Gottfried Leibniz was not the first philosopher to think that we live in the best of all possible worlds. He may have been the unluckiest, suffering the posthumous fate of being skewered in the best of all possible parodies, Voltaire’s “Candide” (1759). When Voltaire was writing, four decades after Leibniz’s death, the German polymath was renowned for his work in several sciences, philosophy, history, law, and, especially, mathematics—he and Newton had, independently, invented calculus, but it’s Leibniz’s notation that’s still used today. Over the years, Leibniz’s reputation continued to grow as more unpublished work came to light, some of which would make him the godfather of the digital age. But he will never quite live down Voltaire’s ridicule.
Leibniz was too logical about God. Like some ancient Stoics, he reasoned that, if God is omnipotent and good, ours has to be the best of all possible worlds, because if a better world had been feasible God would have made that one instead. All our sufferings must therefore be lesser evils that somehow serve to bring about a greater good. This solves the age-old puzzle of why God lets bad things happen. “I cannot show you this in detail,” Leibniz conceded, because no finite mind can see all the connections between events. But God had surely done all the relevant sums. So, Leibniz insisted, we may rest assured that any imagined world that might seem happier than our own would actually have been worse over all.
This cheery train of thought gave Voltaire plenty to work with. In his tale, the young Candide is expelled from a baronial castle in Westphalia and subjected to a procession of colorful and violent disasters around the globe, often in the company of an equally battered tutor, Dr. Pangloss. Pangloss remains upbeat and contented throughout, convinced that all is for the best, because “Leibniz cannot have been wrong.” The good doctor is adept at spinning any setback into a hidden blessing. Even the syphilis that afflicts him is ultimately a good thing, because, from the New World, Columbus brought not only that disease but also chocolate. Pangloss triumphantly infers that without syphilis there would have been no chocolate.
Voltaire took an excusable liberty in “Candide.” The real Leibniz almost always refrained from spelling out Panglossian excuses for particular evils. He kept his theory safely abstract; Voltaire brought it comically down to earth. And the best-of-all-possible-worlds thesis had another self-protective feature that Voltaire’s satire ignores. It referred not to our planet at some specific stage in its history but to the whole universe considered throughout eternity. The claim wasn’t that everything was fine and dandy in the here and now. According to Leibniz, it is up to us to make our corner of the world a better place, and to help bring about the optimal universe that God has made achievable.
Leibniz lived at a splendid time to do plenty of good, or so he thought. The latest advances in knowledge and technology, he wrote in the sixteen-nineties, could soon make people “incomparably happier.” His role, he believed, was to spread news of useful discoveries, to make some discoveries himself, and to persuade rulers to exploit them for the benefit of mankind. Indeed, two new biographies of him—Audrey Borowski’s “Leibniz in His World: The Making of a Savant” (Princeton) and Michael Kempe’s “The Best of All Possible Worlds: A Life of Leibniz in Seven Pivotal Days” (Norton)—show that Leibniz never stopped trying to improve the world, albeit mostly from his desk.
Leibniz was born in 1646 and grew up among bookish Lutherans in Leipzig. At the age of eight, he was let loose in the library of his late father, a professor of moral philosophy, and a part of Leibniz never left. Nobody has ever “read as much, studied as much, meditated more, and written more than Leibniz,” Diderot reflected in his Encyclopédie. The first entry in Leibniz’s own list of his early writings is a three-hundred-verse Latin poem that he composed in a day at the age of thirteen. At around the same time, he presented his teachers with some improvements to Aristotle’s logic. Only a smidgen of Leibniz’s incessant output was published in his lifetime, and there is much still to come. Scholars speculate that it will be at least another half century until a comprehensive edition of his outpourings, in an estimated hundred and thirty volumes, is complete.
Just before his fifteenth birthday, Leibniz began his university studies, and he emerged five years later with a degree in philosophy and a doctorate in law—and a job offer as a professor. He turned it down, because, as he later put it, he had an “ardent desire to earn more glory in the sciences.” At first, Leibniz had to settle for legal work at the court of the prince-archbishop of Mainz, but, luckily, this led to a diplomatic mission to Paris, and with it a path to scientific glory.
When he got to Paris, in 1672, Leibniz was already enthusiastic about Galileo’s and Descartes’s new science of matter in motion—the so-called mechanical philosophy. In order to master it, he began to study mathematics in earnest, mentored by the Dutch mathematician and physicist Christiaan Huygens, a circumstance that resulted in Leibniz’s discovery of calculus. (He started figuring out the system around 1674.) He did sometimes worry, though, about the religious implications of the mechanical philosophy. It seemed to reveal the workings of the physical world, yet it could also lead to “the ruin of holy doctrine” if taken too far. Ever the conciliator, Leibniz was confident he could solve that problem and keep everyone happy by concocting a synthesis of the new thinking and the old.
Paris was the place to be, Leibniz felt, but after four busy years there he had failed to get a suitable position and was forced to leave. The best job on offer was as a court counsellor and librarian in Hanover, working for Duke Johann Friedrich, the first of three Hanoverian dukes to employ him. (The third ascended the British throne as George I, in 1714.) Leibniz spent the rest of his life at least nominally serving the Hanoverians, but his mind was often elsewhere, as, indeed, was his body. He seemed to be constantly in touch with everyone: his literary remains include fifteen thousand letters written to some thirteen hundred people. And he was usually juggling an armful of projects that he kept aloft all at once.
