Book Nobody Understands

In August 1684 a handsome young astronomer named Edmond Halley boarded the London coach for Cambridge and sat back to ponder the events that had sent him on an important mission. Earlier in the year, he had entered into a lively conversation with Robert Hooke and Sir Christopher Wren, noted architect of the new St. Paul's Cathedral in London. Halley suggested that the force of attraction between the planets and the sun decreases in inverse proportion to the square of the distance between them. If this were true, then each planet's orbit should take the form of Kepler's ellipse, a shape like a football, though somewhat more rounded.

Halley recalled that Hooke immediately "affirmed that upon that principle all the Laws of the celestial motions were to be demonstrated."1 Wren, who was also deeply interested in the new science, claimed that he, too, had reached the same conclusion. The problem, as all three admitted, was to find the mathematical means of proving it.

Anxious for a solution, Sir Christopher offered to give a valuable book to the friend who could deliver solid proof within the next two months. Hooke, to whom modesty was a stranger, claimed that he already possessed the required proof. However, he would keep it a secret for the time being so that his friends "might know how to value it, when he should make it public."2

The deadline came and went without a word from Hooke, and spring soon turned to summer. Finally, after seven months of silence, Halley decided to act. He cast an anxious eye in the direction of Cambridge and made a fateful decision. He would visit Trinity College to see if the secretive Isaac Newton could shed some light on the matter.

Newton was living an even more isolated existence than before. Some years earlier his mother, Hannah, had caught what was described as a "malignant fever," a catchall term for any number of fatal illnesses. Newton hurried to Woolsthorpe and took charge of Hannah's care, dressing her blisters and sitting up all night at her bedside. Unfortunately, she was beyond saving and died some days later. As her first child, Isaac inherited most of her property, making him an independently wealthy man.

A more recent blow was the departure from Cambridge of John Wickins, Newton's roommate of twenty years. Wickins became minister of the parish church at Stoke Edith, married, and fathered a son named Nicholas. Though they had been through much together, the two friends would never meet again and exchanged no more than a letter or two in the coming years.

Newton's prescription for loneliness was work, work, and more work. Humphrey Newton observed: "I never saw him take any Recreation or Pastime, either in Riding out to take the Air, Walking, Bowling, or any other Exercise whatever, Thinking all Hours lost that was not spent in his Studies, to which he kept so close that he seldom left his Chamber."3 The reclusive professor had even more time to himself because Cambridge students were little interested in natural philosophy. Humphrey noted that his employer often lectured to the classroom walls. Finally, he stopped going to the lecture hall altogether, placing his texts on deposit in the college library as was required by statute.

Over the years, Newton became the very model of the absent-minded professor. He ate little and often had to be reminded by Humphrey that the dinner delivered to his room had gone untouched. He would express surprise, walk over to the table, and eat a bite or two standing up. "I cannot say," Humphrey noted, "I ever saw Him sit at [the] Table by himself."4

Newton rarely went to bed until two or three in the morning and often slept in his clothes. He rose at five or six, fully refreshed. His long, silver hair was seldom combed, his stockings hung loose, and his shoes were down at the heels. On those rare occasions when he went out, it was usually to take a meal in the dining hall, overlooked by the giant portrait of Henry VIII.

But, according to Humphrey, things did not always go as they should have. Instead of heading almost straight across the Great Court, Newton sometimes made a left turn, only to wind up on Trinity Street. On realizing his mistake, he would turn back, and then "sometimes without going into the Hall return to his Chamber again."5

In good weather Newton was occasionally seen taking a stroll in his garden. Picking up a stick, he drew figures on the graveled walks, which the other Fellows sidestepped for fear of ruining a work of genius—or folly. According to Humphrey, "When he has some Times taken a turn or two he has made a sudden stand, turn'd himself about, run up the Stairs like another Archimedes, and with a eureka fallen to write on his Desk standing, without giving himself the Leisure to draw a chair to sit down on."6 So absorbed was Newton that he lost track of time and place. The days and dates on many of the papers recording his experiments do not match those of the calendar.

As he stepped down from his coach on reaching Cambridge, Halley hardly knew what to expect. He had exchanged no letters with Newton and had met him only once before, in London. Furthermore, Hooke's name was bound to come up. Despite their mutual pledge not to kindle any more coal, Newton and Hooke were still feuding over scientific matters both great and small.

To Halley's surprise, and great relief, Newton was flattered by his visit. They talked of many things before the astronomer revealed his reason for seeking Newton out. What kind of curve, Halley finally asked, "would be described by the planets supposing the force of attraction towards the sun to be reciprocal to the square of their distance from it?"7

Without hesitation, Newton responded that it would be an ellipse! Taken aback, Halley asked him how he knew it.

