The Clockwork Universe Read online

  Through the next day things grew worse. “God grant mine eyes may never behold the like, who now saw above ten thousand houses all in one flame,” wrote the diarist John Evelyn. “The noise and cracking and thunder of the impetuous flames, the shrieking of women and children, the hurry of people, the fall of towers, houses and churches, was like a hideous storm . . . near two miles in length and one in breadth. Thus I left it, burning, a resemblance of Sodom or the Last Day.”

  * * *

  After four days, the wind finally weakened. For the first time, the demolition crews—who had resorted to blowing up houses with gunpowder—managed to corral the flames. As the fires burned down, Londoners surveyed the remnants of their city. Acre after acre was unrecognizable, the houses gone and even the pattern of roads and streets obliterated. People wandered in search of their homes, John Evelyn wrote, “like men in some dismal desert.”

  One Londoner hurried to St. Paul’s Cathedral, long one of the city’s landmarks but now only rubble. “The ground was so hot as almost to scorch my shoes,” William Taswell wrote. The church walls had collapsed, and the bells and the metal areas of the roof had splashed onto the ground in molten puddles. Taswell loaded his pockets with scraps of bell metal as souvenirs.

  Taswell was not the only visitor to St. Paul’s. With their own homes destroyed, many Londoners had sought refuge in the huge, seemingly permanent cathedral. They found little but smoldering rocks. In desperate need of shelter, the refugees crawled inside the underground crypts and took their place alongside the dead.

  The city itself lay silent and devastated. “Now nettles are growing, owls are screeching, thieves and cut-throats are lurking,” one witness cried out. “And terrible hath the voice of the Lord been, which hath been crying, yea roaring in the City, by these dreadful judgments of the Plague and Fire which he hath brought upon us.”

  Chapter Seven

  God at His Drawing Table

  England’s trembling citizens, it would eventually become clear, had the story exactly backward. The 1660s did not mark the end of time but the beginning of the modern age. We can hardly blame them for getting it wrong—the earliest scientists looked out at a world that was filthy and chaotic, a riot of noise, confusion, and sudden, arbitrary death. The sounds that filled their ears were a mix of pigs squealing on city streets, knives shrieking against grinders’ sharpening stones, and street musicians sawing away at their fiddles. The smells were dried sweat and cattle, with a background note of sewage. Chronic pain was all but universal. Medicine was useless, or worse.

  Who could contemplate that chaos and see order?

  And yet Isaac Newton turned his attention to the heavens and described a cosmos as perfectly proportioned as a Greek temple. John Ray, the most eminent naturalist of the age, focused on the living world and saw just as harmonious a picture. Every plant and animal provided yet another example of nature’s perfect design. Gottfried Leibniz, the German philosopher destined to become Newton’s greatest rival, took the widest view of all and reported the sunniest news. Leibniz took as his province Newton’s stars and planets, Ray’s insects and animals, and everything in between. The great philosopher surveyed the universe in all its variety and found, on every scale, an intricate, perfectly engineered mechanism. God had fashioned the best of all possible worlds.

  One reason that seventeenth-century scientists had such faith was mundane. Much of the mayhem all around them went unheeded, like the noise of screeching brakes and whooping sirens on city streets today. But the crucial reasons ran deeper.

  The founding fathers of science looked more or less like us, under their wigs, but they lived in a mental world nothing like ours. The point is not that they took for granted countless features of everyday life that we find horrifying or bewildering—criminals should be tortured in the city square and their bodies cut in pieces and mounted prominently around town, as a warning to others; an excursion to Bedlam to view the lunatics made for ideal entertainment; soldiers captured in wartime might spend the rest of their lives chained to a bench and rowing a galley.

  The crucial differences lay deeper than any such roster of specifics can reveal. On even the broadest questions, our assumptions conflict with theirs. We honor Isaac Newton for his colossal contributions to science, for example, but he himself regarded science as only one of his interests and probably not the most important. The theory of gravity cut into the time he could devote to deciphering hidden messages in the book of Daniel. To Newton and all his contemporaries, that made perfect sense—the heavens and the Earth were God’s work, and the Bible was as well, and so all contained His secrets. To moderns, it is as if Shakespeare had given equal time to poetry and to penmanship, as if Michelangelo had put aside sculpture for basket weaving.

  Look only at scientific questions, and the same gulf yawns. We take for granted, for instance, that we know more than our ancestors did, at least about technical matters. We may not have more insight into human nature than Homer, but unlike him we know that the moon is made of rock and pocked with craters. Newton and many of his peers, on the other hand, believed fervently that Pythagoras, Moses, Solomon, and other ancient sages had anticipated modern theories in every scientific and mathematical detail. Solomon and the others knew not only that the Earth orbited the sun, rather than vice versa, but they knew that the planets travel around the sun in elliptical orbits.

  This picture of history was completely false, but Newton and many others had boundless faith in what they called “the wisdom of the ancients.” (The belief fit neatly with the doctrine that the world was in decline.) Newton went so far as to insist that ancient thinkers knew all about gravity, too, including the specifics of the law of universal gravitation, the very law that all the world considered Newton’s greatest discovery.

