Authors: Neal Stephenson
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.”
S
TRETCH 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 math
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.