Leibniz cleared his throat. “The way to Berlin is long,” he said, “but not that long.”
Daniel said, “The Doctor complains of our digression. I was speaking of the new Institute in Boston.”
“Yes. What is to be the nature of its work?”
Here Daniel was stumped; which was odd, and embarrassing. He did not quite know where to begin. But the Doctor, who knew Caroline much better, said, “If I may,” and gratefully Daniel gave the floor to him.
Leibniz said, “Persons such as your highness, who woolgather, and ponder things, are apt to be drawn into certain labyrinths of the mind—riddles about the nature of things, which one may puzzle over for a lifetime. Perhaps you have already visited them. One is the question of free will versus predestination. The other is the composition of the continuum.”
“The what of the what?”
“Simply that if you begin with observable things around you, such as yonder church-tower, and begin dividing them into their component parts, viz. bricks and mortar, and the parts into parts, where does it lead you in the end?”
“To atoms?”
“Some think so,” said Leibniz, agreeably enough. “At any rate, it happens that even the Principia Mathematica of Mr. Newton does not even attempt to settle such questions. He avoids these two labyrinths altogether—a wise choice! For in no way does he address the topic of free will versus predestination, other than to make it plain that he believes in the former. And he does not touch on atoms. Indeed, he is reluctant even to divulge his work on infinitesimal mathematics! But do not be misled into believing that he does not have an interest in such things. He does, and toils night and day on them. As do I, and as will Dr. Waterhouse in Massachusetts.”
“Do you toil on these two problems separately or—”
“A most important question, and one I should have anticipated,” said Leibniz, clapping his hands. “I should have mentioned that both Newton and I share a suspicion that these two problems are connected. That they are not two separate labyrinths, but a single large one with two entrances! You can enter either way; but by solving one, you solve the other.”
“So, let me see if I am understanding you, Doctor. You believe that if you understood the composition of the continuum—which is to say, atoms and whatnot—”
Leibniz shrugged. “Or monads. But pray continue.”
“If you understood that, it would somehow settle the question of free will versus predestination.”
“In a word: yes,” said the Doctor.
“Atoms I understand better,” began Caroline.
“No, you only phant’sy you do,” said Leibniz.
“What’s to understand? They are wee hard bits of stuff, jostling one another…”
“How big is an atom?”
“Infinitely small.”
“Then how can they touch each other?”
“I don’t know.”
“Supposing they do, by some miracle, come in contact, what happens then?”
“They bounce off each other.”
“Like billiard balls?”
“Precisely.”
“But, your highness, have you any idea just how complicated a billiard ball must be, to bounce? It is a fallacy to think that that most primitive of entities, the atom, can partake of any of the myriad qualities of a polished spherical lump of an elephant’s tusk.”
“Very well, then, but, too, sometimes they stick together, and form aggregates, more or less porous…”
“How does the sticking-together work? Even billiard balls can’t do that!”
“I haven’t the faintest idea, Doctor.”
“Nor does anyone, so do not feel bad about it. Not even Newton has figured out how atoms work, for all his toil.”
“Does Mr. Newton work on atoms too, then?” asked Caroline. It was directed at Daniel.
“All the time,” said Daniel, “but this work is called by the name Alchemy. For a long time I could not fathom his interest in it; but finally I came to understand that when he did Alchemy he was trying to solve this riddle of the two labyrinths.”
“But when you go to Massachusetts you’ll do no Alchemy at your Institute, will you, Dr. Waterhouse?”
“No, your highness, for I am more persuaded by monads than atoms.” He glanced at Leibniz.
“Eeyuh, that’s what I was afraid of!” said Caroline, “for I do not understand those one bit.”
“I believe we have established,” said Leibniz in a gentle voice, “that you do not understand atoms one bit—whatever illusions you may have nourished to the contrary. I hope to disburden your highness of the idea that, in looking for the fundamental particle of the universe, atoms are a simple and natural choice, monads not.”
“What’s the difference between a monad and an atom?”
“Let us first speak of how they are the same, for they have much in common. Monads and atoms both are infinitely small, yet everything is made out of them; and in considering how such a paradox is possible, we must look to the interactions among them: in the case of atoms, collisions and sticking-together, in the case of monads, interactions of an altogether different nature, which I shall come to presently. But either way, we’re obliged to explain the things we see—like the church-tower—solely in terms of those interactions.”
“Solely, Doctor?”
“Solely, your highness. For if God made the world according to understandable, consistent laws—and if nothing else, Newton has proved that—then it must be consistent through and through, top to bottom. If it is made of atoms, then it is made of atoms, and must be explained in terms of atoms; when we get into a difficulty, we cannot suddenly wave our hands and say, ‘At this point there is a miracle,’ or ‘Here I invoke a wholly new thing called Force which has nothing to do with atoms.’ And this is why neither Dr. Waterhouse nor I loves the Atomic theory, for we cannot make out how such phænomena as light and gravity and magnetism can possibly be explained by the whacking and sticking of hard bits of stuff.”
“Does this mean that you can explain them in terms of monads, Doctor?”
