The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World

by Edward Dolnick

Since God himself had fashioned the great chain, it was necessarily perfect and could not be missing any links. So, just as there were countless creatures reaching downward from humans to the beasts, there had to be countless steps leading upward from humans to God. QED.

Each link had its proper place in the hierarchy, king above noble above commoner, husband above wife above child, dog above cat, worm above oyster. The lion was king of beasts, but every domain had a “king”: the eagle among birds, the rose among flowers, the monarch among humans, the sun among the stars. The various kingdoms themselves had specific ranks, too, some lower and some higher—stones, which are lifeless, ranked lower than plants, which ranked lower than shellfish, which ranked lower than mammals, which ranked lower than angels, with innumerable other kingdoms filling all the ranks in between.

Strikingly, no one saw any contradiction in the views of the two camps. In part this reflected a division of labor. The physicists focused on the elegance of God’s aesthetics, the biologists on the range of His inventiveness. Both sides were bound by the shared conviction, deeper than any possible division, that God had designed every feature of the universe. For the physicists, that view led directly to the idea that God was a mathematician, and progress. For biologists, it led down a blind alley and made the discovery of evolution impossible.

Two related beliefs helped rule out any possibility of a seventeenth-century Darwin. The first was the assumption that every feature of the world had been put there for man’s benefit. Every plant, every animal, every rock existed to serve us. The world contained wood, the Cambridge philosopher Henry More explained, because otherwise human houses would have been only “a bigger sort of beehives or birds’ nests, made of contemptible sticks and straw and dirty mortar.” It contained metal so that men could assault one another with swords and guns, rather than sticks, as they enjoyed the “glory and pomp” of war. The second assumption that blinded Newton and his contemporaries to evolution was the idea that the universe was almost brand-new. The Bible put creation at a mere six thousand years in the past. Even if someone had conceived of an evolving natural world, that tiny span of time would not have

offered enough elbow room.

For the mathematically minded, the notion of glimpsing God’s plan has always exerted a hypnotic pull. The seduction is twofold. On the one hand, delving into the world’s mathematical secrets gives a feeling of having one’s hands on nature’s beating heart; on the other, in a world of chaos and disaster, mathematics provides a refuge of eternal, unchallengeable truths and perfect order.

Kepler had followed Copernicus in placing the sun at the center of his model, but then Kepler had moved a crucial step beyond all his predecessors. Not only did all the planets circle the sun, he noted, but the farther a planet was from the sun, the slower it traveled in its orbit. Somehow the sun must propel the planets, and whatever force it employed plainly grew weaker with distance.

“Never in history,” marvels the historian of science Owen Gingerich, “has a book so wrong been so seminal in directing the future course of science.”

Kepler knew, for example, how long it took each planet to orbit the sun—Mercury, 3 months; Venus, 7 months; Earth, 1 year; Mars, 2 years; Jupiter, 12 years; Saturn, 30 years—but try as he might he could not find a rule to connect

those numbers.

This was Kepler’s first law—the planets travel in an ellipse with the sun at one focus.

Kepler’s second law was heretical, too. It had to do with the planets’ speed as they travel, and it involved another assault on uniformity. The planets didn’t travel in

perfect circles, Kepler claimed, and they didn’t travel at a steady pace, either.

It took Kepler two years of false starts to find his second law. (He earned his living, in the meantime, as imperial mathematician to Rudolph II, the Habsburg emperor whose court was in Prague. Kepler’s official duties largely centered on such tasks as preparing horoscopes and making astrology-based forecasts of next season’s weather or a stalemated war’s outcome.)

The natural way to describe a planet’s motion was to chart its position every ten days, say, and then compute the distance between one point and the next. But that procedure turned out not to reveal any general rule. In a moment of inspiration Kepler saw a better way. The key was to think not of distance, which seemed natural, but of area, which seemed irrelevant.

Kepler’s second law: the line from a planet to the sun sweeps out equal areas in equal times.

What Kepler had found was a way—a mysterious, complicated way—to tie the orbits of the various planets together. It required that you perform a messy calculation. Choose a planet, Kepler said, and then take its orbit and cube it (multiply it by itself three times). Next, take the planet’s year and square it (multiply it by itself ). Divide the first answer by the second answer. For every planet, the result of that calculation will be the same. Kepler’s third law is the assertion that if you follow that unappetizing recipe the answer always comes out the same.

Kepler knew, for instance, that Mars’s distance from the sun is 1.53 times Earth’s distance, and Mars’s year is 1.88 times Earth’s year. He saw—somehow—that 1.53 × 1.53 × 1.53 = 1.88 × 1.88. The other planets all told the same story. (Put another way, the length of a planet’s year depends not on its distance from the sun, or on that distance squared, but on something in between—the distance raised to the 3/2 power.) But why? What did it mean?

Galileo not only defended Copernicus against his critics but, in the course of making his argument, devised a theory of relativity. Three centuries before Einstein’s version, Galileo’s theory proved nearly as hard for common sense to grasp.

