Isaac Newton - James Gleick (2004)

Chapter 6. The Oddest If Not the Most Considerable Detection

NEWTON’S STATUS AT TRINITY improved. In October 1667 the college elected fellows for the first time in three years: men entitled to wages (two pounds a year), a room, continuing membership in the academic community, and the use of the library. Each new fellow swore: “I will embrace the true religion of Christ with all my soul.… I will either set Theology as the object of my studies and will take holy orders when the time prescribed by these statutes arrives, or I will resign from the college.”1 Chastity was expected and marriage forbidden. Newton bought shoes and cloth for the gown of a bachelor of arts. Besides his stipend he received small sums from his mother and (very rarely) from pupils he tutored. He bought a set of old books on alchemy, along with glasses, a tin furnace, and chemicals: aqua fortis, sublimate, vinegar, white lead, salt of tar-tar.2 With these he embarked on a program of research more secret than ever.

But he also continued his mathematical investigations, and he shared some of these with Barrow. He began to list cubic equations: curves in three dimensions, more various and complex than the ellipses and hyperbolas of two-dimensional mathematics. He attacked this subject as a classifier, trying to sort all such curves into species and subspecies.3 As he had done with the calculus, he approached this analytic geometry from two directions at once: from the perspective of algebra, where cubic equations begin with the form x3 + ax2 + bx + c = 0; and from a kinematic perspective, describing these creatures in terms of their construction, as the results of points and curves moving through space. He plotted in his notebooks fifty-eight distinct species of cubics. He sought ever greater generality.

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 a few infinite series. For Newton these were merely special cases of the powerful approach to 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.”5 It was the first transmission of Newton’s name south of Cambridge.

At long distance, in messages separated by days or by months, Newton and Collins now engaged in a dance. Newton teased Collins with tantalizing fragments of mathematical insight. Collins begged for more. Newton delayed and withdrew. A table resolving equations of three dimensions was “pretty easy and obvious enough,” he declared. “But I cannot perswade my selfe to undertake the drudgery of making it.”6 Collins bruited some of Newton’s handiwork to several other mathematicians, in Scotland, France, and Italy. He sent books to Newton and posed questions: for example, how to calculate the rate of interest on an annuity. Newton sent a formula for that but insisted that his name be withheld if Collins published it: “For I see not what there is desirable in publick esteeme, were I able to acquire & maintaine it. It would perhaps increase my acquaintance, the thing which I cheifly study to decline.”7 Nonetheless his name was being whispered. James Gregory, the Scots mathematician, heard it. He was struggling with an unsolved problem of analytic geometry that he read in new lectures by Barrow. “I despaire of it my self, and ther-for I doe humblie desire it of any els who can resolve it,” he wrote Collins. “I long to see that peece of Mr Newton which is generallie applied to al curvs.”8

When Barrow prepared his lectures for publication, he asked Newton to help him edit the manuscripts, particularly his Optical Lectures.9 These appeared in 1669, with Barrow’s effusive acknowledgment of “a Man of great Learning and Sagacity, who revised my Copy and noted such things as wanted correction.” Yet Newton knew what Barrow did not: that the whole project wanted correction. Barrow imagined that color had something to do with compression and rarification and excitation of light; that red might be “broken and interrupted by shadowy interstices” while blue involved “white and black particles arranged alternately.”10 Barrow’s protégé had already done private research that rendered these optics obsolete. 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.11

The young professor gained relative security. He could be removed only for serious crime; the statutes specified fornication, heresy, and voluntary manslaughter.12 He was expected to read a lecture on mathematics (broadly construed) each week during the academic term and deposit a copy in the university library. But he disregarded this obligation far more than he fulfilled it. When he did lecture, students were scarce. Sometimes he read to a bare room or gave up and walked back to his chambers.13 The existence of this new professorship reflected a sense that mathematics was an art useful to the growing nation—its architects, tradesmen, and sailors—but cubic curves and infinite series had no use in a trade or on a ship. Such mysteries were as recondite as the researches Newton was beginning to undertake alone in his chambers with his tin crucible.

