Newton had completed this work by the time he received his bachelor’s degree, in April 1665. It would have established him as the greatest mathematician in Europe (and as the most accomplished undergraduate in the history of education) but he published none of it. Publication, he feared, might bring fame, and fame abridge his privacy. As he remarked in a letter written in 1670, “I see not what there is desirable in public esteem, were I able to acquire and maintain it. It would perhaps increase my acquaintance, the thing which I chiefly study to decline.”6
Soon after his graduation the university was closed owing to an epidemic of the plague, and Newton went home. There he had ample time to think. One day (and it seems quite plausibly to have dawned on him all at once) he hit upon the grand theory that had eluded Kepler and Galileo—a single, comprehensive account of how the force of gravitation dictates the motion of the moon and planets. As he recounted it:
In those days I was in the prime of my age for invention & minded Mathematics & Philosophy more than at any time since. … I began to think of gravity extending to the orb of the Moon & … from Kepler’s rule of the periodical times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces which keep the planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: & thereby compared 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.7
Newton is said to have recalled, near the end of his life, that this inspiration came to him when he saw an apple fall from the tree in front of his mother’s house. The story may be true—Newton’s desk in his bedroom looked out on an apple orchard, and even a Newton must occasionally have interrupted his work to gaze out the window—and it serves, in any event, to trace how he arrived at a quantitative description of gravitation that drew together the physics of the heavens and the earth.
Suppose, as Newton did that day, that the same gravitational force responsible for the apple’s fall extends “to the orb of the Moon,” and that its force decreases by the square of the distance over which it propagates.* The radius of the earth is 4,000 miles, meaning that Newton and his apple tree were located 4,000 miles from a point at the center of the earth from which (and this was one of Newton’s key insights) the gravitational force of the earth emanates. The moon’s distance from the center of the earth is 240,000 miles—60 times farther than that of the apple tree. If the inverse-square law holds, the falling apple should therefore experience a gravitational force 602, or 3,600, times stronger than does the moon. Newton assumed, from the principle of inertia, that the moon would fly away in a straight line, were it not constantly tugged from that path by the force of the earth’s gravity. He calculated how far the moon “falls” toward the earth—i.e., departs from a straight line in order to trace out its orbit—every second. The answer was 0.0044 feet per second. Multiplying 0.0044 by 3,600 to match the proposed strength of gravitation at the earth’s surface yielded 15.84 feet per second, or “pretty nearly” the 16 feet per second that an apple, or anything else, falls on Earth. This agreement confirmed Newton’s hypothesis that the same gravitational force that pulls the apple down pulls at the moon, too.
Having done the calculation, Newton silently set it aside. Various explanations can be offered for his quietude: The calculations fit “pretty nearly” but not perfectly, owing to inaccuracies in the estimated distance to the moon; Newton was interested in other matters, among them the binomial series and the nature of color; and, in any event, he seldom felt any impulse to call attention to himself: He didn’t publish the calculus, either, for twenty-seven years, and then anonymously.
The young Newton’s realization on universal gravitation went as follows: If the moon is 60 times as far from the center of the earth as is the apple (4,000 miles for the apple, 240,000 miles for the moon), and gravitation diminishes by the square of the distance, then the apple is subject to a gravitational force 602, or 3,600, times that experienced by the moon. The moon, therefore, should “fall” along the curve of its orbit th each second as does the apple. And so it does (time AB = time CD).
A few academic colleagues did become acquainted with elements of Newton’s research, however, and two years after returning to Trinity College, Cambridge, he was named Lucasian Professor of Mathematics. (The position had been vacated by his favorite teacher, the blustery and witty mathematician Isaac Barrow, who left to take up divinity studies and died seven years later of an opium overdose.) But Newton the teacher had little more in common with his colleagues than had Newton the student. Numerous among the professors were the so-called “wet epicures,” their lives spent, wrote the satirist Nicholas Amherst, “in a supine and regular course of eating, drinking, sleeping, and cheating the juniors.”8 Others were known as much for their eccentricities as for their scholarship; the master of Trinity, for one, was an effeminate shut-in who kept enormous house spiders in his rooms as pets. Not that Newton had any difficulty holding his own when it came to idiosyncrasies. Gaunt and disheveled, his wig askew, he dressed in run-down shoes and soiled linen, seldom stopped working, and frequently forgot to sleep. Once, puzzling over why he seemed to be losing his mental agility while working on a problem, he reflected on the matter, realized that he had not slept for days, and reluctantly went to bed. He forgot to eat as well, often rising from his desk at dawn to breakfast on the congealed remains of the dinner that had been brought to him and left untouched the night before. His rare efforts at conviviality fared poorly; one night while entertaining a few acquaintances he went to his room to fetch a bottle of wine, failed to return, and was found at his desk, hunched over his papers, wine and guests forgotten.
As the years passed, Newton elaborated the calculus, advanced the art of analytical geometry, did pioneering work in optics, and conducted innumerable experiments in alchemy (possibly poisoning himself in the process; some of the symptoms of a mental breakdown he suffered in 1693 are consistent with those of acute mercury toxemia). All this he did in silence. Occasionally he reported on his research in his lectures, but few of the professors and fewer among the students could follow his train of thought, and so few came. Sometimes nobody at all showed up, whereupon Newton, confronted with the empty hall, would trudge back to his rooms, evidently unperturbed.
