“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 ph?nomena as light and gravity and magnetism can possibly be explained by the whacking and sticking of hard bits of stuff.”