Second Reading :: Isaac Newton (with Free PDF File)

   

(0) This text presents some sensible quotes extracted from the book Isaac Newton, written by James Gleick, First Edition, Pantheon Books, New York, 2003. This Isaac Newton’s biography I first read in the middle of 2004, and now, in the middle of 2018, I proposed myself a second reading of such invaluable adventure, which is the Newton’s Life! I hope You Enjoy this Summary of Quotes!

   

(1) His name betokens a system of the world. But for Newton himself there was no completeness, only a questioning – dynamic, protean, an unfinished. He never fully detached matter and space from God. He never purged occult, hidden, mystical qualities from his vision of nature. He sought order and believed in order but never averted his eyes from the chaos. He of all people was no Newtonian. Information flowed faintly and perishably then, through the still human species, but he created a method and a language that triumphed in his lifetime and gained ascendancy with each passing century. He pushed open a door that led to a new universe: set in absolute time and space, at once measureless and measurable, furnished with science and machines, ruled by industry and natural law. Geometry and motion, motion and geometry: Newton joined them as one.

   

(2) He did not know what he wanted to be or do, but was not tend sheep or follow the plow and the dung cart. He spent more time gathering herbs and lying with a book among the asphodel and moonwort, out of the household’s sight. He built waterwheels in the stream while his sheep trampled the neighbors’ barley. He watched the flow of water, over wood and around rocks, noting the whorls and eddies and waves, gaining a sense of fluid motion.

   

(3) He felt learning as a form of obsession, a worthy pursuit, in God’s service, but potentially prideful as well. He taught himself a shorthand of esoteric symbols – this served both to save paper and encrypt his writing – and he used it, at a moment of spiritual crisis, to record a catalogue of his sins. Among them were ‘neglecting to pray’, ‘negligence at the chapel’, and variations on the theme of falling short in piety and devotion.

   

(4) He read Aristotle through a mist of changing languages, along with a body of commentary and disputation. The words crossed and overlapped Aristotle’s was a word of substances. A substance possesses qualities and properties, which taken together amount to a form, depending ultimately on its essence. Properties can change; we call this motion. Motion is action, change, and life. It is an indispensable partner of time; the one could not exist without the other. If we understood the cause of motion, we would understand the cause of the world.

   

(5) By the 1660s – new news every day – readers of esoterica knew well enough that the earth was a planet and that the planets orbited the sun. Newton’s notes began to include measurements of the apparent magnitude of stars. 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.

   

(6) He set authority aside. Later he came back to this page and inscribed an epigraph borrowed from Aristotle’s justification for dissenting from his teacher. Aristotle had said, ‘Plato is my friend, but truth my greater friend.’ Newton inserted Aristotle’s name in sequence: ‘Amicus Plato amicus Aristoteles magis amica veritas.’ He made a new beginning.

   

(7) Cambridge in 1664. At end of that year, just before the winter solstice, a comet appeared low in the sky, its mysterious tail blazing toward the west. Newton stayed outdoors night after night, noting a path against the background of fixed stars, watching till it vanished in the light of each dawn, and only then returned to his room, sleepless and disordered. A comet was a frightening portent, a mutable and irregular traveler through the firmament. Nor was that all: rumors were reaching England of a new pestilence in Holland – perhaps from Italy or the Levant, perhaps from Crete or Cyprus. Hard behind the rumors came the epidemic. Three men in London succumbed in a single house; by January the plague, this disease of population density, was spreading from parish to parish, hundreds dying each week, then thousands. Before the outbreak ran its course, in little more than a year, it killed one of every six Londoners.

   

(8) Newton returned home. He built bookshelves and made a small study for himself. He opened the nearly blank thousand-page commonplace book he had inherited from his stepfather and named it his Waste Book. He began filling it with reading notes. These mutated seamlessly into original research. He set himself problems; considered them obsessively; calculated answers, and asked new questions. He pushed past the frontier of knowledge (though he did not know this). The plague year was his transfiguration. Solitary and almost incommunicado, he became the world’s paramount mathematician. Most of the numerical truths and methods that people had discovered, they had forgotten and rediscovered, again and again, in cultures far removed from one another. Mathematics was evergreen. One scion of Homo sapiens could still comprehend virtually all that species knew collectively.