One feat of juggling took place in early 1686, when Leibniz was thirty-nine and had been working for the Hanoverians for a decade. He was in Zellerfeld, a mining town in the Harz Mountains, in northern Germany, writing a summary of a treatise he’d composed on metaphysics. This was to be sent to a Catholic theologian, whose opinion Leibniz was eager to hear—he was always trying to come up with formulations of ideas that might be acceptable to both Protestants and Catholics. But Leibniz was not in the mountains because it was a peaceful spot to philosophize. He had been trying to help his employers solve a drainage problem in the local silver mines. For six years, he had spent half his time in the region, attempting to drain the mines by harnessing wind power. Unfortunately, Leibniz became all too fascinated by theoretical questions of dynamics, exasperating the miners. His contraptions were sometimes ingenious, but, as Kempe explains in “The Best of All Possible Worlds,” Leibniz’s quixotic windmills kept breaking down, and by the start of 1686 his mining work was gradually coming to an end.
There were plenty of other things to do during that time, anyway. Leibniz collected fossils and conducted geological research, which eventually resulted in an innovative essay on the history of the earth. He had also begun another project, one that proved a bigger boon than any amount of efficiently extracted silver. The Hanoverian dukes were an offshoot of a junior branch of the Welf dynasty, whose long history Leibniz was commissioned to write. He never finished this compendious work—there was always a fascinating new morsel to add—but his relentless archival digging helped the duchy make its case for promotion to an electorate of the Holy Roman Empire.
Medieval history, metaphysics, and geology were not nearly enough to keep Leibniz busy in early 1686. In January, he wrote an article exposing what he took to be a notable blunder in Descartes’s physics. Descartes regarded force as the product of mass and velocity, whereas Leibniz argued that it was better seen as mass times the square of velocity. This move brought Leibniz close to the modern notion of kinetic energy. In April, he began writing a hundred-page “Examination of the Christian Religion,” and not long afterward he composed his most substantial treatise on logic. It contained a pioneering algebra of propositions, similar to the logical calculus invented in the mid-nineteenth century by the English mathematician George Boole. Boole’s creation is a large part of the basis for computer languages. When he learned of Leibniz’s precursor to his handiwork, Boole said that he felt as if Leibniz had shaken hands with him across the centuries.
In the decades that Leibniz spent unearthing documents about distant Welfs for his main employers, he also did side jobs for plenty of other grandees, especially during his fifties. At the behest of Emperor Leopold I, he took part in negotiations to reconcile the churches. He was appointed to one of the Empire’s highest courts of appeal, served as a counsellor to Russia’s tsar, Peter the Great, and became the first president of the Berlin Society of Sciences, which he had persuaded the Elector of Brandenburg to found. Leibniz constantly lobbied to do more, though he couldn’t always get people to listen. Sometimes it was Leibniz who politely declined. He was approached about taking charge of the Vatican Library, but that would have meant becoming a Catholic, and he was not inclined to take ecumenism quite that far.
Leibniz always found time for his abstract pursuits as well. Shortly after his appointment to the Berlin Society, in 1700, he started to work in earnest on the development of a binary arithmetic, something he had long been toying with. The binary system of ones and zeros later became the basis of digital coding, and Leibniz himself attempted to exploit it in some of his designs for machines that could perform calculations. Leibniz loved the simplicity and the suggestiveness of binary: he titled a draft paper “Wonderful Origin of All Numbers from 1 and 0, Which Serves as a Beautiful Representation of the Mystery of Creation, since Everything Arises from God and Nothing Else.” Writing to a Jesuit missionary in China, Leibniz floated the idea that the binary system might help to convert the Chinese to Christianity, by familiarizing them with the Biblical concept of creation ex nihilo.
In his late sixties, Leibniz summarized his distinctive take on what exactly God had created. “Monadology,” which supposedly combined the best of both old and new ideas, proposed that each building block of the universe is a self-contained world of its own. Everything is in some sense made of these “monads,” though the monads are not themselves physical and never interact with one another—they just appear to do so because they are coördinated by what Leibniz calls a “pre-established harmony.” The destiny of each one unfolds according to its own implanted program, and all of them will last until God, who is a uniquely important kind of monad, brings the whole show to an end. Most philosophers have found this story unbelievable; Bertrand Russell’s first impression was that it was “a kind of fantastic fairy tale.” Still, on closer examination, Russell at least came to respect some of Leibniz’s reasoning.
Russell kept a bust of Leibniz on his mantel and held imaginary conversations in which he would “tell him how fruitful his ideas have proved.” He particularly admired Leibniz’s work on logic, but he was contemptuous of his “courtly” existence. Russell disapproved of Leibniz’s decision to turn down a university post at the age of twenty, a choice that he believed led to a life of “undue deference for princes and a lamentable waste of time in the endeavour to please them.” This rather missed the point. Leibniz sought out princes because they had the power to advance the sciences and get things done. They were the “gods of this world,” as he once put it. By persuading such potentates of the wisdom of one’s projects, one might “obtain in a few years what would otherwise have taken several centuries.” If that meant wearing a powdered wig, so be it. (Every portrait of Leibniz shows him in an enormous wig, which served to conceal his baldness, a lump on his head, and his modest height.)
