The Clockwork Universe Part 11

"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 a.s.sistant, "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 cliche 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 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! 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 a.s.sault 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 ma.s.ses 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 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? 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?

Ma.s.s 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 Principia, "is a thing of far greater difficulty than I was aware of."

But Newton did do the business right, and astonis.h.i.+ngly quickly. In April 1686, less than two years after Halley's first visit, Newton sent Halley his completed ma.n.u.script. His nine-page essay had grown into the Principia 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 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 p.r.o.nouncements 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. 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 p.r.o.nouncements 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 s.p.a.ce 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 b.a.l.l.s, 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 Principia immortal. immortal.

Chapter Forty-Eight.

Trouble with Mr. Hooke If not for the Principia Principia's unsung hero, Edmond Halley, the world might never have seen Book III. At the time he was working to coax the Principia 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 n.o.body else seemed to be paying attention. Despite its ill.u.s.trious members.h.i.+p, the Royal Society periodically fell into confusion. This was such a period, with no one quite in charge and meetings often canceled. 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 n.o.body else seemed to be paying attention. Despite its ill.u.s.trious members.h.i.+p, 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 Principia from the printer and delivered the first copies to Newton, Halley never dared even for a moment to relax his guard. 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 ma.n.u.script, 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 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." 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 p.r.i.c.kly 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 surpa.s.sed; Newton's main interests were in other areas altogether. And more trouble lay just ahead, though Hooke could not have antic.i.p.ated 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. .h.i.therto 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 pa.s.sage about how Newton stood "on the shoulders of giants.") Thirty years would pa.s.s-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 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. 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 compet.i.tion. 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.

Chapter Forty-Nine.

The System of the World "I must now again beg you," Halley wrote Newton at the height of the Hooke affair, "not to let your resentments run so high, as to deprive us of your third book." Halley would have pleaded even more fervently if Newton had told him outright what riches he had reserved for Book III. Newton gave in to Halley's pleas. Perhaps he had meant to do so all along, although Newton seldom bothered to bark without also going on to bite.

The key to Book III was one astonis.h.i.+ng theorem. Among the mysteries that Newton had to solve, one of the deepest was this: how could he justify the a.s.sumption that any object whatsoever, no matter how tiny or gigantic, no matter how odd its shape, no matter how complicated its makeup, could be treated mathematically as if it were a single point? Newton hadn't had a choice about simplifying things in that way, because otherwise he could not have gotten started, but it seemed an unlikely fiction.

Then, in Book III, Newton delivered an extraordinarily subtle, calculus-based proof that a complicated object could legitimately be treated as a single point. In reality the Earth was eight thousand miles in diameter and weighed thousands of billions of tons; mathematically it could be treated as a point with that same unimaginable ma.s.s. Make a calculation based on that simplifying a.s.sumption-what was the shape of the moon's...o...b..t, say?-and the result would match snugly with reality.

Everything depended on the inverse-square law. If the universe had been governed by a different law, Newton showed, then his argument about treating objects as points would not have held, nor would the planets have fallen into stable orbits. For Newton, this was yet more evidence that G.o.d had designed the universe mathematically.

The Principia Principia seemed to proclaim that message. What, after all, was the meaning of Newton's demonstration that real-life objects could be treated as idealized, abstract points? It meant that all of the mathematical arguments that Newton had made in Book I turned out to describe the actual workings of the world. Like the world's most fantastic pop-up book, the geometry text of Book I rose to life as the real-world map of Book III. Newton introduced his key findings with a trumpet flourish. "I now demonstrate the frame of the System of the World," he wrote, which was to say, "I will now lay out the structure of the universe." seemed to proclaim that message. What, after all, was the meaning of Newton's demonstration that real-life objects could be treated as idealized, abstract points? It meant that all of the mathematical arguments that Newton had made in Book I turned out to describe the actual workings of the world. Like the world's most fantastic pop-up book, the geometry text of Book I rose to life as the real-world map of Book III. Newton introduced his key findings with a trumpet flourish. "I now demonstrate the frame of the System of the World," he wrote, which was to say, "I will now lay out the structure of the universe."

And so he did. Starting with his three laws and a small number of propositions, Newton deduced all three of Kepler's laws, which dealt with the motions of the planets around the sun; he deduced Galileo's law about objects in free fall, which dealt with the motion of objects here on Earth; he explained the motion of the moon; he explained the path of comets; he explained the tides; he deduced the precise shape of the Earth.

