James Gleick - Isaac Newton

Goodreads

My rating: ★★☆☆☆ (40%)

I wanted to read Newton’s biography because I’ve listened to a lecture about him and realized I know little about how Newton made his scientific discoveries.

• It’s a hard read

  This book helped me, but it was disappointing how hard it was to read it. It tried to be poetic with a heavy citation of resources from Newton’s age. This gave the book an aura of authenticity and authority, but it also made it hard to understand.

• Interesting facts I learned

• Newton’s life

• Newton was super introverted and antisocial.

• Newton was petty and never forgot a grudge.

• From the book, I got a sense that he remained celibate not because of choice but because of social skills.

• Newton’s discoveries

• He found out about white light being made out of different colors by using a prism and trying to split the already-split colors.

• He discovered calculus thanks to his interest in infinitely small numbers.

• There existed no good concept of mass in his time, he had to define that term. This impressed me more than anything. He discovered concepts that his language didn’t support.

• His most important book is “Philosophiæ Naturalis Principia Mathematica”

  • This introduced his 3 laws

• Conclusion

  I wouldn’t recommend this book as the first Newton biography to read.

• private

• Highlights

• 1. What Imployment Is He Fit For?

  Barnabas Smith, a wealthy man twice her age. Smith wanted a wife, not a stepson; under the negotiated terms of their marriage Hannah abandoned Isaac in the Woolsthorpe house, leaving him to his grandmother’s care.

  The triumphant Puritans rejected absolutism and denied the divine right of the monarchy. In 1649, soon after Isaac turned six, Charles Stuart, the king, was beheaded at the wall of his palace.

  Nevertheless, in the fall of 1659, when Isaac was sixteen years old, his mother summoned him home to be a farmer.

• 2. Some Philosophical Questions

  subsizars, who earned their keep by menial service to other students, running errands, waiting on them at meals, and eating their leftovers

  The widowed Hannah Smith was wealthy now, by the standards of the countryside, but chose to provide her son little money; he entered Trinity College as a subsizar.

  “Everything that is in motion must be moved by something,” Aristotle asserted (and proved, by knotted logic).

  Gunners understood that a cannonball, once in flight, was no longer moved by anything but a ghostly memory of the explosion inside the iron barrel; and they were learning, roughly, to compute the trajectories of their projectiles. Pendulums, in clockwork, however crude, demanded a mathematical view of motion. And in turn the clockwork made measurement possible—

  Although the library of Trinity College had more than three thousand books, students could enter only in the company of a fellow. Still, Newton found his way to new ideas and polemics: from the French philosopher René Descartes, and the Italian astronomer Galileo Galilei, who had died in the year of Newton’s birth. Descartes proposed a geometrical and mechanical philosophy. He imagined a universe filled throughout with invisible substance, forming great vortices that sweep the planets and stars forward. Galileo, meanwhile, applied geometrical thinking to the problem of motion. Both men defied Aristotle explicitly—

  Galileo created a concept of uniform acceleration. He considered motion as a state rather than a process. Without ever using a word such as inertia, he nonetheless conceived that bodies have a tendency to remain in motion or to remain motionless. The next step demanded experiment and measure. He measured time with a water-clock. He rolled balls down ramps and concluded, wrongly, that their speed varied in proportion to the distance they rolled.

  Newton began to absorb this, at second or third hand; Galileo had written mostly in Italian, a language few in England could read.

  But light itself played a delicate part in the Cartesian scheme, and Newton, attempting to take Descartes literally, already sensed contradictions. Pressure does not restrict itself to straight lines; vortices whirl around corners. “Light cannot be by pression,” Newton asserted, “for then wee should see in the night a[s] wel or better than in the day we should se[e] a bright light above us becaus we are pressed downewards.…” Eclipses should never darken the sky.

  Another elusive word, gravity, began to appear in the Questiones. Its meanings darted here and there. It served as half of a linked pair: Gravity & Levity. It represented the tendency of a body to descend, ever downward. But how could this happen? “The matter causing gravity must pass through all the pores of a body. It must ascend againe, for else the bowells of the earth must have had large cavitys & inanitys to containe it in.…”19 It must be crowded in that unimaginable place, the center of the earth—all the world’s streams coming home. “When the streames meet on all sides in the midst of the Earth they must needs be coarcted into a narrow roome & closely press together.”

  he sketched a balance scale. He speculated about “rays of gravity.” Then, gravity could also refer to a body’s tendency to move, not downward, but in any direction;

  Violent motion is made continued either by the aire or by motion force imprest or by the natural gravity in the body moved.

