No Man Is a Witness in His Own Cause
WHEN THE SEVENTEENTH CENTURY ENDED, the published work of Isaac Newton amounted to little more than the several hundred copies of the Principia, most in England, a few scattered on the Continent. They were not much read, but scarcity made them valuable. Before a second edition was ready (in 1713, a quarter-century after first publication) a copy cost two guineas. At least one student saved his money and made a copy by hand.1 Newton’s nascent legend diffused only by word of mouth in a tiny community. When an anonymous solution to an esoteric geometry problem made its way to Holland, Johann Bernoulli announced that he recognized the solver “ex ungue leonem”—the lion by his claw.2 In Berlin, Leibniz told the Queen of Prussia that in mathematics there was all previous history, from the beginning of the world, and then there was Newton; and that Newton’s was the better half.3 Tsar Peter of Russia traveled to England in 1698 eager to see several phenomena: shipbuilding, the Greenwich Observatory, the Mint, and Isaac Newton.4
The Royal Society was becalmed, its finances ragged, its membership dwindling. Hooke still dominated. Even living in London, Newton mostly stayed away. Yet numerical thinking was in vogue—calculation of all kinds was permeating the life of the polity—and it conjured Newton’s name above all others. Mariners, architects, and gamblers were understood to depend on mathematical methods. Mathematics had become a pillar raising up the glory and honor of England, “the Academy of the Universe.”5 John Arbuthnot published his Essay on the Usefulness of Mathematical Learning—a study which, he noted, seems to require “a particular genius and turn of head,… few are so happy to be born with.” The incomparable Mr. Newton had now discovered “the grand secret of the whole Machine.” And he assured his readers that the world was made of number, weight, and measure—echoing the Wisdom of Solomon as well as William Petty, the author of another new tract, Political Arithmetick.6 Petty proposed the application of number to affairs of state and trade; the word œconomick barely existed, but he and like-minded scholars were counting what had not been counted before: populations, life expectancy, shipping tonnage, and the national income. Political arithmetic promised wonders, in a technological age:
One Man with a Mill can grind as much Corn, as twenty can pound in a Mortar; one Printer can make as many Copies, as an Hundred Men can write by hand; one Horse can carry upon Wheels, as much as Five upon their Backs; and in a Boat, or upon Ice, as Twenty.7
A decisive technology, and the most venerable example of standard measure, was the coin. Petty reckoned “the whole Cash of England” at about six million pounds, circulating among perhaps six million souls, and by intricate calculation he showed that this was “Mony sufficient to drive the Trade of the Nation.”
By the end of the century, though, England’s money faced a crisis. The silver penny had been the base unit of value for a millennium; for half that time, the only unit. Now gold had joined silver in supporting a vivarium of changing species: groats, shillings, farthings, crowns, guineas. That grand new coin, the guinea, was supposed to be worth twenty shillings, but its value fluctuated unpredictably, as did the price of silver. Untold quantities of English coin were counterfeit. Even more were shrunken in weight and value: worn by decades of handling or deliberately trimmed at the edges by professional clippers, who then made bullion of their accumulated shards. So for thirty years, new machines, powered by horses and men—the mechanisms guarded as a state secret8—had milled a coinage with an ornamented rim to foil the clippers. A mongrel currency was the result. No one would spend a new coin willingly; these were mostly hoarded or, worse, melted down for export to France. “Let one money pass throughout the king’s dominion, and that let no man refuse,” King Edgar had said, centralizing England’s coinage in the tenth century. “Let one measure and one weight be used, such as is observed in London.” No more. The melting houses and press rooms of the Mint, just inside the western rampart of the Tower of London, fell nearly silent as the 1690s began. Most coins circulating were blurry hammered silver, debased, mistrusted, and older than the hands through which they passed.