   

(9) Newton was inspired by the leap of Descarte’s Géométrie, a small and rambling text, the third and last appendix to his Discours de la Méthode. This forever joined two great realms of thought, geometry and algebra. Algebra (a ‘barbarous’ art, Descartes said, but it was his subject nonetheless) manipulated unknown quantities as if they were known, by assigning them symbols. Symbols recorded information, spared the memory, just as the printed book did. Indeed, before texts could spread by printing, the development of symbolism had little point. With symbols came equations: relations between quantities, and changeable relations at that. This was new territory, and Descartes exploited it.

   

(10) 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, tangent and areas. These were visualized, and they were named.

   

(11) No one understands the mental faculty we call mathematical intuition; much less, genius. People’s brains do not differ much, from one to the next, but numerical facility seems rarer, more special, than other talents. It has a threshold quality. In no other intellectual realm does the genius find so much common ground with the idiot savant. A mind turning inward from the world can see numbers as lustrous creatures; can find order in them, and magic; can know numbers as if personally. A mathematician, too, is a polyglot. A powerful source of creativity is a facility in translating, seeing how the same thing can be said in seemingly different ways. If one formulation doesn’t work, try another. Newton’s patience was limitless. Truth, he said much latter, was “the offspring of silence and meditation”. And he said: “I keep the subject constantly before me and wait ‘till the first dawnings open slowly, by little and little, into full and clear light”.

   

(12) Newton seemed now to possess a limitless ability to generalize, to move from one or a few particular cases to the universe of all cases. Yet it turns out that the human mind, though bounded in a nutshell, can discern the infinite and take its measure.

   

(13) Far away across the country multitudes were dying in fire and plague. Numerologists had warned that 1666 would be the Year of the Beast. Most of London lay in black ruins: fire had begun in a bakery, spread in the dry wind across thatch-roofed houses, and blazed out of control for four days and four nights. 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. Here at Woolsthorpe the night was strewn with stars, the moon cast its light through the apple trees, and day’s sun and shadows carved their familiar pathways across the wall. Newton understood now: the projection of curves onto flat planes; the angles in three dimensions, changing slightly each day. He saw an orderly landscape. Its inhabitants were not static objects; they were patterns, process and change. What he wrote, he wrote for himself alone. He had no reason to tell anyone. He was twenty-four and he had made tools.

   

(14) We call the Scientific Revolution an epidemic, spreading across the continent of Europe during two centuries: ‘It would come to rest in England, in the person of Isaac Newton,’ said the physicist David Goodstein. ‘On the way north, however, it stopped briefly in France…’ Or a relay race, run by a team of heroes who passed the baton from one to the next: COPERNICUS to KEPLER to GALILEO to NEWTON. Or the overthrow and destruction of the Aristotelian cosmology: a worldview that staggered under the assaults of Galileo and Descartes and finally expired in 1687, when Newton published a book. For so long the earth had seemed the center of all things. The constellations turned round in their regular procession. Just a few bright objects caused a puzzle – the planets, wanderers, like gods or messengers, moving irregularly against the fixed backdrop of stars. In 1543, just before his death, Nicolaus Copernicus, Polish astronomer, astrologer and mathematician, published the great book De Revolutionibus Orbium Celestium (‘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. 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. Having thus overthrown one kind of celestial perfection, he sought new kinds, believing fervently in a universe built on geometrical harmony. He found an elegant link between geometry and motion by asserting that an imaginary line from a planet to the sun sweeps across equal areas in equal times. Galileo Galilei took spy-glasses – made by inserting spectacle makers’ lenses into hollow tube – and pointed them upward toward the night sky. What he saw both inspired and disturbed him: moons orbiting Jupiter; spots marring the sun’s flawless face; stars that had never been seen – ‘in numbers ten times exceeding the old and familiar stars.’ He learned, ‘with all the certainty of sense evidence,’ that the moon ‘is not robed in a smooth polished surface but is in fact rough and uneven.’ It has mountains, valleys, and chasms.

