IPSWICH HAD BEEN A CLOTH port forever, but that trade had fallen on hard times because of the fatal combination of cheap stuff from India and Dutch shipping that could bring it to Europe. It was the prototype of the ridiculously ancient English town, situated at the place where the River Orwell broadened into an estuary, the obvious spot where anyone from a cave-man to a Cavalier would drive a stake into the muck and settle. Daniel judged that the gaol had been the first structure to go up, some five or six thousand years ago perhaps, and that the rats had moved in a week or two later. Ipswich was the county seat, and so when Charles II had whimsically decided to enforce the Penal Laws, all of Suffolk’s most outstanding Quakers, Barkers, Ranters, Congregationalists, Presbyterians, and the odd Jew had been rounded up and been deposited here. They might just as well have been released a month ago, but it was important to the King that Daniel, his chosen representative, come out and handle the matter in person.
The carriage pulled up in front of the gaol and Exaltation Gather sat in it nervously gripping his strong-box while Daniel went inside and scared the gaoler half to death by brandishing a tablecloth-sized document with a wax seal as big as a man’s heart dangling from it. Then Daniel went into the gaol, interrupting a prayer meeting, and spouted an oration he’d already used in half a dozen other gaols, a wrung-out rag of a speech so empty and banal that he had no idea whether he was making any sense at all, or just babbling in tongues. The startled, wary looks on the faces of the imprisoned Puritans suggested that they were extracting some meaning from Daniel’s verbalizations—he had no idea what exactly. Daniel did not really know how his speech was being interpreted until later. The prisoners had to be released one at a time. Each of them had to pay the bill for his meals and other necessaries—and many had been here for years.
Hence Exaltation Gather and his box of money. The King’s gesture would fall flat if half the prisoners remained in pokey for debts accumulated during their (unjust and un-Christian) imprisonment and so the King had (through Daniel) encouraged special collections to be taken up in sympathetic churches and had (though this was supposed to be grievously secret) supplemented that money with some from his own reserves to make sure it all came off well. In practice it meant that the nonconformists of London and the King of England had used Exaltation Gather’s strongbox as a dust-bin for disposal of all their oldest, blackest, lightest in weight, most clipped, worn, filed-down, and adulterated coins. The true value of each one of these objects had to be debated between the gaoler of Ipswich on one hand, and on the other, Exaltation Gather and any recently freed Puritans who (a) were sharp when it came to money and (b) enjoyed verbal disputes—i.e., all of them.
Daniel staged an orderly retreat to a church-yard with a view down to the harbor, where the sound of the argument was partly masked by the rushing and slapping of the surf. Various Puritans found him, and lined up to give him pieces of their minds. This went on for most of the day—but as an example, Edmund Palling came up and shook Daniel’s hand.
Edmund Palling was a perpetual old man. So it had always seemed to Daniel. Admittedly his strategy of radical hairlessness made it difficult to guess his age. But he’d seemed an old man running around with Drake during the Civil War, and as an old man he had marched in Cromwell’s funeral procession. As an old trader he had frequently showed up at Stourbridge Fair peddling this or that, and had walked into Cambridge to inflict startling visitations on Daniel. Old Man Palling had attended the memorial service for Drake, and during his years living in London, Daniel had occasionally bumped into this elderly man on the streets of London.
Now here he was: “Which is it, Daniel, stupid or insane? You know the King.”
Edmund Palling was a sensible man. He was, as a matter of fact, one of those Englishmen who was so sensible that he was daft. For as any French-influenced courtier could explain, to insist on everything’s being reasonable, in a world that wasn’t, was, in itself, unreasonable.
“Stupid,” Daniel said. Until now he had been every inch the Court man, but he could not dissimulate to such as Edmund Palling. To be with this old man was to be thrown back four decades, to a time when it had become common for ordinary sensible Englishmen to speak openly the widely agreed-upon, but previously unmentionable fact that monarchy was a load of rubbish. The fact that, since those days, the Restoration had occurred and that Europe was in fact ruled by great Kings was of no consequence. At any rate, Daniel felt perfectly at home and at peace among these men, which was a bit alarming given that he was a close advisor to King James II. He could no more defend that King, or any monarch, to Edmund Palling than go to a meeting of the Royal Society and assert that the Sun revolved around the Earth.
