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 from the 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 gravit
ation 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.
7
A PLUMB LINE TO THE SUN
In Tahiti … the women are possessed of a delicate organization, a sprightly turn of mind, a lively, fanciful imagination, a wonderful quickness of parts and sensibility, a sweetness of temper, and a desire to please.
—Johann Georg Forster, 1778
The conception of the solar system that the Western world had attained by the beginning of the eighteenth century was accurate in its proportions but indeterminate in scale. Thanks principally to the theoretical work of Copernicus and Kepler and to the observations of Tycho and Galileo, it had been established beyond dispute that the earth was one of five known planets moving in elliptical orbits around the sun. And, thanks to Newton, these motions could be interpreted and predicted in terms of a mathematically cogent dynamical scheme that embraced terrestrial as well as extraterrestrial physics. But, though the relative distances of the sun and pla
nets were understood, their absolute distances were not.
Copernicus had measured the proportions of the solar system to within 5 percent of the correct values, and Kepler had come closer still. These relative distances customarily were expressed in terms of the distance from the earth to the sun, a quantity known as the astronomical unit. But nobody knew what the distance to the sun might be; in other words, the value of the astronomical unit had not been determined. Here was a clear challenge. Since the proportions of the system already were known, if the distance to the sun or to any one planet could be ascertained, the distances of all the other planets would follow. And, since the apparent diameters of the planets could by now be measured rather well, by using a micrometer eyepiece attached to a good telescope, the sizes of the planets could be ascertained as soon as their distances had been measured. Beyond that lay the exciting prospect that, by using the astronomical unit as a baseline, it might be possible to triangulate nearby stars and measure their distances as well. Accomplishing this feat constituted one of the heroic endeavors of eighteenth-century astronomy.
Traditional estimates of the distance from the earth to the sun were of little help. Beginning with Hipparchus in the second century B.C. and ranging down through Ptolemy, Copernicus, and Tycho, astronomers had assumed as a rule of thumb that the astronomical unit was equal to about twelve hundred times the radius of the earth—in modern figures, some 4.8 million miles. Such a distance seemed appropriately vast; to borrow a conceit from the thirteenth century, had Adam started walking on the day of the creation (usually set at 4004 B.C.) he would have required six hundred years to reach the sun, and would have arrived, footsore, at the planet Jupiter in the twentieth century. Nevertheless, an astronomical unit of twelve hundred earth radii was twenty times smaller than the real distance. Kepler and later observers suspected that it was an underestimate—Kepler guessed that the value was more like thirty-five hundred earth radii, nearly three times the previous estimates—but these early observers lacked observational instruments adequate to test their hunches.
Coming of Age in the Milky Way Page 12