The ship, the sailors, the passengers, the rock falling from the mast, are all in horizontal motion, all of them moving together. The rock lands at the base of the mast because mast and rock are both moving horizontally, in unison, at the same time as the rock is hurtling downward. “Shut yourself up with some friend in the main cabin below decks on some large ship,” Galileo wrote. Bring in some butterflies, a fishbowl with some fish swimming around, a leaky jug dripping water into a pan on the floor. No matter how closely you looked for something out of the ordinary (the fish clustered against one side of their bowl, for instance, or the drops of water missing the pan), Galileo went on, “you could not tell from any of them whether the ship was moving or standing still.” The same holds for the Earth itself, and all its passengers, as it speeds along on its voyage.

Imagine someone firing a gun horizontally, and at the same instant someone standing next to the shooter and dropping a bullet from the same height as the gun. When the two bullets reach the ground, they will be far apart. The one shot from the gun will have traveled hundreds of yards; the other will rest in the grass directly below the spot where it was dropped. Which bullet will hit the ground first? Surprisingly, both reach the ground at exactly the same moment. That’s what it means for the bullet’s vertical motion—its fall—to be independent of its horizontal motion. For Newton, that was enough to draw a remarkable conclusion.

Kepler had taken the first giant steps toward showing that mathematics governed the heavens. Galileo showed that mathematics reigned here on Earth. Newton’s great achievement, to peek ahead for a moment, was to demonstrate that Kepler’s discoveries and Galileo’s fit seamlessly together, and to explain why.

Galileo’s solution was so successful and so radical that everyone today—even those without the slightest knowledge of physics—takes his insight for granted. The breakthrough was to identify time—not distance or temperature or color or any of a thousand other possibilities—as the essential variable that governs the world.

just as a small stone falls at exactly the same rate as a heavy one, a camera falls at exactly the same rate as a diver.

The most ordinary graph—changes in housing prices over the last decade, rainfall this year, unemployment rates for the past six months—is an homage to Descartes.

Negative numbers once posed similar mysteries. Today the concept of a $5 bill is easy to understand, and so is a $5 IOU. A temperature of 10 degrees is straightforward, and so is 10 degrees below zero. But in the history of the human race, for the greatest intellects over the course of millennia, the notion of negative numbers seemed as baffling as the idea of time travel does to us.

In the history of science, abstraction was crucial. It was abstraction that made it possible to look past the chaos all around us to the order behind it.

Galileo won his argument, and science has never turned back. Mathematics remains the language of science because, ever since Galileo, we have taken for granted that abstraction is the pathway to truth.

The very name calculus served as a testimonial to the practical value of this new art; calculus is the Latin word for “pebble,” a reference to the heaps of stones once used as a calculating aid in addition and multiplication.

“Persist,” d’Alembert advised, “and faith will come to you.”

“In the century of Kepler, Galileo, Descartes, Pascal, and Newton,” one historian wrote, “the most versatile genius of all was Gottfried Wilhelm Leibniz.”

The symbols and language that Leibniz devised are still the ones that students learn today. Newton’s discovery was identical, at its heart, and in his masterly hands it could be turned to nearly any task. But Newton’s calculus is a museum piece today, while a buffed and honed version of Leibniz’s remains in universal use.

The story, which is the one thing everyone knows about Isaac Newton, may well be a myth.48 Despite his craving for privacy, Newton was acutely aware of his own legend, and he was not above adding a bit of gloss here and there. Historians who have scrutinized his private papers believe that his understanding of gravity dawned slowly, over several years, rather than in a flash of insight. He threw in the apple, some suspect, simply for color.

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.

Newton’s third law, for instance, was the famous “to every action, there is an equal and opposite reaction.”

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

But the great irony of Newton’s life was that many people looked at his work and drew precisely the opposite moral.

In the year 1600, for the crime of asserting that the Earth was one of an infinite number of planets, a man named Giordano Bruno was burned alive.

Perhaps the most dramatic confirmation came in 1846, when a French mathematician named Urbain Le Verrier looked hard at Newton’s laws, sat down to calculate, and discovered a new planet. This was Neptune, discovered by deduction. Le Verrier and other astronomers of the day knew that the orbit of the planet Uranus was not exactly what theory predicted. The reason, they proposed, was that some unseen planet was tugging it off course. Using Newton’s laws, Le Verrier managed to calculate the vital statistics—the mass, position, and path—of this supposed planet. He sent his results to the German astronomer Joseph Galle. Le Verrier’s letter reached Galle on September 23, 1846. On the same evening, Galle directed his telescope to the spot in the sky that Le Verrier had identified. There, just barely visible, he found Neptune.

Newton would have wept with rage to know that his scientific descendants spent their lifetimes proving conclusively that the clockwork universe ran even more smoothly than he had ever believed. It ran so marvelously well, in fact, that a new consensus quickly arose—just as Newton’s enemies had claimed, Newton had built a universe that had no place within it for God.

“If we evolved a race of Isaac Newtons, that would not be progress,” Aldous Huxley once remarked, with a mix of wonder and horror. “For the price Newton had to pay for being a supreme intellect was that he was incapable of friendship, love, fatherhood, and many other desirable things. As a man he was a failure; as a monster he was superb.”