Measure for Measure: A Musical History of Science
Thomas Levenson
Simon & Schuster, $25

Science and music both need instruments. From this common thread, Thomas Levenson weaves a fascinating tapestry, a colorful panorama of scientific and musical development over three millennia, from Pythagoras and the alchemists' workshops to Yo Yo Ma and the Media Lab at MIT. Despite its scope, this is no dry tome of purely academic interest; it is full of wonderful stories, biographical sketches and accounts of how things work. Levenson is so curious and enthusiastic about his subjects that he excites a reader's interest, whether telling us how Ktesibios of Alexandria built the first organ around 270 b.c.-he adapted a brass water pump he'd invented to put out fires-or why computers, no matter how powerful, will never be able to predict the weather beyond next month.

This is an eclectic history, more subjective than comprehensive, aimed more at showing how scientists and composers think about their pursuits than at cataloguing their works. It is filled with anecdote, obscure detail, curious digression, giving a sense of how history really happens. Of the history of eyeglasses, for instance, we learn that "Petrarch acquired his pair in the last decade of his life, sometime in the mid 1360s." But 14th-century men of science, devoted to revealing God through observation of nature, were suspicious: "Sometimes, given poorly made lenses, eyeglasses would distort shapes, or change the colors an unaided eye would detect. The conclusion was obvious: eyeglasses deceive the eye and degrade the central function of vision-to see the truth directly. Such trickery belonged to conjurers, not to those whose business it was to trace the evidence of the divine through science."

The use of science to know the true, or divine, order of things can be traced to Pythagoras in the sixth century b.c. "The discovery that transfixed the Pythagoreans was that the octave and other intervals that like the octave sounded harmonious and smooth occurred not simply by chance but as if by design. Pythagoras was credited in antiquity with the realization that there was a deep connection between mathematics, numbers and sound: he discovered that the fundamental intervals in music were created by the perfect ratios of the lengths of string or pipe used to generate the notes." In this observation the Greeks saw a universe, describing the orderly movements of the planets in numbers that became "the music of the spheres." "The Pythagoreans were not scientists; they sought magic in numbers," Levenson writes. "But still, here is where science begins."

Before emerging in anything like its modern form, science was shaped by the philosophy of Aristotle, the occult rules of alchemy, and the authority of the church. Levenson sees modern science emerging in the mid-13th century, in Paris, where an Oxford-educated Franciscan, Roger Bacon, posited that questions about nature could be answered by observation, not only by recourse to the Bible. If one wanted to know, for example, whether both parts of a grafted plant retain their individual souls, one could conclude that they do by looking at the fruits they bear. "Bacon's inspiration was to recognize that knowledge of God could be found within the book of nature," Levenson writes.

Bacon studied optics and made some small magnifying lenses of glass droplets, but it took several centuries before Galileo's telescope and Leeuwenhoek's microscope shattered the oldways of seeing. While Galileo's use of the telescope to find new facts in nature brought down the wrath of the church in Rome, Leeuwenhoek was born in the more tolerant Netherlands in the same year (1632) that the Inquisition tried and condemned Galileo.

Leeuwenhoek's investigations of the unseen microscopic world redefined the nature of truth. "The medieval eye, Roger Bacon's eye, was passive," Levenson writes. "Bacon looked at what passed before his eyes and stopped when he had seen enough to recognize the hand of God in nature." Leeuwenhoek became an experimentalist as well as an observer, entering actively into the world his instrument exposed.

With Isaac Newton, the scientist's search for order in nature reached new heights. With a set of mathematically expressed Laws of Nature, Newton could survey the Universe and hope to see the design of God, the "First Cause." But, as Levenson points out, Newton's God was to be found in nature and its laws, not any longer through them, and this brought about a profound change in science itself: "Medieval men could stop when they had achieved their object, when they had seen enough. The new, modern kind of scientist had no such luck; [this science] . . . required them to continue to seek new evidence that would confirm or disprove their ideas . . . with no end in sight."

Newton and his contemporaries had achieved a method of knowing nature that seemed elegant and certain. In music, this sense of order was brought to perfection in the works of Johann Sebastian Bach. But just as the 19th century would replace Bach's sublime order with Beethoven's clashing harmonies and discords, the certainty of Newton's order was to give way to a new mathematics and science of uncertainty, quantum theory and chaos.

The scope of change is shown by Levenson in two revealing anecdotes. Early in the 19th century, the French astronomer Pierre Simon de Laplace predicted that science would "embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom." And when asked by Napoleon why he had left God out of his equations, Laplace responded, "I have no need of that hypothesis." But by the end of the century, the French mathematician Henri Poincare would conclude, "Not only science cannot teach us the nature of things, but nothing is capable of teaching it to us, and if any god knew it, he could not find the words to express it."

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.