   

(15) He read them in a new book from London, titled Micrographia: ‘The Science of Nature has been already too ling made only a work of the Brain and the Fancy. It is now high time that it should return to the plainness and soundness of Observations on material and obvious things.’ The author was Robert Hooke, a brilliant and ambitious man seven years Newton’s senior, who wielded the microscope just as Galileo had the telescope. These were the instruments that penetrated the barrier of scale and opened a view into countries of the very large and the very small. Wonders were revealed there.

   

(16) Newton’s status at Trinity improved. In October 1667 the college elected fellows for the first time in three years. He bought a set of old books on alchemy, along with glasses, a tin furnace, and chemicals: aqua fortis, sublimate, vinegar, white lead, salt and tartar. With these he embarked on a program of research more secret than ever.

   

(17) 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. Mercator had constructed an entire book – a useful book, at that – from few infinite series. For Newton these were merely special cases of powerful approach to infinite series he had worked out at Woolsthorpe. Provoked, he revealed 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, 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.’ It was the first transmission of Newton’s name south of Cambridge.

   

(18) Like no institution before it, the Royal Society was born dedicated to information flow. It exalted communication and condemned secrecy. ‘So far are the narrow conceptions of a few private Writers, in a dark Age, from being equal to so vast a design,’ its founders declared. Science did not exist – not as an institution, not as an activity – but they conceived it as a public enterprise. They imagined a global network, an ‘Empire in Learning.´ Those striving to grasp the whole fabric of nature ‘ought to have their eyes in all parts, and to receive information from every quarter of the earth, they ought to have a constant universal intelligence: all discoveries should be brought to them: the Treasuries of all former times should be laid open before them.’

   

(19) Far away in Cambridge Newton inhaled all this philosophical news. He took fervid notes. Rumors of lunar influence: ‘Oysters & Crabs are fat at the new moone & leane at the full.’ Then in 1671 he heard directly from the voice of the Royal Society. ‘Sr’, Oldenburg wrote, ‘Your Ingenuity is the occasion of this addresse by a hand unknowne to you…’ He said he wished to publish an account of Newton’s reflecting telescope. He urged Newton to take public credit. This peculiar historical moment – the manners of scientific publication just being born – was alert to the possibilities of plagiarism.

   

(20) It led him (or so he reported) to the Experimentum Crucis – the signpost at a crossroads, the piece of experience that shows which path to trust. Years before, in his earliest speculation, he had asked himself, ‘Try if two Prismas the one casting blue upon the other’s red doe not produce a white.’ They did not. Blue light stayed blue and red stayed red. Unlike white (Newton deduced) those colors were pure. ‘And so the true cause of the length of that Image was detected,’ Newton declared triumphantly – ‘that Light consists of Rays differently refrangible.’ Some colors are refracted more, and not by any quality of the glass but their own predisposition. Color is not a modification of light but an original, fundamental property. Above all: white light is a heterogeneous mixture. ‘But the most surprising, and wonderful composition was that of Whiteness. There is no one sort of Rays which alone can exhibit this. ‘Tis ever compounded, and to its composition are requisite all the aforesaid primary Colours, mixed in due proportion. I have often in Admiration beheld, that all the Colours of the Prisme being made to converge, and thereby to be again mixed,… reproduced light, intirely and perfectly white.’

   

(21) In 1675 Newton journeyed to London and finally appeared at the Royal Society. He met in person these men who had till then been friends and antagonists twice removed, their spirits channeled through Oldenburg’s mail.

   

(22) This sheaf of papers posted to Oldenburg blended calculation and faith. It was a work of the imagination. It sought to reveal nothing less than the microstructure of matter. For generations it reached no further than the few man who heard it read and then raptly debated it through all the meetings of the Royal Society from December 1675 to the next February. Newton had peered deeper into the core of the matter than could be justified by the power of the microscopes. Through a series of experiments and associations he seemed to feel nature’s fundamental particles just beyond the edge of the vision. Indeed, he predicted that instruments magnifying three or four thousand times might bring atoms into view.