Edmund Palling was fascinated, and nodded sagely. “Some have been saying insane, you know—because of the syphilis.”
“Not true.”
“That is extraordinary, because everyone is convinced he has syphilis.”
“He does. But having gotten to know His Majesty reasonably well, Mr. Palling, it is my opinion, as Secretary of the Royal Society, that when he, er…”
“Does something that is just amazingly ludicrous.”
“As some would say, Mr. Palling, yes.”
“Such as letting us out of gaol in the hopes that we’ll not perceive it as a cynical ploy, and supposing that we’ll rally about his standard as if he really gives a farthing for Freedom of Conscience!”
“Without staking myself to any position concerning what you’ve just said, Mr. Palling, I would encourage you to look towards mere stupidity in your quest for explanations. Not to rule out fits of syphilitic insanity altogether, mind you…”
“What’s the difference then? Or is it a distinction without a difference?”
“This sort of thing,” Daniel said, waving towards the Ipswich gaol, “is stupidity. By contrast, a fit of syphilitic insanity would lead to results of a different character entirely: spasms of arbitrary violence, mass enslavements, beheadings.”
Mr. Palling shook his head, then turned toward the water. “One day soon the sun will rise from across yonder sea and chase the fog of stupidity and the shadows of syphilitic insanity away.”
“Very poetic, Mr. Palling—but I have met the Duke of Monmouth, I have roomed with the Duke of Monmouth, I have been vomited on by the Duke of Monmouth, and I am telling you that the Duke of Monmouth is no Charles II! To say nothing of Oliver Cromwell.”
Mr. Palling rolled his eyes. “Very well, then—if Monmouth fails I’m on the next ship to Massachusetts.”
STRETCH A LINE, and another intersecting it, and rotate the former about the latter and it will sweep out a cone. Now shove this cone through a plane (fig. 1) and mark every point on the plane where the cone touches it. Commonly the result is an ellipse (fig. 2), but if the cone’s slope is parallel to the plane it makes a parabola (fig. 3), and if it’s parallel to the axis it makes a two-part curve called a hyperbola (fig. 4).
An interesting feature of all of these curves—the ellipse, the parabola, and the hyperbola—was that they were generated by straight things, viz. two lines and a plane. An interesting feature of the hyperbola was that far away its legs came very close to being straight lines, but near the center there was dramatic curvature.
Greeks, e.g., Euclid, had done all of these things long ago and discovered various more or less interesting properties of conic sections (as this family of curves was called) and of other geometric constructions such as circles and triangles. But they’d done so as an exploration of pure thought, as a mathematician might compute the sum of two numbers. Every assertion that Euclid, et al., made concerning geometry was backed up by a chain of logical proofs that could be followed all the way back to a few axioms that were obviously true, e.g., “the shortest distance between two points is a straight line.” The truths of geometry were necessary truths; the human mind could imagine a universe in which Daniel’s name was David, or in which Ipswich had been built on the other side of the Orwell, but geometry and mat
h had to be true, there was no conceivable universe in which 2 + 3 was equal to 2 + 2.
LIBRI I. CONICORVM APOLLONII
Occasionally one discovered correspondences between things in the real world and the figments of pure math. For example: Daniel’s trajectory from London to Ipswich had run in nearly a straight line, but after every one of the Dissenters had been let out of gaol, Daniel had executed a mighty change in direction and the next morning began riding on a rented horse towards Cambridge, following a trajectory that became straighter the farther he went. He was, in other words, describing a hyperbolic sort of path across Essex, Suffolk, and Cambridgeshire.