"I have calculated it," Newton replied.8

When Halley asked to see the calculations, Newton began rummaging through his many stacks of papers while his excited visitor held his breath. As luck would have it, he was unable to find the critical documents, forcing Halley to depart without the written proof he required. However, all was not lost. Before they parted company, Newton promised to redo his calculations and send them on to Halley by the London post.

Once again Halley's patience was sorely tested. Three months passed without a single word from Cambridge. What Halley did not know was that Newton had solved the problem of the elliptical orbit by employing a different mathematical method than before, but he was not satisfied. He spent much of those three months working on a nine-page manuscript titled De Motu Corporum in Gyrum (On the Motion of Revolving Bodies). Finally, in November 1684, nearly eleven months after Halley, Hooke, and Wren had taken part in the discussion that had started the quest, a copy of De Motu arrived at Halley's doorstep in London.

Halley was astounded, for in his hands were the mathematical seeds of a general science of dynamics—the study of the relationship between motion and the forces that affect it. Not wasting a moment, he headed north to Cambridge a second time. He must find out whether Newton would agree to have his paper set before the Royal Society and published for all the scientific world to see.

On December 10, Halley rose to address his fellow members of the Royal Society and its new president, Samuel Pepys. He gave an account of his most recent visit with Newton and of a "curious treatise," De Motu. Halley's report was duly recorded in the minutes, and he was urged to push Newton to publish his little work as soon as possible.

At first Newton may have thought of De Motu as an end in itself. But once his creative powers were loosed, there was no checking their momentum. "Now that I am upon this subject," he wrote Halley in January 1685, "I would gladly know the bottom of it before I publish my papers."9 In his mind's eye De Motu would serve as the germ of his masterpiece, the greatest book of science ever written.

Thus began eighteen months of the most intense labor in the history of science. In April 1686 Newton presented and dedicated to the Royal Society the first third of his illustrious work. He titled it Philosophiae Naturalis Principia Mathematica (Mathematical Principles ofNatural Philosophy), commonly known as the Principia. A month later the Fellows agreed that the society should pay the cost of the book's publication, but that decision was reversed two weeks later when it was reported that the treasury was empty for having funded a slow-selling history of fishes. The members turned to Halley, who agreed to finance publication out of his own pocket and to act as the difficult Newton's editor.

It was a fortunate choice. No sooner had Newton presented his first installment than Robert Hooke raised his all-too-familiar cry of theft. He claimed to have formulated the inverse square law six years earlier, which he had communicated in a letter to Newton. While it is true that Hooke had corrected a rare blunder Newton made regarding the path of a falling body, this was a far stretch from proving that the greater the distance between a planet and the sun the less intense the gravitational attraction between them. In addressing Hooke's claim that Newton had stolen from him, the eighteenth-century French scientist Alexis Claude Clairaut later observed, "what a distance there is between a truth that is glimpsed and a truth that is demonstrated."10

Newton was predictably outraged when word of Hooke's charge reached him in Cambridge. He immediately dashed off an angry letter to Halley in which he threatened to withhold the rest of the Principia. "Philosophy is such an impertinently litigous Lady," he wrote, "that a man had as good be engaged in lawsuits, as have to do with her. I found it so formerly, and now I am no sooner come near to her again, but she gives me warning."11

Tall, dark-eyed, soft of face and manner, Halley was a presence pleasing to almost everyone. Despite many frustrations, his treatment of Newton was unwavering, ever polite and respectful from their first meeting to their last letter, a relationship destined to endure forty more years. He moved swiftly to calm the troubled waters. All Hooke desired, Halley wrote Newton, was to be mentioned in the preface of the Principia. It would be a fine gesture on Newton's part, and one that would cost him nothing. A still infuriated Newton reacted by going over his manuscript and crossing out every reference to Hooke. With that the storm passed and Newton agreed to go ahead with publication.

The Principia was not an easy book to read in Newton's day, nor is it now. After it was published, Newton was passed on the street by a student who is said to have remarked, "There goes the man that writt a book that neither he nor anybody else understands."12 The same would be said of Einstein when his papers on the theory of relativity were published some 250 years later.

The first of the Principiaos three books deals with problems of motion involving no friction or resistance. Book II is concerned with the motions of fluids and the effect of friction on the motions of solid bodies in fluids. Important though these books are, it is Book III, entitled System of the World, that most concerns us.

According to Newton's first law, "Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it." As we have seen, Galileo was actually the first to formulate this principle. Taking up where the Italian left off, Newton recast and incorporated it into his own system of mechanics, or the behavior of matter. If no outside force acts on a body, it will continue to move at a constant speed in the same direction. If left alone, a planet will orbit the sun eternally.