  Yet how could the cannonball be helped along by the air? He noted that the air crowds more upon the front of a projectile than on the rear, “& must therefore rather hinder it.” So the continuing motion must come from some natural tendency in the object. But—gravity?

• 3. To Resolve Problems by Motion

  wollstrup may the 6. 16654 The colleges of Cambridge began shutting down. Fellows and students dispersed into the countryside

  As Newton learned Latin and Greek, he experimented with shorthand alphabets and phonetic writing, and when he entered Trinity College he wrote down a scheme for a “universal” language, based on philosophical principles, to unite the nations of humanity. “The Dialects of each Language being soe divers & arbitrary,” he declared, “a generall Language cannot bee so fitly deduced from them as from the natures of things themselves.”

  symbols came equations: relations between quantities, and changeable relations at that. This was new territory, and Descartes exploited it. He treated one unknown as a spatial dimension, a line; two unknowns thus define a plane. Line segments could now be added and even multiplied. Equations generated curves; curves embodied equations

  He taught himself to find real and complex roots of equations and to factor expressions of many terms—polynomials. When the infinite number of points in a curve correspond to the infinite solutions of its equation, then all the solutions can be seen at once, as a unity. Then equations have not just solutions but other properties: maxima and minima, tangents and areas. These were visualized, and they were named.

  Newton’s patience was limitless. Truth, he said much later, was “the offspring of silence and meditation.”

  On one page he drew a hyperbola and set about calculating the area under it—“squaring” it. He stepped past the algebra Descartes knew. He would not confine himself to expressions of a few (or many) terms; instead he constructed infinite series: expressions that continue forever.17 An infinite series need not sum to infinity; rather, because the terms could grow smaller and smaller, they could close in on a goal or limit. He conceived such a series to square the hyperbola— —and carried out the calculation to fifty-five decimal places:

  Mathematicians had a glimmering notion of how to raise the sum of two quantities, a + b, to some power. Through infinite series, Newton discovered in the winter of 1664 how to expand such sums to any power, integer or not: the general binomial expansion.

  special aspect of infinity troubled Newton; he returned to it again and again, turning it over, restating it with new definitions and symbols. It was the problem of the infinitesimal—the quantity, impossible and fantastic, smaller than any finite quantity, yet not so small as zero

  could not escape it, so he pressed it into service, employing a private symbol—a little o—for this quantity that was and was not zero. In some of his diagrams, two lengths differed “but infinitely little,” while two other lengths had “no difference at all.” It was essential to preserve this uncanny distinction. It enabled him to find areas by infinitely partitioning curves and infinitely adding the partitions. He created “a Method whereby to square those crooked lines which may bee squared”26—to integrate (in the later language of the calculus

  paradox of Achilles and the tortoise. The tortoise has a head start. Achilles can run faster but can never catch up, because each time he reaches the tortoise’s last position, the tortoise has managed to crawl a bit farther ahead. By this logic Zeno proved that no moving body could ever reach any given place

  culture lacking technologies of time and speed also lacked basic concepts that a mathematician needed to quantify motion. The English language was just beginning to adapt its first unit of velocity: the term knot, based on the sailor’s only speed-measuring device, the log line heaved into the sea. The science most eager to understand the motion of earthly objects, ballistics, measured the angles of gun barrels and the distances their balls traveled, but scarcely conceived of velocity; even when they could define this quantity, as a ratio of distance and time, they could not measure it

  geometrical task matched a kinetic task: to measure curvature was to find a rate of change. Rate of change was itself an abstraction of an abstraction; what velocity was to position, acceleration was to velocity. It was differentiation (in the later language of the calculus

  Repeatedly he started a new page—in November 1665, in May 1666, and in October 1666—in order to essay a system of propositions needed “to resolve Problems by motion.”34 On his last attempt he produced a tract of twenty-four pages, on eight sheets of paper folded and stitched together.

  In creating this mathematics Newton embraced a paradox. He believed in a discrete universe. He believed in atoms, small but ultimately indivisible—not infinitesimal. Yet he built a mathematical framework that was not discrete but continuous, based on a geometry of lines and smoothly changing curves. “All is flux, nothing stays still,” Heraclitus had said two millennia before. “Nothing endures but change.” But this state of being—in flow, in change—defied mathematics then and afterward.