The crown called for guidance from eminent citizens, Locke, Wren, and Newton among them. Wren proposed a decimal system; he was ignored. 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 burning around the clock, teams of horses and men crowding in upon one another, garrisoned soldiers standing watch. It was a 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 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.) He found a house in Jermyn Street, bought luxurious, mainly crimson furniture,10 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.11
By tradition the Mint posts offered easy income; Montague had promised Newton “ ’tis worth five or six hundred pounds per An, and has not too much bus’nesse to require more attendance than you may spare.”12 Newton did not mind treating his professorship as a sinecure—he drew his Cambridge salary in absentia—but he ran the Mint until his death, with diligence and even ferocity. He was, after all, the master of melters and assayers and metallurgists who multiplied gold and silver on a scale that alchemists could only dream of. He wrestled with issues of unformed monetary theory and international currency.13 There was nothing lofty about the requisite arithmetic, yet few could have persevered through the intricacies of accounting:
The Assaymasters weights are 1, 2, 3, 6, 11, 12.… The weight 12 is about 16 or 20 grains more or less as he pleases.… His scales turn with the 128th part of a grain, that is with the 2560th part of the weight 12 which answers to less then the 10th part of a penny weight.… The Melter runs from 600 or 700 to 800 lb of late 1000 lb weight of silver in a pot & melts 3 potts a day.… The pots shrink in the fire … 4 Millers, 12 horses two Horskeepers, 3 Cutters, 2 Flatters, 8 sizers one Nealer, thre Blanchers, two Markers, two Presses with fourteen labourers to pull them.…14
In pursuing clippers and counterfeiters, he called on long-nurtured reserves of Puritan anger and righteousness. False coinage was a capital crime, high treason. Jane Housden and Mary Pitman, for example, were condemned (but pardoned) after having been caught with coining tools and trying to escape by dropping a parcel of counterfeit money into the Thames.15 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. He ignored the convict’s final plea:
Some body must have lost something to prove the Thiefe Some person robbd to prove the highwayman … Save me from being murthered O Dear Sr do this mercifull deed O my offending you has brought this upon me … O God my God I shall be murderd unless you wave me O I hope God will move your heart with mercy and pitty.…16
Newton did not consider the uttering of bad money to be a victimless crime; he took it personally. For that matter, the crown held the Master of the Mint responsible for the weight and purity of its coinage, subject to enormous fines. At intervals he underwent the so-called Trial of the Pyx, named for the official coin chest, the pyx, protected by three independent locks and keys. A jury of the Goldsmiths’ Company would test select coins “by fire, by water by touch, or by weight or by all or by any of them,” Newton noted in a memorandum he drafted and redrafted eight times.17 Then, with solemn ceremony, it would present the King’s Council with the verdict. Newton prepared carefully for these trials, carrying out his own assays. They showed that he had brought the standardization of England’s coins to new heights of exactness. 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.
A portent of future trouble came from Leibniz, 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.”19 In passing this on, the elderly mathematician John Wallis begged Newton to let some of his treasure out from the darkness. Newton was seen now as the curator of a hoard of knowledge, its extent unknown. Wallis told Newton he owed to the public his hypothesis of light and color, which Wallis knew he had suppressed for more than thirty years, and much more—a full optical treatise. “You say, you dare not yet publish it,” Wallis argued. “And why not yet? Or, if not now, when then? You adde, lest I create you some trouble. What trouble now, more then at another time?… Mean while, you loose the Reputation of it, and we the Benefit.”
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. Past presidents had often been honorary, political figures. Newton seized power now and exercised it authoritatively. He quickly named his own Curator of Experiments. As president he attended almost every meeting; he commented from the chair on the reading of almost every paper.20 He asserted control over the selection of council members. He shored up the society’s sagging finances, in part from his own pocket. He imposed a rule that the royal mace be displayed when and only when he was presiding.
With Hooke dead, he also finally took Wallis’s advice and released for publication his second great work—in English, rather than Latin,21 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 an “Advertisement” in which he explained why he had suppressed this work since 1675. The reason: “To avoid being engaged in Disputes.”22
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. In the Opticks Newton described his experiments vividly and revealed far more of his working style—at least, a plausible working style—than in the Principia. He leaped across optical wonders as across stepping stones: from the trigonometry of refraction to the use of spectacles and mirrors; from thin transparent plates to bubbles; from the composition of the rainbow to the refraction of crystals. Much of the available data was raw and imprecise, but he shrank from nothing: friction, heat, putrefaction; the emission of light when bodies burn and when their parts vibrate. He considered the mysterious property called “electricity”—a vapor, or fluid, or vital force that seemed to arise from the excitation of glass, or cloth, as in his 1675 experiment with bits of paper.
But was light to be understood as waves or particles? He still believed, hypothetically, that light was a stream of material particles, but he explored wavy-seeming phenomena, too: “Do not rays of light move sometimes like an eel?” With Hooke buried, Newton also buried the ether as a medium that might vibrate with light waves, as a pond carries waves when struck by a stone. Such an ether would interfere with the planets’ permanent motion, otherwise so perfectly established now.
