Isaac Newton - James Gleick (2004)

Chapter 4. Two Great Orbs

HISTORIANS CAME TO SEE Newton as an end-point: the “culmination” and “climax” of an episode in human affairs conventionally called the Scientific Revolution. Then that term began to require apologies or ironic quotation marks.1Ambivalence is appropriate, when one speaks of the turning point in the development of human culture, the time when reason triumphed over unreason. The Scientific Revolution is a story, a narrative frame laid down with hindsight. Yet it exists and existed, not just in the backward vision of historians but in a self-consciousness among a small number of people in England and Europe in the seventeenth century. They were, as they thought, virtuosi. They saw something new in the domain of knowledge; they tried to express the newness; they invented academies and societies and opened channels of communication to promote their break with the past, their newscience.

We call the Scientific Revolution an epidemic, spreading across the continent of Europe during two centuries: “It would come to rest in England, in the person of Isaac Newton,” said the physicist David Goodstein. “On the way north, however, it stopped briefly in France.…”2 Or a relay race, run by a team of heroes who passed the baton from one to the next: COPERNICUS to KEPLER to GALILEO to NEWTON. Or the overthrow and destruction of the Aristotelian cosmology: a worldview that staggered under the assaults of Galileo and Descartes and finally expired in 1687, when Newton published a book.3

For so long the earth had seemed the center of all things. The constellations turned round in their regular procession. Just a few bright objects caused a puzzle—the planets, wanderers, like gods or messengers, moving irregularly against the fixed backdrop of stars. In 1543, just before his death, Nicolaus Copernicus, Polish astronomer, astrologer, and mathematician, published the great book De Revolutionibus Orbium Coelestium (“On the Revolutions of the Heavenly Spheres”). In it he gave order to the planets’ paths, resolving them into perfect circles; he set the earth in motion and placed an immobile sun at the center of the universe.4

Johannes Kepler, looking for more order in a growing thicket of data, thousands of painstakingly recorded observations, declared that the planets could not be moving in circles. He suspected the special curves known to the ancients as ellipses. Having thus overthrown one kind of celestial perfection, he sought new kinds, believing fervently in a universe built on geometrical harmony. He found an elegant link between geometry and motion by asserting that an imaginary line from a planet to the sun sweeps across equal areas in equal times.5

Galileo Galilei took spy-glasses—made by inserting spectacle makers’ lenses into a hollow tube—and pointed them upward toward the night sky. What he saw both inspired and disturbed him: moons orbiting Jupiter; spots marring the sun’s flawless face; stars that had never been seen—“in numbers ten times exceeding the old and familiar stars.”6 He learned, “with all the certainty of sense evidence,” that the moon “is not robed in a smooth polished surface but is in fact rough and uneven.” It has mountains, valleys, and chasms. (He also thought he had detected an atmosphere of dense and luminous vapors.)

He took pains to detail an unfamiliar fact of arithmetic: that, because in his spy-glass the moon’s diameter appeared thirty times larger, its apparent area was magnified by 900 and its apparent volume by 27,000—a square law and a cube law. This was essentially the only mathematics in his report, The Starry Messenger.7

It was strange to think of these dots of light as worlds, and more strange to think of a world—the whole world—as a body in motion, comparable to a mere stone. Yet without understanding motion, no one could place the heavenly bodies. There could be no cosmology without dynamics. Galileo felt this. What he saw in the skies of Florence in 1610, English pamphleteers tried to convey a generation later. In London a young chaplain, John Wilkins, began writing anonymous screeds. First, in 1638, The Discovery of a New World; or, a Discourse tending to prove, that it is probable there may be another habitable World in the Moon.8

Among all the celestial mysteries, the moon was special—so near, so changeling, so portentous. It stirred madness in weak minds; people were known to grow lunatic on a monthly cycle. Empedocles saw the moon as “a globe of pure congealed air, like hail inclosed in a sphere of fire.” Aristotle held it to be solid and opaque, whereas Julius Caesar said it must be transparent and pure, of the same essence as the heavens. Plain observation, night after night, failed to settle such matters. “You may as soon persuade some country peasants that the moon is made of green cheese (as we say) as that it is bigger than his cart-wheel,” wrote Wilkins, “since both seem equally to contradict his sight, and he has not reason enough to lead him farther than his senses.”9

How far could reason lead, without help? Francis Bacon, who had practiced logic and disputation as the king’s Learned Counsel and Attorney-General, lamented a natural philosophy built solely on words, ostentation, the elaborate knitting together of established ideas.

