The Clockwork Universe (5 page)

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?

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 of some dark corner.”

Leibniz was a lawyer and a diplomat by profession, but he seemed, almost literally, to know everything. He knew theology and philosophy and history, he published new theorems in mathematics and new theories in ethics, he taught himself Latin at seven and wrote learned essays on Aristotle at thirteen, he had invented a calculating machine that could multiply and divide (when rival machines could do no more than add and subtract). No subject fell outside his range. He knew more about China than any other European. Frederick the Great declared him “a whole academy in himself.”

Leibniz's view of his own abilities was fully in line with Frederick's. On the rare occasions when praise was lacking, he supplied it himself. “I invariably took the first rank in all discussions and exercises, whether public or private,” he remarked happily, recalling his school days. His favorite wedding gift to young brides was a collection of his own maxims. But somehow his vanity was so over-the-top, as was his flattery of the royal patrons he was forever wooing, that his exuberance seemed almost endearing. Throughout his long life, Leibniz retained the frantic eagerness of the smartest boy in fifth grade, desperately waving his hand for attention.

Newton and Leibniz never met. They would have made a curious-looking pair. Unlike Newton, who often slept in his clothes, Leibniz was a dandy who had a weakness for showy outfits with lace-trimmed cuffs, gleaming boots, and silk cravats. He favored a wig with long, black curls. Newton had a vain side, too, despite his austere manner—eventually he would pose for some seventeen portraits—and in his prime he cut a handsome figure. He was slim, with a cleft chin, a long, straight nose, and shoulder-length hair that turned silver-gray while he was still in his twenties. (Newton's early graying inspired his only recorded foray into the vicinity of humor. He had spent so much time working with mercury in his alchemical experiments, he once said, “as if from thence he took so soon that Colour.”)

In appearance Leibniz was an odder duck. He was small, jumpy, and so nearsighted that his nose almost scraped the page as he wrote. Even so, he knew how to charm and chat, and he could set his earnestness aside. “It's so rare,” the Duchess of Orl
é
ans declared happily, “for intellectuals to be smartly dressed, and not to smell, and to understand jokes.”

Leibniz was greatly impressed by a demonstration of “a Machine for walking on water,” which was apparently akin to this arrangement of inflatable pants and ankle paddles.

Today we slap the word
genius
on every football coach who wins a Super Bowl, but both Newton and Leibniz commanded intellectual powers that dazzled even their enemies. If their talents were on a par, their styles were completely different. In his day-to-day life, as well as in his work, Leibniz was always riding off boldly in all directions at once. “To remain fixed in one place like a stake in the ground” was torture, he remarked, and he acknowledged that he “burned with the desire to win great fame in the sciences and to see the world.”

Endlessly energetic and fascinated by everything under the sun, Leibniz was perpetually setting out to design a new sort of clock or write an account of Chinese philosophy and then dropping that project halfway through in order to build a better windmill or investigate a silver mine or explain the nature of free will or go to look at a man who was supposedly seven feet tall. At the same time that he was inventing calculus, in Paris in 1675, Leibniz interrupted his work and scurried off to the Seine to see an inventor who claimed he could walk on water.

No man ever had less of the flibbertigibbet about him than Isaac Newton. He had not a drop of Leibniz's impatience or wanderlust. Newton spent the eighty-four years of his life entirely within a triangle a bit more than one hundred miles on its longest side, formed by Cambridge, London, and Woolsthorpe, Lincolnshire, his birthplace. He made the short trip to Oxford for the first time at age seventy-seven, and he never ventured as far as the English Channel. The man who explained the tides never saw the sea.

Newton was a creature of serial obsessions, focusing single-mindedly on a problem until it finally gave way, however long that took. When an admirer asked him how he had come up with the theory of gravitation, he replied, simply and intimidatingly, “By thinking on it continually.” So it was with alchemy or the properties of light or the book of Revelation. Week after week, for months at a stretch, Newton did without sleep and nearly without food (“his cat grew very fat on the food he left standing on his tray,” one acquaintance noted).

“His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it,” wrote John Maynard Keynes, who was one of the first to examine Newton's unpublished papers. “I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted.” An economist of towering reputation and intelligence, Keynes could only marvel at Newton's mental stamina. “Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one's mind and apply all one's powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret.”

Newton's journal, showing his experiments on his own eye. Reproduced by kind permission of The Syndics of Cambridge University
Library
.

Nothing diverted Newton. To test whether the shape of the eyeball had anything to do with how we perceive color, Newton wedged a bodkin—essentially a blunt-ended nail file—under his own eyeball and pressed hard against his eye. “I took a bodkin & put it betwixt my eye & ye bone as neare to ye backside of my eye as I could,” he wrote in his notebook, as if nothing could be more natural, “and pressing my eye with ye end of it . . . there appeared several darke and coloured circles.” Relentlessly, he followed up his original experiment with one painful variation after another. What happened, he wondered, “when I continued to rub my eye with ye point of ye bodkin”? Did it make a difference “if I held my eye and ye bodkin still”?