The outer world eventually intruded nonetheless. In the case of Newton, who shunned notoriety, as in that of Galileo, who welcomed it, the agency responsible was the telescope.
Newton was handy, and liked to build experimental devices. (A good thing, said a colleague, for he took no exercise and had no hobbies and would otherwise have killed himself with overwork.) He wanted a telescope with which to observe comets and the planets. The only type of telescope in use at the time was the refractor—the sort that Galileo built, with a large lens at the front end to gather light. Newton disliked refractors; his extensive studies of optics had acquainted him with their tendency to introduce spurious colors. To overcome this defect he invented a new kind of telescope, one that employed a mirror rather than a lens to collect light. Efficient, effective, and cheap, the “Newtonian reflector” was to become the most popular telescope in the world. It brought Newton’s name to the attention of the Royal Society of London, which elected him to membership and prevailed upon him to publish a short paper he had written on colors. This decision he soon regretted; the paper drew twelve letters, prompting Newton to complain to Henry Oldenburg, the society’s secretary, that he had “sacrificed my peace, a matter of real substance.”9
The Royal Society was the most influential of the several scientific societies that had sprung up in the seventeenth century, each devoted to the empirical study of nature without interference by Church or State. The first of these, the Italian Academy of the Lynx, was founded in 1603 and had formed a platform from which Galileo, its most famous member, conducted his polemics. Founded under the amateur physicist King
Charles II, the Royal Society was too poor to afford a laboratory or even an adequate headquarters, but was fiercely independent and proudly unfettered by tradition or superstition. Its temper had been expressed by Oldenburg in a letter to the philosopher Benedict Spinoza:
Reflecting telescopes gather light by means of a curved mirror, refracting telescopes by a curved lens.
We feel certain that the forms and qualities of things can best be explained by the principles of mechanics, and that all effects of Nature are produced by motion, figure, texture, and the varying combinations of these and that there is no need to have recourse to inexplicable forms and occult qualities, as to a refuge from ignorance.10
This clear new cast of mind was personified by the three members of the Royal Society—Edmond Halley, Christopher Wren, and Robert Hooke—who lunched together in a London tavern one cold January afternoon in 1684. Wren, who had been president of the Royal Society, was an astronomer, geometer, and physicist, and the architect of St. Paul’s Cathedral—where his body is entombed, with an epitaph composed by his son inscribed on the cathedral wall that reads, IF YOU SEEK A MONUMENT, LOOK AROUND. Hooke was an established physicist and astronomer, the discoverer of the rotation of Jupiter; it was he who had worded the society’s credo: “To improve the knowledge of natural things, and all useful Arts, Manufactures, Mechanic practices, Engines and Inventions by Experiments (not meddling with Divinity, Metaphysics, Morals, Politics, Grammar, Rhetoric or Logic).”11 Halley at twenty-seven years old was a generation younger than his two companions, but he had already made a name for himself in astronomy, charting the southern skies from the island of St. Helena in the South Atlantic and there conducting pendulum experiments that showed a deviation in gravitational force caused by the centrifugal force of the earth’s rotation. Ahead lay a distinguished career highlighted by Halley’s compiling of actuarial tables, drawing maps of magnetic compass deviations and a meteorological map of the earth, and identifying as periodic the comet that has since borne his name.
Over lunch, Halley and Hooke discussed their shared conviction that the force of gravitation must diminish by the square of the distance across which it is propagated. They felt certain that the inverse-square law could explain Kepler’s discovery that the planets move in elliptical orbits, each sweeping out an equal area within its orbit in an equal time. The trouble was, as Halley noted, that he could not demonstrate the connection mathematically. (Part of the problem was that nobody, except the silent Newton, had realized that the earth’s gravitational force could be treated as if it were concentrated at a point at the center of the earth.) Hooke brashly asserted that he had found the proof, but preferred to keep it a secret so that others might try and fail and thus appreciate how hard it had been to arrive at it. Perhaps he meant to echo Descartes’s Geometry, which ends with the infuriating declaration that the author has “intentionally omitted” elements of his proofs “so as to leave to others the pleasure of discovery.”12 In any event, Wren had his doubts about Hooke’s mathematical ability if not Descartes’, and he offered as a prize to Hooke or Halley a book worth up to forty shillings—an expensive book—if either could produce such a demonstration within two months. Hooke immediately agreed, but the two months passed and he failed to come up with the proof. Halley tried, and failed, but kept thinking about the matter.
The man who might be able to answer it, he realized, was Newton. Newton was forbidding, to be sure; his amanuensis, Humphrey Newton (no relation), said he had seen his master laugh only once in five years, this when Newton inquired of an acquaintance what he thought of a copy of Euclid he had loaned him, and the man asked what use or benefit its study might be in his life, “upon which Sir Isaac was very merry.”13 But when the two men had met a couple of years earlier, Newton pumping Halley for data on the great comet of 1680, they had got along reasonably well. So, in August, while visiting Cambridge, Halley stopped in to see Newton again.