All the philosophy of nature which is now received, is either the philosophy of the Grecians, or that other of the alchemists.… The one is gathered out of a few vulgar observations, and the other out of a few experiments of a furnace. The one never faileth to multiply words, and the other ever faileth to multiply gold.10

He argued for experiment—the devising of “Crucial Instances” to divide the true from the false. Was the moon flame-like and airy or solid and dense? Since the moon reflects the sun’s light, Bacon proposed, a crucial instance would be a demonstration that a flame or other rare body does or does not reflect light. Perhaps the moon also “raises the waters,” Bacon suggested, and “makes moist things swell.” He proposed to call this effect Magnetic Motion.11

Wilkins cited the lunar observations of many authorities: Herodotus, the venerable Bede, the Romish divines, the Stoics, Moses, and Thomas Aquinas. But at last he chose a new witness.

I shall most insist on the observation of Galilæus, the inventor of that famous perspective, whereby we may discern the heavens hard by us; whereby those things which others have formerly guessed at, are manifested to the eye, and plainly discovered beyond exception or doubt.12

With his glass, Galileo could see plainly at a distance of sixteen miles what the naked eye could scarcely see at a mile and a half. He saw mountains and valleys; he saw a sphere of thick vaporous air; from these it was but a short step to infer wind and rain, seasons and weather, and so, Wilkins concluded, inhabitants. “Of what kind they are, is uncertain,” he conceded. “But I think that future ages will discover more; and our posterity, perhaps, may invent some means for our better acquaintance with these inhabitants.” As soon as the art of flying is discovered, he said, we should manage to transplant colonies to that other world. After all, time is the father of truth; ages passed before men crossed the seas and found other men at the far side of the world; surely other excellent mysteries remain to be discovered.

Wilkins urged that the strangeness of his opinions should be no reason to reject them. The surprising discovery of another New World weighed heavily: “How did the incredulous gaze at Columbus, when he promised to discover another part of the earth?”

Still, he agreed that the idea of multiple worlds brought paradoxical difficulties. The most troublesome was the tendency of heavy bodies to fall down: their gravity. “What a huddling and confusion must there be, if there were two places for gravity and two places for lightness?”13 Which way should bodies of that other world fall? To where should its air and fire ascend? Can we expect pieces of the moon to fall to earth?

He answered these questions in the terms of Copernicus and Kepler: by proposing that two worlds must have two centers of gravity. “There is no more danger of their falling into our world, than there is fear of our falling into the moon.” He reminded his readers of the simple nature of gravity: “nothing else, but such a quality as causes a propension in its subject to tend downwards towards its own centre.”14

The discovery of new worlds had lit a fuse leading to the destruction of the Aristotelian conception of gravity. It was inevitable. A multitude of worlds implied a multitude of reference frames. Up and down became relative terms, in the imaginations of philosophers, contrary to common experience. Wilkins did not shrink from considering the problem of what would happen to an object—a bullet, perhaps—sent to such a great height that it might depart “that magnetical globe to which it did belong.” It might just come to rest, he decided. Outside the earth’s sphere of influence, pieces of earth should lose their gravity, or their susceptibility to gravity. He offered a “similitude”:

As any light body (suppose the sun) does send forth its beams in an orbicular form; so likewise any magnetical body, for instance a round loadstone, does cast abroad his magnetical vigour in a sphere.… Any other body that is like affected coming within this sphere will presently descend towards the centre of it, and in that respect may be styled heavy. But place it without this sphere, and then the desire of union ceaseth, and so consequently the motion also.15

Newton read Wilkins as a boy in Grantham, at the apothecary Clarke’s.16 Whatever else he thought about the moon, he knew it was a great planetary object traveling through space at high speed. The mystery was why. Carried along, as Descartes said, in a vortex? Newton knew how big the moon was and how far away. By virtue of a coincidence, the moon’s apparent size was almost exactly the same as the sun’s, about one-half degree of arc, the coincidence that makes a solar eclipse such a perfect spectacle. It was necessary now to forge mental links across many orders of magnitude in scale: between the everyday and the unimaginably vast. Sitting in the orchard behind his farmhouse, musing continually on geometry, Newton could see other globes, dangling from their stems. A two-inch apple at a distance of twenty feet subtended the same half-degree in the sky. These ratios were second nature now, the congruent Euclidean triangles inscribed in his mind’s eye. When he thought about the magnitude of these bodies, another automatic part of the picture was an inverse square law: something varies as 1/x2. A disk twice as far away would seem not one-half as bright but one-fourth.

Newton was eager, as the Greeks had not been, to extend the harmony and abstraction of mathematics to the crude sublunary world in which he lived. An apple was no sphere, but he understood it to be flying through space along with the rest of the earth’s contents, spinning across 25,000 miles each day. Why, then, did it hang gently downward, instead of being flung outward like a stone whirled around on a string? The same question applied to the moon: what pushed it or pulled it away from a straight path?

