Coming of Age in the Milky Way - Timothy Ferris (2003)
Part I. SPACE
Chapter 6. NEWTON’S REACH
Watch the stars, and from them learn.
To the Master’s honor all must turn,
each in its track, without a sound,
forever tracing Newton’s ground.*
Nearer the gods no mortal may approach.
on Newton’s Principia
Newton created a mathematically quantified account of gravitation that embraced terrestrial and celestial phenomena alike. In doing so he demolished the Aristotelian bifurcation of the universe into two realms, one above and one below the moon, and established a physical basis for the Copernican universe. The thoroughness and assurance with which he accomplished this task were such that his theory came to be regarded, for more than two centuries thereafter, as something close to the received word of God. Even today, when Newtonian dynamics is viewed as but a part of the broader canvas painted by Einstein’s relativity, most of us continue to think in Newtonian terms, and Newton’s laws still work well enough to guide spacecraft to the moon and planets. (“I think Isaac Newton is doing most of the driving now,” said astronaut Bill Anders, when asked by his son who was “driving” the Apollo 8 spacecraft carrying him to the moon.)
Yet the man whose explication of the cosmos lives on in a billion minds was himself one of the strangest and most remotely inaccessible individuals who ever lived. When John Maynard Keynes purchased a trunk full of Newton’s papers at auction, he was startled to find that it was full of notes on alchemy, biblical prophecy, and the reconstruction from Hebraic texts of the floor plan of the temple of Jerusalem, which Newton took to be “an emblem of the system of the world.” “Newton was not the first of the age of reason,” a shaken Keynes told a gathering at the Royal Society. “He was the last of the magicians, the last of the Babylonians and Sumerians.”1 Newton was isolated, too, by the singular power of his intellect. Richard Westfall spent twenty years writing a highly perceptive scholarly biography of Newton, yet confessed, in the first paragraph of its preface, that
The more I have studied him, the more Newton has receded from me. It has been my privilege at various times to know a number of brilliant men, men whom I acknowledge without hesitation to be my intellectual superiors. I have never, however, met one against whom I was unwilling to measure myself, so that it seemed reasonable to say that I was half as able as the person in question, or a third or a fourth, but in every case a finite fraction. The end result of my study of Newton has served to convince me that with him there is no measure. He has become for me wholly other, one of the tiny handful of supreme geniuses who have shaped the categories of the human intellect, a man not finally reducible to the criteria by which we comprehend our fellow beings.2
Newton was an only child, the posthumous son of an illiterate yeoman. Born prematurely—so small, his mother used to say, that he could have fit in a quart bottle—he was not expected to survive. His mother, a widow with a farm to manage, soon remarried, and her new husband, the Reverend Barnabus Smith, sent the child off to be raised by his maternal grandmother; there he grew up, only a mile and a half away, within sight of the house where dwelt his loving mother and usurping stepfather. The product of all this— a fatherless birth on Christmas Day, survival against the odds, separation from his mother, and possession of a mind so powerful that he was as much its vassal as its master—was a brooding, simmering boy, sullen and bright and quick to anger. At age twenty Newton compiled a list of his youthful sins; among them were “threatening my father and mother Smith to burne them and the house over them,” “peevishness with my mother,” “striking many,” and “wishing death and hoping it to some.”3
The young Newton was as sensitive to the rhythms of nature as he was indifferent to those of men. As a child he built clocks and sundials and was known for his ability to tell time by the sun, but he habitually forgot to show up for meals, a trait that persisted throughout his life, and he was far too fey to help out reliably on the farm. Sent to gather in livestock, he was found an hour later standing on the bridge leading to the pasture, gazing fixedly into a flowing stream. On another occasion he came home trailing a leader and bridle, not having noticed that the horse he had been leading had slipped away. A sometime practical joker, he alarmed the Lincolnshire populace one summer night by launching a hot-air flying saucer that he constructed by attaching candles to a wooden frame beneath a wax paper canopy.* He seldom studied and customarily fell behind at grammar school, but applied himself at the end of each term and surpassed his classmates on final examinations, a habit that did little to enhance his popularity. A contemporary of Newton’s reported that when the boy left for Cambridge, the servants at Woolsthorpe Manor “rejoiced at parting with him, declaring, he was fit for nothing but the ’Versity.”4
