The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World - Edward Dolnick (2011)
Part III. Into the Light
Chapter 49. 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 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 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.