The Clockwork Universe (28 page)

Chapter Forty-Seven
Newton Bears Down

The paper was not really lost. Newton, the most cautious of men, wanted to reexamine his work before he revealed it to anyone. Looking over his calculations after Halley's visit, Newton did indeed catch a mistake. He corrected it, expanded his notes, and, three months later, sent Halley a formal, nine-page treatise, in Latin, titled “On the Motion of Bodies in an Orbit.” It did far, far more than answer Halley's question.

Kepler's discovery that the planets travel in ellipses, for instance, had never quite made sense. It was a “law” in the sense that it fit the facts, but it seemed dismayingly arbitrary. Why ellipses rather than circles or figure eights? No one knew. Kepler had agonized over the astronomical data for years. Finally, for completely mysterious reasons, ellipses had turned out to be the curves that matched the observations. Now Newton explained where ellipses came from. He showed, using calculus-based arguments, that if a planet travels in an ellipse, then the force that attracts it
must
obey an inverse-square law. The flip side was true, too. If a planet orbiting around a fixed point does obey an inverse-square law, then it travels in an ellipse.
⁵⁰
All this was a matter of strict mathematical fact. Ellipses and inverse-square laws were intimately connected, though it took Newton's genius to see it, just as it had taken a Pythagoras to show that right triangles and certain squares were joined by hidden ties.

Newton had solved the mystery behind Kepler's second law, as well. It, too, summarized countless astronomical observations in one compact, mysterious rule—planets sweep out equal areas in equal times. In his short essay, Newton deduced the second law, as he had deduced the first. His tools were not telescope and sextant but pen and ink. All he needed was the assumption that some force draws the planets toward the sun. Starting from that bare statement (without saying anything about the shape of the planets' orbits or whether the sun's pull followed an inverse-square law), Newton demonstrated that Kepler's law had to hold. Mystery gave way to order.

Bowled over, Halley rushed back to Cambridge to talk to Newton again. The world needed to hear what he had found. Remarkably, Newton went along. First, though, he would need to improve his manuscript.

Thus began one of the most intense investigations in the history of thought. Since his early years at Cambridge, Newton had largely abandoned mathematics. Now his mathematical fever surged up again. For seventeen months Newton focused all his powers on the question of gravity. He worked almost without let-up, with the same ferocious concentration that had marked his miracle years two decades before.

Albert Einstein kept a picture of Newton above his bed, like a teenage boy with a poster of LeBron James. Though he knew better, Einstein talked of how easily Newton made his discoveries. “Nature to him was an open book, whose letters he could read without effort.” But the real mark of Newton's style was not ease but power. Newton focused his gaze on whatever problem had newly obsessed him, and then he refused to look away until he had seen to its heart.

“Now I am upon this subject,” he told a colleague early in his investigation of gravity, “I would gladly know ye bottom of it before I publish my papers.” The matter-of-fact tone obscures Newton's drivenness. “I never knew him take any Recreation or Pastime,” recalled an assistant, “either in Riding out to take ye Air, Walking, Bowling, or any other Exercise whatever, thinking all Hours lost that was not spent in his Studyes.” Newton would forget to leave his rooms for meals until he was reminded and then “would go very carelessly, with Shooes down at Heels, Stockings unty'd . . . & his Head scarcely comb'd.”

Such stories were in the standard vein of anecdotes about absentminded professors, already a cliché in the 1600s,
⁵¹
except that in Newton's case the theme was not otherworldly dreaminess but energy and singleness of vision. Occasionally a thought would strike Newton as he paced the grounds near his rooms. (It was not quite true that he never took a walk to clear his head.) “When he has sometimes taken a Turn or two he has made a sudden Stand, turn'd himself about, run up ye stairs & like another Archimedes, with a
Eureka!
, fall to write on his Desk standing, without giving himself the Leasure to draw a Chair to sit down in.”

Even for Newton the assault on gravity demanded a colossal effort. The problem was finding a way to move from the idealized world of mathematics to the messy world of reality. The diagrams in Newton's “On Motion” essay for Halley depicted points and curves, much as you might see in any geometry book. But those points represented colossal, complicated objects like the sun and the Earth, not abstract circles and triangles. Did the rules that held for textbook examples apply to objects in the real world?

Newton was exploring the notion that all objects attracted one another and that the strength of that attraction depended on their masses and the distance between them. Simple words, it seemed, but they presented gigantic difficulties. What was the distance between the apple and the Earth? For two objects separated by an enormous distance, like the Earth and the moon, the question seemed easy. In that case, it hardly mattered precisely where you began measuring. For simplicity's sake, Newton took “distance” to mean the distance between the centers of the two objects. But when it came to the question of the attraction between an apple and the Earth, what did the center of the Earth have to do with anything? An apple in a tree was thousands of miles from the Earth's center. What about all those parts of the Earth that
weren't
at the center? If everything attracted everything else, wouldn't the pulls from bits of ground near the tree have to be taken into account? How would you tally up all those millions and millions of pulls, and wouldn't they combine to overcome the pull from a faraway spot like the center of the Earth?