   

(23) Irregular motions, he emphasized – and he saw no way to explain them mechanically, purely in terms of matter pressing on matter. It was no static world, no orderly world he sought to understand now. Too much to explain at once: the world in flux; a world of change and even chaos. He gave out poetry: ‘For nature is a perpetuall circulatory worker, generating fluids out of solids, and solids out of fluids, fixed things out of volatile, & volatile out of fixed, subtile out of gross, and gross out of subtile, Some things to ascend & make the upper terrestriall juices, Rivers and the Atmosphere; and by consequence others to descend…’ The ancients had often supposed the existence of ether, a substance beyond the elements, purer than air or fire. Newton offered the ether as a hypothesis now, describing it as a ‘Medium much of the same constitution with the air, but far rarer, subtiler & more strongly Elastic.’ As sound is a vibration of the air, perhaps there are vibrations of the ether – these would be swifter and finer. He estimated the scale of sound waves at a foot or half-foot, vibrations of ether at less than a hundred thousandth of an inch.

   

(24) Oldenburg – no friend to Hooke – chose to surprise him with a public reading of Newton’s rejoinder at the next Royal Society meeting. Finally, after years of jousting by proxy, Hooke decided to take pen in hand and address his adversary personally. He adopted a meek and philosophical tone. Newton’s famous reply came a fortnight later. He called Hooke a ‘true Philosophical spirit.’ And then, for the matter of their dispute, he put on record a finely calibrated piece of faint praise and lofty sentiment: ‘What Des-Cartes did was a good step. You have added much several ways, & especially in taking the colours of thin plates into philosophical consideration. If I have seen further it is by standing on the sholders of Giants.’ The private philosophical dialogue between Newton and Hooke never took place. Almost two years passed before they communicated again at all. By then Oldenburg had died, Hooke had succeeded him as Secretary of the Royal Society, and Newton had withdrawn ever more deeply into the seclusion of his Trinity chambers.

   

(25) His devotion to philosophical matters grew nonetheless. He built a special chimney to carry away the smoke and the fumes. No one could understand till centuries latter – after his papers, long hidden and scattered, began finally to be reassembled – that he had been not only a secret alchemist but, in the breadth of his knowledge and his experimentation, the peerless alchemist of Europe. Much later, when the age of reason grew mature, a fork was seen to have divided the road to the knowledge of substances. On one path, chemistry: a science that analyzed the elements of matter with logic and rigor. Left behind, alchemy: a science and an art, embracing the relation of the human to the cosmos; invoking transmutation and fermentation and procreation. Alchemists lived in a realm of exuberant, animated forces. In the Newtonian world of formal, institutionalized science, it became disreputable. But Newton belonged to the pre-Newtonian world. Alchemy was in its heyday. Newton was a mechanist and a mathematician to his core, but he could not believe in a nature without spirit.

   

(26) To alchemists nature was alive with process. Matter was active, not passive; vital, not inert. Many processes began in the fire: melting, distilling subliming, and calcining. Newton studied them and practiced them, in his furnaces of tin and bricks and firestones. In sublimation vapors rose from the ashes of burned earths and condensed again upon cooling. In calcination fire converted solids to dust; ‘be you not weary of calcination,’ the alchemical fathers had advised; ‘calcination is the treasure of a thing.’ When a crimson-tinged earth, cinnabar, passed through the fire, a coveted substance emerged: ‘silvery water’ or ‘chaotic water’ – quicksilver. It was liquid and a metal at once, lustrous white, eager to form globules. Some though a wheel rimmed with quicksilver could turn unaided – perpetual motion. Alchemists knew quicksilver as Mercury (as iron was Mars, copper Venus, and gold the Sun); in their clandestine writings they employed the planet’s ancient symbol. Or they alluded to quicksilver as ‘the serpents.’

   

(27) Rather than turn away from what he could not explain, he plunged in more deeply. Dry powders refuse to cohere. Flies walked on water. Heat radiated through a vacuum. Metallic particles impregnated mercury. Mere though caused muscles to contract and dilate. 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 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 alchemistical 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.

   

(28) He had seldom returned home to Lincolnshire since the sojourn of the plague years, but in the spring of 1679 his mother succumbed to a fever. He left Cambridge and kept vigil with her over days and nights, till she died. He, the first-born son, not his half-brothers or sisters, was her heir and executor, and he buried her in the Colsterworth churchyard next to the grave of his father.

