13
The Logarithmic Spiral
It had been three years before, when I was fifteen, that I wrote my thesis on Descartes. It was precocious of a child who knew so little to attempt so much. I blushed now to think of my gray-haired Masters, steeped in decades of long thought, regarding my chubby cheeks and naïve, earnest eyes as I, the dwarf, described my opinions of giants. And even more, that I compared Newton with Descartes, to the faculty of Basel, the Mathematical hotbed of anti-Newtonism, and the theological nemesis of Cartesians. It was a miracle that I even still existed! But those generous and patient professors allowed me past, and Master Johann, who could have sunk the whole battleship with one raised eyebrow or finger tap of annoyance, instead allowed me passage across his cannon, and himself signed the parchment of my Master’s degree. For a while afterward a few people called me Master, but I’d never wanted that. Even with a tricorne, I still felt I was no Master.
Between those two, Newton and Descartes, I believed Mr. Newton to be more correct; and three years later, I was more convinced. Many criticisms of Mr. Newton complained that his theories were too precise: they applied such a severe Mathematical exactitude to the beauty and gentle motions of nature. This was, besides, the completely invisible Gravity that he proposed, and others rejected as absurd. But the comparison was to Monsieur Descartes, who believed that the only truth was what we experienced, and could know with our own senses. If the universe was to be measured by Mathematic rules, or else by man’s experience, then I knew that Mathematics was superior. I believed that the universe would exist and follow its Mathematic orbits even if no man ever lived to see it. I even believed that if there was no universe, the laws of Mathematics would still exist. And I thought Mathematics was beautiful itself, and added to the exquisite harmony of creation rather than degrading it. And for Gravity, well, I very greatly believed in invisible things.
It was still early on Saturday, though already the day was warm, when I sat at my desk to read Herr Leibniz. I’d read Nova methodus pro maximis et minimis many, many times, but it still put me in the best frame for my meeting with Master Johann. The two had been correspondents and friends. I thought this was one real reason that Master Johann sided so passionately with Herr Leibniz over Mr. Newton on the discovery of the Calculus. His passion had carried all the Mathematicians in the continent with him, turning the whole continent of Europe against England, and England against Europe.
It was strange that a subject as perfect and rational as Mathematics could stir disagreements and conflict. Yet it did in two ways: first, in discovery, where a man’s pride would lead him to grasp a new theorem as a dog did a bone, and yield to no other that it was his original; and second, in proof, where claims might be shaky or unfounded, and the rigorous deduction to prove or disprove was beyond knowledge. So, the Newton camp and the Leibniz camp had warred over which champion first discovered the Calculus. Then, there was a civil war within each camp over what had actually been truly proven and what had not but would be, and what was actually false.
Then, there was a third hostility that arose from Mathematics, founded in the first two conflicts, and that was outright, which was the pursuit of Publications, of Eminence and Esteem, and most of all, of Chairs. So reading Leibniz, I thought much more about these qualities of humanity, and not as much about the qualities of polynomials.
On my dresser, beside my friend the wood head, and my marvel, the conch shell, and the small charred slat with the Logarithmic spiral, I had two other items, my bowls. They were pottery and seemed very normal. Each was only eight inches from rim to rim and somewhat shallow, just a few inches deep, with the sides becoming steep at their outer edge. They might even have seemed identically shaped, though they weren’t. In color they were plain but had interiors which were very polished. However, each had its own unique and amazing property: one was brachistochronic, the other was tautochronic.
The tautochrone was the easier to demonstrate. Set a small flat pebble that would slide on the smooth surface, or a very round pebble that would roll, near the rim and it would accelerate down and quickly travel the long distance to the center. Place it farther from the rim, closer to the center, where the slope was less, and it would accelerate more slowly, but would still reach the center quickly because it was closer. Indeed, place the stone anywhere in the bowl, and the combination of the steepness and distance from the center at any point would contribute to the stone’s reaching the center in the exact same time. Tautochrone meant identical time. Set two stones, or three, or as many as would fit and could be held, anywhere in the bowl from rim to nearly the center, and after they were all let go at the same time, they would all reach the center simultaneously.
That the second bowl was a brachistochrone was more difficult to demonstrate. In this bowl, the pebble set anywhere would reach the center faster than it would in a bowl of any other shape. If the side were steeper, the stone could accelerate more quickly but have a greater distance to travel; if it were more shallow, the reverse applied. Brachistochrone meant the fastest time.
These bowls showed another reason why Master Johann was so hostile to Mr. Newton.
The shape of either bowl could only be derived with a special set of the Calculus. The shapes were first sought by Galileo nearly a hundred years ago, but were beyond the Mathematics of the time. Only after Herr Leibniz published his Nova Methodus were the necessary theorems available. The equation of the tautochrone was fairly easy. But Master Johann, thirty years ago, and only a little older than I was now, published the first solution to the brachistrochrone, which was much more difficult. Yet only his solution was correct.