Instead of mathematics he chose to lecture on light and color. The invention of telescopes had spurred intense interest in the properties of light, he noted, yet the geometers had “hitherto erred.” So he proposed to add his own discoveries “to what my reverend predecessor last delivered from this Place.”14 He considered the phenomenon of refraction, the bending of light when it passes from one medium to another, as from air to glass (lenses being the offspring of refraction and geometry). Wearing a professor’s gown of scarlet, he stood before the few students who attended and delivered news: rays of colored light differ from one another in how sharply they are refracted. Each color has its own degree of refraction. This was a bare, mathematical claim, with none of the romance or metaphor that usually ornamented the philosophy of light.

Newton was not just drawing and calculating; he was also grinding glass and polishing lenses in difficult, nonspherical curves. Telescope makers had learned to their sorrow that spherical lenses blurred their images, inevitably, because rays of light failed to meet at a single point. Also, the larger they made the lenses, the more they saw rings of unwanted color—and Newton understood these now. The problem lay not in imperfect craft but in the very nature of white light: not simple but complex; not pure but mixed; a heterogeneous mixture of differently refrangible rays.15 Lenses were after all prisms at their edges. He tried a new kind of telescope, based on a reflecting mirror instead of a refracting lens.16 A big mirror would gather more light than a small lens—in proportion to its area, or to the square of its diameter. The difficulty was a matter of craft: how to polish metal to the smoothness of glass. With his furnace and putty and pitch he cast a tin and copper alloy and refined its surface, grinding with all his strength. In 1669 he had a stubby little tube six inches long and magnifying forty times—as much as the best telescopes in London and Italy, and as much as a refracting telescope ten times longer.17 He kept it for two years. He saw the disk of Jupiter with its satellites, and Venus distinctly horned, like a crescent moon. Then he lent it to Barrow. Barrow carried it to London, to show his friends at the Royal Society.

The reflecting telescope(illustration credit 6.1)

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.18

And in what language? The society’s work included translation, contending with scores of vernacular dialects in Europe, and even stranger languages were reported to exist in faraway India and Japan. Latin served for standardization, but the society’s founders explicitly worried about the uses of any language. Philosophy had mired itself in its own florid eloquence. They sought “not the Artifice of Words, but a bare knowledge of things.” Now it was time for plain speaking, the most naked expression, and when possible this meant the language of mathematics.19

Words were truant things, elusive of authorities, malleable and relative. Philosophers had much work to do merely defining their terms, and words like think and exist and word posed greater challenges than tree and moon. Thomas Hobbes warned:

The light of humane minds is perspicuous words, but by exact definitions first snuffed, and purged from ambiguity; reason is the pace. And, on the contrary, metaphors, and senseless and ambiguous words are like ignes fatui; and reasoning upon them is wandering amongst innumerable absurdities.20

Galileo, having observed sunspots through his telescope in 1611, could not report the fact without entering a semantic thicket:

So long as men were in fact obliged to call the sun “most pure and most lucid,” no shadows or impurities whatever had been perceived in it; but now that it shows itself to us as partly impure and spotty; why should we not call it “spotted and not pure”? For names and attributes must be accommodated to the essence of things, and not the essence to the names, since things come first and names afterwards.21

It has always been so—this is the nature of language—but it has not always been equally so. Diction, grammar, and orthography were fluid; they had barely begun to crystallize. Even proper names lacked approved spelling. Weights and measures were a hodgepodge. Travelers and mail made their way without addresses, unique names and numbers as coordinates for places. When Newton sent a letter to the Secretary of the Royal Society, he directed it To Mr Henry Oldenburge at his house about the middle of the old Palmail in St Jamses Fields in Westminster.22

Oldenburg was an apostle for the cause of collective awareness—born Heinrich Oldenburg in the trading city of Bremen (he was never sure what year), later Henricus, and now Henry. He had come to England during the Civil War as an envoy on a mission to Oliver Cromwell. He began corresponding with learned men such as Cromwell’s Latin Secretary, John Milton; Cromwell’s brother-in-law, John Wilkins; the young philosopher Robert Boyle; and others—soon to be the nucleus of the Royal Society. Then, as an acquaintance put it, “this Curious German having well improved himself by his Travels, and … rubbed his Brains against those of other People, was … entertained as a Person of great Merit, and so made Secretary to the Royal Society.”23 He was a master of languages and the perfect focal point for the society’s correspondence. He employed both the ordinary post and a network of diplomatic couriers to receive letters from distant capitals, especially Paris and Amsterdam. In 1665 he began printing and distributing this correspondence in the form of a news sheet, which he called the Philosophical Transactions. This new creature, a journal of science, remained Oldenburg’s personal enterprise till the end of his life.24 He found a printer and stationer with carriers who could distribute a few hundred copies across London and even farther.