  The new king, Charles II—having survived his father’s beheading and his own fugitive years, and having outlasted the Lord Protector, Cromwell—fled London with his court.

• 4. Two Great Orbs

  1543, just before his death, Nicolaus Copernicus, Polish astronomer, astrologer, and mathematician, published the great book De Revolutionibus Orbium Coelestium (“On the Revolutions of the Heavenly Spheres”). In it he gave order to the planets’ paths, resolving them into perfect circles; he set the earth in motion and placed an immobile sun at the center of the universe.4

  Johannes Kepler, looking for more order in a growing thicket of data, thousands of painstakingly recorded observations, declared that the planets could not be moving in circles. He suspected the special curves known to the ancients as ellipses.

  Galileo Galilei took spy-glasses—made by inserting spectacle makers’ lenses into a hollow tube—and pointed them upward toward the night sky. What he saw both inspired and disturbed him: moons orbiting Jupiter;

  Newton knew how big the moon was and how far away. By virtue of a coincidence, the moon’s apparent size was almost exactly the same as the sun’s, about one-half degree of arc, the coincidence that makes a solar eclipse such a perfect spectacle.

  Newton could see other globes, dangling from their stems. A two-inch apple at a distance of twenty feet subtended the same half-degree in the sky. These ratios were second nature now, the congruent Euclidean triangles inscribed in his mind’s eye.

  An apple was no sphere, but he understood it to be flying through space along with the rest of the earth’s contents, spinning across 25,000 miles each day. Why, then, did it hang gently downward, instead of being flung outward like a stone whirled around on a string? The same question applied to the moon: what pushed it or pulled it away from a straight path?

  Many years later Newton told at least four people that he had been inspired by an apple in his Woolsthorpe garden—perhaps an apple actually falling from a tree, perhaps not.

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

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

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

  He took the mile to be 5,000 feet.20 He set one degree of the earth’s latitude at the equator equal to sixty miles, an error of about 15 percent. Some units were English, some antique Latin, others Italian: mile, passus, brace, pedes. He came up with a datum for the speed of the revolving earth: 16,500,000 cubits in six hours.

  Yet, with the data he had, he could not quite make the numbers work. He still found it necessary to attribute some of the moon’s motion to the vortices of Descartes.

  If a quantity once move it will never rest unlesse hindered by some externall caus. 2. A quantity will always move on in the same streight line (not changing the determination nor celerity of its motion) unless some externall cause divert it.26

  He continued through dozens more axioms, comprising a logical whole, but a tangled one. He was hampered by the chaos of language—words still vaguely defined and words not quite existing.

  twenty-four, Newton believed he could marshal a complete science of motion, if only he could find the appropriate lexicon, if only he could set words in the correct order

• 5. Bodys & Senses

  With this paradox in mind, Newton, experimental philosopher, slid a bodkin into his eye socket between eyeball and bone. He pressed with the tip until he saw “severall white darke & coloured circles.…

• 6. The Oddest If Not the Most Considerable Detection

  Barrow showed him a new book from London, Logarithmotechnia, by Nicholas Mercator, a mathematics tutor and member of the Royal Society. It presented a method of calculating logarithms from infinite series and thus gave Newton a shock: his own discoveries, rediscovered.

  infinite series he had worked out at Woolsthorpe. Provoked, he revealed to Barrow a bit more of what he knew. He drafted a paper in Latin, “On Analysis by Infinite Series.” He also let Barrow post this to another Royal Society colleague, a mathematician, John Collins,4 but he insisted on anonymity. Only after Collins responded enthusiastically did he let Barrow identify him: “I am glad my friends paper giveth you so much satisfaction. his name is Mr Newton; a fellow of our College, & very young … but of an extraordinary genius and proficiency in these things.

  Yet Newton knew what Barrow did not: that the whole project wanted correction.

  Anyway, Barrow had ambitions elsewhere. He was a favorite of the king, hoped for advancement, and thought of himself more as a theologian than a mathematician. Before the end of the year, he resigned his post as Lucasian professor, yielding it to Newton, twenty-seven years old.

• 7. Reluctancy and Reaction

  The crucial idea was to isolate a beam of colored light and send that through a prism. For this he needed a pair of prisms and a pair of boards pierced with holes

  Most persuasive, though, was that the second prism never created new colors or altered the colors shining from the first prism.

  “And so the true cause of the length of that Image was detected,” Newton declared triumphantly—“that Light consists of Rays differently refrangible.”

  Above all: white light is a heterogeneous mixture.

