a vast range of fields[1] including set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics and game theory, computer science, numerical analysis, hydrodynamics (of explosions), and statistics,
Truly, a staggering amount of fields. His 1944 work, with Morgenstern, Theory of Games and Economic Behavior , basically founded what we call game theory. Game theory is truly everything. Sports, poker, evolution, economics, warfare, it describes everything we do, and is truly one of the most powerful theories of modern society. He contributed heavily to the Manhattan Project, and his genius added greatly to it.

Have you heard of a computer? Probably, since you're reading this. What you might not know is that your processor is almost certainly based on the Von Neumann architecture . He also contributed to the development on the Monte Carlo method, the idea that random algorithms could provide performance without complicated ideas being needed. Finally, Knuth credits him as the creator of the Merge sort, which is not as impressive as say, Quick Sort, but it was 15 years before, and as far as I can tell, the first sorting algorithm with O(n*lg(n)), and almost certainly the first to be implemented. To a computer scientists, this is incredible.

He was also know for his personality and wit.
He once reported one of his many car accidents in this way: "I was proceeding down the road. The trees on the right were passing me in orderly fashion at 60 miles per hour. Suddenly one of them stepped in my path.

Finally, one of my favorite stories ever, possibly apocryphal , is
two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time a fly that travels at a steady 15 m.p.h. 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."

1 comment:

Jeff Matzke said...

As an evolutionary biologist in training, I have great respect for this man. Without his contributions to game theory, our understanding of animal behavior would be severely limited.