The Clockwork Universe Read online

  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 Orléans 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”?

  In his zeal to learn about light, Newton risked permanent darkness.

  Chapter Nine

  Euclid and Unicorns

  In the early days of the Royal Society nearly anyone could attend its weekly meetings. Geniuses sat side by side with gentleman amateurs. The Society was less an ivory tower than a place to see and be seen. Giants like Robert Boyle and Christopher Wren presented their newest work, and so did such men as Sir Kenelm Digby, notable mainly for his faith in a potion called “weapon salve.” Digby claimed he had used the salve to cure a man injured in a duel and given up for dead by the king’s surgeons. The mysterious ointment included some unlikely ingredients—“moss from the skull of an unburied man,” for one9—but the treatment was even odder than the medicine. Weapon salve was applied not to the wound but to the sword that had inflicted it, even if sword and victim were miles apart. (The wound itself was covered with a clean piece of linen and left alone, which in those pre-antibiotic days was probably a good thing.)

  Along with stories of miraculous cures, tales of faraway lands were always popular. So was show-and-tell. On one October day in 1660, “the Society received a present of a living chameleon,” after which Wren
gave a talk about Saturn’s rings. At another meeting in 1660, the Society gravely scrutinized a unicorn’s horn and then tested the ancient belief that a spider set down in the middle of a circle made from powdered unicorn’s horn would not be able to escape. (The spider, unfazed, “immediately ran out several times repeated.”)

  Spiders turned up more often than one might have expected. On a winter afternoon in 1672 Isaac Newton made his first formal presentation to the Society. (Reclusive as always, Newton stayed away while someone else read aloud a paper he had sent.) Newton explained how he had found, using prisms, the true nature of light. White light was not pure but was made up of all the colors of the rainbow. This discovery was one of the milestones in the history of science. Newton’s paper followed one on tarantula bites.

  The Royal Society quickly accumulated so many strange and wondrous objects that it set up a museum. Visitors ogled such marvels of nature as “a tooth taken out of the womb of a woman, half an inch long,” and “a piece of bone voided with his urine by Sir William Throgmorton.”

  Meetings were a hodgepodge because for every genius there was a crank or a charlatan. The surprise, from today’s vantage point, is that so often the genius and the crank were the same person. Robert Boyle, for instance, was not merely a brilliant scientist and the most respected member of the Royal Society in its first decades but also the very model of circumspection and respectability. Boyle believed that the best cure for cataracts was to blow powdered, dried human excrement into the patient’s eyes.

  Ideas like that, and even more outlandish ones, were perfectly respectable. Three hundred years ago the boundary that separates the possible from the impossible was far fuzzier than it is today. In 1670 the Royal Society thrilled to reports of a new invention from Europe, a “flying chariot” that moved through the air powered by oars and a sail. Such optimism had its roots in genuine discoveries. Explorers had recently found entire “new” continents. The telescope had revealed astonishing new worlds, and the microscope, which was even newer, had shown that this world contained a multitude of unsuspected wonders. The humblest drop of pond water teemed with life.

  The Royal Society’s response to Kenelm Digby’s claims for his magical “weapon salve” shows how much even learned men were prepared to believe. Since reliable men vouched for Digby’s remedy, one highly regarded Society member remarked, “I need not be solicitous of the Cause.” The world was so full of marvels, in other words, that the truly scientific approach was to reserve judgment about what was possible and what wasn’t, and to observe and experiment instead. Digby’s supposed cure strikes modern ears as a relic from an older, superstitious age. His contemporaries drew precisely the opposite moral—taking Digby’s claims seriously displayed not backwardness and credulity but up-to-the-minute open-mindedness.

  John Locke, a philosopher of decidedly levelheaded views (and, incidentally, a friend of Isaac Newton), considered it likely that the seas contained mermaids. Learned journals in the second half of the seventeenth century published articles with titles that sound like headlines from an ancient National Enquirer. “A Girl in Ireland, who has several Horns growing on her Body,” “Description of an Extraordinary Mushroom,” “Of Four Suns, which very lately appear’d in France.”

  Anything was possible.

  We think of scientists as chucking out old ideas when something newer and more plausible comes along, but that is not the usual pattern. More often, scientists take up the new but cling to the old as well. In science’s early days that was emphatically so. That made for some unlikely pairings. New ideas and old shared space in the same mind, like tattooed teens and hard-of-hearing dotards in uneasy coexistence in the same apartment.

  Boyle, for example, held peculiar ideas about dead men and hangings. Eight times a year, on Hanging Days, immense crowds swarmed to London’s gallows to see the show. The “Tyburn tree” had room for twenty-four swaying bodies at a time. Hanging Days were holidays, and crowds in dense, jolly packs lined the route from the prison gate to the gallows, like spectators at a parade. “All the Way, from Newgate to Tyburn, is one continued Fair, for Whores and Rogues of the meaner sort,” one observer noted. The condemned man rode past the gawkers in a cart, seated atop his own coffin, his hands in manacles and his neck in a noose.