   

(29) In the next year a comet came. In England it arose faint in the early morning sky for a few weeks in November till it approached the sun and faded in the dawn. Few saw it. A more dramatic spectacle appeared in the nights of December. Newton saw it with naked eye on December 12: a comet whose great tail, broader than the moon, stretched over the full length of King’s College Chapel. He tracked it almost nightly through the first months of 1681. A young astronomer travelling to France, Edmond Halley, a new Fellow of the Royal Society, was amazed at its brilliance. Robert Hooke observed it several times in London. Across the Atlantic Ocean, where a handful of colonists were struggling to survive on a newfound continent, Increase Mather delivered a sermon, ‘Heaven’s Alarm to the World,’ to warn Puritans of God’s displeasure.

   

(30) 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, far 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. They were dancing around a pair of questions, one the mirror of the other: What curve will be traced by a body orbiting another in an inverse-square gravitational field? (An ellipse). What gravitational force law can be inferred from a body orbiting another in a perfect ellipse? (An inverse-square law). 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. 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.

   

(31) Four years latter Edmond Halley made a pilgrimage to Cambridge. Halley had been discussing planetary motion in coffee-houses with Hooke and the architect Cristopher Wren. Some boasting ensued. Halley himself had worked out (as Newton had in 1666) a connection between an inverse-square law and Kepler’s rule of periods – that the cube of the planet’s distance from the sun varies as the square of its orbital year. Wren claimed that he himself had guessed at the inverse-square law years before Hooke, but could not quite work out the mathematics. 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. Halley doubted that Hooke knew as much as he claimed. Halley put the question to Newton directly in August 1684: supposing an inverse square law of attraction toward the sun, what sort of curve would a planet make? Newton told him: an ellipse. He said he had calculated this long before. He would not give Halley the proof – he said he could not lay his hands on it – but promised to redo it and send it along.

   

(32) He could not, or would not, give Halley a simple answer. First he sent a treatise of nine pages, ‘On the Motions of Bodies in Orbit.’ It firmly tied a centripetal force, inverse proportional to the square of distance, not only to specific geometry of the ellipse but to all Kepler’s observations of orbital motion. Halley rushed back to Cambridge. His one copy had become an object of desire in London. Flamsteed complained: ‘I believe I shall not get a sight of [it] till our common friend Mr Hooke & the rest of the towne have been first satisfied.’ Halley begged to publish the treatise, and he begged for more pages, but Newton was not finished.

   

(33) The alchemical furnaces went cold; the theological manuscripts were shelved. 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, walk erratically, turn and stop for no apparent reason, and disappear inside once again. Though he had dropped alchemy for now, Newton had learned from it. He embraced invisible forces. He knew he was going to have to allow planets to influence one another from distance. He was writing the principles of philosophy. But not just that: the mathematical principles of natural philosophy. ‘For the whole difficult of philosophy’, he wrote, ‘seems to be to discover the forces of nature from the phenomena of motions and then demonstrate the other phenomena from these forces’. The planets, the comets, the moon, the sea. He promised a mechanical program – no occult qualities. He promised proof. Yet there was mystery in forces still.

   

(34) Our eyes perceived only relative motion: a sailor’s progress along his ship, or the ship’s progress on the earth. But the earth, too, moves, in reference to space – itself immovable because it is purely mathematical, abstracted from our senses. Of time and space he made a frame for the universe and a credo for a new age.

   

(35) ‘It was ordered, that a letter of thanks be written to Mr Newton’, recorded Halley, as clerk of the Royal Society, on April 28, 1686, ‘…and that in the meantime the book be put into the hands of Mr Halley’. Only Halley knew what was in ‘the book’ – a first sheaf of manuscript pages, copied in Cambridge by Newton’s amanuensis and dispatched to London with the grand title Philosophiae Naturalis Principia Mathematica. Halley had been forewarning the Royal Society: ‘a mathematical demonstration of the Copernican hypothesis’; ‘makes out all the phenomena of the celestial motions by the only supposition of a gravitation towards the centre of the sun decreasing as the squares of the distances therefrom reciprocally’. Hooke heard him.