  God had revealed those truths long ago, but they had been lost. The ancient Egyptians and Hebrews had rediscovered them. So had the Greeks, and, now, so had Newton. The great thinkers of past ages had expressed their discoveries in cryptic language, to hide them from the unworthy, but Newton had cracked the code.

  So Newton believed. The notion is both surprising and poignant. Isaac Newton was not only the supreme genius of modern times but also a man so jealous and bad-tempered that he exploded in fury at anyone who dared question him. He refused to speak to his rivals; he deleted all references to them from his published works; he hurled abuse at them even after their deaths.

  But here was Newton arguing vehemently that his boldest insights had all been known thousands of years before his birth.

  The belief in ancient wisdom was overshadowed by other doctrines. By far the most important of the seventeenth century’s bedrock beliefs was this: the universe had been arranged by an all-knowing, all-powerful creator. Every aspect of the world—why there is one sun and not two, why the ocean is salty, why lobster is delicious and deer are swift and gold is scarce, why one man died of plague but another survived—represented an explicit decision by God. We may not grasp the plan behind those decisions, we may see only disarray, but we can be certain that God ordained it all.

  “All disorder,” wrote Alexander Pope, was “harmony not understood.” The world was an orderly text to those who knew how to read it, a tangle of blotches and squiggles to those who did not. God was the author of that text, and mankind’s task was to study His creation, secure in the knowledge that every word and letter reflected divine purpose. “Things happen for a reason,” we tell one another nowadays, by way of consolation after a tragedy, but for our forebears everything happened for a reason. At the core, the reason was always the same: God had willed it.7 God was a daily presence and used events great and small—earthquakes, fires, victories in war, illness, a stumble on the stairs—to demonstrate his wrath or his mercy. To imply that anything in the world happened by chance or accident was to malign Him. One should not speak of “fate,” Oliver Cromwell had scolded, because it was “too paganish a word.”

  God saw every sparrow that falls, but t
hat was only for starters. If God were to relax his guard even for a moment, the entire world would immediately collapse into chaos and anarchy. The very plants in the garden would rebel against their “cold, dull, inactive life,” one Royal Society physician declared, and strive instead for “self motion” and “nobler actions.”

  To a degree we can scarcely imagine, the 1600s were a God-drenched era. “People rarely thought of themselves as ‘having’ or ‘belonging to’ a religion,” notes the cultural historian Jacques Barzun, “just as today nobody has ‘a physics’; there is only one and it is automatically taken to be the transcript of reality.” Atheism was literally unthinkable. In modern times, we presume that either God exists or He doesn’t. We can fight about the evidence, but the statement itself seems perfectly clear, no different in principle from either there are mountains on the moon or there are not.

  In the seventeenth century no one reasoned that way. The idea that God might not exist made no sense. Even Blaise Pascal, one of the farthest-ranging thinkers who ever lived, declared flatly that it would be “absurd to affirm of an absolutely infinite and supremely perfect being” that He did not exist. The idea was meaningless. To raise the question would be to ponder an impossibility, like asking if today might come before yesterday.

  For Newton and the other intellectuals of the day, God also had another aspect entirely. Not only had He created the universe and designed every last feature of every single object within it, not only did He continue to supervise His domain with an all-seeing, ever-vigilant eye. God was not merely a creator but a particular kind of creator. God was a mathematician.

  That was new. The Greeks had exalted mathematical knowledge above all others, but their gods had other concerns. Zeus was too busy chasing Hera to sit down with compass and ruler. Greek thinkers valued mathematics so highly for aesthetic and philosophical reasons, not religious ones. The great virtue of mathematics was that its truths alone were certain and inevitable—in any conceivable universe, a straight line is the shortest distance between two points, and so on.8 In the Greek way of thinking, all other facts stood on shakier ground. A mountain might be precisely 10,257 feet tall, but it could just as well have been a foot higher or lower. To the Greeks, historical facts seemed contingent, too. Darius was king of the Persians, but he might have drowned as a young boy and never come to the throne at all. Even the facts of science had an accidental feel. Sugar is sweet, but there seemed no particular reason it could not have tasted sour. Only the truths of mathematics seemed tamper-proof. Not even God could make a circle with corners.

  Seventeenth-century thinkers rejected the Greeks’ distinction between truths that have to be—two and two make four—and truths that happen to be—gold is soft and easy to scratch. Since every facet of the universe reflected a choice made by God, chance had no role in the universe. The world was rational and orderly. “It just so happens” was impossible.

  But the seventeenth century found its own reasons for regarding mathematics as the highest form of knowledge. The huge excitement among the new scientists was the discovery that the abstract mathematics that the Greeks had esteemed for its own sake turned out in fact to describe the physical world, both on Earth and in the heavens. On the face of it this was absurd. You might as well expect to hear that a newly discovered island had proved to be a perfect circle or a newfound mountain an exact pyramid.

  Sometime around 300 B.C., Euclid and his fellow geometers had explored the different shapes you get if you slice a cone with a knife. Cut straight across and you get a 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, 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?

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p; 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, independently, 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.”