The news took many forms. Mr. Samuel Colepress, near Plymouth, reported his observations of the height and velocity of the daily tides; from March to September, he asserted, the tides tended to be a foot higher (“perpendicular, which is always to be understood”) in the morning than in the evening.25 An author in Padua, Italy, claimed to have discovered new arguments against the motion of the earth, and a mathematician there disputed him, citing an experiment by a Swedish gentleman, who fired shots from “a Canon perpendicular to the Horizon” and observed whether the balls fell toward the west or the east. Mr. Hooke saw a spot on the planet Jupiter. A very odd monstrous calf was born in Hampshire. A newly invented instrument of music arrived: a harpsichord, with gut-strings. There were poisonous vipers and drops of poison from Florence. The society examined the weaving of asbestos—a cloth said to endure the fiercest fire—and models of perpetual motion.26

No sooner had the virtuosi begun to gather than England’s poets satirized their fixations and their questions. Hooke himself made an easy target—his fantastic world of fleas and animalcules. The natural philosopher could easily be portrayed as a preoccupied pedant, and not so easily distinguished from the astrologer and the alchemist. “Which way the dreadful comet went / In sixty-four and what it meant?” asked Samuel Butler (his mockery tinged with wonder).

Whether the Moon be sea or land

Or charcoal, or a quench’d firebrand …

These were their learned speculations

And all their constant occupations,

To measure wind, and weigh the air

And turn a circle to a square.27

In fact, travel and trade, more than speculation or technology, fueled the society’s business; bits of exotic knowledge came as fellow travelers on ships bearing foreign goods. Spider webs were seen in faraway Bermuda and 300-foot cabbage trees in the Caribe Islands.28 A worthy and inquisitive gentleman, Captain Silas Taylor of Virginia, reported that the scent of the wild Penny-royal could kill Ratle-Snakes. A German Jesuit, Athanasius Kircher, revealed secrets of the subterranean world: for example, that the ocean waters continually pour into the northern pole, run through the bowels of the earth, and regurgitate at the southern pole.

Far away in Cambridge Newton inhaled all this philosophical news. He took fervid notes. Rumors of a fiery mountain: “Batavia one afternone was covered with a black dust heavyer then gold which is thought came from an hill on Java Major supposed to burne.”29 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. Oldenburg raised the specter of “the usurpation of foreigners” who might already have seen Newton’s instrument in Cambridge, “it being too frequent, the new Inventions and contrivances are snatched away from their true Authors by pretending bystanders.”30 The philosophers were proposing Newton for election as a fellow of the society. Still, there were questions. Some of the skillful examiners agreed that Newton’s tube magnified more than larger telescopes, but others said this was hard to measure with certainty.31 Some, ill at ease with the technology, complained that such a powerful telescope made it difficult “to find the Object.” Meanwhile Hooke told the members privately that he himself had earlier made a much more powerful tiny telescope, in 1664, just an inch long, but that he had not bothered to pursue it because of the plague and the fire. Oldenburg chose not to mention Hooke’s claim.

Newton wrote back with conventional false modesty:

I was surprised to see so much care taken about securing an invention to mee, of which I have hitherto had so little value. And therefore since the R. Society is pleased to think it worth the patronizing, I must acknowledg it deserves much more of them for that, then of mee, who, had not the communication of it been desired, might have let it still remained in private as it hath already done some yeares.32

A fortnight later he set modesty aside. He wished to attend a meeting, he told Oldenburg dramatically.

I am purposing them, to be considered of & examined, an accompt of a Philosophicall discovery which induced me to the making of the said Telescope, & which I doubt not but will prove much more gratefull then the communication of that instrument, being in my Judgment the oddest if not the most considerable detection which hath hitherto been made in the operations of Nature.33

And by the way, what would his duties be, as Fellow of the Royal Society?