   

(36) 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 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. He presented these axioms, to serve as the foundation for an edifice of reasoning and proof. ‘Law’ – lex – was a strong and peculiar choice of words. Bacon had spoken of laws, fundamental and universal. It was no coincidence that Descartes, in his own book called Principles of Philosophy, had attempted a set of three laws, regulae quaedam sive leges naturae, specifically concerning motion, including a law of inertia. For Newton, the laws formed the bedrock on which a whole system would lie. A law is not a cause, yet it is more than a description. A law is a rule of conduct: here God’s law, for every piece of creation. A law is to be obeyed, by inanimate particles as well as sentient creatures. Newton chose to speak not so much of God as of nature. ‘Nature is exceedingly simple and conformable to herself. Whatever reasoning holds for great motions, should hold for lesser ones as well’.

   

(37) Book III gave The System of the World. It gathered together the phenomena of the cosmos. It did this flaunting an exactitude unlike anything in the history of philosophy, Phenomenon 1: the four known satellites of Jupiter. Newton had four set of observations to combine. He produced some numbers: their orbital periods in days, hours, minutes, and seconds, and their greatest distance from the planet, to the nearest thousandth of Jupiter’s radius. He did the same for the five planets, Mercury, Venus, Mars, Jupiter, and Saturn. And for the moon.

   

(38) He said he had tested gold, silver, lead, glass, sand, salt, wood, water, and wheat – suspending them in a pair of identical pendulums so precisely that he could detect a difference of one part in a thousand. Furthermore, he proposed, the heavenly bodies must perturb one another: Jupiter influencing Saturn’s motion, the sun influencing the earth, and the sun and moon both perturbing the sea. ‘All the planets are heavy toward one another’. He pronounced: ‘It is now established that this force is gravity, and therefore we shall call it gravity from now on’.

   

(39) These elements meshed and turned together like the parts of a machine, the work of a perfect mechanic, like an intricate clock, a metaphor that occurred to many as news of the Principia spread. Yet Newton himself never succumbed to this fantasy of pure order and perfect determinism. Continuing to calculate where calculation was impossible, he saw ahead to the chaos that could emerge in the interactions of many bodies, rather than just two or three. The center of the planetary system, he saw, is not exactly the sun, but rather than just two or three. The center of the planetary system, he saw, is not exactly the sun, but rather the oscillating common center of gravity. Planetary orbits were not exact ellipses after all, and certainly not the same ellipse repeated. ‘Each time a planet revolves it traces a fresh orbit, as happens also with the motion of the Moon, and each orbit is dependent upon the combined motions of all planets, not to mention their actions upon each other’, he wrote.

   

(40) Yet he solved another messy, bewildering phenomenon, the tides. He had assembled data, crude and scattered though they were. Samuel Sturmy had recorded observations from the mouth of the River Avon, three miles below Bristol. Samuel Colepress had measured the ebb and flow in Plymouth Harbor. Newton considered the Pacific Ocean and the Ethiopic Sea, bays in Normandy and at Pegu in the East Indies. Halley himself had analyzed observations by sailors in Batsha Harbor in the port of Tunking in China. None of these lent themselves to a rigorous chain of calculation, 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.

   

(41) He had declared at the outset that his mission was to discover the forces of nature. He deduced forces from celestial bodies’ motion, as observed and recorded. He made a great claim – the System of the World – and yet declared his program incomplete. In fact, incompleteness was its greatest virtue. He bequeathed to science, that institution is its throes of birth, a research program, practical and open-ended. There was work to do, predictions to be computed and verified.

   

(42) Besides mathematics Newton has returned to the most tortuous unfinished problem in the Principia: a full theory of the moon’s motion. This was no mere academic exercise; given a precise recipe for predicting the moon’s place in the sky, sailors with handheld astrolabes should finally be able to calculate their longitude at sea. A lunar theory should follow from Newton’s theory of gravity: the ellipse of the lunar orbit crosses the earth’s own orbital plane at a slant angle; the sun’s attraction twists the lunar orbit, apogee and perigee revolving over a period of roughly nine years. But the force of solar gravity itself varies as the earth and moon, in their irregular dance, approach and recede from the sun. With a revised edition of the Principia in mind, he needed more data, and this meant calling upon the Astronomer Royal. Late in the summer of 1694 he boarded a small boat to journey down the river Thames and visit, for the first time, Flamsteed in Greenwich. He pried loose fifty lunar observations and a promise of one hundred more.