“Not yet. Not in the sense of being able to write out an equation that predicts the refraction of light, or the pointing of a compass-needle, in terms of interactions among monads. But I do believe that this type of theory is more fundamentally coherent than the Atomic sort.”
“Madame la duchesse d’Arcachon has told me that monads are akin to little souls.”
Leibniz paused. “Soul is a word frequently mentioned in connexion with monadology. It is a word of diverse meanings, most of them ancient, and much chewed over by theologians. In the mouths of preachers it has come in for more abuse than any other word I can think of. And so perhaps it is not the wisest choice of term in the new discipline of monadology. But we are stuck with it.”
“Are they like human souls?”
“Not at all. Allow me, your highness, to attempt to explain how this troublesome word soul became entangled in this discourse. When a philosopher braves the labyrinth, and sets about dividing and subdividing the universe into smaller and smaller units, he knows that at some point he must stop, and say, ‘Henceforth I’ll subdivide no further, for I have at last arrived at the smallest, elemental, indivisible unit: the fundamental building-block of all Creation.’ And then he can no longer dodge and evade, but must finally stick his neck out, as it were, and make an assertion as to what that building-block is like: what its qualities are, and how it interacts with all the others. Now, nothing is more obvious to me than that the interactions among these building-blocks are stupefyingly numerous, complicated, fluid, and subtle; just look about yourself for irrefutable proof, and try to think what can explain spiders, moons, and eyeballs. In such a vast web of dependencies, what laws are to govern the manner in which one particular monad responds to all of the other monads in the universe? And I do mean all; for the monads that make up you and me, your highness, feel the gravity of the Sun, of Jupiter, of Titan, and of the distant stars, which m
eans that they are sensitive of, and responsive to, each and every one of the myriad monads that make up those immense bodies. How can they keep track of it all, and decide what to do? I submit that any theory based on the assumption that Titan spews out atoms that hurtle across space and whack into my atoms is very dubious. What is clear is that my monads, in some sense, perceive Titan, Jupiter, the Sun, Dr. Waterhouse, the horses drawing us to Berlin, yonder stable, and everything else.”
“What do you mean, ‘perceive’? Do monads have eyes?”
“It must be quite a bit simpler. It is a logical necessity. A monad in my fingernail feels the gravity of Titan, does it not?”
“I believe that is what the law of Universal Gravitation dictates.”
“I deem that to be perception. Monads perceive. But monads act as well. If we could transport ourselves much closer to Saturn, and get into the sphere of influence of its moon Titan, my fingernail, along with the rest of me, would fall into it—which is a sort of collective action that my monads take in response to their perception of Titan. So, your highness: What do we know of monads thus far?”
“Infinitely small.”
“One mark.”
“All the universe explainable in terms of their interactions.”
“Two marks.”
“They perceive all the other monads in the universe.”
“Three. And—?”
“And they act.”
“They act, based on what?”
“Based on what they perceive, Dr. Leibniz.”
“Four marks! A perfect score. Now, what must be true about monads, to make all of these things possible?”
“Somehow all of these perceptions are flooding into the monad, and then it sort of decides what action to take.”
“That follows unavoidably from all that has gone before, doesn’t it? And so, summing up, it would appear that monads perceive, think, and act. And this is where the idea comes from, that a monad is a little soul. For perception, cogitation, and action are soul-like, as opposed to billiard-ball-like, attributes. Does this mean that monads have souls in the same way that you and I do? I doubt it.”
“Then what sorts of souls do they have, Doctor?”
“Well, let us answer that by taking an inventory of what we know they do. They perceive all the other monads, then think, so that they may act. The thinking is an internal process of each monad—it is not supplied from an outside brain. So the monad must have its own brain. By this I do not mean a great spongy mass of tissue, like your highness’s brain, but rather some faculty that can alter its internal state depending on the state of the rest of the universe—which the monad has somehow perceived, and stored internally.”
“But would not the state of the universe fill an infinite number of books!? How can each monad store so much knowledge?”
“It does because it has to,” said the Doctor. “Don’t think of books. Think of a mirrored ball, which holds a complete image of the universe, yet is very simple. The ‘brain’ of the monad, then, is a mechanism whereby some rule of action is carried out, based upon the stored state of the rest of the universe. Very crudely, you might think of it as like one of those books that gamblers are forever poring over: let us say, ‘Monsieur Belfort’s Infallible System for Winning at Basset.’ The book, when all the verbiage is stripped away, consists essentially of a rule—a complicated one—that dictates how a player should act, given a particular arrangement of cards and wagers on the basset-table. A player who goes by such a book is not really thinking, in the higher sense; rather, she perceives the state of the game—the cards and the wagers—and stores that information in her mind, and then applies Monsieur Belfort’s rule to that information. The result of applying the rule is an action—the placing of a wager, say—that alters the state of the game. Meanwhile the other players around the table are doing likewise—though some may have read different books and may apply different rules. The game is, au fond, not really that complicated, and neither is Monsieur Belfort’s Infallible System; yet when these simple rules are set to working around a basset-table, the results are vastly more complex and unpredictable than one would ever expect. From which I venture to say that monads and their internal rules need not be all that complicated in order to produce the stupendous variety, and the diverse mysteries and wonders of Creation, that we see all about us.”