What, Halley asked Newton, would be the shape of the orbits of the planets if the gravitational force holding them in proximity to the sun decreased by the square of their distance from the sun?
An ellipse, Newton answered without hesitation.
Halley, in a state of “joy and amazement” as Newton recalled the moment, asked Newton how he knew this answer to be true.
Newton replied that he had calculated it.
Halley asked if he might see the calculation.
Newton searched through some of the stacks of papers that littered his quarters. There were thousands of them. Some bore the spiderweb tracings of his diagrams in optics. Others, adorned with medieval symbols and ornate diagrams of the philosophers’ stone, recorded his explorations of alchemy. A paper crammed with columns of notes compared twenty different versions of the Book of Revelations, part of the theological research Newton had conducted in substantiating his opposition to the doctrine of the Trinity—this a deep secret for the Lucasian Professor of Mathematics at Trinity College. Other pages were devoted to Newton’s attempts to show that the Old Testament prophets had known that the universe is centered on the sun, and that the geocentric cosmology upheld by the Roman Catholic Church was therefore a corruption. But-, Newton said, he could not find his calculations connecting the inverse-square law to Kepler’s orbits. He told Halley he would write them out anew and send them to him.
Newton had calculated elliptical orbits five years earlier, upon his return from a stay of nearly six months at his mother’s farm in Woolsthorpe, where he had gone when he learned that she had fallen mortally ill with a fever. His behavior there displayed a tenderness we do not normally associate with this frosty man: “He attended her with a true filial piety, sat up whole nights with her, gave her all her Physic himself, dressed all her blisters with his own hands, and made use of that manual dexterity for which he was so remarkable to lessen the pain which always attends the dressing,” reported John Conduitt, who wrote notes for a memoir on Newton’s life.14 The semiliterate Hannah Newton Smith could not have understood much of what her firstborn son did and thought, but her devotion to him was unwavering. A letter she wrote him shortly before his graduation from Cambridge survives; one edge has been burned away (perhaps by Newton, who destroyed many of his papers) and a few words are missing, but what remains contains the word “love” three times in two lines:
Isack
received your leter and I perceive you
letter from mee with your cloth but
none to you your sisters present thai
love to you with my motherly lov
you and prayers to god for you I
your loving mother
hanah15
She was buried on June 4, 1679. Conduitt described her as a woman of “extraordinary … understanding and virtue.”
When Newton returned to Cambridge after his mother’s death, he returned as well to the study of universal gravitation. He had paid little attention to the problem since the time, years before, when he had watched the apple fall outside the window of his room in his mother’s farmhouse. But now he was blessed with an antagonist—none other than Hooke himself, the tight-lipped claimant to the inverse-square law, who had written him with questions concerning the trajectory described by an object falling straight toward a gravitationally attractive body. Newton, aloof as usual, replied by declining Hooke’s invitation to correspond further, but took the trouble to answer Hooke’s questions, and in so doing made a mistake. Hooke seized upon the error, pointing it out in a letter of reply. Furious at himself, Newton concentrated on the matter for a time, and in the process verified to his own satisfaction that gravity obeying an inverse-square law could be shown to account for the orbits of the planets. Then he put his calculations aside. These were the papers he referred to when Halley came calling.
But they, too, turned out to contain an error—which may explain why the cautious Newton said he was “unable” to find them in the first place—and so Newton was obligated to resume work on the problem in order to satisfy
his promise to Halley. This he did, and three months later, in November, he sent Halley a paper that successfully derived all three of Kepler’s laws from the precept of universal gravitation obeying an inverse-square law. Halley, immediately recognizing the tremendous importance of Newton’s accomplishment, hastened to Cambridge and urged him to write a book on gravitation and the dynamics of the solar system. Thus was born Sir Isaac Newton’s Mathematical Principles of Natural Philosophy and His System of the World—the Principia.
Work on the book took over Newton’s life. “Now I am upon this subject,” he wrote the astronomer John Flamsteed, in a letter soliciting data on the orbits of Saturn’s satellites, “I would gladly know the bottom of it before I publish my papers.”16 The effort only intensified his air of preoccupation. His amanuensis Humphrey Newton observed that
he ate very sparingly, nay, ofttimes he has forget [sic] to eat at all, so that going into his Chamber, I have found his Mess untouched of which when I have reminded him, [he] would reply, Have I; and then making to the Table, would eat a bit or two standing. … At some seldom Times when he design’d to dine the Hall, would turn to the left hand, & go out into the street, where making a stop, when he found his Mistake, would hastily turn back, & then sometimes instead of going into the Hall, would return to his Chamber again.17
Newton still wandered alone in the gardens, as he had since his undergraduate days, and when fresh gravel was laid in the walks he drew geometric diagrams in it with a stick (his colleagues carefully stepping around the diagrams so as not to disturb them). But now his walks were more often interrupted by bolts of insight that sent him running back to his desk in such haste, Humphrey Newton noted, that he would “fall to write on his Desk standing, without giving himself the Leisure to draw a Chair to sit down in.18”
Coming of Age in the Milky Way Page 11