   

(43) He did ultimately produce a practical formula for calculating the moon’s motion: a hybrid sequence of equations and measurements that appeared first in 1702, as five Latin pages inside David Gregory’s grand Astronomiae Elementa. Gregory called it Newton’s theory, but in the end Newton had omitted any mention of gravitation and buried his general picture under a mass of details. Halley quickly reprinted Newton’s text as a booklet in English, saying, ‘I though it would be a good service to our Nation… For as Dr. Gregory’s Astronomy is a large and scarce Book, it is neither everyone’s Money that can purchase it’. Halley hailed the theory’s exactness and hoped to encourage people to use it, but ‘the Famous Mr. Isaac Newton’s Theory of the Moon’ was little noted and quickly forgotten. 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. As he emphatically told Flamsteed, he was now occupied by the King’s business. He had taken charge of the nation’s coin.

   

(X) Reader’ Personal Note :: 1696 was a turning point in Newton’s life. He left not only Trinity, but the Natural Philosophy principles. From Good to evil, he became obsessively engaged in politics and power struggles. Newton embraced the dark side of himself from 1696 on. He was fifty-three.

   

(44) The new Chancellor of the Exchequer, Charles Montague, set a radical program in motion: a complete recoinage – all old coins to be withdrawn from circulation. Montague had known Newton at Cambridge and with this support the king named him Warden of the Mint in April 1696, just as the recoinage began. Newton supervised an urgent industrial project, charcoal fires burned around the clock, teams of horses and men crowding in upon one another, garrisoned soldiers standing watch. It was tumultuous time at the Tower and in London: the terms of the recoinage had strangled the supply of money essential to daily commerce and, not incidentally, effected a transfer of national wealth from the poor to the rich. Newton grew rich himself, as Warden and then, from 1770 onward, Master. (From his first months he complained to the Treasury about his remuneration, but as Master he received not only a salary of 500 pounds but also a percentage of every pound coined, and these sums were far greater). He found a house in Jermyn Street, bought luxurious, mainly crimson furniture, engaged servants, and invited his twenty-year-old niece, Catherine Barton, the daughter of his half-sister, to live with him as housekeeper. She became renowned in London society for beauty and charm. Jonathan Swift was an admirer and frequent visitor. Within a half-decade she became the lover of Newton’s patron Montague, by now the Earl of Halifax.

   

(45) A portent of future trouble came from Leibnitz, by second hand: ‘to Mr. Newton, that man of great mind, my most devoted greeting’ – and ‘another matter, not only did I recognize that the most profound Newton’s Method of Fluxions was like my differential method, but I said so… and I also informed others’. In passing this on, the elderly mathematician John Wallis begged Newton to let some of his treasure out from darkness. His (Newton’s) return to the Royal Society ha waited, all these years, for Hooke’s exit. Hooke died in March 1703; within months Newton was chosen president. Past presidents had often been honorary, political figures. Newton seized power now and exercised it authoritatively.

   

(46) With Hooke dead, he also finally took Wallis’s advice and released for publication his second great work – in English, rather than Latin, and, more important, in prose rather than mathematics. This time he needed no editor. He had three ‘books’ based on his work from thirty years earlier on the nature of light and color: the geometry of reflection and refraction; how lenses form images; and the workings of the eye and the telescope. The origin of whiteness; prisms; the rainbow. He added much more, in the form of ‘Queries’: queries on heat; queries on the ether; occult qualities, action at a distance, inertia. For good measure he included a pair of mathematical papers, the first he ever published. He titled the book Opticks – or, a Treatise on the Reflexions, Refractions, Inflexions and Colours of Light. He presented it to the Royal Society with the ‘Advertisement’ in which he explained why he had suppressed this work since 1675. The reason: ‘To avoid being engaged in Disputes’. Not only had Hooke died but the world had changed. Newton’s style, integrating theories with mathematical experimentation, had become familiar to philosophers, and they accepted readily the same propositions that had stirred skepticism and scorn in the 1670s.