At college he filled his lonely life with books. “Amicus Plato amicus Aristoteles magis arnica Veritas,’” he wrote in his student notebook—“Plato is my friend, Aristotle is my friend, but my greatest friend is truth.”5 He seems to have made the acquaintance of only one of his fellow students, John Wickins, who found him walking in the gardens “solitary and dejected” and took pity on him. Newton’s studies, like those of many a clever undergraduate, were eclectic—he looked into everything from universal languages to perpetual motion machines—but he pursued them with a unique intensity. Nothing, least of all his personal comfort, could deter him when he was on to a question of interest: To investigate the anatomy of the eye he stuck a bodkin “betwixt my eye and the bone as near to the backside of my eye as I could,” and he once stared at the sun for so long that it took days of recuperation in a dark room before his vision returned to normal.
For a time he drew inspiration from the books of Rene Descartes, a kindred spirit. Descartes like Newton had been a frail child, brought up by his grandmother, and both men were seized by an all-embracing vision while in their early twenties: Newton’s epiphany was universal gravitation; Descartes’s involved nothing less than a science of all human knowledge. Descartes died in 1650, more than a decade before Newton arrived at Cambridge, but his works were very much alive among the “brisk part” of the faculty—those whose intellectual horizons were not bounded by Aristotle’s.*
But if Newton learned a great deal from Descartes’s Principia Philosophiae—which included, among many other things, an assertion that inertia involves resistance to changes in motion and not just to motion itself—he was always happiest in contention, and Descartes’s philosophy promoted in him an equal and opposite reaction. Descartes’s disapproval of atomism helped turn Newton into a confirmed atomist. Descartes’s vortex theory of the solar system became the foil for Newton’s demonstration that vortices could not account for Kepler’s laws of planetary motion. Descartes’s emphasis on depicting motion algebraically encouraged Newton to develop a dynamics written in terms of algebra’s alternative, geometry; as this was not yet mathematically feasible, Newton found it necessary to invent a new branch of mathematics, the calculus. Infinitesimal calculus set geometry in motion: The parabolas and hyperbolas Newton drew on the page could be analyzed as the product of a moving point, like the tip of the stick with which Archimedes drew figures in the sand. As Newton put it, “Lines are described, and thereby generated not by the opposition of parts, but by the continued motion of points.” Here the unbending Newton danced.
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:
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
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”
Newton’s surviving drafts of the Principia support Thomas Edison’s dictum that genius is one percent inspiration and ninety-nine percent perspiration. Like Beethoven’s drafts of the opening bars of the Fifth Symphony, they are characterized less by sudden flashes of insight than by a constant, indefatigable hammering away at immediate, specific problems; when Newton was asked years later how he had discovered his laws of celestial dynamics, he replied, “By thinking of them without ceasing.”19 Toil was transmuted into both substance and veneer, and the finished manuscript, delivered to Halley in April 1686, had the grace and easy assurance of a work of art. For the modern reader the Principia shares with a few other masterworks of science—Euclid’s Elements among them, and Darwin’s Origin of Species—a kind of inevitability, as if its conclusions were self-evident. But the more we put ourselves into the mind-set of a seventeenth-century reader, the more it takes on the force of revelation. Never before in the history of empirical thought had so wide a range of natural phenomena been accounted for so precisely, and with such economy.
