The Clockwork Universe by Edward Dolnick Read Free Book Online

circle; at an angle and you get an ellipse; parallel to one side, a parabola. Euclid had studied circles, ellipses, and parabolas because he found them beautiful, not useful. (In the Greek world, where manual labor was the domain of slaves, to label an idea “useful” would have been to sully it. Even to work as a tradesman or a shopkeeper was contemptible; Plato proposed that a free man who took such a job be subject to arrest.)

    Nineteen centuries later, Galileo found the laws that govern falling objects on Earth. After he showed the way, the discoveries came in a flood. Rocks thrown in the air and arrows shot from a bow travel in parabolas, and comets and planets move along ellipses exactly as if a colossal diagram from Euclid had been set among the stars. The universe had been meticulously arranged, Galileo and Kepler and Newton demonstrated, and the arrangement was the work of a brilliant geometer.
    Then came an amazing leap. It was not simply that one aspect of nature or another followed mathematical law; mathematics governed every aspect of the cosmos, from a pencil falling off a table to a planet wandering among the stars. Galileo and the other seventeenth-century giants discovered a few golden threads and inferred the existence of a broad and gorgeous tapestry.
    If God was a mathematician, it went without saying that He was the most skilled of all mathematicians. And since nature’s laws are God’s handiwork, they must necessarily be flawless—few in number, compact, elegant, and perfectly meshed with one another. “It is ye perfection of God’s works that they are all done with ye greatest simplicity,” Isaac Newton declared. “He is ye God of order and not of confusion.”
    The primary mission that seventeenth-century science set itself was to find His laws. The problem was that someone would first have to invent a new kind of mathematics.

Chapter Eight
The Idea That Unlocked the World
    The Greeks had been brilliant mathematicians, but for centuries afterward that was the end of the story. Europe knew less mathematics in 1500, wrote Alfred North Whitehead, than Greece had in the time of Archimedes. A century later, matters had begun to improve. Descartes, Pascal, Fermat, and a small number of others had made genuine advances, though almost no one outside a tiny group of thinkers had any idea what they had been working on. The well educated in Newton’s day knew Greek and Latin fluently, but a mathematical education typically ended with arithmetic, if it reached that far. “It was common,” one historian writes, “for boys entering university to be unable to decipher the page and chapter numbers in a book.” When Samuel Pepys took a high-level job as an administrator with the British navy, in 1662, he hired a tutor to teach him the mysteries of multiplication.
    As able as the Greeks had been, they never found a way around one fundamental obstacle. They had nothing to say about motion. But if mathematics was going to describe the real world, it had to find a way to deal with moving objects. If a bullet is shot into the air , how fast does it fly? How high does it rise?
    Alone on his mother’s farm, twenty-three-year-old Isaac Newton set himself to unraveling the mystery of motion. (His mother hoped he would help run her farm, but he ignored her.) Newton’s self-imposed task had two parts, and each was imposing. First, he had to invent a new language, some not-yet-known form of mathematics that would let him translate questions in English into numbers and equations and pictures. Second, he had to find a way to answer those questions.
    It was a colossal challenge, but the Greeks’ silence on the topic spoke more of distaste than of confusion. To the Greek way of thinking, the everyday world was a grimy, imperfect version of an ideal, unchanging, abstract one. Mathematics was the highest art because it was the discipline that, more than any other,