The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World - Edward Dolnick (2011)

Part III. Into the Light

Chapter 40. Talking Dogs and Unsuspected Powers

Leibniz gave the impression that he intended to pursue every one of nature’s secrets himself. “In the century of Kepler, Galileo, Descartes, Pascal, and Newton,” one historian wrote, “the most versatile genius of all was Gottfried Wilhelm Leibniz.” The grandest topics intrigued him, and so did the humblest. Leibniz invented a new kind of nail, with ridged sides to keep it from working free. He traveled to see a talking dog and reported to the French Academy that it had “an aptitude that was hard to find in another dog.” (The wondrous beast could pronounce the French words for tea, coffee, and chocolate, and some two dozen more.)

He drew up detailed plans for “a museum of everything that could be imagined,” roughly a cross between a science exhibition and a Ripley’s Believe It or Not museum. It would feature clowns and fireworks, races between mechanical horses, rope dancers, fire eaters, musical instruments that played by themselves, gambling halls (to bring in money), inventions, an anatomical theater, transfusions, telescopes, demonstrations of how the human voice could shatter a drinking glass or how light reflected from a mirror could ignite a fire.

Leibniz’s energy and curiosity never flagged, but he could scarcely keep up with all the ideas careening around his head. “I have so much that is new in mathematics, so many thoughts in philosophy, so numerous literary observations of other kinds, which I do not wish to lose, that I am often at a loss what to do first,” he lamented.

Many of these ventures consumed years, partly because they were so ambitious, partly because Leibniz tackled everything at once. He continued to work on his calculating machine, for example, and on devising a symbolic language that would allow disputes in ethics and philosophy to be solved like problems in algebra. “If controversies were to arise, there would be no more need of disputing between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, to sit down to their slates, and to say to each other (with a friend as witness, if they liked): ‘Let us calculate.’ ”

Leibniz wrote endlessly, at high speed, often while bumping along the road in a coach. Today a diligent team of editors is laboring to turn well over one hundred thousand manuscript pages into a Collected Works, but they do not expect to complete the project in their lifetimes. Volume 4, to choose an example at random, comes under the heading of “Philosophical Writings,” and consists of three “books.” Each book contains over a thousand pages. The editors envision sixty such volumes.

Thinkers who take on the whole world, as Leibniz did, are out of fashion today. Even in his own era, he was a hard man to get the measure of. Astonishingly brilliant, jaw-droppingly vain, charming, overbearing, a visionary one minute and a self-deluded dreamer the next, he was plainly a lot of work. Not everyone was inclined to make the effort. Still, in Bertrand Russell’s words, “Leibniz was one of the supreme intellects of all time.” If anything, his reputation among scientists and mathematicians has grown through the centuries, as ideas of his that once seemed simply baffling have come into focus.

More than three hundred years ago, for instance, Leibniz envisioned the digital computer. He had discovered the binary language of 0s and 1s now familiar to every computer programmer,46 and, more remarkably, he had imagined how this two-letter alphabet could be used to write instructions for an all-purpose reasoning machine.

The computer that Leibniz had in mind relied not on electrical signals—this was almost a century before Benjamin Franklin would stand outdoors with a kite in a lightning storm—but on marbles tumbling down chutes in a kind of pinball machine. “A container shall be provided with holes in such a way that they can be opened and closed,” Leibniz wrote. “They are to be open at those places that correspond to a 1 and remain closed at those that correspond to a 0. Through the opened gates small cubes or marbles are to fall into tracks, through the others nothing.”

Leibniz was born in Germany, but he spent his glory years in the glittering Paris of Louis XIV, when the Sun King had just begun building Versailles and emptying the royal treasury. Leibniz arrived in Paris in 1672, at age twenty-six, a dapper young diplomat sporting a long wig. The dark curls and silk stockings were standard fare, but the torrent of words that spilled forth from the new arrival dazed his listeners. Leibniz had come to Paris with characteristically bold plans. Germany dreaded an invasion by the French, who had grand territorial ambitions. Leibniz’s mission was to convince Louis XIV that an incursion into Germany would do him little good. What he ought to do instead, what would prove a triumph worthy of so illustrious a monarch, was to conquer Egypt.