He was committed to his corpuscular theory: that rays of light are “very small Bodies emitted from shining Substances.”23 Thus he seemed to take a wrong turn: over the next two centuries, researchers thrived by treating light as waves, choosing smoothness over granularity in their fundamental view of energy. The mathematical treatment of colors depended on wavelength and frequency. Until, that is, Einstein showed that light comes in quanta after all. Yet it was Newton, more than any other experimenter, who established the case for light waves. With an accuracy measured in hundredths of an inch, he had studied colored rings in thin films.24 He found it impossible to understand this as anything but a form of periodicity—oscillation or vibration. Diffraction, too, showed unmistakable signs of periodicity. He could neither reconcile these signs with his corpuscular theory nor omit them from his record. He could not see how a particle could be a wave, or embody waviness. He resorted to an odd word: fits, as in “fits of easy reflection” and “fits of easy transmission.” “Probably it is put into such fits at its first emission from luminous bodies, and continues in them during all its progress. For these Fits are of a lasting nature.”25
Opticks stretched to cosmology and metaphysics—the more as Newton extended it in new printings. He could speak with authority now. He used his pulpit to issue a manifesto. He repeated again and again these dicta: that nature is consonant; that nature is simple; that nature is conformable to herself.26 Complexity can be reduced to order; the laws can be found. Space is an infinite void. Matter is composed of atoms—hard and impenetrable. These particles attract one another by unknown forces: “It is the Business of experimental Philosophy to find them out.”27 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.
As President of the Royal Society he employed two new Curators of Experiments.29 Sometimes he had them demonstrate or extend features of the Principia—once, for example, dropping lead weights and inflated hogs’ bladders from a church tower—but more often he tried to spur experiments on light, heat, and chemistry. One line of experiments explored the electric effluvium, creating a luminous glow, for example, in a glass tube rubbed with cloth, and testing the tube’s attractive power with a feather. Some spirit, it seemed, could penetrate glass, move small objects, and emit light—but what? In revising the Opticks he drafted new “Queries”: for example, “Do not all bodies therefore abound with a very subtle, but active, potent, electric spirit by which light is emitted, refracted, & reflected, electric attractions and fugations are performed …?”30 He suppressed these; even so, the trail of electrical research in the next century seemed to lead back to the Opticks.
“I have only begun the analysis of what remains to be discover’d,” he wrote, “hinting several things about it, and leaving the Hints to be examin’d and improv’d by the farther Experiments and Observations of such as are inquisitive.”31 Active principles—shades of alchemy—remained to be found out: the cause of gravity, of fermentation, of life itself. Only such active principles could explain the persistence and variety of motion, the constant heating of the sun and the inward parts of the earth. Only such principles stand between us and death. “If it were not for these Principles,” he wrote,
the Earth, Planets, Comets, Sun, and all things in them, would grow cold and freeze, and become inactive Masses; and all Putrefaction, Generation, Vegetation and Life would cease.32
Word of the Opticks spread slowly through Europe; then a bit faster after a Latin edition appeared in 1706.33 Father Nicolas Malebranche, aging theologian and Cartesian, reviewed the Opticks with the remark, “Though Mr. Newton is no physicist, his book is very interesting …”34 Rivals who had never managed to dispute his mathematics found new opportunities in his metaphysics. He had spoken of infinite space as the “sensorium” of God, by which he meant to unify omnipresence and omniscience. God, being everywhere, is immediately and perfectly aware. But the difficult word, suggesting a bodily organ for divine sensation, left him vulnerable to theological counterattack: “I examined it and laughed at the idea,” Leibniz told Bernoulli—these eminent admirers now turned enemies of Newton. “As if God, from whom everything comes, should have need of a sensorium. This man has little success with Metaphysics.”35 And again Leibniz abhorred Newton’s vacuum. A world of vast emptiness—unacceptable. Planets attracting one another across this emptiness—absurd. He objected to Newton’s conception of absolute space as a reference frame for analyzing motion, and he mocked the idea of gravitation. For one body to curve round another, with nothing pushing or impelling it—impossible. Even supernatural. “I say, it could not be done without a miracle.”36
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. One long letter from Newton, for Leibniz via Oldenburg, asserted possession of a “twofold” method for solving inverse problems of tangents “and others more difficult” and then concealed the methods in code:
At present I have thought fit to register them both by transposed letters … 5accdæ10effh11i4l3m9n6oqqr8s11t9v3x: 11ab3cdd10eæg10illrm7n603p3q6r5s11t8vx, 3acæ4egh 5i414m5n8oq4r3s6t4vaaddæeeeeeiijmmnnooprrsssssttuu.37
Communicating with Leibniz: The key to the cryptogram. (illustration credit 14.1)
He retained the key in a dated “memorandum” to himself. Still, impenetrable though this cryptogram was, Newton had shown Leibniz powerful methods: the binomial theorem, the use of infinite series, the drawing of tangents, and the finding of maxima and minima.