The heart of the Principia Principia was a breathtaking generalization. Galileo had made a leap from objects sliding down a ramp to objects falling through the air. Newton leaped from the Earth's pulling an apple to every pair of objects in the universe pulling one another. "There is a power of gravity," Newton wrote, "pertaining to all bodies, proportional to the several quant.i.ties of matter which they contain." was a breathtaking generalization. Galileo had made a leap from objects sliding down a ramp to objects falling through the air. Newton leaped from the Earth's pulling an apple to every pair of objects in the universe pulling one another. "There is a power of gravity," Newton wrote, "pertaining to all bodies, proportional to the several quant.i.ties of matter which they contain." All bodies All bodies, everywhere. everywhere.

This was the theory of "universal gravitation," a single force and a single law that extended to the farthest reaches of the universe. Everything pulled on everything else, instantly and across billions of miles of empty s.p.a.ce, the entire universe bound together in one vast, abstract web. The sun pulled the Earth, an ant tugged on the moon, stars so far away from Earth that their light takes thousands of years to reach us pull us, and we pull them. "Pick a flower on Earth," said the physicist Paul Dirac, "and you move the farthest star."

With a wave of Newton's wand, the world fell into place. The law of gravitation-one law-explained the path of a paperweight knocked off a desk, the arc of a cannonball shot across a battlefield, the orbit of a planet circling the sun or a comet on a journey that extended far, far beyond the solar system. An apple that fell a few feet to the ground, in a matter of seconds, obeyed the law of gravitation. So did a comet that traveled hundreds of millions of miles and neared the Earth only once every seventy-five years.

And Newton had done more than explain the workings of the heavens and the Earth. He had explained everything using the most familiar, literally the most down-to-earth force of all. All babies know, before they learn to talk, that a dropped rattle falls to the ground. Newton proved that if you looked at that observation with enough insight, you could deduce the workings of the cosmos.

The Principia Principia made its first appearance, in a handsome, leatherbound volume, on July 5, 1687. The scientific world searched for superlatives worthy of Newton's achievement. "Nearer the G.o.ds no mortal may approach," Halley wrote, in an adulatory poem published with the made its first appearance, in a handsome, leatherbound volume, on July 5, 1687. The scientific world searched for superlatives worthy of Newton's achievement. "Nearer the G.o.ds no mortal may approach," Halley wrote, in an adulatory poem published with the Principia Principia. A century later the reverence had scarcely died down. Newton was not only the greatest of all scientists but the most fortunate, the French astronomer Lagrange declared, for there was only one universe to find, and he had found it.

Halley watched over the Principia Principia all the way to the end, and past it. The Royal Society had only ventured into publis.h.i.+ng once before. In 1685 it had published a lavish volume called all the way to the end, and past it. The Royal Society had only ventured into publis.h.i.+ng once before. In 1685 it had published a lavish volume called The History of Fishes The History of Fishes and lost money. Now the Society instructed Halley to print the and lost money. Now the Society instructed Halley to print the Principia Principia at his own expense, since he was the one who had committed it to publication in the first place. Halley agreed, though he was far from rich. The work appeared, to vast acclaim, but the Society's finances fell further into disarray. It began paying Halley his salary in unsold copies of at his own expense, since he was the one who had committed it to publication in the first place. Halley agreed, though he was far from rich. The work appeared, to vast acclaim, but the Society's finances fell further into disarray. It began paying Halley his salary in unsold copies of The The History of Fishes. History of Fishes.

Chapter Fifty.

Only Three People From the beginning, the Principia Principia had a reputation for difficulty. When Newton brushed by some students on the street one day, he heard one of them mutter, "There goes the man that writt a book that neither he nor any body else understands." It was almost true. When the had a reputation for difficulty. When Newton brushed by some students on the street one day, he heard one of them mutter, "There goes the man that writt a book that neither he nor any body else understands." It was almost true. When the Principia Principia first appeared, it baffled all but the ablest scientists and mathematicians. (The first print run was tiny, between three and four hundred.) "It is doubtful," wrote the historian Charles C. Gillispie, "whether any work of comparable influence can ever have been read by so few persons." first appeared, it baffled all but the ablest scientists and mathematicians. (The first print run was tiny, between three and four hundred.) "It is doubtful," wrote the historian Charles C. Gillispie, "whether any work of comparable influence can ever have been read by so few persons."

