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December 10, 2009

Dear Colleague:  

     When we ordinary people fantasize, it is all too often just daydreaming and wishful thinking. When a great scientist does, it may well be a disciplined flight of the mind at the end of which reality takes on a greater strangeness and beauty than it did before. What are the pre-conditions for such flight? They are exceptional curiosity, a temperament that favors the simple, a spirit of fun, and a keen aesthetic sense. Let me give an example of each.

      First, exceptional curiosity. Physicist Hans Bethe, when he was five years old, said to his mother while they were taking a walk, "Isn’t it strange that if a zero comes at the end of the number it means a lot, but if it is at the beginning of a number it doesn’t mean anything at all?" At age five, I could do simple sums by following the rules. With proper coaching, even a chimpanzee can do as much. Neither of us, however, will find the position of zero worth puzzling over. Our level of curiosity just doesn’t reach that level.

     Second, simplicity. Temperamentally, I appreciate complexity and richness in human works. I would enjoy a beautiful and ornate church service, for example. Not so, apparently, Galileo. When he was compelled to attend, he filtered out all the ritual and spectacle in order to concentrate on one of the sacred lamps that swung back and forth on its chain. He pondered over the forces at work, and decided that the motion depended on the length of the chain and on earth's force of gravity. He was able to express the relationship is a mathematical equation that gave physics students much pleasure in his time and in the succeeding centuries. At a practical level, Galileo’s formulation made it possible to make accurate clocks.

     Third, a spirit of fun, a delight in games. I never liked games of any sort, finding them artificial and a waste of time. But I know of bright children who liked nothing better than to make up rules and see where they led if logically and systematically pursued. Some of the greatest discoveries in mathematics and science are the result of this sort of game playing. My favorite example is Girolamo Sacchari. In 1733, in a spirit of sheer playfulness, he substituted Euclid’s axioms of parallels with the "nonsensical" axiom that through a given point two lines may be drawn parallel to a given line. From this start, he constructed a self-consistent non-Euclidean geometry that eventually gave birth to a whole constellation of geometries, including the Riemannian, which Einstein used in equations that led to the release of atomic energy.

     Fourth, a keen sense of beauty. A curious whim of the modern art world is to shun the word "beauty." To art mandarins of our time, "beauty" has come to mean the bland and the trivial. Banished by artists, "beauty" as a word of approval is now firmly installed among scientists. This isn’t really surprising, for scientists are after some sort of harmony in the chaos that is nature; and, obviously, the simpler and more elegant the harmony they find, the better they are pleased and the more likely they are to call it "beautiful." An unsuccessful theory is cumbersome, so full of arbitrary parameters that it threatens to approximate nature’s own chaos. Such a theory, it goes without saying, is not only useless but ugly.

Best wishes,

Yi-Fu