Yet the planets, as Newton had demonstrated mathematically, circle the sun, tracing out elliptical orbits. Why is it that they do not move off into space in a straight line, as would be expected according to his first law? This is where Newton's second law comes into play: "The change of motion [of a body] is proportional to the motive force impressed; and is made in the direction of the straight line in which that force is impressed." Stated in less rigorous terms, this law tells us that the orbiting planet is pulled at a right angle toward the sun. Its natural tendency to move outward into space, or what Christiaan Huygens called its "centrifugal" force, is perfectly balanced by the sun's inward pull, or what Newton termed "centripetal" force. One of the best ways to illustrate this principle is to whirl an object on a rope or a string over one's head. The object can be likened to a planet, the anchoring hand to the sun, while the string acts as the "force" that keeps the object from flying off into the blue.

But what of the string itself? No such visible tether binds a planet to the sun. Enter Newton's third law, which was uniquely his own: "To every action there is always opposed an equal reaction: or, the mutual action of two bodies upon each other are always equal, and directed to contrary parts." Hence, if one body acts upon another at a distance, the second also acts on the first with an equal and opposite force. The moon pulls the Earth with the same force with which the Earth pulls the moon. This is no less true of the Earth and an apple, except that in this instance the force exerted causes the apple to visibly change its position, while the Earth, because of its far greater size, seems totally unaffected. With these three laws of motion, Newton founded the branch of modern physics we call dynamics.

The genius of Newton's achievement becomes even clearer when we focus on the third law. Gravity acting at a distance could no longer be thought of as something peculiar to the sun and the planets; it applies to every object in existence, no matter how large or how small. As a universal property of all bodies, its force is dependent solely on the amount of matter each body contains. Or, as Newton announced in Proposition VII of Book III: "Every particle of matter attracts every other particle with a force proportional to the product of the masses and inversely proportional to the square of the distances between them." With this elegant principle, he had made the universe a "democracy" by treating all objects as equals. Everything—from the smallest of atoms to the largest of planets—obeys the same unchanging law, as profound a thought as has ever crossed a human mind.

Newton was ready now to demonstrate how the law of universal gravitation accounts for phenomena that had confounded the greatest minds in history for centuries. Or, in his words, "to admit no more causes of natural things than are both true and sufficient to explain their appearances."13

He focused his attention on Saturn's orbit of the sun, which he had attempted to calculate accurately for several years. Had it only been a matter of determining the mutual attraction of two bodies, the solution would have been relatively easy. But, as Newton well knew, the problem is complicated by the fact that Saturn's movement is influenced by other bodies as well, most notably its neighboring planet Jupiter. Although the sun, which contains a thousand times more matter than all the planets put together, is the solar system's dominant body, Jupiter is sufficiently large to produce small changes, or perturbations, in Saturn's orbit. Thus while Saturn follows an elliptical path around the sun, it wavers during the course of itsjourney, as though buffeted by an ill wind. Even Newton, armed as he was with the calculus, could not come up with anything more than a general solution to what is called

"the three-bodied problem," one of the most difficult in physics. Indeed, he once remarked that trying to resolve it made his head ache, which he treated by tying a band of cloth around his head and twisting it with a stick until the reduced circulation dulled the pain. His pioneering study of planetary perturbation was refined over the decades until, in 1846, the planet Neptune was discovered by means of its gravitational pull on Uranus, the first such body to be discovered on the basis of theoretical calculations alone.

No less intriguing to Newton were the marked irregularities in the moon's orbit, a phenomenon that had puzzled astronomers for centuries. While the lunar orbit is dictated by the pull of Earth, it too is influenced by the enormous mass of the sun. And unlike the perturbations of the planets, those of the moon are both more numerous and more pronounced. By employing a complex system of calculations, Newton was able to account for most of these major disturbances. He did the same for Jupiter and its satellites, which Galileo had discovered in 1609 while gazing through his homemade telescope.

Among the more interesting deductions found in the Principia is Newton's assertion that the Earth and the other planets are oblate bodies. This means that they are flattened somewhat at their poles, or axes, and bulge to some degree at their equators. In terms of Earth, the equatorial bulge means the planet's surface is a few miles higher at its central belt than at the North and South Poles, a seemingly small difference but one fraught with significant implications.

Elsewhere in the Principia, Newton had demonstrated that a perfect sphere attracts another body as if its mass were concentrated at its center. However, oblate bodies, such as Earth, do not.

