The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World - Edward Dolnick (2011)
Part III. Into the Light
Chapter 47. 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.