“Is Dr. Waterhouse going to study monads in Massachusetts, then?” Caroline asked.
“Allow me to frame an analogy, once more, to Alchemy,” Daniel said. “Newton wishes to know more of atoms, for it is through atoms that he’d explain Gravity, Free Will, and everything else. If you visited his laboratory, and watched him at his labours, would you see atoms?”
“I think not! They are too small,” Caroline laughed.
“Just so. You instead would see him melting things in crucibles or dissolving them in acids. What do such activities have to do with atoms? The answer is that Newton, unable to see atoms with even the finest microscope, has said, ‘If my notion of atoms is correct, then such-and-such ought to happen when I drop a pinch of this into a beaker of that.’ He gives it a go and sees neither success nor failure but some other thing he did not anticipate; then he goes off and broods over it, and re-jiggers his notions of atoms, and devises a new experimentum crucis, and re-iterates. Likewise, if your highness were to visit Massachusetts and see me at work in my Institute, you’d not see any monads lying about on counter-tops. Rather you would see me toiling over machines that are to thinking what beakers, retorts, et cetera, are to atoms: Machines that, like monads, apply simple rules to information that is supplied to them from without.”
“How will you know that these machines are working as they ought to? A clock may be compared to the wheeling of the heavens to judge whether it is working aright. But what is the action that your machine will take, after it has applied the rule, and made up its mind? And how will you know whether it is correct?”
“That is easier than you might suppose. For as Dr. Leibniz has pointed out, the rules need not be complicated. The Doctor has written out a system for conducting logical operations through manipulation of symbols, according to certain rules; think of it as being to propositions what algebra is to numbers.”
“He has already taught me some of that,” said Caroline, “but I never phant’sied it had anything to do with monads and so forth.”
“That system of logic may be imbued into a machine without too much difficulty,” said Daniel. “And a quarter of a century ago, Dr. Leibniz, building upon the work of Pascal, built a machine that could add, subtract, divide, and multiply. I mean simply to carry the work forward. That is all.”
“How long will it take?”
“Years and years,” said Daniel. “Longer, if I were to try to do it amid the distractions of London. So, as soon as I have delivered you to Berlin, I shall begin heading west, and not stop for long until I have reached Massachusetts. How long shall it take? Suffice it to say that by the time I have anything to show for my labors, you’ll be full-grown, and a Queen of some Realm or other. But perhaps in an idle moment you may recall the day you went to Berlin in a coach with two strange Doctors. It may even occur to you to ask yourself what became of the one who went off to America to build the Logic Mill.”
“Dr. Waterhouse, I am certain you shall come to mind more frequently than that!”
“Difficult to say—your highness shall have many distractions. But I hope I am not being too forward in saying that I should be honored to receive a letter from your highness at any time, if you should wish to inquire about the state of the Logic Mill. Or, for that matter, if I may be of service to your highness in any other way whatsoever!”
“I promise you, Dr. Waterhouse, that if any such occasion arises, I shall send you a letter.”
As best he could in a moving carriage, Daniel—who had sat up admirably straight all through the interview—bowed. “And I promise your highness that I shall respond—cheerfully and without a moment�
��s hesitation.”
A House Overlooking the Meuse Valley
APRIL 1696
BEFORE THE MANOR-HOUSE’S GATES, two equestrians parleyed: a stout, peg-legged Englishman in a coat that had been drab, before it had got so dirty, and a French cavalier. They were ignored by two hundred gaunt, shaggy men with shovels and picks, who were turning the house’s formal garden into a system of earthen fortifications with interlocking fields of fire.
The Englishman spoke French in theory, but perhaps not so well in practice. “Where are we?” he wanted to know, “I can’t make out if this is France, the Spanish Netherlands, or the Duchy of bloody Luxembourg.”
“Your men appear to believe it is part d’Angleterre!” said the cavalier reproachfully.
“Perhaps they are confused because an Englishman is said to reside here,” said the other. He gave the Frenchman an anxious look. “This is—is it not—the winter quarters of Count Sheerness?”
“Monsieur le comte de Sheerness has chosen to establish a household here. During intervals between campaigns, he withdraws to this place to recover his health, to read, hunt, play the harpsichord—”
“And dally with his mistress?”
“Men of France have been known to enjoy the company of women; we do not consider it a remarkable thing. Otherwise I should have appended it to the list.”
“But what I’m getting at is: There is a feminine presence here? Maids and whatnot?”
“There was, when I went out this morning to ride. Whether there is any more, I can only speculate, Monsieur Barnes, as the place has been invested, and I cannot get into it!”
“Pity, that. Say, monsieur, do tell me, is this French soil or not?”
“Like a banner in the wind, the border is ever-shifting. The soil we stand upon is not presently claimed by La France, unless le Roi has issued some new proclamation of which I have not been made aware yet.”
“Ah, that’s good—these chaps have not invaded France, then—now, that would be embarrassing.”
The Baroque Cycle: Quicksilver, the Confusion, and the System of the World Page 202
