Clockwork Futures

by Brandy Schillace

  A century and a half later, William Herschel, a British astronomer of German origin and the inventor of the most advanced telescopes of his day, published “Observations on the Mountains of the Moon” in 1780. Half scientific treatise, half dreamlike musing, Herschel’s extravagant claims keep pace with Kepler’s little book: “[Perhaps] the Moon is the planet and the Earth the satellite! Are we not a larger moon to the Moon, than she is to us? [. . .] What a glorious view of the heavens from the Moon! How beautifully diversified with hills and valleys! [. . .] Do not all the elements seem at war here, when we compare the earth with the Moon?”26 Herschel does not make the journey there, but he does discover a new planet, and as with Brahe’s discovery and Kepler’s mathematics, the “new” turned the “old” on its head. Again. Everything men understood in the eighteenth century about stability and creation was about to shift—but that assumes a stability to start with. In other words, by Herschel’s day, plotting the moon’s geography no longer seemed impossible. Far from it. In the age that followed Kepler, measuring the cosmos and measuring the natural world made equal sense to most educated people. Despite the chaos of the 1600s, despite the plague and disaster, despite the mad upheaval of the heavenly cosmos in the hands of Copernicus and Galileo (and the more mad response of the Church to either), by 1780 educated people took order for granted. Order was light in the darkness, life from death and decay. Galileo and Kepler had proven that God spoke in numbers, but for a full triumph of order over chaos we return again to the lone thinker on a farm in the year 1665. Newton would countenance no competitors.

  History remembers Newton as a beacon, an unearthly figure capable of feats no other had achieved before—and possibly since, at least until Einstein. Newton was inclined to agree. Born during Christmas,‡ he felt that his own birth portended “apartness” from others; God had ordained him, destined him, for greatness. And God, as Edward Dolnick puts it, did indeed seem to “whisper secrets” into Newton’s ear.27 Though, if we look at Newton’s methods, his persistence, his dogged determination to accept no seconds, we see something else. Johannes Kepler’s life burst forward in fits and starts of inspiration; he grasped God’s plan as one captures lightning in a jar. Newton, by contrast, did not wait for divine inspiration; he pursued her and ran her to ground. He would align himself to a problem with laser focus, and he would not let it go—not even for bodily necessities of food and water and exercise. Newton believed the Bible’s code had been reserved only for “a remnant”; like Galileo before him, he did not suppose that this knowledge belonged to the masses, but to the chosen. Newton’s fondest phrase comes from Isaiah: “I will give thee the treasures of darkness, and hidden riches of secret places.” The fact that Newton sought them out, more like the adventurers and explorers of the next century than the quiet thinkers of the previous one, never diminished in his own mind the nature of the “gift.” What God and Nature do not give easily, Newton himself would grasp with a tenacity that surpassed his contemporaries almost as often as his intellect overmastered them.

  Newton’s fervent nature and his dedication to mathematics does not disqualify in the least his belief in a Creator-God. In fact, he turned the Latin version of his own name into an anagram: Jeova Sanctus Unus, or God’s Holy One.28 There may be reasons beyond the convenience of Latin (and his belief in his own supernatural intelligence) to choose Jehovah instead of Christus to name the Divine. Newton did not believe in the Trinity, but rather that God the father and Jesus the son were entirely separate entities; the three-in-one he considered a mathematical absurdity, and he nearly ruined his career as Lucasian Professor of Mathematics at Cambridge’s Trinity College as a result.29 Famed Newton historian Betty Jo Teeter Dobbs explains his ardent belief in unity (rather than Trinity) as “a way to reunite his many brilliant facets, which however well-polished, now remain incomplete fragments.”30 There was room for only one singular God in Newton’s math—a recipe of parts joining in mystic unity of truth. If Newton’s mystic conscriptions sound like the convictions of alchemists, they should: Newton practiced alchemy from his youth. We are used to thinking of the alchemists as wizards turning lead into gold, and it’s true that this did remain a preoccupation for centuries. However, alchemy also serves as the origination of chemistry, and even the earliest recipes from Egypt sound more like lab applications than witch’s brew: “Lime, one dram; sulfur, previously ground [. . .] add sharp vinegar or the urine of a youth; heat from underneath until the mixture looks like blood. Filter it from sediments and use it pure.”31 While the foul-smelling solution that results likely served in the search for transforming metals, Newton’s applications had more to do with his own body. He mixed potions from turpentine, rose water, beeswax, olive oil, red sandalwood and more, and he recommended it internally for “consumption” and externally for “green wounds.”32 He did not think that man could be made divine, nor could he grasp immortality from his bizarre exploits. But Newton did want to preserve the sacred orderliness of the body for as long as he could. Self-experimentation continued well into adulthood as he began studying the principles of light, most famously when he stuck a pin or “bodkin” between his eye and eye bone. It may seem rash—and considering he may have killed himself off before his greatest discoveries, it very likely was—but Newton had a method. He believed in inspiration, but of a kind that required deep attention and observation. It was the mind, and not the body, that approached God.

