The Clockwork Universe by Edward Dolnick Read Free Book Online Page A

dealt with eternal truths. In the world of mathematics, nothing dies or decays. The angles of a triangle add up to 180 degrees, and they did so a thousand years ago, and they will a thousand years in the future. To try to create a mathematics of change would be purposely to introduce impermanence and decline into the realm of perfect order.
    Challenge a Greek mathematician with even the most elaborate question about a triangle or a circle or a sphere, then, and he would immediately have solved it. But triangles and spheres just sit there. Instead of drawing a picture of a sphere on a page, take a cannonball and shoot it into the sky. How high will it go? What path will it follow? How fast will it be moving when it crashes to the ground? In place of a cannonball, take a comet. If it passes overhead tonight, where will it be a month from now?
    The Greeks had no idea. Until Isaac Newton and Gottfried Leibniz came along to press the “on” button and set the static world in motion, no one else did, either. After they revealed their secrets, every scientist in the world suddenly held in his hands a magical machine. Pose a question that asked, how far? how fast? how high? and the machine spit out the answer.
    The conceptual breakthrough was called calculus. It was the key that opened the way to the modern age, and it made possible countless advances throughout science. The word calculus conjures up little more, in the minds of most educated people today, than vague images of long equations and arcane symbols. But the world we live in is made of ideas and inventions as much as it is made of steel and concrete. Calculus is one of the most vital of those ideas. In an era that gave birth to the telescope and the microscope, to Hamlet and Paradise Lost , it was calculus that one distinguished historian proclaimed “by all odds the most truly revolutionary intellectual achievement of the seventeenth century.”
    Isaac Newton and Gottfried Leibniz invented calculus, indepen dently, Newton on his mother’s farm and Leibniz in the glittering Paris of Louis XIV. Neither man ever suspected for a moment that anyone else was on the same trail. Each knew he had made a stupendous find. Neither could bear to share the glory.
    No hero ever rose from less auspicious roots than Isaac Newton. His father was a farmer who could not sign his name, his mother scarcely more learned. Newton’s father died three months before his son was born. The baby was premature, so tiny and weak that no one expected him to survive; the mother was a widow, not yet thirty; the country was embroiled in civil war.
    Newton did live, and lived to see honors heaped upon him. The fatherless boy, who was born on Christmas Day, believed throughout his life that he had been singled out by God. His story is so implausible that it almost seems that he might have been right. When Newton finally died, in 1727, at age eighty-four, a stunned Voltaire watched dukes and earls carry his casket. “I have seen a professor of mathematics, simply because he was great in his vocation, buried like a king who had been good to his subjects.”
    Newton’s great opponent was a near contemporary—Leibniz was four years younger—and every bit as formidable as Newton himself. A boy wonder who had grown into an even more accomplished adult, Gottfried Leibniz had two strengths seldom found together: he was a scholar of such range that he seemed to have swallowed a library, and he was a creative thinker who poured forth ideas and inventions in half a dozen fields so new they had not yet been named. Even supremely able and ambitious men quailed at the thought of Leibniz’s powers. “When one . . . compares one’s own small talents with those of a Leibniz,” wrote Denis Diderot, the philosopher/poet who had compiled an encyclopedia of all human knowledge, “one is tempted to throw away one’s books and go die peacefully in the depths