The historian A. Rupert Hall fleshed out Gillispie's remark. Perhaps half a dozen scientists, Hall reckoned, fully grasped Newton's message on first reading it. Their astonished praise, coupled with efforts at recasting Newton's arguments, quickly drew new admirers. In time popular books would help spread Newton's message. Voltaire wrote one of the most successful, Elements of Newton's Philosophy Elements of Newton's Philosophy, much as Bertrand Russell would later write ABC of Relativity. ABC of Relativity. An Italian writer produced An Italian writer produced Newtonianism for Ladies Newtonianism for Ladies, and an English author using the pen name Tom Telescope wrote a hit children's book.

But in physics a mystique of impenetrability only adds to a theory's allure. In 1919, when the New York Times New York Times ran a story on Einstein and relativity, a subheadline declared, "A Book for 12 Wise Men." A smaller headline added, "No More in All the World Could Comprehend It." A few years later a journalist asked the astronomer Arthur Eddington if it was true that only three people in the world understood general relativity. Eddington thought a moment and then replied, "I'm trying to think who the third person is." ran a story on Einstein and relativity, a subheadline declared, "A Book for 12 Wise Men." A smaller headline added, "No More in All the World Could Comprehend It." A few years later a journalist asked the astronomer Arthur Eddington if it was true that only three people in the world understood general relativity. Eddington thought a moment and then replied, "I'm trying to think who the third person is."

Two features, beyond the difficulty of its mathematical arguments, made the Principia Principia so hard to grasp. The first reflected Newton's hybrid status as part medieval genius, part modern scientist. Through the whole vast book Newton relies on concepts from calculus-infinitesimals, limits, straight lines homing in ever closer to curves-that he had invented two decades before. But he rarely mentions calculus explicitly or explains the strategy behind his arguments, and he makes only indirect use of calculus's labor-saving machinery. so hard to grasp. The first reflected Newton's hybrid status as part medieval genius, part modern scientist. Through the whole vast book Newton relies on concepts from calculus-infinitesimals, limits, straight lines homing in ever closer to curves-that he had invented two decades before. But he rarely mentions calculus explicitly or explains the strategy behind his arguments, and he makes only indirect use of calculus's labor-saving machinery.

Instead he makes modern arguments using old-fas.h.i.+oned tools. What looks at a glance like cla.s.sical geometry turns out to be a more exotic beast, a kind of mathematical centaur. Euclid would have been baffled. "An ancient and venerable mathematical science had been pressed into service in a subject area for which it seems inappropriate," writes one modern physicist. "Newton's geometry seems to shriek and groan under the strain, but it works perfectly."

There are almost no other historical examples of so strange a performance as this use/nonuse of calculus. To get something of its flavor, we have to imagine far-fetched scenarios. Think, for instance, of a genius who grew up using Roman numerals but then invented Arabic numerals. And then imagine that he conceived an incredibly complex theory that relied heavily on the special properties of Arabic numerals-the way they make calculations easy, for instance. Finally, imagine that when he presented that theory to the world he used no Arabic numerals at all, but only Roman numerals manipulated in obscure and never-explained ways.

Decades after the Principia Principia, Newton offered an explanation. In his own investigations, he said, he had used calculus. Then, out of respect for tradition and so that others could follow his reasoning, he had translated his findings into cla.s.sical, geometric language. "By the help of the new a.n.a.lysis [i.e., calculus] Mr. Newton found out most of the Propositions in his Principia Philosophiae Principia Philosophiae," he wrote, referring to himself in the third person, but then he recast his mathematical arguments so that "the System of the Heavens might be founded upon good Geometry."

Newton's account made sense, and for centuries scholars took it at face value. He knew he was presenting a revolutionary theory. To declare that he had reached startling conclusions by way of a strange, new technique that he had himself invented would have been to invite trouble and doubt. One revolution at a time.