In four years Leibniz never managed to win an audience with the king. (France, as everyone had feared, spent the next several decades embroiling Europe in one war after another.) Leibniz spent his time productively nonetheless, somehow combining an endless series of visits with one count or duke or bishop after another with the deepest investigations into science and mathematics.

Leibniz’s conquest of mathematics came as a surprise. Unlike nearly all the other great figures in the field, he came to it late. Leibniz’s academic training had centered on law and diplomacy. In those fields, as well as philosophy and history and a dozen others, he knew everything. But at twenty-six, one historian writes, Leibniz’s knowledge of mathematics was “deplorable.”

He would remedy that. In Paris he set to work under the guidance of some leading mathematicians, notably the brilliant Dutch scientist Christiaan Huygens. For the most part, though, he taught himself. He took up classic works, like Euclid, and recent ones, like Pascal and Descartes, and dipped in and out at random like a library patron flipping through the books on the “new arrivals” shelf. Even Newton had found that newfangled doctrines like Descartes’ geometry slowed him to a crawl. Not Leibniz. “I read [mathematics] almost as one reads tales of romance,” he boasted.

He read voraciously and competitively. These were difficult, compact works by brilliant men writing for a tiny audience of peers, not textbooks meant for students, and Leibniz measured himself against the top figures in this new field. “It seemed to me,” he wrote shortly after beginning his crash course, “I do not know by what rash confidence in my own ability, that I might become the equal of these if I so desired.” The time had come to stop reading about what other people had done and to make discoveries of his own.

By now it was 1675. Leibniz was thirty but still, at that advanced mathematical age, at the peak of his powers. The riddle that taunted every mathematician was the infinitesimal, the key to understanding motion at a given instant. Nearly a decade before, Newton had solved the mystery and invented what is now called calculus. He had told almost no one, preferring to wrap that secret knowledge around himself like a warm cloak. Now, unaware of what Newton had already done, Leibniz set out after the same prize.

In the course of one astonishing year—a miracle year of his own—he found it. Newton had kept his discovery to himself, because of his hatred of controversy and because the security of his professorship at Cambridge meant he did not have to scramble for recognition. Leibniz did not publish an account of his discovery of calculus for nine years, but his silence is harder to explain. Leibniz never had a safe position like Newton’s. Throughout his long career, he was dependent on the whims of his royal patrons, forever trapped in the role of an intellectual court jester. That might have made him more eager to publish, anything to make his status less precarious, but it did not.

The reasons for his delay have disappeared into a biographical black hole. Leibniz wrote endlessly on every conceivable topic—his correspondence alone consisted of fifteen thousand letters, many of them more essays than notes—but he remained silent on the question of his long hesitation. Scholars can only fill the void with guesses.

Perhaps he was gun-shy as a result of a fiasco at the very beginning of his mathematical career. On his first trip to England, in 1672, Leibniz had met several prominent mathematicians (but not Newton) and happily rattled on about his discoveries. The bragging was innocent, but Leibniz was such a mathematical novice that he talked himself into trouble. At an elegant dinner party in London, presided over by Robert Boyle, Leibniz claimed as his own a result (involving the sum of a certain infinitely long sequence of fractions) that was in fact well-known. Another guest set him straight. In time the episode blew over. Still, Leibniz may have decided to make sure that he stood on firm ground before he announced far bolder mathematical claims.

Or perhaps he decided that formal publication was beside the point because the audience he needed to reach had already learned of his achievement through informal channels—rumors and letters. Or the task of developing a full-fledged theory, as opposed to a collection of techniques for special cases, may have proved unexpectedly difficult. Or Leibniz may have judged that he needed to make a bigger splash—from an impossible-to-miss invention like the telescope or from some diplomatic coup—than any mathematical discovery could provide.

Eventually, in 1684, Leibniz told the world what he had discovered. By then he and Newton had exchanged friendly but guarded letters discussing mathematics in detail but tiptoeing around the whole subject of calculus. (Rather than tell Leibniz directly what he had found, Newton concealed his most important discoveries in two encrypted messages. One read, “6accdae13eff7i319n4o4qrr4s8t12ux.”) In the published article announcing his discovery of calculus, Leibniz made no mention of Newton or any of his other predecessors.

In the case of Newton, at least, that oversight was all but inevitable, since Leibniz had no way of knowing what Newton had found. A perfect alibi, one might think, but it proved anything but. Leibniz’s “oversight” was destined to poison the last decades of his life.