Isaac Newton (10 page)

Yet all in all he claimed to have explained everything; to have given—“newly” given—the causes

capable of explicating all the Phenomena of colours, not onely of those appearing in the Prisme, Water-drop, or Rainbow … but of all that are in the world, whether they be fluid or solid bodies, whether in thick or thin, whether transparent, or seemingly opacous.”
²¹

Newton absorbed this bold claim.
²²
He had no microscope and no chance of obtaining one. For that matter, he had no room with more than one window. He did have a prism. He darkened his study and made a hole in the window shutter to let in a sunbeam, white light, the purest light, light with no intrinsic color, philosophers still thought. He performed his own experiments—even, he felt, an
experimentum crucis
. He noted the results and told no one.

Bacon had also warned: “God forbid that we should give out a dream of our own imagination for a pattern of the world.”
²³

The plague abating, Newton returned to Cambridge, where among those he did not tell of his experiments was the professor of mathematics, Isaac Barrow.

6
 
The Oddest If Not the Most Considerable Detection

N
EWTON’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
x
³
+ ax
²
+
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