But it now turns out that Newton did not not use calculus's shortcuts in private and then reframe them. "There is no letter," declared one of the most eminent Newtonians, I. Bernard Cohen, "no draft of a proposition, no text of any kind-not even a lone sc.r.a.p of paper-that would indicate a private mode of composition other than the public one we know in the use calculus's shortcuts in private and then reframe them. "There is no letter," declared one of the most eminent Newtonians, I. Bernard Cohen, "no draft of a proposition, no text of any kind-not even a lone sc.r.a.p of paper-that would indicate a private mode of composition other than the public one we know in the Principia Principia." The reason that Newton claimed otherwise was evidently to score points against Leibniz. "He wanted," wrote Cohen, "to show that he understood and was using the calculus long before Leibniz."

This is curious, for Newton had had understood calculus long before Leibniz, and so it would have made perfect sense for him to have drawn on its hugely powerful techniques. But he did not. The reason, evidently, was that he was such a geometric virtuoso that he felt no impulse to deploy the powerful new a.r.s.enal that he himself had built. "As we read the understood calculus long before Leibniz, and so it would have made perfect sense for him to have drawn on its hugely powerful techniques. But he did not. The reason, evidently, was that he was such a geometric virtuoso that he felt no impulse to deploy the powerful new a.r.s.enal that he himself had built. "As we read the Principia Principia," the nineteenth-century scientist William Whewell would write, "we feel as when we are in an ancient armoury where the weapons are of gigantic size; and as we look at them, we marvel what manner of men they were who could use as weapons what we can scarcely lift as a burden."

Chapter Fifty-One.

Just Crazy Enough The second reason that the Principia Principia was so baffling is more easily stated-the theory made no sense. This is not to deny that the theory of gravitation "works." It works astonis.h.i.+ngly well. When NASA sent a man to the moon, every calculation along the way turned out precisely as Newton would have forecast centuries before. Nor does the model break down when applied to the farthest corners of the universe or the largest structures in nature. A theory that Newton devised by pondering the solar system and its one sun turns out to apply to galaxies made up of billions upon billions of suns, galaxies whose existence was unknown in Newton's day. was so baffling is more easily stated-the theory made no sense. This is not to deny that the theory of gravitation "works." It works astonis.h.i.+ngly well. When NASA sent a man to the moon, every calculation along the way turned out precisely as Newton would have forecast centuries before. Nor does the model break down when applied to the farthest corners of the universe or the largest structures in nature. A theory that Newton devised by pondering the solar system and its one sun turns out to apply to galaxies made up of billions upon billions of suns, galaxies whose existence was unknown in Newton's day.

But early scientists found themselves bewildered even so. The problem was that the theory predicted, but it did not explain. Why do rocks fall? "Because of gravity," the world has said ever since Newton, but that answer only pins a name to our ignorance. Moliere long ago made fun of the doctor who explained that opium makes us sleepy because it has a "dormitive potency." When Newton published the Principia Principia, many scientists hailed his mathematics but denounced "gravity" as the same sort of empty explanation. They demanded to know what it meant to say that the sun pulled the planets. How How did it pull them? What did the pulling? did it pull them? What did the pulling?

Another difficulty cut deeper. Today we've grown accustomed to thinking of modern science as absurd and unfathomable, with its talk of black holes and time travel and particles that are neither here nor there. "We are all agreed that your theory is crazy," Niels Bohr, one of the twentieth century's foremost physicists, once told a colleague. "The question that divides us is whether it is crazy enough to have a chance of being correct." We think of cla.s.sical science, in contrast, as a world of order and structure. But Newton's universe was as much an affront to common sense as anything that modern science has devised, and Newton's contemporaries found his his theory crazy, too. theory crazy, too.

One of the great mysteries of modern science is where consciousness comes from. How can a three-pound hunk of gray meat improvise a poem or spin out a dream? In Newton's day, gravity was just as bewildering.52 How could it be that every hunk of matter pulls every other? Newton's scheme seemed fantastically elaborate-the Alps pulled the Atlantic Ocean, which pulled back and pulled the Tower of London at the same time, which pulled Newton's pen, which pulled the Great Wall of China. How could all those pulls also stretch to the farthest corners of s.p.a.ce, and do so instantly? How does gravity snag a comet speeding outward past the farthest planets and yank it back toward us? How could it be that every hunk of matter pulls every other? Newton's scheme seemed fantastically elaborate-the Alps pulled the Atlantic Ocean, which pulled back and pulled the Tower of London at the same time, which pulled Newton's pen, which pulled the Great Wall of China. How could all those pulls also stretch to the farthest corners of s.p.a.ce, and do so instantly? How does gravity snag a comet speeding outward past the farthest planets and yank it back toward us?