Gone forever was Aristotle’s misconception that the dynamics of objects depended upon their elemental composition, so that water, say, had a different law of motion from fire. In the Newtonian universe every object is described by a single quantity, its mass—Newton invented this concept—and mass possesses inertia, the tendency to resist any change in its state of motion. This is Newton’s first law—that “every body perseveres in its state of rest, or of uniform motion in a right [i.e., straight] line, unless it is compelled to change that state …”20
Whenever an immobile object is set into motion, or a moving object changes its velocity or direction of motion, Newton infers that a force is responsible. Such a change may be expressed as acceleration, the rate of change of velocity with time. This is Newton’s second law—that force equals mass times acceleration:
F = ma
The price paid for the application of force is that the action it produces must also result in an equal and opposite reaction. Thus, Newton’s third law—that “to every action there is always opposed an equal reaction.”21
Applied to the motions of the planets, these concepts explicated the entire known dynamics of the solar system. The moon circles the earth; the law of inertia tells us that it would move in a straight line unless acted upon by an outside force; as it does not move in a straight line, we can infer that a force—gravity—is responsible for bending its trajectory into the shape of its orbit. Newton demonstrates that gravitational force diminishes by the square of the distance, and establishes that this generates Kepler’s laws of planetary motion. It is because gravitation obeys the inverse-square law that Halley’s Comet or the planet Mars moves rapidly when near the sun and moves more slowly when far from the sun, sweeping out equal areas along its orbital plane in equal times. The amount of gravitational force exerted by each body is directly proportional to its mass. (From these considerations Newton was able to account for the tides as being due to the gravitational tug of both the sun and the moon, thus clearing up Galileo’s confusion on that score.)
From Newton’s third law (for every action an equal and opposite reaction) we can deduce that gravitational force is mutual. The earth not only exerts a gravitational force on the moon, but is subjected to a gravitational force fromthe moon. The mutuality of gravitational attraction introduces complexities into the motions of the planets. Jupiter, for instance, harbors 90 percent of the mass of all the planets, and so perturbs the orbits of the nearby planet Saturn to a degree “so sensible,” Newton comments dryly, “that astronomers are puzzled with it.” With the publication of the Principia, their puzzlement was at an end. Newton had provided the key to deciphering all observed motion, whether cosmic or mundane.
Halley had to exert himself to get the Principia published in financially thirsty times. The Royal Society had taken a loss the year before by publishing John Ray’s History of Fishes, a handsome book that nevertheless had not exactly flown from the booksellers’ shelves. Unsold copies lay stacked in the society storeroom, and at one point, Halley’s salary was being paid in copies of the History of Fishes. Further complications arose when Hooke proposed, groundlessly, that Newton had stolen the theory of universal gravitation from him, and Newton responded by threatening to leave the Principia unfinished by omitting Part Three, a more popularized section that Halley hoped would “much advance the sale” of the book.*
But Halley persisted, paying the printing costs out of his own pocket, and the Principia appeared in 1687, in an edition of some three or four hundred copies. The book was (and is) difficult to read, owing in part to Newton’s having, as he told his friend William Derham, “designedly made his Principia abstruse … to avoid being baited by little Smatterers in Mathematicks.”22 But Halley promoted it tirelessly, sending copies to leading philosophers and scientists throughout Europe, presenting King James II with a gloss of it, and going so far as to review it himself, for the Philosophical Transactions of the Royal Society. Thanks in large measure to his efforts, the Principia had a resounding impact. Voltaire wrote a popular account of it, and John Locke, having verified with Christian Huygens that Newton’s mathematics could be trusted, mastered its contents by approaching it as an exercise in logic. Even those who could not understand the book were awed by what it accomplished; the Marquis de l’Hopital, upon being presented with a copy by Dr. John Arbuthnot, “asked the Doctor every particular thing about Sir Isaac,” recalled a witness to their exchange, “even to the color of his hair, said does he eat & drink & sleep. Is he like other men?”23
