Authors: Neal Stephenson
On a desk he saw letters in Latin from gentlemen in Prague, Naples, St.-Germain, addressed to JEOVA SANCTUS UNUS. Through gaps between them Daniel saw parts of a large drawing that had been pinned down to the surface of the table. It looked like a floor plan of a building. Daniel moved some papers and books out of the way to expose more of it. He was wondering whether Isaac—like Wren, Hooke, and Daniel himself—had gone into Architecture.
Isaac appeared to be designing a square, walled court with a rectangular structure in the middle. Sweeping a trapezoid of lantern-light over a block of writing, Daniel read the following:
The same God gave the dimensions of the Tabernacle to Moses and Temple with its Courts to David & Ezekiel & altered not the proportion of the areas but
only doubled them in the Temple…So then Solomon and Ezekiel agree, and are double to Moses.
“I am only trying to recover what Solomon knew,” Isaac said.
Knowing that the lantern would blind Isaac’s burnt eyes, Daniel raised it up and blew it out before turning around. Isaac had come in silence down a stone staircase. His atelier on the first story had candles burning, and these warmed the stone behind Isaac with orange light. He was a black silhouette robed in a dressing-gown, his head cloaked with silver. He had not grown any heavier since College days, which was no surprise if the rumors about his dining habits were to be credited.
“I can’t help but wonder if you—perhaps even
I
—don’t know a hell of a lot more about practically every subject than Solomon ever did,” Daniel said.
Isaac said nothing for a moment, but something about his silhouette looked wounded, or sad.
“It’s right there in the Bible, Daniel. First chapter: the Garden of Eden. Last chapter: the Apocalypse.”
“I know, I know, the world started out perfectly good and has gotten worse and worse since then, and the only question is how bad will it get before God brings down the curtain. I was raised to believe that this tendency was as fixed and unavoidable as gravity, Isaac. But the Apocalypse did not come in 1666.”
“It will occur not long after 1867,” Isaac said. “That is the year when the Beast will fall.”
“Most Anglican cranks are guessing 1700 for the demise of the Catholic Church.”
“It is not the only way that the Anglicans are wrong.”
“Could it be, Isaac, that things are getting
better,
or at worst remaining more or less
the same,
rather then getting
worse
all the time? Because I really think you may know certain things that never entered Solomon’s head.”
“I am working out the System of the World upstairs,” Isaac said offhandedly. “It is not beyond reason to think that Solomon and other ancients knew that System, and encrypted it in the design of their Temples.”
“But according to the Bible those designs were given to them directly by God.”
“But go outside and look up at the stars and you see God trying to give you the same thing, if only you will pay attention.”
“If Solomon knew all of this, why didn’t he just come out and say, ‘The sun is in the middle of the solar system and planets go round about it in ellipses?’”
“I believe he did say so, in the design of his temple.”
“Yes, but why are God and Solomon alike so damned oblique in everything? Why not just come out and say it?”
“It is good that you do not waste my time with tedious letters,” Isaac said. “When I read a letter I can follow the words, but I cannot fathom the mind, of him who sent it. It is better that you come to visit me in the night-time.”
“Like an alchemist?”
“Or an early Christian in pagan Rome…”
“Scratching curves in the dust?”
“…or any Christian who dares oppose the idolators. If you were to use me thus in a letter, I would conclude you were in the employ of the Beast, as some say you are.”
“What, merely for suggesting that the world does something other than rot?”
“Of course it rots, Daniel. There is no perpetual motion machine.”
“Except for the heart.”
“The heart rots, Daniel. Sometimes it even begins to rot while its owner still lives.”
Daniel dared not follow that one up. After a silence Isaac continued, in a throatier voice: “Where do we find God in the world? That is all I want to know. I have not found Him yet. But when I see anything that does
not
rot—the workings of the solar system, or a Euclidean proof, or the perfection of gold—I sense I am drawing nearer to the Divine.”
“Have you found the Philosophick Mercury yet?”
“In ’77, Boyle was certain he had it.”
“I remember.”
“I agreed with him for a short time—but it was wishful thinking. I am seeking it in geometry now—or rather I am seeking it where geometry fails.”
“Fails?”
“Come upstairs with me Daniel.”
D
ANIEL RECOGNIZED THE
first proof as easily as his own signature. “Objects governed by a centripetal force conserve angular momentum and sweep out equal areas in equal times.”