Every aspect of the picture was mystifying. Gravity traveled across millions of miles of empty s.p.a.ce? How? How could a force be transmitted with nothing to transmit it? Leibniz was only one of many eminent thinkers who hailed the brilliance of Newton's mathematics but scoffed at his physics. "He claims that a body attracts another, at whatever distance it may be," Leibniz jeered, "and that a grain of sand on earth exercises an attractive force as far as the sun, without any medium or means."

It was Newton's notion of "action at a distance" that particularly galled Leibniz and many others. Newton agreed that there was no resolving this riddle, at least for the time being, but he put it to one side. "Mysterious though it was," historian John Henry writes, by way of summarizing Newton's view, "G.o.d could make matter act at a distance-to deny this was to deny G.o.d's omnipotence."

The skeptics were not so easily satisfied. Without some mechanism that explained how physical objects pulled one another, they insisted, this new theory of universal gravitation was not a step forward but a retreat to medieval doctrines of "occult forces." Proper scientific explanations involved tangible objects physically interacting with other tangible objects, not a mysterious force that flung invisible, undetectable la.s.sos across endless regions of s.p.a.ce. Invoking G.o.d, said Leibniz, was not good enough. If gravity was a force that G.o.d brought about "without using any intelligible means," then that would not make sense "even if an angel, not to say G.o.d himself, should try to explain it."

Nor was the mystery merely that gravity operated across vast distances. Unlike light, say, gravity could not be blocked or affected in any way whatsoever. Hold your hand in front of your eyes and the light from a lamp on the other side of the room cannot reach you. But think of a solar eclipse. The moon pa.s.ses between the Earth and the sun and blocks the sun's light, but it certainly doesn't block the gravitational force between Earth and sun-the Earth doesn't fly out of its...o...b..t. The force seems to pa.s.s through the moon as if it weren't there.

The closer you examined Newton's theory, the more absurd it seemed. Consider, for instance, the Earth in its...o...b..t. It travels at a fantastic speed, circling the sun at about 65,000 miles per hour. According to Newton, it is the sun's gravitational pull that keeps the Earth from flying off into s.p.a.ce. Now imagine a giant standing atop the sun and swinging the Earth around his head at that same speed of 65,000 miles per hour. Even if the t.i.tan held the Earth with a steel cable as thick as the Earth itself, the steel would snap at once, and Earth would shoot off into the void. And yet, with no sort of cable at all, gravity holds the Earth in an unbreakable grip.

Seen that way, gravity seems incredibly powerful. But compared with nature's other forces, like electricity and magnetism, it is astonis.h.i.+ngly feeble. If you hold a refrigerator magnet a tiny distance from the fridge, the magnet leaps through the air and sticks to the door. Which is to say, the magnetic pull of a refrigerator door outmuscles the gravitational pull of the entire Earth.

It was just as hard to understand how gravity could cut instantaneously across the cosmos. Newton maintained that it took no time whatsoever, not the briefest fraction of a second, for gravity to span even the vastest distance. If the sun suddenly exploded, one present-day physicist remarks, then according to Newton the Earth would instantly instantly change in its...o...b..t. (According to Einstein, we would be every bit as doomed, but we would have a final eight minutes of grace, blithely unaware of our fate.) change in its...o...b..t. (According to Einstein, we would be every bit as doomed, but we would have a final eight minutes of grace, blithely unaware of our fate.) None of this made sense. Kepler and Galileo, the first great scientists of the seventeenth century, had toppled the old theories that dealt with an everyday, commonsensical world where carts grind to a halt and cannonb.a.l.l.s fall to Earth. In its place they began to build a new, abstract work of mathematical architecture. Then Newton had come along to complete that mathematical temple.

So far, so good. Other great thinkers of the day, such men as Leibniz and Huygens, shared those mathematical ambitions. But when those peers and rivals of Newton looked closely at the Principia Principia, they drew back in shock and distaste. Newton had installed at the heart of the mathematical temple not some gleaming new centerpiece, they cried, but a shrine to ancient, outmoded, occult forces.