Leibniz, in his turn, chose not to acknowledge these when, in 1684 and 1686, he published his related mathematical work as “A New Method for Maxima and Minima, and Also for Tangents, Which Stops at Neither Fractions nor Irrational Quantities, and a Singular Type of Calculus for These” in the new German journal Acta Eruditorum. He offered rules for computing derivatives and integrals, and an innovative notation: dx, f(x), ∫x. This was a pragmatic mathematics, a mathematics without proof, an algorithm for solving “the most difficult and most beautiful problems.”38 With this new name, calculus, it traveled slowly toward England, just before word of the Principia, with its classic geometrical style concealing new tools of analysis, made its way across the Continent.
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 through 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.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. 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.”40 Between each of these thrusts and parries, 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.”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. 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.43 It vindicated Newton with 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. Thus he anonymously reviewed his own anonymous report, and in doing so he spoke of candor:
It lies upon [Leibniz], in point of Candor, to tell us what he means by pretending to have found the Method before he had found it.
It lies upon him, in point of Candor, to make us understand that he pretended to this Antiquity of his Invention with some other Design than to rival and supplant Mr. Newton.
When he wrote those Tracts he was but a Learner, and this he ought in candour to acknowledge.
He declared righteously: “no Man is a Witness in his own Cause. A Judge would be very unjust, and act contrary to the Laws of all Nations, who should admit any Man to be a Witness in his own Cause.”44
Newton wrote many private drafts about Leibniz, often the same ruthless polemic again and again, varying only by a few words. The priority dispute spilled over into the philosophical disputes, the Europeans sharpening their accusation that his theories resorted to miracles and occult qualities. What reasoning, what causes, should be permitted? In defending his claim to first invention of the calculus, Newton stated his rules for belief, proposing a framework by which his science—any science—ought to be judged. Leibniz observed different rules. In arguing against the miraculous, the German argued theologically. By pure reason, for example, he argued from the perfection of God and the excellence of his workmanship to the impossibility of the vacuum and of atoms. He accused Newton—and this stung—of implying an imperfect God.
Newton had tied knowledge to experiments. Where experiments could not reach, he had left mysteries explicitly unsolved. This was only proper, yet the Germans threw it back in his face: “as if it were a Crime to content himself with Certainties and let Uncertainties alone.”
“These two Gentlemen differ very much in Philosophy,” Newton declared under cover of anonymity.
The one teaches that Philosophers are to argue from Phænomena and Experiments to the Causes thereof, and thence to the Causes of those Causes, and so on till we come to the first Cause; the other that all the Actions of the first Cause are Miracles, and all the Laws imprest on Nature by the Will of God are perpetual Miracles and occult Qualities, and therefore not to be considered in Philosophy. But must the constant and universal Laws of Nature, if derived from the Power of God or the Action of a Cause not yet known to us, be called Miracles and occult Qualities?45
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. Newton had 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 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.46
The Newton-Leibniz duel continued long after the deaths of the protagonists. It constricted the development of English mathematics, as orthodoxy hardened around Newton’s dot notation.47 The more historians came to understand what happened, the uglier it looked. No one could dispute Lenore Feigenbaum’s simple précis: “Grown men, brilliant and powerful, betrayed their friends, lied shamelessly to their enemies, uttered hateful chauvinistic slurs, and impugned each others’ characters.”48 Newton’s rage, Leibniz’s bitterness—the darkest emotions of these protoscientists almost overshadowed their shared achievement.
Yet the priority dispute contributed to the transition of science from private obsessions to public enterprise. It exposed texts that Newton had meant to keep hidden and concentrated the interest of philosophers in these new methods: their richness, their fungibility, their power. The competition between formalisms—superficially so different—brought into focus the shared underlying core.
The obsessions of Newton’s later years disappointed modernity in some way. Later Newtonians came to find them as troubling as his pursuit of alchemy and biblical prophecy, if not for quite the same reasons. 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. (Flamsteed, summoned to appear before Newton, “complained then of my catalogue being printed by Halley, without my knowledge, and that I was robbed of the fruits of my labors. At this he fired, and called me all the ill names, puppy &c. that he could think of.”49) D. T. Whiteside, who became the twentieth century’s preeminent scholar and shepherd of Newton’s mathematical work, could not but remark:
Only too few have ever possessed the intellectual genius and surpassing capacity to stamp their image upon the thought of their age and that of centuries to follow. 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.
Still, it did not seem so to Newton.50 He had been a man on God’s mission, seeking his secrets, interpreting his design, but he had never meant to draw philosophers to his side. He had not meant to lead a cult or a school. Nevertheless he had gathered disciples and enemies as well. Leibniz never stopped hoping for a moral victory. Adieu, he wrote. “Adieu the vacuum, the atoms, and the whole Philosophy of M. Newton.”51
Leibniz died in 1716, having spent his last years at Hanover as librarian to the Duke. Newton’s death was still to come.