  The only reason, Newton maintained, that no one had yet discovered the secrets of God (not even Kepler) was that no one had yet been good enough or smart enough or “chosen” enough to do it. Newton addressed himself to Nature and to the bounds of the earth through physics and alchemy; he addressed himself to the Divine and to the Heavens through a mathematics devised and developed for the sole purpose of understanding the actions of Providence. It wasn’t as simple as seeing God in the clockwork—and Newton does not expressly refer to a clockwork universe. All the same, his quest was for “the simple machinery through which God creates, governs, sustains and replenishes.”33 The simple machinery, however, turns out to be remarkably complicated in application, and it required God’s constant maintenance or risked collapsing inward into nothingness. He was “a God of order and not of confusion,” Newton maintained, and yet in his understanding of the corruptible universe, Newton also encouraged an idea of entropy. Chaos threatens always. We need God always to establish or reestablish order, and we need a man like Newton to find his laws and to explain them. For that, Newton didn’t need alchemy; he needed a new kind of math. And so, by “thinking of it continually,” he invented calculus.

  By Newton’s own account, the time between 1665 and 1666 was a year of “magical thinking.” He published the order of events late in his life, mentioning almost casually his progress into an idea that changed science and physics forever. It makes for some convoluted reading, but it’s worth the effort if only to see the master displaying his treasures:

  In the beginning of the year 1665, I found the Method of approximating series & the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of Tangents . . ., & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wcl globe revolving within a sphere presses the surface of the sphere) from Kepler’s rule . . . I deduced that the forces which keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about will they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665 & 1666.34

  Newton’s definitive biographer, Richard Westfall, calls this passage “the foundation of the myth of Newton’s annus mirabilis, his marvelous year of di
scovery.”35 Tycho Brahe may have been a showman, and Kepler a mystic, but Newton is the Hero of Science. He has all the qualities that make for Elting’s “men of genius”: an auspicious and mysterious beginning, born on a fateful date and to a world that clearly needed his clarity and intellect. A loner, irascible, distant, and yet domineering, Newton arrived as a man set apart, a man with an origin myth, and most importantly, a man with a quest. He set out to invent a new language for translating mystery to math, and then to apply that math to the universe around him. It’s hard to miss the importance of calculus, but let’s recall that the seventeenth century world could not, before Newton, answer even the most basic questions: Why does an apple fall? Why does a cannonball travel in an arc? How fast is it moving? Can I predict when it will arrive? The ubiquity of our technology allows us access to the greatest discoveries of the greatest minds in seconds; we have invented machines to calculate for us, but Newton was, himself, a calculation machine. Everything that follows, invention, mechanics, engineering, physics—the launching of satellites and the landing of spacecraft, and more importantly, the ability of one sphere spinning at 1,040 mph to launch something and hit another (spinning at 539 mph) with a Mars rover the size of a Land Rover—comes of this one, incredible discovery: calculus, the language of God.

  Newton had a rare capacity for ecstasy, what Richard Westfall describes as “stepping outside of himself and becoming wholly absorbed in the problems on which he worked,” forgetting to sleep and eat.36 But Westfall also points out the fact that Newton’s private papers do not agree with Newton’s year of magic. His achievements remain mind-boggling, certainly. But that he found the answers easily, and in so short of a time, tells only half the tale—and this, by design. Newton’s published narrative of events changed his achievements from human endeavors to superhuman feats. The journals, however, point to years of thinking, of sustained inquiry, of mistakes and false steps, of forward and backward motion as well greased as any piston. This more correct version emerges from history, but it makes for a far less interesting story. Newton might not have acknowledged his debts to those coming before him, but he’d surely learned from Galileo (who hadn’t acknowledged them either) that the way to greatness involved mythmaking. Newton had prophesied his own godlike greatness, and he made sure to tell the story that best revealed that truth. The trouble was that he started too late. The hero had a rival.

  Newton believed he alone had been tapped to reveal that God’s universe operated in simple elegance, a mathematical structure that could be extrapolated from the heavenly bodies to earthly ones. Gottfried Leibniz, a German polymath fresh from the excitement and turmoil of European philosophy (and pointed in every direction at once), had rather different plans. Leibniz was a rationalist, not a mystic: “nothing in heaven or on earth, no mystery in religion, no secret in nature” defied the power of human reason.37 Rather than considering cosmic principles as secret treasures of the few, Leibniz felt God’s laws were intended for everyone, or at least as many as would turn their attention to mathematical study. To Leibniz, the world was universally good—mathematics existed to prove it could not have been otherwise. He did not see chaos as an enemy to be defeated. Given the unbelievable breadth of his interests and the hectic way he pursued them, he probably didn’t see chaos anywhere at all. If Newton was a solitary stoic, Leibniz was his darker angel; attractive, charming, social, and visionary, he didn’t make conversation so much as high-velocity impact. Dressed in silk stockings and curls and newly arrived from the French court, the savant conquered mathematics along the way to more elaborate schemes, nearly falling into the works that Newton labored over. In the midst of plans for “a museum of everything” that would have rivaled the carnivals and pseudoscientific sideshows of the Victorian era with its jumble of telescopes, tightropes, tumblers, and fire-eaters—Leibniz discovered Newton’s discovery. He’d found calculus, nearly two decades after Newton, but before Newton published his work—and he found it, like the “little men in black coats” by “thinking all the time of something else.”