Curiously, Newton fully shared the misgivings about gravity's workings. The idea that gravity could act across vast, empty stretches of s.p.a.ce was, he wrote, "so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it." He returned to the point over the course of many years. "To tell us that every Species of Things is endow'd with an occult specific Quality [like gravity] by which it acts and produces manifest Effects, is to tell us nothing."

Except... except that the theory worked magnificently. Newton's mathematical laws gave correct answers-fantastically accurate answers-to questions that had long been out of reach, or they predicted findings that no one had ever antic.i.p.ated. No one until Newton had explained the tides, or why there are two each day, or why the Earth bulges as it does, or why the moon jiggles as it orbits the Earth.

Description and prediction would have to do, then, and explanation would have to wait. How the universe managed to obey the laws he had discovered-how gravity could possibly work-Newton did not claim to know. He would not guess.

He painted himself as the voice of hardheaded reason, Leibniz as the spokesman for airy speculation. When Leibniz rebuked him for proposing so incomplete a theory, Newton maintained that restraint was only proper. He would stick to what he could know, even though Leibniz talked "as if it were a Crime to content himself with Certainties and let Uncertainties alone." Newton opted for caution. "Ye cause of gravity is what I do not pretend to know," he wrote in 1693, "& therefore would take more time to consider of it."

Twenty years later, he had made no progress. "I have not been able to discover the cause of those properties of gravity," Newton wrote in 1713, "and I frame no hypotheses." Another two centuries would pa.s.s before Albert Einstein framed a new hypothesis.

In the meantime, Newton declared his peace with his own considerable achievement. "And to us it is enough that gravity does really exist, and act according to the laws which we have explained," he wrote, in a kind of grand farewell to his theory, "and abundantly serves to account for all the motions of the celestial bodies, and of our sea."

Chapter Fifty-Two.

In Search of G.o.d A different feature of Newton's theory of gravitation raised the most troubling question of all: where did G.o.d fit into Newton's universe? For seventeenth-century thinkers in general, and for Newton in particular, no question could have been more important. Today, the talk of G.o.d may seem misplaced. The Principia Principia is not a sacred text but a scientific work that makes specific, quant.i.tative predictions about the world. Those predictions are either true or false, regardless of what your religious views happen to be. is not a sacred text but a scientific work that makes specific, quant.i.tative predictions about the world. Those predictions are either true or false, regardless of what your religious views happen to be.53 But to judge the But to judge the Principia Principia by the accuracy of its predictions is to see only part of it. In a similar sense, you can admire Michelangelo's by the accuracy of its predictions is to see only part of it. In a similar sense, you can admire Michelangelo's Pieta Pieta as a gorgeous work of art even if you have no religious beliefs whatsoever. But to know what Newton thought he was doing, or Michelangelo, you need to take account of their religious motivation. as a gorgeous work of art even if you have no religious beliefs whatsoever. But to know what Newton thought he was doing, or Michelangelo, you need to take account of their religious motivation.

Newton had ambitions for his discoveries that stretched far beyond science. He believed that his findings were not merely technical observations but insights that could transform men's lives. The transformation he had in mind was not the usual sort. He had little interest in flying machines or labor-saving devices. Nor did he share the view, which would take hold later, that a new era of scientific investigation would put an end to superst.i.tion and set men's minds free. Newton's intent in all his work was to make men more pious and devout, more reverent in the face of G.o.d's creation. His aim was not that men rise to their feet in freedom but that they fall to their knees in awe.

So for Newton himself, the answer to the question where does G.o.d fit in the universe? where does G.o.d fit in the universe? was plain. G.o.d sat enthroned at the center of creation. Newton had always known it; he had always seen his work as a hymn to G.o.d's glory, though one written in curves and equations rather than notes on a staff. Now his dazzling success in the was plain. G.o.d sat enthroned at the center of creation. Newton had always known it; he had always seen his work as a hymn to G.o.d's glory, though one written in curves and equations rather than notes on a staff. Now his dazzling success in the Principia Principia provided still further evidence of the magnificence of G.o.d's design. provided still further evidence of the magnificence of G.o.d's design.