Leibniz, as Borowski shows in her biography, was an awkward and somewhat reluctant courtier. He could be gauche and undiplomatic when selling himself and his projects. In a memorandum to Duke Johann Friedrich, he immodestly described himself as a “walking encyclopedia,” and he once boasted that he had turned down several grandees so that he could conduct his research “more freely, and perhaps with greater benefit to the public.”
Leibniz’s wish lists of schemes for the public benefit were always ambitious and sometimes utopian. One early proposal for a reformed and fairer economy, which he wrote in his twenties, envisaged an end to unemployment and food shortages, and a merry band of workers singing away as they exchanged useful work-related tips. These carefree artisans would be encouraged to tell “all sorts of funny stories,” though not to drink, and would be spared the fatigue of child care, as their offspring would be raised in state institutions.
During his Paris years, an exhibition of machinery on the Seine prompted Leibniz to write a memo in which he really let himself go. He proposed a European network of scientific academies that would entertain the public with technological marvels, including “speaking trumpets,” artificial gems and dragons, and self-playing musical instruments. These circuses of science would be profitable—by hosting lotteries and selling trinkets—and could feature gaming houses in which hidden pipes and mirrors would be used to spy on the populace, thus providing the state with political intelligence. Substitute “Big Tech” for Leibniz’s “state” and his snooping, money-making entertainments seem not unfamiliar.
Leibniz conceded that this reverie of gadgets and wonders might sound rather odd, but such projects would stimulate further inventions. The time seemed ripe for awesome advances, and Leibniz was confident that he was just the man to scour the world for exploitable discoveries. There was treasure to be found in the work of countless half-mad inventors, if only one knew where to look. A case in point was phosphorus, which a German alchemist, Hennig Brand, had isolated from urine. Leibniz had been enthused by the potential military and civilian applications of this “eternal fire” and negotiated a deal with Brand on behalf of Duke Johann Friedrich. (In his determination to secure the benefits of phosphorus, Leibniz cut corners and seems to have tricked Brand, who subsequently compared Leibniz to a clown.) Leibniz’s other pitches to the Duke included a system of disaster insurance, techniques for mechanizing silk production, various medicinal remedies, improved watches, and designs for a novel kind of wagon.
Leibniz was still fizzing with ideas in the last year of his life, 1716. In July, he had just turned seventy and was excited about a recent encounter with the tsar. Peter I was taking the waters at a German spa, and Leibniz deluged him with proposals for reforming Russian science along with the country’s schools, economy, and armed forces. He was particularly eager for the tsar to support a research expedition to Siberia and the Pacific coast of Asia. “I hope that with his help we shall learn whether Asia is connected to America,” Leibniz wrote to a friend. He also corresponded about a debate with an English philosopher and cleric, Samuel Clarke, regarding the implications of Newton’s views on space and time. In an argument that Albert Einstein later partly endorsed, Leibniz maintained, against Newton and Clarke, that time and space exist only as relations between things, not as absolutes—an idea that was, as it were, ahead of its time. Leibniz was also still tinkering with a mechanical calculator that he had told a friend, back in 1673, was on the verge of completion. And there was the Welf history to finish. In the last weeks of his life, Leibniz suffered severe pain from inflammation in his arms and legs, but he did not stop writing until eight days before his death, in November.
How many of Leibniz’s schemes and inventions came to any sort of fruition? Historians have not been able to say much on the subject. It is safe to assume that many of his plans went nowhere; it is not even certain that his mechanical calculator ever worked properly. An exception was his campaign to set up institutions for the exchange of scientific information, which did eventually bear fruit in several countries. Voltaire, in one of his historical works, rightly gave him credit for that.
Leibniz’s weary secretary once complained that his boss tried to do everything and could therefore finish nothing, “not even if he had angels as assistants.” Constantly distracted by an influx of fresh information, Leibniz was wont to switch attention to a new task while the old ones were still pending. This is perhaps another way in which he reaches across the centuries and shakes hands with us, if we consider the digital devices that do much to divert our attention, technology for which Leibniz’s work on logic and binary did much to lay the ground.
Leibniz’s life was inevitably full of frustrations because he aimed so impossibly high. Yet he always pressed on, certain that everything would go better next time. He would not have regarded himself as an optimist, though; the concept had not been invented. A French journal coined optimisme after his death, to refer to his account of God’s choice between possible worlds. It later came to mean some of the things that Leibniz personally was—energized by hope, inclined to underestimate the chances of failure, ready to see a bright side. When the pain in his legs kept him indoors, it was “a blessing in disguise,” he half joked to a friend, because it meant that he could get even more done at his desk. That sounds like Voltaire’s Pangloss. But, unlike Pangloss, Leibniz was never satisfied with the present state of things, because he couldn’t stop dreaming up ways to make the world better. ♦
