“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?”
“ Thissort 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 math had to be true, there was no conceivable universe in which 2 + 3 was equal to 2 + 2.
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 ?ther 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?