The Clockwork Universe (29 page)

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 astonishing theorem. Among the mysteries that Newton had to solve, one of the deepest was this: how could he justify the assumption 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 mass. Make a calculation based on that simplifying assumption—what was the shape of the moon's orbit, 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 God had designed the universe mathematically.

The
Principia
seemed to proclaim that message. What, after
all, was the meaning of Newton's demonstration that real-life ob
jects 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
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 quantities of matter which they contain.”
All bodies
,
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 space, 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
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 gods no mortal may approach,” Halley wrote, in an adulatory poem published with the
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
all the way to the end, and past it. The Royal Society had only ventured into publishing once before. In 1685 it had published a lavish volume called
The History of Fishes
and lost money. Now the Society instructed Halley to print the
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
The
History of Fishes.

Chapter Fifty
Only Three People

From the beginning, the
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
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.”

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
, much as Bertrand Russell would later write
ABC of Relativity.
An Italian writer produced
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
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
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-fashioned tools. What looks at a glance like classical 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
, 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 classical, geometric language. “By the help of the new Analysis [i.e., calculus] Mr. Newton found out most of the Propositions in his
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
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 scrap of paper—that would indicate a private mode of composition other than the public one we know in the
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
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 arsenal that he himself had built. “As we read the
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
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 astonishingly 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. Molière 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
, 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
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 classical 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
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 space, 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 space? 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, “God could make matter act at a distance—to deny this was to deny God'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 lassos across endless regions of space. Invoking God, said Leibniz, was not good enough. If gravity was a force that God brought about “without using any intelligible means,” then that would not make sense
“even if an angel, not to say God 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 passes 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 orbit. The force seems to pass 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 orbit. 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 space. 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 titan 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 astonishingly 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
change in its orbit. (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 cannonballs 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
, 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 space 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 anticipated. 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 pass 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.”