But he was not doing so because it was a hyperbola, or (to look at it another way) it was not a hyperbola because he was doing so. This was simply the route that traders had always taken, going from market to market as they traveled up out of Ipswich with wagon-loads of imported or smuggled goods. He could have followed a zigzag course. That it looked like a hyperbola when plotted on a map of England was luck. It was a contingent truth.
It did not mean anything.
In his pocket were some notes that his patron, the good Marquis of Ravenscar, had stuffed into his pocket with the explanation “Here is a pretext.” They’d been written out by John Flamsteed, the Astronomer Royal, apparently in response to inquiries sent down by Isaac. Daniel dared not unwrap and read this packet—the uncannily sensitive Isaac would smell Daniel’s hand-prints on the pages, or something. But the cover letter was visible. Wedged into the chinks between its great blocks of Barock verbiage were a few dry stalks of information, and by teasing these out and plaiting them together Daniel was able to collect that Newton had requested information concerning the comet of 1680; a recent conjunction of Jupiter and Saturn; and the ebb and flow of tides in the ocean.
If any other scholar had asked for data on such seemingly disparate topics he’d have revealed himself to be a crank. The mere fact that Isaac was thinking about all of them at the same time was as good as proof that they were all related. Tides obviously had something to do with the moon because the formers’ heights were related to the latter’s phase; but what influence could connect the distant sphere of rock to every sea, lake, and puddle on the earth? Jupiter, orbiting along an inside track, occasionally raced past Saturn, lumbering along on the outer boundary of the solar system. Saturn had been seen to slow down as Jupiter caught up with it, then to speed up after Jupiter shot past. The distance separating Jupiter from Saturn was, at best, two thousand times that between the moon and the tides; what influence could span such a chasm? And comets, almost by definition, were above and outside of the laws (whatever they might be) that governed moons and planets—comets were not astronomical bodies, or indeed natural phenomena at all, so much as metaphors for the alien, the exempt, the transcendent—they were monsters, thunderbolts, letters from God. To bring them under the jurisdiction of any system of natural laws was an act of colossal hubris and probably asking for trouble.
But a few years earlier a comet had come through inbound, and a bit later an outbound one had been tracked, each moving on a different line, and John Flamsteed had stuck his neck out by about ten miles and asked the question, What if this was not two comets but one?
The obvious rejoinder was to point out that the two lines were different. One line, one comet; two lines, two comets. Flamsteed, who was as painfully aware of the vagaries and limitations of observational astronomy as any man alive, had answered that comets didn’t move along lines and never had; that astronomers had observed only short segments of comets’ trajectories that might actually be relatively straight excerpts of vast curves. It was known, for example, that most of a hyperbola was practically indistinguishable from a straight line—so who was to say that the supposed two comets of 1680 might not have been one comet that had executed a sharp course-change while close to the Sun, and out of astronomers’ view?
In some other era this would have ranked Flamsteed with Kepler and Copernicus, but he was living now, and so it had made him into a sort of data cow to be kept in a stall in Greenwich and milked by Newton whenever Newton became thirsty. Daniel was serving in the role of milk-maid, rushing to Cambridge with the foaming pail.
There was much in this that demanded the attention of any European who claimed to be educated.
(1) Comets passed freely through space, their trajectories shaped only by (still mysterious) interactions with the Sun. If they moved on conic sections, it was no accident. A comet following a precise hyperbolic trajectory through the æther was a completely different thing from Daniel’s just happening to trace a roughly hyperbolic course through the English countryside. If comets and planets moved along conic sections, it had to be some kind of necessary truth, an intrinsic feature of the universe. It did mean something. What exactly?