“You have read my
De Motu Corporum in Gyrum
?”
“Mr. Halley has made its contents known to the Royal Society,” Daniel said drily.
“Some supporting lemmas come out of this,” Isaac said, pulling another diagram over the first.
“and thence we can move on immediately to” “That is the great one,” Daniel said. “If the centripetal force is governed by an inverse-square law, then the body moves on an ellipse, or at any rate a conic section.”
“I would say, ‘That heavenly bodies
do
move on conic sections proves the inverse-square law.’ But we are only speaking of fictions, so far. These proofs only apply to infinitesimal concentrations of mass, which do not exist in the real world.
Real
heavenly bodies possess geometry—they comprise a vast number of tiny particles arranged in the shape of a sphere. If Universal Gravitation exists, then each of the motes that make up the Earth attracts every other, and attracts the moon as well, and vice versa. And each of the moon’s particles attracts the water in Earth’s oceans to create tides. But how does the spherical geometry of a planet inform its gravity?”
Isaac produced another sheet, much newer-looking than the rest.
Daniel did not recognize this one. At first he thought it was a diagram of an eyeball, like the ones Isaac had made as a student. But Isaac was speaking of planets, not eyes.
A few awkward moments followed.
“Isaac,” Daniel finally said, “
you
can draw a diagram like this one and say, ‘Behold!’ and the proof is finished.
I
require a bit of explanation.”
“Very well.” Isaac pointed to the circle in the middle of the diagram. “Consider a spherical body—actually an aggregate of
countless particles, each of which produces gravitational attraction according to an inverse square law.” Now he reached for the nearest handy object—an inkwell—and set it on the corner of the page, as far away from the “spherical body” as it could go. “What is felt by a satellite, here, on the outside, if the separate attractions of all of those particles are summed and fused into one aggregate force?”
“Far be it from me to tell you how to do physics, Isaac, but this strikes me as an ideal problem for the integral calculus—so why are you solving it geometrically?”
“Why not?”
“Is it because Solomon didn’t have the calculus?”
“The calculus, as
some
call it, is a harsh method. I prefer to develop my proofs in a more geometric way.”
“Because geometry is ancient, and everything ancient is good.”
“This is idle talk. The result, as anyone can see from contemplating my diagram, is that a spherical body—a planet, moon, or star—having a given quantity of matter, produces a gravitational attraction that is the same as if all of its matter were concentrated into a single geometric point at the center.”
“The
same
? You mean
exactly
the same?”
“It is a geometrical proof,” Isaac merely said. “That the particles are spread out into a sphere
doesn’t make any difference
because the geometry of the sphere is what it is. The gravity is the same.”
Daniel now had to locate a chair; all the blood in his legs seemed to be rushing into his brain.
“If that is true,” he said, “then everything you proved
before
about point objects—for example that they move along conic section trajectories—”
“Applies without alteration to spherical bodies.”
“To
real things.
” Daniel had a queer vision just then of a shattered Temple reconstituting itself: fallen columns rising up from the rubble, and the rubble re-aggregating itself into cherubim and seraphim, a fire sparking on the central altar. “You’ve done it then…created the System of the World.”
“
God
created it. I have only
found
it. Rediscovered what was forgot. Look at this diagram, Daniel. It is
all here,
it is Truth made manifest,
epiphanes.
”
“Now you said before that you were looking for God where Geometry failed.”
“Of course. There is no
choice
in this,” Isaac said, patting his diagram with a dry hand. “Not even God could have made the world otherwise. The only God here—” Isaac slammed the page hard “—is the God of Spinoza, a God that is everything and therefore nothing.”
“But it seems as if you’ve explained everything.”
“I’ve not explained the inverse square law.”
“You’ve a proof right there saying that if gravity follows an inverse square law, satellites move on conic sections.”
“And Flamsteed says that they do,” Isaac said, yanking the sheaf of notes out of Daniel’s hip pocket. Ignoring the cover letter, he tore the ribbon from the bundle and began to scan the pages. “Therefore gravity does indeed follow an inverse square law. But we may only say so because it is consistent with Flamsteed’s observations. If tonight Flamsteed notices a comet moving in a spiral, it shows that all my work is wrong.”
“You’re saying, why do we need Flamsteed at all?”
“I’m saying that the fact that we do need him proves that God is making choices.”