  Fifteen months after his election to the Royal Society, Newton announced that he wished to withdraw—and not just from the society but from all correspondence

  Oldenburg did not hear from him again for more than two years

  had discovered a great truth of nature. He had proved it and been disputed. He had tried to show how science is grounded in concrete practice rather than grand theories. In chasing a shadow, he felt, he had sacrificed his tranquillity

• 8. In the Midst of a Whirlwind

  Hooke grew irate. In evenings that followed he met with friends in coffee-houses and told them that Newton had commandeered his pulse theory. After all, Newton was talking about color in terms of “vibrations of unequal bignesses.” Large vibrations are red—or, as he said more carefully, cause the sensation of red. Short vibrations produce violet. The only difference between colors was this: a slight, quantifiable divergence in the magnitude of vibration. Newton did not speak of waves. Nor for that matter had Hooke: waves were still a phenomenon of the sea. A lack of vocabulary hindered both men;

• 9. All Things Are Corruptible

  He feared disease—plague and pox—and treated himself preemptively by drinking a self-made elixir of turpentine, rosewater, olive oil, beeswax, and sack. In fact he was poisoning himself, slowly, by handling mercury

  the Newtonian world of formal, institutionalized science, it became disreputable. But Newton belonged to the pre-Newtonian world

  Over time, mercury builds up in the body, causing neurological damage: tremors, sleeplessness, and sometimes paranoid delusions.

  The virtuosi of the Royal Society wished to remove themselves from charlatans, to build all explanations from reason and not miracles. But magic persisted. Astronomers still doubled as astrologers; Kepler and Galileo had trafficked in horoscopes.

  There were forces in nature that he would not be able to understand mechanically, in terms of colliding billiard balls or swirling vortices. They were vital, vegetable, sexual forces—invisible forces of spirit and attraction. Later, it had been Newton, more than any other philosopher, who effectively purged science of the need to resort to such mystical qualities. For now, he needed them.

  When he was not stoking his furnaces and stirring his crucibles, he was scrutinizing his growing hoard of alchemical literature. By the century’s end, he had created a private Index chemicus, a manuscript of more than a hundred pages, comprising more than five thousand individual references to writings on alchemy spanning centuries. This, along with his own alchemical writing, remained hidden long after his death.

• 10. Heresy, Blasphemy, Idolatry

  But in the seventh year of his fellowship, 1675, a further step would be required: he would take holy orders and be ordained to the Anglican clergy, or he would face expulsion. As the time approached, he realized that he could no longer affirm his orthodoxy. He would not be able to take a false oath. He prepared to resign.

  The very existence of the Bible in English—long opposed by the church establishment and finally authorized only a generation before Newton’s birth—had inspired the Puritan cause.

  At the last moment, in 1675, Newton’s precarious position at Cambridge was rescued. The king granted his request for a dispensation, an act that released the Lucasian professorship, in perpetuity, from the obligation to take holy orders.

  He would not even label years as AD, preferring AC: Christ, but not the Lord. Jesus was more than a man but less than God. He was God’s son, a mediator between God and humanity,

• 11. First Principles

  Whatever comets were, omens or freaks, their singularity was taken for granted: each glowing visitor arrived, crossed the sky in a straight path, and departed, never to be seen again. Kepler had said this authoritatively, and what else could a culture of short collective memory believe?

  Instead he suggested that the comet could have gone all the way around the sun and then returned.10 He diagrammed this alternative, too. And he conceded a crucial point to Flamsteed’s intuition: “I can easily allow an attractive power in the whereby the Planets are kept in their courses about him from going away in tangent lines.” He had never before said this so plainly.

  Hooke’s essay offered a “System of the World.”13 It paralleled much of Newton’s undisclosed thinking about gravity and orbits in 1666, though Hooke’s system lacked a mathematical foundation. All celestial bodies, Hooke supposed, have “an attraction or gravitating power towards their own centers.”

  Hooke pounced. Having promised days earlier to keep their correspondence private, he now read Newton’s letter aloud to the Royal Society and publicly contradicted it

  Both men were thinking in terms of a celestial attractive force, binding planets to the sun and moons to the planets.

  Hooke and Newton had both jettisoned the Cartesian notion of vortices. They were explaining the planet’s motion with no resort to ethereal pressure (or, for that matter, resistance). They had both come to believe in a body’s inherent force—its tendency to remain at rest or in motion—a concept for which they had no name.