Many years later Newton told at least four people that he had been inspired by an apple in his Woolsthorpe garden—perhaps an apple actually falling from a tree, perhaps not. He never wrote of an apple. He recalled only:

I began to think of gravity extending to the orb of the Moon …

—gravity as a force, then, with an extended field of influence; no cutoff or boundary—

& computed the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth … & found them answer pretty nearly. All this was in the two plague years of 1665–1666. For in those days I was in the prime of my age for invention & minded Mathematicks and Philosophy more than at any time since.17

Voltaire did mention the apple, as did other memoirists, and their second- and third-hand accounts gradually formed the single most enduring legend in the annals of scientific discovery.18 And the most misunderstood: Newton did not need an apple to remind him that objects fell to earth. Galileo had not only seen objects fall but had dropped them from towers and rolled them down ramps. He had grasped their acceleration and struggled to measure it. But most emphatically he declined to explain it. “The present does not seem to be the proper time to investigate the cause of the acceleration,” Galileo wrote, “… [but] merely to investigate and to demonstrate some of the properties of accelerated motion (whatever the cause of this acceleration may be).”19

Nor did Newton comprehend universal gravitation in a flash of insight. In 1666 he was barely beginning to understand. What he suspected about gravity he kept private for decades to come.

The apple was nothing in itself. It was half of a couple—the moon’s impish twin. As an apple falls toward the earth, so does the moon: falling away from a straight line, falling around the earth. Apple and moon were a coincidence, a generalization, a leap across scales, from close to far and from ordinary to immense. In his study and in his garden, in his state of incessant lonely contemplation, his mind alive with new modes of geometry and analysis, Newton made connections between distant realms of thought. Still, he was unsure. His computations were ambiguous; he only found them answer pretty nearly. He was attempting rare exactitude, more than any available raw data could support. Even the units of measure were too crude and variable. He took the mile to be 5,000 feet.20 He set one degree of the earth’s latitude at the equator equal to sixty miles, an error of about 15 percent. Some units were English, some antique Latin, others Italian: mile, passus, brace, pedes. He came up with a datum for the speed of the revolving earth: 16,500,000 cubits in six hours.21 He struggled to arrive at a datum for the rate of fall due to gravity. He had Galileo’s calculations, in a new translation: one hundred cubits in five seconds.22 He tried to derive his own measurements using a weight hanging on a cord and swinging in circles—a conical pendulum. This needed patience. He noted the pendulum making 1,512 “ticks” in an hour.23 He arrived at a constant for gravity more than double Galileo’s. He concluded that a body on the earth’s surface is drawn downward by gravity 350 times stronger than the tendency of the earth’s rotation to fling it outward.

To make the arithmetic work at all, he had to suppose that the power of attraction diminished rapidly according to distance from the center of the earth. Galileo had said that bodies fall with constant acceleration, no matter how far they are from the earth; Newton sensed that this must be wrong. And it would not be enough for gravity to fade in proportion to distance. He estimated that the earth attracted an apple 4,000 times as powerfully as it attracted the distant moon. If the ratio—like brightness, and like apparent area—depended on the square of distance, that might answer pretty nearly.24

He reckoned the distance of the moon at sixty times the earth’s radius; if the moon were sixty times farther than the surface of the earth from the center of the earth, then the earth’s gravity might be 3,600 times weaker there. He also derived this inverse-square law by an inspired argument from an observation of Kepler’s: the time a planet takes to make one orbit grows as the 3/2 power of its distance from the sun.25 Yet, with the data he had, he could not quite make the numbers work. He still found it necessary to attribute some of the moon’s motion to the vortices of Descartes.

He needed new principles of motion and force. He had tried some out in the Questiones, and now, in the plague year, he tried again. He wrote “axioms” in the Waste Book:

1. If a quantity once move it will never rest unlesse hindered by some externall caus.

2. A quantity will always move on in the same streight line (not changing the determination nor celerity of its motion) unless some externall cause divert it.26

Thus circular motion—orbital motion—demanded explanation. So far, the external cause was missing from the picture. And Newton posed himself a challenge: it ought to be possible to quantify this cause.

3. There is exactly so much required so much and noe more force to reduce a body to rest as there was to put it upon motion.

He continued through dozens more axioms, comprising a logical whole, but a tangled one. He was hampered by the chaos of language—words still vaguely defined and words not quite existing. He conceived of force as a thing to be measured—but in what units? Was force inherent in bodies, as Descartes thought? Or was force an external agent, impinging on bodies and changing a differently named quantity: quantity of motion; or quantity of mutation in its state27; or whole motion; or force of motion? Whatever this missing concept was, it differed from velocity and direction. Axiom 100:

A body once moved will always keepe the same celerity, quantity and determination of its motion.28

At twenty-four, Newton believed he could marshal a complete science of motion, if only he could find the appropriate lexicon, if only he could set words in the correct order. Writing mathematics, he could invent his own symbols and form them into a mosaic. Writing in English, he was constrained by the language at hand.29 At times his frustration was palpable in the stream of words. Axiom 103:

 … as the body (a) is to the body (b) so must the power or efficacy vigor strength or virtue of the cause which begets the same quantity of velocity. 30

Power efficacy vigor strength virtue—something was missing. But these were the laws of motion, in utero.