   

(47) By now he and Newton were in open conflict. Leibniz, four years Newton’s junior, had seen far more of the world – a stoop-shouldered, tireless man of affairs, lawyer and diplomat, cosmopolitan traveler, courtier to the House of Hanover. The two men had exchanged their first letters – probing and guarded – in the late 1670s. In the realm of mathematics, it was paradoxically difficult to stake effective claims to knowledge without disclosure.

   

(48) Now, decades later, Newton had a purpose in publishing his pair of mathematical papers with the Opticks, and he made his purpose plain. In particular, ‘On the Quadrature of Curves’ laid out for the first time his method of fluxions. In effect, despite the utterly different notation, this was Leibniz’s differential calculus. Where Leibniz worked with successive differences, Newton spoke of rates of flow changing throughout successive moments of time. Leibniz was chunklets – discrete bits. Newton was the continuum. A deep understanding of the calculus ultimately came to demand a mental bridge from one to the other, a translation and reconciliation of two seemingly incompatible symbolic systems. 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. 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. Newton’s disciples fired back in the Philosophical Transactions, suggesting that it was Leibniz who, having read Newton’s description of his methods, then published ‘the same Arithmetic under a different name and using a different notation’. Between each of these thrusts and parties, years passed. But a duel was under way. Partisans joined both sides, encouraged by tribal loyalties more than any real knowledge of the documentary history. Scant public record existed on either side. 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’. The society named a committee to investigate ‘old letters and papers’. 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. No clearer account of the calculus existed, but exposition was not the point; the report was meant as a polemic, to condemn Leibniz, accusing him of a whole congeries of plagiarisms. It judged Newton’s method to be not only the first – ‘by many years’ – but also more elegant, more natural, more geometrical, more useful, and more certain. It vindicated Newton eloquence and passion, and no wonder: Newton was its secret author. The Royal Society published it rapidly. It also published a long assessment of the report, in the Philosophical Transactions – a diatribe, in fact. This, too, was secretly composed by Newton.

   

(49) 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 invention was his. Newton has made his discoveries first, and he had discovered more, but Leibniz had done what Newton had not: published his work for the world to use and to judge. It was secrecy that spawned competition and envy. The plagiarism controversy drew its heat from the gaps in the dissemination of the knowledge. 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.

   

(50) The obsessions of Newton’s later years disappointed modernity in some way. Just when science began to coalesce as an English Institution, Newton made himself its autocrat. He purged the Royal Society of all remnants of Hooke. He gained authority over the Observatory and wrested from Flamsteed the astronomer’s own life’s work, a comprehensive catalogue of the stars.

   

(51) He had concealed so much, till the very end. As his health declined, he kept writing. His niece’s new husband, John Conduitt, saw him in his last days working in near darkness on an obsessional history of the world – he wrote at least a dozen drafts – The Chronology of Ancient Kingdoms Amended. In his chambers, after a painful fit of gout, he sat with Conduitt before a wood fire and talked about comets. In 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’.

   

(52) In eight-four years he had amassed a fortune: household furniture, much of it upholstered in crimson; crimson curtains, a crimson mohair bed, and crimson cushions; a clock; a parcel of mathematical instruments and chemical glasses; several bottles of wine and cider; thirty-nine silver medals and copies in plaster of Paris; a vast library with nearly two thousand books and his many secret manuscripts; gold bars and coins – the whole state valued at 31,821 pounds, a considerable legacy. Yet he left no will.

   

(53) The relativity of Einstein appeared as a revolutionary assault on absolute space and time. Motion distorts the flow of time and the geometry of space, he found. Gravity is not just a force, ineffable, but also a curvature of space-time itself. Mass, too, had to be redefined; it became interchangeable with energy. Einstein did shake space-time loose from pins which Newton had bound it, but he lived in Newton’s space-time nonetheless: absolute in its geometrical rigor and its independence of the world we see and feel. He happily brandished the tools Newton had forged. Einstein’s is no everyday or psychological relativity. ‘Let no one suppose’, he said in 1919, ‘that the mighty work of Newton can really be superseded by this or any other theory. His great and lucid ideas will retain their unique significance for all time as the foundation of our whole modern conceptual structure in the sphere of natural philosophy’.

   

Compression Rate = 18 quotation’ pages / 191 read pages = 9,42%

   

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