  Hooke finally did put this to Newton: “My supposition is that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall”—that is, inversely as the square of distance.

  now remaines to know the proprietys of a curve Line … made by a centrall attractive power … in a Duplicate proportion to the Distances reciprocally taken

  Hooke had finally formulated the problem exactly. He acknowledged Newton’s superior powers. He set forth a procedure: find the mathematical curve, suggest a physical reason. But he never received a reply.

  Hooke asserted that he could show how to base all celestial motion on the inverse-square law and that he was keeping the details secret for now, until more people had tried and failed; only then would they appreciate his work.22 Halley doubted that Hooke knew as much as he claimed.

  He wrote only in Latin now, the words less sullied by everyday use. Quantitas materiæ—quantity of matter. What did this mean exactly? He tried: “that which arises from its density and bulk conjointly.” Twice the density and twice the space would mean four times the amount of matter. Like weight, but weight would not do; he could see ahead to traps of circular reasoning. Weight would depend on gravity, and gravity could not be presupposed. So, quantity of matter: “This quantity I designate under the name of body or mass.”23 Then, quantity of motion: the product of velocity and mass. And force—innate, or impressed, or “centripetal”—a coinage, to mean action toward a center.

  For the reasoning to come, he needed a foundation of words that did not exist in any language.

  A fever possessed him, like none since the plague years. He ate mainly in his room, a few bites standing up. He wrote standing at his desk. When he did venture outside, he would seem lost,

  specially understood and owned by the virtuosi—the scientists. Absolute, true, and mathematical time, in and of itself, and of its own nature, without reference to anything external, flows uniformly.…

• 12. Every Body Perseveres

  After much discussion the council members did vote to order the Principia printed—but by Halley, at his own expense. They offered him leftover copies of History of Fishes in place of his salary. No matter. The young Halley was a believer

  Without further ado, having defined his terms, Newton announced the laws of motion. Law 1. Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed. A cannonball would fly in a straight line forever, were it not for air resistance and the downward force of gravity. The first law stated, without naming, the principle of inertia, Galileo’s principle, refined. Two states—being at rest and moving uniformly—are to be treated as the same. If a flying cannonball embodies a force, so does the cannonball at rest. Law 2. A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed. Force generates motion, and these are quantities, to be added and multiplied according to mathematical rules. Law 3. To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction. If a finger presses a stone, the stone presses back against the finger. If a horse pulls a stone, the stone pulls the horse. Actions are interactions—no preference of vantage point to be assigned. If the earth tugs at the moon, the moon tugs back.

  Newton formed his argument in classic Greek geometrical style: axioms, lemmas, corollaries; Q.E.D. As the best model available for perfection in knowledge, it gave his physical program the stamp of certainty. He proved facts about triangles and tangents, chords and parallelograms, and from there, by a long chain of argument, proved facts about the moon and the tides.

  He had to create a dynamics for velocities changing from moment to moment, both in magnitude and in direction, in three dimensions. No philosopher had ever conceived such a thing, much less produced it.

  The force points toward the centers of bodies, not because of anything special in the centers, but as a mathematical consequence of this final claim: that every particle of matter in the universe attracts every other particle. From this generalization all the rest followed. Gravity is universal.

  He explained the slow precession of the earth’s rotation axis, the third and most mysterious of its known motions. Like a top slightly off balance, the earth changes the orientation of its axis against the background of the stars, by about one degree every seventy-two years. No one had even guessed at a reason before. Newton computed the precession as the complex result of the gravitational pull of the sun and moon on the earth’s equatorial bulge.

  but the pattern of two high tides per twenty-five hours was clear and global. Newton marshaled the data and made his theoretical claim. The moon and sun both pull the seas; their combined gravity creates the tides by raising a symmetrical pair of bulges on opposite sides of the earth.

  But the mechanical philosophy already had rules, and Newton was flouting one of them in spectacular fashion. Physical causes were supposed to be direct: matter striking or pressing on matter,

  It could not be denied, even if its essence could not be understood

• 13. Is He Like Other Men?

  Halley heralded the Principia in 1687 with the announcement that its author had “at length been prevailed upon to appear in Publick.”2 Indeed, Newton, in his forty-fifth year, became a public man. Willy-nilly he began to develop into the eighteenth-century icon of later legend.

  The King asserted his authority over this bastion of Protestantism by issuing royal mandates, placing Catholics as fellows and college officers. Tensions rose—the abhorrence of popery was written into Cambridge’s statutes as well as its culture.