  The throng at Tyburn might number twenty thousand. The rich, perched on wooden bleachers, had the best views. The poor fought for position. The crowd roared its approval for those prisoners who managed a defiant last word or a jaunty wave. A hangman who had been slipped a coin or two might make sure that his victim died quickly, but some condemned men twisted and choked, still half alive, at the end of a dangling rope. It made for extra excitement if the victim’s friends flung themselves at his swinging body, frantically tugging his legs downward to try to speed his death.

  For nearly everyone the spectacle itself was lure enough. Boyle and other connoisseurs knew better. One of the hangman’s perks was the right to auction off souvenirs. Death ropes sold in one-foot lengths. But the hangman’s most coveted trophies were an executed prisoner’s severed hands, because a hand’s “death sweat” held the power to heal. Robert Boyle, a giant of science, recommended this cure for those afflicted with a goiter.

  The greatest figures in the pantheon of science gave equal weight to discoveries that we still celebrate and to ideas that strike us as mad. Take René Descartes, the brilliant mathematician and philosopher. He was one of the most important scientists of the generation just before Newton. If science is a cathedral, it was Descartes who set many of its foundation stones in place. Descartes was the ultimate skeptic, so reluctant to take anything for granted that he worried that the world and everything in it might simply be his dream. But he proposed a careful, scientific explanation for the well-known fact that if a person had been murdered and the killer later approached the victim’s body, the corpse “identified” its killer by gushing blood.

  William Harvey, renowned to this day for explaining how blood circulates in the body, was another who discovered the new while adhering to the old. Harvey was a contemporary of Descartes, which is to say that both men came of age at a time when the belief in witches was at its high point. Everyone knew a great deal about witches. They knew, for instance, that witches rubbed their bodies with “devil’s grease,” made from the fat of murdered babies, so that they could slither their way through tiny cracks into their victims’ homes. They knew, as well, that witches had animal companions, cats or toads or rats, provided by Satan and magically able to do their mistress’s evil bidding. Harvey, a man who straddled two ages, painstakingly dissected one witch’s diabolical toad to see if he might find anything supernatural.

  Alchemy, which was a scientific quest for a magical-sounding goal, provides perhaps the most striking example of the coexistence of old and new. The aim was to find a substance called the “philosopher’s stone,” despite its name a liquid, which held the power to transform ordinary substances into silver and gold and to convey immortality to anyone who drank it. A devout belief in alchemy was standard in the seventeenth century, but no one exceeded Isaac Newton in persistence. His small, crabbed handwriting fills notebook after notebook with the records of his alchemical experiments. In all Newton lavished some half million words on alchemy, about as many as in War and Peace.

  He and countless other researchers spent long hours at their flasks and fires mixing potions according to closely guarded recipes. (Leibniz’s only fear was that if gold became too readily available its price would fall.) An assistant watched Newton’s experiments with reverence but without understanding. “Whatever his aim might be, I was not able to penetrate into, but his Pains, his Diligence at those Times made me think he aimed at something beyond the Reach of human Art & Industry.”

  A peek inside Newton’s notebooks would have left an observer scarcely more enlightened. He never spoke of anything as crass as growing rich; his focus, it seems, was solely on uncovering nature’s secrets. In any case, alchemical fo
rmulas were too valuable to state openly. All the language was encoded—“Saturn” stood for “lead,” for instance—and the procedures sound like something from an X-rated Hogwarts spell-book. Newton jotted down recipes with such ingredients as “the Green Lion” and “the menstrual blood of the sordid whore.”

  The language is so strange, and Newton’s scientific reputation is so high, that the temptation is to assume that the odd phrases merely indicate the difficulty of describing new techniques in an antique vocabulary. And it is true that in time alchemy gave rise to chemistry, and that Newton’s approach to alchemy was methodical and absolutely rigorous. But it would be a mistake to conclude that Newton was a chemist in a sorcerer’s hat.

  On the contrary, Newton started out by studying chemistry but abandoned it in favor of what he saw as the deeper mysteries of alchemy. This was effectively a return to the past. Chemistry dealt with matter-of-fact questions like what salt is made from. Alchemy sought to explain the invisible forces of living nature. This was sacred, secret research. Throughout his long life Newton hardly breathed a word of what he was up to, and no wonder. “Just as the world was created from dark Chaos . . . ,” he confided in a notebook, “so our work brings forth the beginning out of black chaos.”

  Newton’s theological and alchemical writings went largely unexamined for two centuries after his death. In 1936, John Maynard Keynes purchased a trove of Newton’s notes at auction. He read aghast. Newton was not the first inhabitant of the modern world, Keynes declared, but “the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than ten thousand years ago.”