The Hunt for Vulcan

by Thomas Levenson

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  There you have it: one of the great non-apologies in the history of science.

  It was a controversial gibe at the time—inflammatory, really, for all its august air of unconcern. Historians and philosophers still argue about what, exactly, Newton meant. But at a minimum, it’s clear that Newton drew a sharp distinction between the way he thought natural philosophy should be done and how his opponents believed nature needed to be explained.

  Here’s the context. One of the most consistent requirements of pre-Newtonian natural philosophy comes in the demand for explicit determination of the causes, answers to the “why” and “how” for any phenomenon. From antiquity, this requirement led to explanations like the one Aristotle gave of the mechanism of planetary motion: the planets ride on rotating spheres, he said, which themselves move through eternity thanks to a shove from the original source, the prime mover. In medieval reworkings of that idea, God takes over from Aristotle’s formless author, but the concept of a direct connection between motion and a mover remains. See, for example, a gorgeous image found in the fourteenth-century manuscript Breviari d’Amor (an Abstract of Love): two angels, elegant in their robes of green, seated outside the sphere of the fixed stars, turning deep blue cranks. Those divine agents become, in the words of the artist Michael Benson, an image of “changeless supernatural beings winding the clockwork of temporality.”

  Credit col1.2

  In the cosmic order depicted in Matfre Ermengau’s fourteenth-century manuscript Breviari d’Amor, everything beyond the moon is pure and perfect, and the machinery of heaven drives the ceaseless round of the sublunary sphere.

  By Newton’s time such divine engineers had surrendered to more purely inanimate drivetrains, but the need to provide a direct account of cause and effect remained. Thus, when René Descartes set out to create a modern cosmology, he suggested that space had to be full of some mysterious fluid in which the motion of celestial objects could be driven by whirlpools, vortices that could impart the necessary impetus to the planets. That notion solved what was seen as the essential problem. Here was machinery that could be imagined to make a cosmos go.

  Unfortunately for such a mechanistic explanation, Newton showed in Principia that vortex physics was wrong both in particular (the mathematics Descartes developed to describe his vortices failed to predict planetary positions correctly) and, much more important, was unnecessary. Once you allow a handful of axioms—gravity acts according to an inverse square law; it does so everywhere; and the force imparted by gravity to an object moves that object in accordance to three simple laws of motion—then that’s it.* You don’t need anything else to provide an accurate account of falling fruit here on Earth or the tracks of moons, comets, and planets through the night sky. This gravity is disembodied, abstract, something Newton called a force, without ever quite defining the term, and without saying just how that force imparts its impulse to whatever it touched. No levers here, no gears, no mover, prime or not. Instead, action at a distance, something that seemingly leapt from one mass to another, incorporeal, instant in its effects.

  This is what so offended Newton’s critics, themselves no slouches as natural philosophers and mathematicians. To them, Newton had abandoned the direct “local” explanations of Cartesian physics (and Aristotelian, for that matter)—the way that such explanations brought cause directly into contact with effect right where any effects occur. Once he denied the demand to explain how nature worked, he undermined (seemingly) the very nature of physical explanation. Gottfried Leibniz, the nearest Newton had to an intellectual equal, complained publicly that absent an explanation for how it made things go, Newton’s theory verged on blasphemy: “without any mechanism…[gravity] is an unreasonable and occult quality, and so very occult that it is impossible that it should ever be done though an angel or God himself should undertake to explain it.” To Leibniz as to many of his contemporaries, the argument that gravity was somehow just the way nature did it was an unacceptable surrender. Newton’s view was, in their eyes, a bizarre unwillingness to accept what seemed obvious. If a planet orbits the sun in a path that suggests a tug between the two bodies, then it must be the natural philosopher’s job to find out what “really” connects the two.