  Newton abandoned his Cambridge cloister for good in 1696. His smoldering ambition for royal preferment was fulfilled. Trinity had been his home for thirty-five years, but he departed quickly and left no friends behind.35 As he emphatically told Flamsteed, he was now occupied by the King’s business. He had taken charge of the nation’s coin.

• 14. No Man Is a Witness in His Own Cause

  Newton grew rich himself, as Warden and then, from 1700 onward, Master. (From his first months he complained to the Treasury about his remuneration,9 but as Master he received not only a salary of £500 but also a percentage of every pound coined, and these sums were far greater.)

  Newton often opposed such pardons. Counterfeiting was difficult to prove; he had himself made a Justice of the Peace and oversaw prosecutions himself, all the way to the gallows. William Chaloner not only coined his own guineas but tried to cover his tracks by accusing the Mint of making its own false money. Newton, managing a network of agents and prison informers, ensured that he was hanged

  For the coronation of Queen Anne, in 1702, he manufactured medals of gold and silver, for which he billed the Treasury, twice, precisely £2,485 18s. 3½d.18 It was three years later, by Her Majesty’s Special Grace, that he was knighted.

  His return to the Royal Society had waited, all these years, for Hooke’s exit. Hooke died in March 1703; within months Newton was chosen president.

  He presented it to the Royal Society with an “Advertisement” in which he explained why he had suppressed this work since 1675. The reason: “To avoid being engaged in Disputes.”

  He was charging his heirs and followers with a mission, the perfection of natural philosophy. He left them a task of further study, “the Investigation of difficult Things by the Method of Analysis.”28 They need only follow the signs and the method

  Newton declared not only that he had made his discoveries by 1666 but also that he had described them to Leibniz. He released the correspondence, anagrams and all.39 Soon an anonymous counterattack appeared in Acta Eruditorum suggesting that Newton had employed Leibniz’s methods, though calling them “fluxions” instead of “Leibnizian differences.” This anonymous reviewer was Leibniz.

  The principals joined the fray openly in 1711. A furious letter from Leibniz arrived at the Royal Society, where it was read aloud and “deliver’d to the President to consider the contents thereof.”41 The society named a committee to investigate “old letters and papers.”42 Newton provided these. Early correspondence with John Collins came to light; Leibniz had seen some of it, all those years before. The committee produced a document without precedent: a detailed, analytical history of mathematical discovery.

  vindicated Newton with eloquence and passion, and no wonder: Newton was its secret author

  Newton understood the truth full well: that he and Leibniz had created the calculus independently. Leibniz had not been altogether candid about what he had learned from Newton—in fragments, and through proxies—but the essence of the invention was his.

  In a young and suddenly fertile field like the mathematics of the seventeenth century, discoveries had lain waiting to be found again and again by different people in different places.

  “Grown men, brilliant and powerful, betrayed their friends, lied shamelessly to their enemies, uttered hateful chauvinistic slurs, and impugned each others’ characters.”

  Watching over the minting of a nation’s coin, catching a few counterfeiters, increasing an already respectably sized personal fortune, being a political figure, even dictating to one’s fellow scientists: it should all seem a crass and empty ambition once you have written a Principia.

• 15. The Marble Index of a Mind

  The Principia marked a fork in the road: thenceforth science and philosophy went separate ways. Newton had removed from the realm of metaphysics many questions about the nature of things—about what exists—and assigned them to a new realm, physics. “This preparation being made,” he declared, “we argue more safely.”26 And less safely, too: by mathematizing science, he made it possible for its facts and claims to be proved wrong.

  This vulnerability was its strength. By the early nineteenth century Georges Cuvier was asking enviously, “Should not natural history also one day have its Newton

  The observer whom Einstein and his followers returned to science scarcely resembled the observer whom Newton had removed. That medieval observer had been careless and vague; time was an accumulation of yesterdays and tomorrows, slow and fast, nothing to be measured or relied upon. Time and space had first to be rescued—made absolute, true, and mathematical

  “Newton was not the first of the age of reason,” Keynes told a few students and fellows in a shadowed room at Trinity College. “He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago.”

  On his deathbed he refused the sacrament of the church. Nor could a pair of doctors ease his pain. He died early Sunday morning, March 19, 1727. On Thursday the Royal Society recorded in its Journal Book, “The Chair being Vacant by the death of Sir Isaac Newton there was no Meeting this Day.”

  In eighty-four years he had amassed a fortune: