The Confusion

DOCTOR

THE RECENT EVENTS IN THE BALLROOM OF THE HOTEL ARCACHON WERE OF SUCH A DRAMATICK NATURE THAT I CANNOT BUT THINK YOU HAVE ALREADY HAD ACCOUNTS OF THEM FROM DIVERSE SOURCES HOWEVER MY VERSION FOLLOWS…

Beyond that point all was swallowed up between the pages of the enclosing book, which was expensively bound in red leather, ornately gilded with both Roman and Chinese characters.

“Any possibility of tea?” Fatio inquired, spying a kettle that had been left on one of the steps of the flaming ziggurat. Shielding his face in the crook of one arm, Leibniz ventured closer, seized a poker, and lunged like a fencing-master at the kettle to see whether it contained any water. Meanwhile Fatio peeled back the topmost sheet to reveal a letter written on different paper, in a different hand: Eliza’s!

To G. W. Leibniz from Eliza, the Marrying Maiden

Doctor,

You will want to know everything about the dress I was married in. The stomacher is made of Turkish watered silk decorated with several thousand of the tiny pearls that come from Bandar-Kongo on the Persian Gulf…

Leibniz had been rummaging in a drawer. He pulled up a black slab about the size of a folio book, impressed with a single huge Chinese character, and snapped off a corner. “Caravan tea,” he explained. “Unlike your English and Dutch tea, which comes loose off of ships, this stuff was brought overland, via Russia-it is a million dried leaves pressed together into a brick.”

Fatio did not seem to be as fascinated by this as Leibniz had hoped. Leibniz tried another gambit: “Huygens wrote to me recently, and mentioned you had come over from London.”

“Monsieur Newton and I devoted the month of March to reading Mr. Huygens’s Treatise on Light and were so taken with it that we agreed to divide forces for the year-I have been studying with Huygens-”

“And Newton toils at his Alchemy.”

“Alchemy, theology, philosophy-call it what you will,” Fatio said coolly, “he is close to an achievement that will dwarf the Principia.”

“I don’t suppose it has anything to do with gold?” asked Leibniz.

Fatio-generally so birdlike-quick in his answers-allowed some moments to pass. “Your question is a bit vague. Gold is important to Alchemists,” he allowed, “as comets are to astronomers. But there are some, of a vulgar turn of mind, who suppose that Alchemists are interested in gold only in the same sense as bankers are.”

“C’est juste. Though there is a troublesome banker, not far from here, who seems to value it in both the monetary and the Alchemical sense.” Leibniz, who until this point in the conversation had been the embodiment of good cheer, deflated as he was saying these words, as if he had been reminded of something very grave, and his eye strayed over to the outlandish red-leather book. This topic had had the same effect on his spirits as a handful of earth tossed into a fire. Again, Fatio allowed some moments to pass before he responded; for he was studying Leibniz carefully.

“I think I know who you mean,” Fatio said finally.

“It is most curious,” Leibniz said. “Perhaps you have heard some of the same stories concerning this as I have. The entire controversy, as I understand it, revolves around a belief that there is a particular sample of gold, whose precise whereabouts are unknown, but that possesses some properties that make it more valuable, to Alchemists, than ordinary gold. I would expect a banker to know better!”

“Do not make the error of believing that all gold is the same, Doctor.”

“I thought Natural Philosophy had proved at least that much.”

“Why, some would say it has proved the opposite!”

“Perhaps you have read something new in London or Paris that I have not seen yet?”

“Actually, Doctor, I was thinking of Isaac’s Principia.”

“I have read it,” Leibniz said drily, “and do not recollect seeing anything about gold.”

“And yet it is clear enough that two planets of equal size and composition will describe different trajectories through the heavens, depending on their distances from the sun.”

“Of course-that is necessarily true, by the inverse-square law.”

“Since the two planets themselves are equal in every way, how can this difference in their trajectories be accounted for, unless you enlarge your scope of observations to include the difference in their situations vis-a-vis the sun?”

“Monsieur Fatio, a cornerstone of my philosophy is the identity of indiscernibles. Simply put, if A cannot be discerned from B, then A and B are the same object. In the situation you have described, the two planets are indiscernible from each other, which means that they ought to be identical. This includes having identical trajectories. Since they are obviously not identical, in that their trajectories differ, it follows that they must in some way be discernible from each other. Newton discerns them by assigning them differing positions in space, and then presuming that space is somehow pervaded by a mysterious presence that accounts for the inverse-square force. That is, he discerns one from the other by appealing to a sort of mysterious external quality of space…”

“You sound like Huygens!” Fatio snapped, suddenly annoyed. “I might as well have stayed in the Hague.”

“I am sorry if the tendency of me and Huygens to agree causes you grief.”

“You may agree with each other all you like. But why will you not agree with Isaac? Can you not perceive the magnificence of what he has achieved?”

“Any sentient man can perceive that,” Leibniz returned. “Almost all will be so blinded by its brilliance that they will be unable to perceive its flaws. There are only a few of us who can do that.”

“It is very easy to carp.”

“Actually it is rather difficult, in that it leads to discussions such as this one.”

“Unless you can propose an alternative theory that mends these supposed flaws, I believe you should temper your criticisms of the Principia.”

“I am still developing my theory, Monsieur Fatio, and it may be a long time before it is capable of making testable predictions.”

“What conceivable theory could explain the discernibility of those two planets, without making reference to their positions in absolute space?”

THIS LED TO AN INTERLUDE in the snow outside. Doctor Leibniz packed two handfuls of snow together between his hands, watched warily by Fatio. “Don’t worry, Monsieur Fatio, I’m not going to throw it at you. If you would be so helpful as to make two more, about the size of melons, as like to each other as possible.”

Fatio was not quick to warm to such a task, but eventually he squatted down and began to roll a pair of balls, stopping every couple of paces to pound away the rough edges.

“They are as close to indiscernible as I can make them under these conditions-which is to say, in twilight with frozen hands,” shouted Fatio towards Leibniz, who was a stone’s throw off, wrestling with a snowball that weighed more than he did. When no response came back, he muttered, “I shall go in and warm my hands if that is acceptable.”

But by the time Nicolas Fatio de Duillier had got back to Leibniz’s office, his hands were warm enough to do a few things. He took another look at the papers stuck into the Chinese book. The letter from Eliza was inordinately long, and appeared to consist entirely of gaseous chatter about what everyone was wearing. Yet on top of it was the other document, addressed to the Doctor but written in the Doctor’s hand. A mystery. Perhaps the book was a clue? It was called I Ching. Fatio had seen it once before, in the library of Gresham’s College, where Daniel Waterhouse had fallen asleep over it. The sheaf of papers had been used to mark a particular chapter entitled: 54. Kuei Mei: The Marrying Maiden. The chapter itself was a bucket of claptrap and mystickal gibberish.

He put it back where he’d found it, and went over to the shed’s single tiny window. Leibniz now had his back pressed against an immense snowball and was trying to topple it over by thrusting with both legs. Fatio strolled once around the room, pausing to riffle through any prominent stacks of papers that presented themselves to his big pale eyes. Of which there were several: letters from Huygens, from Arnauld, from the Bernoullis, the late Spinoza, Daniel Waterhouse, and everyone else in Christendom who had a flicker of sense. But one of the larger stacks consisted of letters from Eliza. Fatio reached into the middle, grabbed half a dozen leaves between his thumb and index finger, and snapped them out. He folded them and stuffed them into his breast pocket. Then he ventured back outside.

“Are your hands warm, Monsieur Fatio?”

“Exceeding warm, Doctor Leibniz.”

The Doctor had arranged the three snowballs-one giant one and the two small indiscernibles-on the field between the stable, the Schlo?, and the nearby Arsenal. The triangle defined by these balls was nothing special, being neither equilateral nor isosceles.

“Isn’t this how Sir Francis Bacon died?”

“Descartes, too-froze to death in Sweden,” the Doctor returned cheerfully, “and if Leibniz and Fatio can go down in the annals next to Bacon and Descartes our lives will have been well concluded. Now, if you would be so good as to go to that one and tell me of your perceptions.” The Doctor pointed to a small snowball a few paces in front of Fatio.

“I see the field, the Schlo?, Arsenal, and Library-to-be. I see you, Doctor, standing by a great snowball, and over there to the right, not so far away, a lesser one.”

“Now pray do the same from the other snowball that you made.”

A few moments later Fatio was able to report: “The same.”

“Exactly the same?”

“Well, of course there are slight differences. Now, Doctor, you and the large snowball are to my right, and closer than before, and the small snowball is to my left.”

Leibniz now deserted his post and began stomping towards Fatio. “Newton would have it that this field possesses a reality of its own, which governs the balls, and makes them discernible. But I say the field is not necessary! Forget about it, and consider only the balls’ perceptions.”

“Perceptions?”

“You said yourself that when you stood there you perceived a large snowball on the left, far away, and a small one on the right. Here you perceive a large one on the right, near at hand, and a small one on the left. So even though the balls might be indiscernible, and hence identical, in terms of their external properties such as size, shape, and weight, when we consider their internal properties-such as their perceptions of one another-we see that they are different. So they are discernible! And what is more, they may be discerned without reference to some sort of fixed, absolute space.”

By now they had, without discussion, begun trudging back towards the Schlo?, which looked deceptively warm and inviting as twilight deepened.

“You seem to be granting every object in the Universe the power to perceive, and to record its perceptions,” Fatio ventured.

“If you are going to venture down this road of subdividing objects into smaller and smaller bits, you must somewhere stop, and stick your neck out by saying, ‘This is the fundamental unit of reality, and thus are its properties, on which all other ph?nomena are built,’ ” said the Doctor. “Some think it makes sense that these are like billiard balls, which interact by colliding.”

“I was just about to say,” said Fatio, “what could be simpler than that? A hard wee bit of indivisible matter. That is the most reasonable hypothesis of what an atom is.”

“I disagree! Matter is complicated stuff. Collisions between pieces of matter are more complicated yet. Consider: If these atoms are infinitely small, why, then, is it not true that the likelihood of one atom colliding with another is essentially zero?”

“You have a point,” said Fatio, “but I hardly think it is somehow simpler to endow these atoms, instead, with the ability to perceive and to think.”

“Perception and thought are properties of souls. It is no worse to posit that the fundamental building-block of the Universe is souls than to say it is wee bits of hard stuff, moving about in an empty space that is pervaded by mystickal Fields.”

“Somehow a planet’s perception of the sun and all the other planets, then, causes it to behave exactly as if it were in such a ‘mystickal Field,’ to an uncanny degree of precision.”

“I know it sounds difficult, Monsieur Fatio, but ’twill work out better in the long run.”

“Physics, then, becomes a sort of vast record-keeping exercise. Every object in the Universe is distinguished from every other object by the uniqueness of its perceptions of all the other objects.”

“If you think on it long enough you will see it is the only way to distinguish them.”

“Why, it is as if every atom or particle-”

“I call them monads.”

“Monad, then, is a sort of Knowledge Engine unto itself, a Bucherrad-rad-rad-rad…”

Leibniz summoned a weak smile.

“Its gears grind away like the ones in your Arithmetickal Engine, and it decides what to do of its own accord. You knew Spinoza, did you not?”

Leibniz held up a warning hand. “Yes. But pray do not put me in with him.”

“If I may just return to the topic that got us started, Doctor, it seems to me that your theory allows for a possibility you scoffed at-namely, that two lumps of gold might be different from each other.”

“Any two such lumps are different, but it is because, being differently situated, they have different perceptions. I am afraid that you want to assign mystickal properties to some gold and not other.”

“Afraid why?”

“Because the next thing you’ll do is melt it down to extract that mystery and put it in a phial.”

Fatio sighed. “In truth, all these theories have their problems.”

“Agreed.”

“Why not admit it, then? Why this stubborn refusal to consider Newton’s system, when yours is just as fraught with difficulties?”

Leibniz drew to a halt before the front stoop of the Schlo?, as if he’d rather freeze than continue the discussion where it might be overheard. “Your question is dressed up in the guise of Reason, to make it appear innocent. Perhaps it is. Perhaps not.”

“Even if you do not think me innocent, pray believe that my confusion is genuine.”

“Isaac and I had this conversation long ago, when we were young, and matters stood quite differently.”

“How odd. You are the only person, other than Daniel Waterhouse, who has ever called him by his Christian name.”

The look of uncertainty on Leibniz’s face now hardened into open disbelief. “What do you call him, when the two of you are alone together in your London house?”

“I stand corrected, Doctor. There are three of us who have known him thusly.”

“That is a very clever sentence you just uttered,” Leibniz exclaimed, sounding genuinely impressed. “Like a silken cord turned in on itself and knotted into a snare. I commend you for it, but I will not put my foot in it. And I will thank you to keep Daniel out of it as well.”

Fatio had turned red. “The only thing I wish to snare is a clearer understanding of what has passed between you and Isaac.”

“You want to know if you have a rival.”

Fatio said nothing.

“The answer is: you do not.”

“That is well.”

“You do not have a rival, Fatio. But Isaac Newton does.”