The answer, of course, was no. Newton was a force of nature, brilliant and unapproachable as a star. “As a man he was a failure,” wrote Aldous Huxley, “as a monster he was superb.” We remember the monster more than the man, and the specter of a glacial Newton portraying the universe as a machine has furthered the impression that science itself is inherently mechanical and inhuman. Certainly Newton’s personality did little to alleviate this misconception. Indifferent to the interdependence of science and the humanities, Newton turned a deaf ear to music, dismissed great works of sculpture as “stone dolls,” and viewed poetry as “a kind of ingenious nonsense.”24
He spent his last forty years in the warming and stupefying embrace of fame, his once lean face growing pudgy, the dark luminous eyes becoming puffy, the wide mouth hardening from severity to petulance. His penetrating gaze and unyielding scowl became the terror of the London counterfeiters he enjoyed interrogating as warden of the mint, sending many to the gallows. He denied requests for interviews submitted by the likes of Benjamin Franklin and Voltaire. He was friendlier with Locke, with whom he studied the Epistles of Saint Paul, and with the diarist Samuel Pepys, who had been president of the Royal Society, but alarmed them when in 1693 he succumbed to full-scale insomnia and suffered a mental breakdown, writing them strange, paranoid letters in a spidery scrawl in which he implied that Pepys was a papist and told Locke that “being of opinion that you endeavoured to embroil me with woemen & by other means I was so much affected with it as that when one told me you were sickly & would not live I answered twere better if you were dead.”25 Newton was confined to bed by friends who, unable otherwise to assess the health of an intellect so far above the timberline, judged him well when at last he regained the ability to make sense of his own Principia. Elected to Parliament, he is said during the 1689–1690 session to have spoken but once, when, feeling a draft, he asked an usher to close the window. He died a virgin.
Newton cast a long shadow, and is said to have retarded the progress of science by seeming to settle matters that might otherwise have been further investigated. But he himself was acutely aware that the Principia left many questions unanswered, and he was forthright in confronting them.
Of these, none was more puzzling than the mystery of gravitation itself. If nature operated according to cause and effect, its paradigm the cue ball that scatters the billiard balls, then how did the force of gravitation manage to make itself felt across gulfs of empty space, without benefit of any medium of contact between the planets involved? This absence of a causal explanation for gravity in Newton’s theory prompted sharp criticism: Leibniz branded Newton’s conception of gravity “occult,” and Huygens called it “absurd.”
Newton agreed, calling the idea of gravity acting at a distance “so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it,”26 and conceding that he had no solution to the riddle: “The Cause of Gravity is what I do not pretend to know,” he said.27 In the Principia appears his famous phrase Hypotheses non fingo—“I have not been able to discover the cause of those properties of gravity from phenomena, and [so] I frame no hypothesis.”28 He would have approved of the quatrain that adorned one of his portraits:
See the great Newton, he who first surveyed
The plan by which the universe was made;
Saw Nature’s simple yet stupendous laws,
And proved the effects, though not explained the cause.
One might say, then, that evidence of Newton’s genius survives in his questions as well as in his answers. Human understanding of gravitation has been greatly improved by Einstein’s conception of gravity as a manifestation of the curvature of space, but the road to full comprehension still stretches on ahead; its next, dimly perceived way station is thought to be a hyperdimensional unified theory or a quantum account of general relativity. Until that goal is achieved, and perhaps even thereafter, Newton’s prudent tone will remain the byword of gravitational physics.