Mass was just as bad. The Earth certainly wasn't a point, though Newton had drawn it that way. It wasn't even a true sphere. Nor was it uniform throughout. Mountains soared here, oceans swelled there, and, deep underground, strange and unknown structures lurked. And that was just on Earth. What of the sun and the other planets, and what about all their simultaneous pulls? “To do this business right,” Newton wrote Halley in the middle of his bout with the
Principia
, “is a thing of far greater difficulty than I was aware of.”

But Newton did do the business right, and astonishingly quickly. In April 1686, less than two years after Halley's first visit, Newton sent Halley his completed manuscript. His nine-page essay had grown into the
Principia
's five hundred pages and two-hundred-odd theorems, propositions, and corollaries. Each argument was dense, compact, and austere, containing not a spare word or the slightest note of warning or encouragement to his hard-pressed readers. The modern-day physicist Subrahmanyan Chandrasekhar studied each theorem and proof minutely. Reading Newton so closely left him more astonished, not less. “That all these problems should have been enunciated, solved, and arranged in logical sequence in seventeen months is beyond human comprehension. It can be accepted only because it is a fact.”

The
Principia
was made up of an introduction and three parts, known as Books I, II, and III. Newton began his introduction with three propositions now known as Newton's laws. These were not summaries of thousands of specific facts, like Kepler's laws, but magisterial pronouncements about the behavior of nature in general. Newton's third law, for instance, was the famous “to every action, there is an equal and opposite reaction.” Book I dealt essentially with abstract mathematics, focused on topics like orbits and inverse squares. Newton discussed not the crater-speckled moon or the watery Earth but a moving point P attracted toward a fixed point S and moving in the direction AB, and so on.

In Book II Newton returned to physics and demolished the theories of those scientists, most notably Descartes, who had tried to describe a mechanism that accounted for the motions of the planets and the other heavenly bodies. Descartes pictured space as pervaded by some kind of ethereal fluid. Whirlpools within that fluid formed “vortices” that carried the planets like twigs in a stream. Something similar happened here on Earth; rocks fell because mini-whirlpools dashed them to the ground.

Some such “mechanistic” explanation had to be true, Descartes insisted, because the alternative was to believe in magic, to believe that objects could spring into motion on their own or could move under the direction of some distant object that never came in contact with them. That couldn't be. Science had banished spirits. The only way for objects to interact was by making contact with other objects. That contact could be direct, as in a collision between billiard balls, or by way of countless, intermediate collisions with the too-small-to-see particles that fill the universe. (Descartes maintained that there could be no such thing as a vacuum.)

Much of Newton's work in Book II was to show that Descartes' model was incorrect. Whirlpools would eventually fizzle out. Rather than carry a planet on its eternal rounds, any whirlpool would sooner or later be “swallowed up and lost.” In any case, no such picture could be made to fit with Kepler's laws.

Then came Book III, which was destined to make the
Principia
immortal.

Chapter Forty-Eight
Trouble with Mr. Hooke

If not for the
Principia
's unsung hero, Edmond Halley, the world might never have seen Book III. At the time he was working to coax the
Principia
from Newton, Halley had no official standing to speak of. He was a minor official at the Royal Society—albeit a brilliant scientist—who had taken on the task of dealing with Newton because nobody else seemed to be paying attention. Despite its illustrious membership, the Royal Society periodically fell into confusion. This was such a period, with no one quite in charge and meetings often canceled.

So the task of shepherding along what would become one of the most important works in the history of science fell entirely to Halley. It was Halley who had to deal with the printers and help them navigate the impenetrable text and its countless abstruse diagrams, Halley who had to send page proofs to Newton for his approval, Halley who had to negotiate changes and corrections. Above all, it was Halley who had to keep his temperamental author content.

John Locke once observed that Newton was “a nice man to deal with”—“nice” in the seventeenth-century sense of “finicky”—which was true but considerably understated. Anyone dealing with Newton needed the delicate touch and elaborate caution of a man trying to disarm a bomb. Until he picked up the
Principia
from the printer and delivered the first copies to Newton, Halley never dared even for a moment to relax his guard.

On May 22, 1686, after Newton had already turned in Books I and II of his manuscript, Halley worked up his nerve and sent Newton a letter with unwelcome news. “There is one thing more I ought to informe you of,” he wrote, “viz, that Mr Hook has some pretensions upon the invention of ye rule of the decrease of Gravity. . . . He says you had the notion from him.” Halley tried to soften the blow by emphasizing the limits of Hooke's claim. Hooke maintained that he had been the one to come up with the idea of an inverse-square law. He conceded that he had not seen the connection between inverse squares and elliptical orbits; that was Newton's insight, alone. Even so, Halley wrote, “Mr Hook seems to expect you should make some mention of him.”