But the great irony of Newton's life was that many people looked at his work and drew precisely the opposite moral. Newton had not honored G.o.d, they insisted, but had made Him irrelevant. The more the universe followed laws that held everywhere and always, the less room G.o.d had to exercise his sovereignty. This critique was seldom directed at Newton personally (except by Leibniz). No one questioned the sincerity of his religious faith. Both his major works, the Principia Principia and the and the Opticks Opticks, concluded with long, heartfelt outpourings of praise for the Creator. "He is eternal and infinite, omnipotent and omniscient," Newton wrote in the Principia. Principia. "That is, his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things and knows all things that are or can be done." "That is, his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things and knows all things that are or can be done."

Still, the faithful insisted, Newton had inadvertently given aid and comfort to the enemy. He had bolstered the cause of science, and science had shown itself to be an enterprise devoted to demoting G.o.d. Everyone knew that the history of religion was filled with miraculous interventions-floods, burning bushes, the sick healed, the dead returned to life. G.o.d did not merely watch his creation. On countless occasions He had stepped in and directly altered the course of events. And now, it seemed, science threatened to push G.o.d aside.

This made for a debate over gravity that in some ways antic.i.p.ated the nineteenth-century battle over evolution. Such fights may seem to turn on arcane issues-planets and mathematical laws, fossils and apes-but in intellectual history, giant wars are fought on narrow battlegrounds. The real issue is always man's place in the cosmos.

Like evolution, gravity raised questions that tangled up science, politics, and theology. By hemming in G.o.d, religious thinkers railed, science promoted atheism. Atheist Atheist, in the seventeenth century, was an all-purpose slur that embraced a range of suspicious beliefs, much as commie commie or or pinko pinko would in Cold War America. But the fear it exposed was real, for to challenge religion was to call the entire social order into question. "Is nothing sacred?" was not an empty bit of rhetoric but a howl of anguish. If religion were undermined, s.e.xual license and political anarchy were sure to follow. would in Cold War America. But the fear it exposed was real, for to challenge religion was to call the entire social order into question. "Is nothing sacred?" was not an empty bit of rhetoric but a howl of anguish. If religion were undermined, s.e.xual license and political anarchy were sure to follow.

Nor did science aim only at toppling age-old beliefs. Even worse, in the eyes of its detractors, the new thinkers meant to replace time-honored doctrines with their own dubious subst.i.tutes. "Scientists, like whoring Jerusalem and Babylon, have turned away from G.o.d and have put in His stead their own systems and explanations," writes one modern historian, in summarizing the antiscience case. "And these are the idols they wors.h.i.+p: not the world created by G.o.d, but the mechanistic representations-like idols, devoid of spirit-that are the works of their own crazed imaginations."

If the universe was a machine, as science seemed to teach, then humans were just one more form of matter and there was no such thing as the soul, or choice, or responsibility. In such a world, morality would have no meaning, and, everyone would know, as one appalled writer put it, that "they may do any thing that they have a mind to."

So Newton and Leibniz squared off one last time, this time in an ideological clash over G.o.d and gravity. The battleground was the issue of G.o.d's intervention in the world. Each man accused the other of maligning G.o.d and attacking Christianity. Newton began by insisting that his theory of gravitation did did have an explicit role for G.o.d. It was not simply that, at creation, G.o.d had set the whole solar system in motion. More than that, He had continued ever since to fine-tune His creation. The planets could not be left to run on their own, Newton's calculations showed; their ever-changing pulls on one another meant that their orbits were not quite stable. Left unattended, the solar system would fall out of kilter and, eventually, tumble into chaos. have an explicit role for G.o.d. It was not simply that, at creation, G.o.d had set the whole solar system in motion. More than that, He had continued ever since to fine-tune His creation. The planets could not be left to run on their own, Newton's calculations showed; their ever-changing pulls on one another meant that their orbits were not quite stable. Left unattended, the solar system would fall out of kilter and, eventually, tumble into chaos.

And so the world had not been left unattended. This was, Newton maintained, still further proof of G.o.d's wisdom. If He had designed the universe to run unsupervised, He would have left room for the foolish and skeptical to argue that if G.o.d is absent now now, perhaps He was absent always. always. G.o.d had known better. G.o.d had known better.

The question of whether G.o.d had neglected his creation was so touchy that Newton's followers produced a second argument to demonstrate His ongoing presence. The miracles recorded in the Bible had taken place long ago. How to show that the age of miracles had not pa.s.sed?