Newton was equally straightforward in pointing out that he could not hope to calculate all the minute variations in the orbits of the planets produced by their mutual gravitational interactions. As he put it in the Principia:
The orbit of any one planet depends on the combined motion of all the planets, not to mention the action of all these on each other. But to consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the force of the entire human intellect.29
Today this is known as the “many body problem,” and it remains unsolved, just as Newton foresaw. Calculation of the precise interactions of all the planets in the solar system—much less that of all the stars in the Milky Way—may as Newton prophesied forever elude “the force of the entire human intellect,” or it may one day yield, if not to the mind, then to the inhuman power of giant electronic computers. No one knows. For now, let Einstein pronounce Newton’s eulogy: “Genug davon. Newton verzeih’ mir,” Einstein wrote, in his “Autobiographical Notes,” after discussing weaknesses in Newton’s assumptions:
Enough of this. Newton, forgive me; you found the only way which, in your age, was just about possible for a man of highest thought and creative power. The concepts, which you created, are even today still guiding our thinking physics, although we now know that they will have to be replaced by others farther removed from the sphere of immediate experience, if we aim at a profounder understanding.30
In any case, the ultimate unsolved questions were for Newton not scientific but theological. His career had been one long quest for God; his research had spun out of this quest, as if by centrifugal force, but he had no doubt that his science like his theology would redound to the greater glory of the Creator. “When I wrote my treatise upon our System I had an eye upon such Principles as might work with considering men for the belief of a Deity & nothing can rejoice me more than to find it useful for that purpose,” he replied to a query from a young chaplain, the Reverend Richard Bentley, who was writing a series of sermons on God and natural law.31 At the conclusion of the Principia, Newton asserted that “this most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.”
Newton saw science as a form of worship, yet Newtonian mechanics had a dolorous effect upon traditional belief in a Christian God. Its determinism seemed to deny free will; as Voltaire wrote, “It would be very singular that all nature, all the planets, should obey eternal laws, and that there should be a little animal, five feet high, who, in contempt of these laws, could act as he pleased.”32
Newton himself did not believe that his theory had diminished the role of the deity. As he saw it, the real miracle is existence itself, and he invoked the hand of God at the origin of the universe: “The Motions which the Planets now have could not spring from any natural Cause alone, but were impressed by an intelligent Agent,” he wrote Bentley.33 In modern scientific terminology the question he was addressing is called the problem of initial conditions. We think that the formation of the solar system can be explained in terms of the workings of natural law, but the authorship of the laws remains a mystery. If for every effect there must have been a cause, then what, or who, was responsible for the first cause? But to ask such questions is to leave science behind, and to enter precincts still ruled by Saint Augustine of Hippo and Isaac Newton the theologian.
*Translation by Dave Fredrick.
*I have tried this one myself and can testify that, like many of Newton’s inventions, it works very well indeed.
*A devotee of warmth who had experienced his transcendent moment in an overheated room he called “the oven,” Descartes succumbed at age fifty-two to the impetuous attentions of the twenty-three-year-old Queen Christina of Sweden, who insisted that he brave the Nordic chill to tutor her in science and philosophy each morning at five. The less accommodating Newton declined most invitations, never traveled abroad, and lived to be eighty-five.
*This, the “inverse square” law, can be arrived at intuitively if we imagine the force of gravity as being spread out across the surface of a sphere. Consider two planets orbiting a star in such a way that the distance of planet B from the star is twice that of planet A. Let each planet rest on the surface of an imaginary sphere centered on the star. Since the radius of the sphere encompassing the orbit of planet B is twice that for planet A, its surface area is equal to the square of the surface area of planet B’s sphere. (The area of the surface of a sphere equals 4 π r2, where r is the radius of the sphere.) This means that the total amount of gravitational force emanating from the star must be spread out over sphere B with a surface equal to that of sphere A squared. The gravitational force experienced by planet B will, therefore, be the inverse square of that experienced by planet A. Newton derived this much from Kepler’s third law, but Kepler himself had failed to obtain it, evidently because he thought of gravitation as being propagated in only two dimensions, not three.
*“He was of an active, restless, indefatigable Genius even almost to the last, and always slept little to his death, seldom going to Sleep till two three, or four a Clock in the Morning, and seldomer to Bed, often continuing his Studies all Night, and taking a short Nap in the Day. His Temper was Melancholy….” Sound familiar? That’s Hooke, not Newton, as described by a contemporary. Inevitably, we tend to quarrel most bitterly with those who most nearly resemble ourselves.