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  But what if that necessity was an illusion? Newton’s refusal to assert what he did not know was more subtle than a simple rejection of mechanical dogma. Instead, the deeper truth hidden within Newton’s seeming intellectual modesty comes from the realization that there is a real gap between mathematics and physics. Newtonian theory exists in mathematical form, in equations. There, gravity is simply a quantity, some number of units of force that can be calculated in a context of other quantities: the mass on which the force acts; the acceleration experienced by that mass. There is no need to invoke a specific set of physical connections. The test of such a relationship, of a claim about the motion of bodies, is to observe, to measure, and to match calculation to what can be seen.

  That’s how Newton’s math became physics: an abstract relationship like force is equal to mass times acceleration:

  F = ma

  Or, for the gravitational force between two bodies:

  —enables anyone to figure out where Mars would be next Tuesday.

  “I feign no hypotheses” may mean many things, but at the least, it says this: the mathematical form of physical law is its own hypothesis, a proposition about the material world, subject to the judgment of measurement and observation. Once it meets that test, such an unfeigned hypothesis gets woven into the fabric of reality; it becomes, as Newton had proclaimed, an explanation that “cannot fail but to be true.”

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  Looking back, finding Neptune so precisely where calculation said it should lie may seem merely one more in the line of confirmations of the most successful scientific idea in history. But that’s only part of the story. The objections Newton faced in his lifetime did not simply disappear on his say-so, that regal “I Do Not Feign!” The heart of the Newtonian revolution lay with the claim that a purely mathematical argument was a sufficient account of events in the physical world—all of it, the full, unmeasured sweep of the heavens and our own mundane experience here on Earth: the same laws governing a ball dropping from a child’s hand or the tide sweeping away a sand castle to Neptune appearing first on the page and then in the eyepiece of Galle’s telescope. But the conviction that equations do in fact represent reality did not triumph in a day.

  It didn’t even for Newton himself. He wasn’t—he couldn’t be—truly a Newtonian, utterly convinced of the sufficiency of mathematical explanations. Like anyone, he was a man of his time and place—and there was as much (or more) in him of the past that made him as of the future he helped make. He was a secret alchemist, committed to esoteric studies to uncover how change happens in nature. That alchemical spirit infused his ideas about gravity, including how the material fact of a planet could, disembodied, reach across open space to move another body. He saw God’s hand at work throughout the solar system, the entire cosmos—no abstract spirit but the ultimate agent in the material world. Newton’s heirs downplayed, and then simply ignored, this side of their hero’s convictions. (The University of Cambridge would even decline to accept a donation of Newton’s alchemical papers as “of very little interest in themselves.”) Instead, thinkers like Euler and Lagrange and Laplace and finally Le Verrier constructed in Newton’s name a worldview in which mathematics and not mechanism became the scaffolding of the universe—math, without God—to the point where Laplace’s “I have no need of that hypothesis,” could both echo and overwhelm Newton’s “I do not feign…”

  These Newtonians extended Newton’s ideas to more and more complicated problems. They vindicated them again and again throughout the solar system until, at last, Neptune crushed all doubt. Le Verrier’s calculation signaled not just advance but victory: the approach to nature established by Newton and developed since was no mere set of clever tools. Rather, it
offered the definitive account of how the cosmos actually works.

  It is for this reason that Newton is remembered not simply as a great thinker for his day, but as the greatest scientist ever. For all the secrets he kept, the private thoughts he harbored—for all the (to our eyes, not his) crazy, almost magical beliefs that informed his natural philosophy—the legacy of “I feign no hypotheses” remains. It is the cornerstone of the scientific account of material experience: rigorous observation and measurement of the physical world, expressed and analyzed in the language of number.

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  * These laws are simple in the sense the physicist Richard Feynman meant when he described solving a problem in Newton’s Principia: “ ‘Elementary’ does not mean easy to understand. ‘Elementary’ means that very little is required to know ahead of time in order to understand it, except to have an infinite amount of intelligence.”