This means that the intensity of the planet's gravitational field will not be exactly the same everywhere. The Earth pulls and is in turn pulled by the moon with a slightly off-center attraction, the line of pull being strongest at the equatorial bulge, where matter is most concentrated. In effect we are dealing with a giant top slightly overloaded on one side. This causes the planet's axis to change its angle of rotation very slowly, so as to trace out the shape of a cone in the heavens. Astronomers call this "the precession of the equinoxes." It was first observed by Hipparchus, a Greek astronomer of the late second century B.C., but its explanation defied solution by the best of minds, including a deeply frustrated Copernicus. Newton undertook the calculation of this conical motion, which he accurately attributed to the slightly off-center attractions of the moon. He found that it takes 26,000 years for the Earth's axis to complete the cone. Once again genius had triumphed by explaining a mystifying phenomenon and calculating the time frame in which it occurs, a far cry from the simple suggestion that an apple falls to the ground because the Earth attracts it.

Of all the riddles that bedeviled astronomers, none had proved more baffling than the eternal rise and fall of the seas. Isaac Newton ended their frustration with a stroke of his pen: "That the flux and reflux of the sea arise from the actions of the sun and moon."14 By applying the law of gravitation to the problem, Newton found that the power of attraction is greater on the waters facing the attracting body than on the Earth as a whole, and greater on the Earth as a whole than on the waters on the opposite side. Because of the moon's nearness to Earth (240,000 vs. 93,000,000 miles for the sun), the satellite's gravitational pull gives rise to the main tides. Its chief effect is to cause a pair of waves, or ocean humps, of tremendous area to travel around the Earth once in a lunar day, or a little less than twenty-five hours. The sun's attraction produces a similar but lower pair of waves that circle Earth once in a solar day of twenty-four hours. The effect of these two pairs of waves periodically overtaking each other accounts for the spring and neap tides. The spring tides, the more marked of the two, occur when the sun, moon, and Earth are in a line and exert maximum gravitational pull. The weaker neap tides result when the sun and moon pull at right angles to each other. While Newton's calculations were not refined enough to accurately predict the height of a tide at any given place in the world, another tremendous advance in scientific knowledge was his to claim.

As a young man, Newton had written of staying up all night to watch comets, and of becoming ill for lack of rest. Until shortly before his birth, these mysterious visitors had been regarded as nothing more than vaporous exhalations from Earth released into the higher regions of the atmosphere. More recently, comets were thought of as independent celestial bodies, but no one had been able to account for their seemingly irregular movements across the midnight sky.

Believing comets to be composed of solid matter, Newton reasoned that they must be subject to the same gravitational forces as the planets. Yet when he employed observational data collected in part by the astronomer royal, John Flamsteed, with whom he quarreled almost as violently as he did with Hooke, he found that the motions of comets were much more complex than those of the planetary bodies. As a result, he set out to prove that besides elliptical orbits, celestial bodies could move in paths tracing out sharper curves than previously imagined. He soon gave substance to this conjecture by determining that comets "move in some of the conic sections" about the sun. The natural philosopher then plotted the curve of the so-called Great Comet of 1681.

Based on what he read in the Principia, Halley was attracted to cometary theory as well. The gifted astronomer took particular interest in the orbit of another brilliant comet, which he had closely observed in 1682. Then, through a painstaking search of past records worthy of Newton himself, he found that there had been similar sightings in 1607 and 1531, or about once every seventy-five years. Could not these sightings, Halley thought to himself, indicate the periodic return of the same object? He calculated the orbit on the assumption that it was, and predicted its return in 1758, give or take a year. The streaming body, which now bears Halley's name, was next observed on Christmas Day, 1758 (the 116th anniversary of Newton's birth), by an amateur astronomer named George Palitsch. Like clockwork, Halley's comet has since shown up three more times, reaffirming Newton's reduction of yet another great mystery to mathematical rule.

When we step back and look at Newton's universe from afar, what is it, exactly, that we see? According to the Principia, we peer into a seemingly endless void of which only a tiny part is occupied by material bodies moving through the boundless and bottomless abyss. Newton's followers would liken it to a colossal machine, much like the clocks located on the faces of medieval buildings. All motions are reduced to mechanical laws, a universe where human beings and their world of the senses have no effect. Yet for all its lack of feeling, it is a realm of precise, harmonious, and rational principles. Mathematical laws bind each particle of matter to every other particle, barring the gate to disorder and chaos. By flinging gravity across the void, Isaac Newton united physics and astronomy in a single science of matter in motion, fulfilling the dreams of Pythagoras, Copernicus, Kepler, Galileo, and countless others in between. And while Newton was unable to discover the true cause of gravity itself, a giant riddle still, the laws he formulated provide convincing proof that we inhabit an orderly and knowable universe.

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