  Leibniz’s thoughts ricocheted a bit like the projectiles Galileo spent so much time measuring, but one theme persists—and would recur in the grim end of his career: the calculation of conflict. He wanted to build a machine for turning philosophical disputes into a numeric language. Problems could be fed into the design and the solutions rendered without recourse to argument: logic prevailed because the numbers, he theorized, wouldn’t lie. “If controversies were to arise,” he suggests, philosophers could kindly invite one another to “calculate.” He even theorized a means of translating everything to the very simplest forms—to 0s and 1s—which is precisely how our computers work today. That doesn’t mean Leibniz didn’t value words themselves; historians lament that though an editorial team is right now trying to turn over 100,000 of his manuscript pages into a collection, they despair of finishing in their lifetimes.38 He valued discourse. But when Leibniz turned over and over the problems and solutions in his mind, he conversed with the greats—reading René Descartes’s complex geometry as though it were a novel rather than the long terrible slog that Newton (and most of the rest of us) found it. But there are riddles, still. For one, how did all of this result in two simultaneous and independent discoveries of calculus? It’s a bit like Douglas Adams’s quandary in The Hitchhiker’s Guide to the Galaxy. The “Answer to the Ultimate Question of Life, the Universe, and Everything” turns out to be the number forty-two. The interesting bit isn’t the answer, but the question.

  The riddle that puzzled the masters had been infinity. Calculus revealed for the first time how speed, distance, and acceleration were linked; it helped you get from one to the other, to measure the previously immeasurable, with an equation. To put it more simply, as Dolnick does, “questions about bests and worsts,” comparison about whether a quantity was at its maximum or minimum, could be readily and easily answered.39 That’s a bit like measuring something’s speed after it has ceased to move. Much of our world isn’t about stopped motion, however; it’s about acceleration, about how speed changes over time. The frenetic discovery of quantum physics, of E=mc2, of the speed of light that never changes, and a galaxy where everything else, including space and time, does, could never have been possible if not for this: How do objects fall, and how fast do they travel at each infinitesimal point along the way? Calculus “was a device for analyzing how things change as time passes.”40 But if we look closer, we see that the Great Simple Truth of calculus strikes a killing blow at the very order Newton, and even Leibniz, thought they were defending.

  Killing the Gods

  I want to return, for a moment, to the dark void of night we’ve all faced at one point or another in our lives. Growing up, as we have, in an age where the exposure of nature’s secrets is a necessary part of education, we can miss the significance of the great and wondrous beyond, the mystical realm of gods and demons and sorcerers. Steampunk aficionados resist being considered “fantasy” or “escapist,” but that prefigures these as negative terms. For Newton and his contemporaries, “science” infused natural philosophy with mystery and made room for flights of fancy. Kepler wrote fiction, Newton practiced alchemy and apocalyptic code-breaking, and Leibniz believed that dogs might be trained to speak. They all lived with contradiction, believing that God ordered the world and spoke in mathematical proofs that we could decipher and use to study the natural as well as the celestial world, and also believing in a great host of things we today would call fantasy and superstition. Like them, we have both a desire for and dread of the unknown. Because of them, we believe those secrets are discoverable, and while we might not think in terms of magic numbers, it’s the numbers that made this possible. Calculus, like Oliver in Whitechapel Gods, is the key to the machine. And in the same way, calculus reduced supernatural to natural, and gods to men. When Newton and Leibniz battled over the math, they poked critical holes in the mythology of discovery. Newton would win the war—but Leibniz rent holes in Newton�
�s careful theorems by introducing a cloud of doubt. Newton argued that the world was like a machine, and God was the master mathematician. But if the world worked perfectly, ordered by numbers and stalwart equations, then it didn’t need a God at all.

  The battle began with clear lines; each man claimed to have discovered calculus first, and independently, and neither could believe it possible that another genius had come up, separately, with the same thing.§ Another clear difference had to do with style. Leibniz aimed to make calculus available to anyone, even to the “unworthy” and “unchosen” souls that Newton disdained. Newton’s failure to publish probably stems from just that: it was his duty to discover God’s order, not to let every peeping eye see it working. Even the means by which Leibniz wrote his discovery surpassed Newton’s in terms of accessibility, and it’s noteworthy that the calculus of today uses Leibniz’s symbols, which are principally “Roman” letters, like x and y, with symbols like δ for delta function and ∞ for infinity. But though we start with a definite and specific feud, the lines become far more blurry—steeped in venom and anger and even hatred—as the feud progressed. “When lions battle,” Newton wrote to Leibniz as an opening shot, “the jackals flee.”41 Whatever else the feud represents, it returned, ultimately, to God and to the faith-based order of the clockwork cosmos at large.