  THIRTY-EIGHT SECONDS

  Success mellows some. Not everyone, though, and certainly not Urbain-Jean-Joseph Le Verrier. The man who discovered Neptune “at the tip of his pen,” received—and very rapidly came to expect—a hero’s reception. His professional peers understood what he had done, while the public received him with all the reverence due a magician who could conjure a planet out of equations. As the mathematician Ellis Loomis wrote in 1850, “the sagacity of Le Verrier was felt to be almost superhuman. Language could hardly be found strong enough to express the general admiration.” Loomis himself was slightly less moved, noting that the outcry was “somewhat extravagant.” No matter, he added. Even a more sober assessment of Le Verrier’s achievement would still have earned him, Loomis concluded, “the title of FIRST ASTRONOMER OF THE AGE.”

  Le Verrier concurred. He was first among not-quite-equals, as he emphasized in what was almost his first professional act after Galle’s sighting was confirmed by other observers. At issue: what to call the new planet. Le Verrier had an obvious answer, given the naming convention for the rest of the planets, drawn from the Roman pantheon (with Uranus the one Greek outlier). He proposed Neptune, god of the sea and Jupiter’s brother. That choice tangled the sequence of the family tree—Saturn was both Jupiter and Neptune’s dad and Uranus was Saturn’s father. Still, Le Verrier’s choice fit with the broad sense of how to address a respectable planet, the same sentiment that attached names like Ceres and Pallas to the largest of asteroids discovered earlier in the century.

  So far so good, though there was some dissent from the English, who preferred Oceanus in a nod toward the claim that an astronomer from their sea-girt island had a hand in the discovery. But while that move may have irritated Le Verrier—with cause—it seems to have occurred to him rather quickly that he might have undersold his triumph. So he withdrew from the naming stakes and turned to his colleague François Arago, director of the Paris Observatory, to represent him at the new planet’s christening. Arago did so, making a proposal that might have aroused some suspicion in uncharitable minds: Le Verrier’s planet should be called…Le Verrier!

  The honoree made an unconvincing show of humility, a public stance undercut by his sudden shift on what to call the seventh planet from the sun. Now, for the first time in his career, he took to addressing Uranus by the name only English astronomers still (occasionally) used: Herschel. As for Britain in the eighteenth century, so for France—and M. Le Verrier—in the glorious nineteenth. The maneuver failed (obviously), in part because Herschel’s son John rejected the idea of relabeling his father’s find, and more because no astronomers beyond Paris, and not many there, could stomach a celestial Le Verrier glowering down on them night after night. The earthbound version ultimately gave up the attempt, and the consensus remained with what had from the start seemed like the obvious choice: Neptune.

  Still, plenty of rewards did come his way. As Herschel had before him, Le Verrier won the royal notice, receiving the Légion d’Honneur from the hands of Louis Philippe of France. More practically, from this moment in his career he began to gain real power in and ultimately dominance over the French astronomical establishment. Just months after the discovery, French officials asked him to submit a proposal for his future research. In reply, he proposed to out-Laplace the master himself, to “encompass in a single work the entire ensemble of the planetary system…” Such a project would, he wrote, “reconcile and render everything harmonious, if possible, and when this cannot be done, to declare with certainty that there exist causes of perturbations still unknown, whose origins are then and only then revealed.”

  Urbain-Jean-Joseph Le Verrier, as the French public at mid-century knew him.

  Le Verrier himself had no illusions of the scale of the project. Consider, he told the ministry, what was involved: first, he would have to gather a comprehensive catalogue of observations of each planet in turn. Then came the building of the system of equations that could account for every known influence on the individual objects under scrutiny, one by one, on the Neptune-validated faith that Newton’s universal gravitation governed all such interactions. Next, with the observational data fully incorporated into a mathematical model of the planet, he (and his assistant) would calculate the planet’s table—the specific numbers that predict its position at any arbitrarily chosen time. Finally, with all the planets thus rendered on paper, it would at last be possible to see whether any measured motion in the observed solar system escaped Le Verrier’s written account. If any such an anomaly appeared, there the next Neptune would lie, trembling on the point of discovery.

