Poincare had earned the right to say this, as it were, by proving mathematically that Newton's equations for planetary motion, while they worked for Earth and Moon (which was as far as Newton took them) could never work for even three celestial bodies, let alone the whole planetary system. "We cannot know all the facts," Poincare argued, "and it is necessary to choose those which are worthy of being known."
Scientists and composers of music alike, Levenson says, are still engaged in the Pythagorean search for abstract order-whether scientifically discovered in nature or invented by the composer's mind. There has seemed to be a great difference between these kinds of order, between discovery and invention, reality and imagination, truth and beauty. But the heart of Levenson's story is the slow and steady erosion, since Newton, of this clear distinction.
Poincare's words were soon followed by a recognition among this century's physicists and philosophers that nature's secrets were only selectively-and subjectively-available to us. Einstein's relativity tied knowledge to an observer's particular perspective. Heisenberg's uncertainty principle showed that one could never know both the position and the velocity of an atomic particle, for in measuring one you altered the other. Similarly, it was found that light appears as a wave or a particle depending on how it is measured.
All of this, Levenson suggests, was implicit in the early triumphs of Galileo and Leeuwenhoek. "Telescopes and microscopes," he writes, "do not simply extend human sight. They narrow it, confining the field of view. Leeuwenhoek, squinting at the microbes swimming in the water at Berkelse Mere, could see a city in a single drop, but not the pond itself."
Ultimately, this kind of observation leads to a vanishing point, the point where we can't know everything and must choose what's worth knowing. And here Levenson sees the deepest connection between science and music. The test of a piece of music is its beauty; in a universe where truth depends on our choice of facts, this may also be the best test of a scientific theory.
To Einstein, Levenson reports, a theory could be too beautiful to be false: Einstein's most famous epigram was prompted by the question of what he would do if the measurements of bending starlight at the 1919 eclipse contradicted his general theory of relativity. He said, "Then I would feel sorry for the good Lord. The theory is correct."
Paul Trachtman is a freelance writer based in rural New Mexico.