(2) The notion that the Sun exerted some centripetal force on the planets was now becoming pretty well accepted, but by asking for data on the interactions of moon and sea, and of Jupiter and Saturn, Isaac was as much as saying that these were all of a piece, that everything attracted everything—that the influences on (say) Saturn of the Sun, of Jupiter, and of Titan (the moon of Saturn that Huygens had discovered) were different only insofar as they came from different directions and had different magnitudes. Like the diverse goods piled up in some Amsterdam merchant’s warehouse, they might come from many places and have different values, but in the end all that mattered was how much gold they could fetch on the Damplatz. The gold that paid for a pound of Malabar pepper was melted and fused with the gold that paid for a boatload of North Sea herring, and all of it was simply gold, bearing no trace or smell of the fish or the spice that had fetched it. In the case of Cœlestial Dynamics, the gold—the universal medium of exchange, to which everything was reduced—was force. The force exerted on Saturn by the Sun was no different from that exerted by Titan. In the end, the two forces were added together to make a vector, a combined resultant force bearing no trace of its origins. It was a powerful kind of alchemy because it took the motions of heavenly bodies down from inaccessible realms and brought them within reach of men who had mastered the occult arts of geometry and algebra. Powers and mysteries that had been the exclusive province of Gods, Isaac was now arrogating to himself.
A SAMPLE CONSEQUENCE OF THIS alchemical fusing of forces would be that a comet fleeing the Sun on the out-bound limb of a hyperbola, traveling an essentially straight line, would, if it happened to pass near a planet, be drawn towards it. The Sun was not an absolute monarch. It did not have any special God-given power. The comet did not have to respect its force more than the forces of mere planets—in fact, the comet could not even perceive these two influences as being separate, they’d already been converted to the universal currency of force, and fused into a single vector. Far from the Sun, close to the planet, the latter’s influence would predominate, and the comet would change course smartly.
And so did Daniel, after riding almost straight across the fenny country northeast of Cambridge for most of a day, and traversing the pounded, shit-permeated mud flat where Stourbridge Fair was held, suddenly swing round a bend of the Cam and drop into an orbit whose center was a certain suite of chambers just off to the side of the Great Gate of Trinity College.
Daniel still had a key to the old place, but he did not want to go there just yet. He stabled his horse out back of the college and came in through the rear entrance, which turned out to be a bad idea. He knew that Wren’s library had started building, because Trinity had dunned him, Roger, and everyone else for contributions. And from the witty or despairing status reports that Wren gave the R.S. at every meeting, he was aware that the project had stopped and started more than once. But he hadn’t thought about the practical consequences. The formerly smooth greens between the Cam and the back of the College were now a rowdy encampment of builders, their draft-animals, and their camp-followers (and not just whores but itinerant publicans, tool-sharpeners, and errand-boys, too). So there was a certain amoun
t of wading through horse-manure, wandering into blind alleys that had once been bowling-greens, tripping over hens, and declining more or less attractive carnal propositions before Daniel could even get a clear view of the library.
Most of Cambridge had fallen into twilight while Daniel had been seeking a route through the builders’ camp. Not that it made much of a difference, since the skies had looked like hammered lead all day. But the upper story of the Wren Library was high enough to look west into tomorrow’s weather, which would be fine and clear. The roof was mostly on, and where it wasn’t, its shape was lofted by rafters and ridge-beams of red oak that seemed to resonate in the warm light of the sunset, not merely blocking the rays but humming in sympathy with their radiance. Daniel stood and looked at it for a while because he knew that any moment of such beauty could never last, and he wanted to describe it to the long-suffering Wren when he got back to London.
The bell began to toll, calling the Fellows to the dining hall, and Daniel slogged forward through the Library’s vacant arches and across Neville’s Court just in time to throw on a robe and join his colleagues at the High Table.
The faces around that table were warmed by port and candlelight, and exhibiting a range of feelings. But on the whole they looked satisfied. The last Master who’d tried to enforce any discipline on the place had suffered a stroke while hollering at some rowdy students. There was no preventing students and faculty from drawing weighty conclusions from such an event. His replacement was a friend of Ravenscar, an Earl who’d showed up reliably for R.S. meetings since the early 1670s and reliably fallen asleep halfway through them. He came up to Cambridge only when someone more important than he was there. The Duke of Monmouth was no longer Chancellor; he’d been stripped of all such titles during one of his banishments, and replaced by the Duke of Tweed—a.k.a. General Lewis, the L in Charles II’s CABAL.