  In all, Le Verrier estimated, it would take at least a decade to complete the task, probably more—and meeting even that deadline would require the services of an assistant to take on the monotonous labor of calculation along with his own complete freedom to pursue his inquiry for as long as it would take.

  The excellencies at the Ministry of Public Instruction raised no objections—and why would they? One cheaply paid assistant and the license to do research for which he was clearly suited was hardly a difficult request to grant the man who conquered Neptune. Perhaps predictably, though, Le Verrier didn’t start right away. He had applause to reap—a tour of England in 1847 was only one such distraction—and Paris between 1848 and 1850 was roiled by the political transition that ultimately produced France’s Second Empire, with the original Napoleon’s nephew seizing power as Napoleon III. Le Verrier, like Laplace before him, took part in revolutionary politics—and like his intellectual ancestor, managed to navigate treacherous shifts in power unscathed. By 1850, with his position stable and the power struggle resolved, he could once again focus on problems in celestial mechanics. Arrogant ass though he may have seemed—and been—to a growing number of his peers, he quickly demonstrated that he was, in fact, the first astronomer of his age.

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  If Le Verrier had a secret superpower—some special gift that propelled him to insights his contemporaries missed—it lay with his knack for sniffing out the subtleties of the physics implied by his calculations. As good as he was as a mathematical astronomer, none of his peers would have seen him as the best mathematician of his day. Nor was he an observational maestro. When he became director of the Paris Observatory in 1854, he managed men who stood to the eyepieces, but it wasn’t his job (or inclination) to do so himself. Instead, his signal contribution came in reasoning from equations to their solutions to an interpretation of what the numbers implied about the actual events in the world. He was able to remind his peers of this as soon as he stepped off the carousel of fame and returned to the concentrated labor of celestial analysis. He tackled a seemingly minor problem—a close examination of the orbits of what were then still known as the minor planets, the asteroids. At stake was a question of origins: how could astronomers explain the growing heap of rubble found in the gap between Mars and Jupiter?

  The first (and, unsurprisingly, the largest) asteroid, Ceres, had been discovered in 1801. The next year, Pallas was identified by the German astronomer Heinrich Olbers. Olbers published the first guess as to
why there was more than one object sweeping through orbital tracks that, in the rest of the known solar system, would belong to just one much larger object, a “major” planet. His idea: the two little objects identified so far were what was left from a planetary catastrophe: once, he argued, there must have been a much larger body out there—a hypothetical fifth planet from the sun.

  That planet would be dubbed Phaeton—Apollo’s son, struck down by Zeus (Jupiter) after he lost control of his father’s sun-chariot. Olbers suggested that the asteroids were all that were left after the celestial Phaeton had been destroyed in an early solar system cataclysm. Later notions included the idea that Phaeton had passed too close to Jupiter, to shatter under the stress of the gravitational force imposed by the largest planet in the solar system, or that it had been whacked by another large object at some earlier moment. Whatever the particular history involved, Olbers made one clear prediction: if that missing planet had once existed, only to be blown apart, then there should be dozens, hundreds—who knew how many?—asteroids to be discovered in the same general area that had already yielded up Ceres and Pallas.

  He was quite right about that, of course, as he proved by becoming the first observer to discover a second asteroid, Vesta, in 1807. It’s also important to note that his idea that the early solar system experienced some kind of a demolition derby can’t be dismissed out of hand. After all, the best current reconstruction of how our Earth got its moon is the so-called giant impact hypothesis: an object about the size of Mars colliding with the proto-Earth one hundred million years or less after the birth of the solar system as a whole. At least one such hypothetical whack-and-hover object even has its own name, Theia (for the Titan whose daughter was Selene, goddess of the moon).*