Instead, Newton went through the
Principia
page by page, diligently striking out Hooke's name virtually every time he found it. “He has done nothing,” Newton snarled to Halley. Newton bemoaned his mistake in revealing his ideas and thereby opening himself up to attack. He should have known better. “Philosophy [i.e., science] is such an impertinently litigious Lady that a man had as good be engaged in Law suits as have to do with her,” he wrote. “I found it so formerly & now I no sooner come near her again but she gives me warning.”

The more Newton brooded, the angrier he grew. Crossing out Hooke's name was too weak a response. Newton told Halley that he had decided not to publish Book III. Halley raced to soothe Newton. He could not do without Newton's insights; the Royal Society could not; the learned world could not.

* * *

Newton could have dismissed the controversy with a gracious tip of the hat to Hooke, for Hooke had indeed done him a favor. In 1684, as we have seen, Halley had asked Newton a question about the inverse-square law, and Newton had immediately given him the answer.

The reason Newton knew the answer is that Hooke had written him a letter four years before that asked the identical question. What orbit would a planet follow if it were governed by an inverse-square law? “I doubt not but that by your excellent method you will easily find out what that Curve must be,” Hooke had written Newton, “and its proprietys [properties], and suggest a physicall Reason of this proportion.”

Newton had solved the problem then and put it away. He never replied to Hooke's letter. This was perhaps inevitable, for Hooke and Newton had been feuding for years. Back in 1671, the Royal Society had heard rumors of a new kind of telescope, supposedly invented by a young Cambridge mathematician. The rumors were true. Newton had designed a telescope that measured a mere six inches but was more powerful than a conventional telescope six feet long. The Royal Society asked to see it, Newton sent it along, and the Society oohed and aahed.

Newton's reputation was made. This was Newton's first contact with the Royal Society, which at once invited him to join. He accepted. Only Hooke, until this new development England's unchallenged authority on optics and lenses, refused to add his voice to the chorus of praise.

Even a better-natured man than Hooke might have bristled at all the attention paid to a newcomer (Hooke was seven years older than Newton), but Hooke was fully as proud and prickly as Newton himself. In 1671 Hooke was an established scientific figure; Newton was unknown. Hooke had spent a career crafting instruments like the telescopes that Newton's new design had so dramatically surpassed; Newton's main interests were in other areas altogether. And more trouble lay just ahead, though Hooke could not have anticipated it. In a letter to the Royal Society thanking them for taking such heed of his telescope, Newton added a tantalizing sentence. In the course of his “poore & solitary endeavours,” he had found something remarkable.

Within a month, Newton followed up his coup with the telescope by sending the Royal Society his groundbreaking paper on white light. The nature of light was another of Hooke's particular interests. Once again, the outsider had barged into staked-out territory and put down his own marker. Deservedly proud of what he had found, Newton for once said so openly. His demonstration that white light was made up of all the colors was, Newton wrote, “the oddest, if not the most considerable detection, which has hitherto been made in the operation of nature.”

The paper, later hailed as one of the all-time landmarks in science, met with considerable resistance at first, from Hooke most of all. He had already done all of the same experiments, Hooke claimed, and, unlike Newton, he had interpreted them correctly. He said so, dismissively, lengthily, and unwisely. (It was at this point that Newton sent a letter to the hunchbacked Hooke with a mock-gracious passage about how Newton stood “on the shoulders of giants.”) Thirty years would pass—until 1704, the year following Hooke's death—before the world would hear any more about Newton's experiments on light.

Now, in 1686, with the first two books of the
Principia
in Halley's hands, Hooke had popped up again. For Hooke to venture yet another criticism, this time directed against Newton's crowning work, was a sin beyond forgiving. In Newton's eyes Hooke had done nothing to contribute to a theory of gravitation. He had made a blind guess and not known how to follow it up. The challenge was not to suggest that an inverse-square law might be worth looking at, which anyone might have proposed, but to work out what the universe would look like if that law held.

Hooke had not even known how to get started, but he had airily dismissed Newton's revelations as if they were no more than the working out of a few details that Hooke had been too busy for. “Now is not this very fine?” Newton snapped. “Mathematicians that find out, settle & do all the business must content themselves with being nothing but dry calculators & drudges & another that does nothing but pretend & grasp at all things must carry away all the invention. . . .”

Hooke was a true genius, far more than Salieri to Newton's Mozart, but he did not come up to Newton's level. Hooke's misfortune was to share so many interests with a man fated to win every competition. That left both men trapped. Newton could not bear to be criticized, and Hooke could not bear to be outdone. The two men never did make peace. On the rare occasions when they found themselves thrown together, Hooke stalked out of the room. Newton was just as hostile. Even twenty years after Hooke's death, Newton could not hear his name spoken without losing his temper.

During the many years when Hooke was a dominant figure at the Royal Society, Newton made a point of staying away. When Hooke finally died, in 1703, Newton immediately accepted the post of Royal Society president. At about the same time, the Royal Society moved to new quarters. In the course of the move the only known portrait of Hooke vanished.