His proof was not. Often in Mathematics this would happen. It would be the same as stating that the source of the Barefoot Square fountain was the Birsig, which I believed was true but was not certain; and having given as my proof that it was water in the fountain, and it was water in the stream, so the one must feed the other. This would not be a valid proof, and neither were Master Johann’s calculations of the brachistochrone.
This soon came to light, and Master Johann’s proof was invalidated. A challenge was sent out to the Mathematicians of Europe in the journal Acta Eruditorum to find the correct proof, and also presented several variations to the problem. The challenge was actually posted by Master Johann himself, but anonymously, as he had a scheme to remove the stain on his reputation.
Only five men among all then living could have solved the problem, and they each did. Herr Leibniz solved it, of course. Monsieur L’Hospital also sent in a solution, though it was apparent that he’d corresponded with Herr Leibniz and had mainly repeated that Master’s answer.
Two others able were the brothers Jacob and Johann. Master Jacob solved it in an original way, and as the two brothers were then still cordial, he showed his proof to Master Johann. Master Johann, expecting this, took his brother’s proof and attempted to pass it as his own.
All of these proofs were published in the Acta, anonymously as always, though each of the men quickly recognized the others’ work. Accusations flew and the brothers were permanently sundered. They’d all spent days and weeks at their calculations, each sure of his own unique genius.
There was, though, a fifth proof published in that same edition, superior actually to all the others. Mr. Newton in England, it was said, had solved the problem in a few moments the very night he received the journal, after a tiring day of work. Though the attribution was anonymous, the notations made it obvious that they’d all been bested by the Englishman.
As Master Johann said when he read it, “I recognize the lion by his paw.” The saying had persisted in his family. The feelings between them had also persisted.
After Leibniz, I read Newton. The Principia was a book that would stand forever: it bested all his peers, just as his proof had bested them. Whether Mr. Newton or Herr Leibniz first understood the Calculus, I did not know. I did know that Mr. Newton’s work reached farther, and his principal that Mathematics ruled, and also explained, the motions of both planets and pebbles, of both raindrops and rainbows, was a new beginning of history. He would be famous forever. Whenever he died, and he was now very old, his fame would only keep growing.
My Master Johann would also hold a place in history. Again whether Mr. Newton or Herr Leibniz first discovered the Calculus, it was without doubt that everyone who now knew the subject learned it through Master Johann’s explanation. His books were not on the same pinnacle as the Principia, but they would always be known. He had the renown that Master Faust sought.
Daniel and Nicolaus and Gottlieb would also be remembered. In Mathematics, their family had been a constellation. Daniel wanted to outshine his father and would have paid a dear price to do it, and Nicolaus had more ambitions than he showed. And, in some obscure journal, an author might even be remembered for the first proof of the Reciprocal Squares.
It seemed to be the warmest day yet of the spring, and the sky was cloudless. All sound was deadened.
When I was admitted into Master Johann’s house, there was a thickness to the silence. I could hardly hear my own footsteps in the stairs, and Mistress Dorothea’s knock on the inner door was like a leaf fall. The call from within sounded as from a grave.
“What have you been reading this week?” he asked, and he seemed much older and worn.
I was able truthfully to give an answer pleasing to him. “Herr Leibniz.”
Though less, he was still omniscient and omnipotent in his dark room. He’d known. “I have been, also,” he said. “Even now.”
“The Nova Methodus?” I didn’t see a book on the table, only some papers. But these were what he set his hand on as he answered.
“Our correspondence.”
“From himself?” I asked, awed. I knew, of course, that there had been many letters between them, but these were those letters themselves.
“I was younger then. Leonhard, why do you pursue Mathematics?”
“I can’t not.”
“How does Mr. Newton describe the study of Mathematics?”
This was disturbing. It may have been the first time I’d ever heard that name from my Master’s lips. It was dangerous, as well. To deny my respect would be foolish, as he certainly remembered my thesis of three years before. But to show too much admiration would also be unwise. “The Principia states that Mathematics explains the revolving of earth and the motion of water and the colors of light,” I said.
“How can Mathematics do this?”
“I believe there are deep laws that govern motion and substance.”
“So is that Mathematics?” he asked, and I sensed his dissatisfaction with my answer. “It is just a principal of natural philosophy?”
“Then what?”
“I think that natural philosophy, and Physics, and all of such things are built on Mathematics like a castle is built on a mountain. There is more to the mountain than just the portion that holds the castle.”
“There is more of Mathematics,” he said, and now he was satisfied, “than is used in the earth and heavens.”
“I believe so. Master, what do you understand that Mathematics is?”
“It is an invisible world,” he answered. “Greater and deeper than anything we see.”
“I do see invisible things,” I admitted. “Sometimes.”
“Then you see that world,” he said, “also.”
“Where did it come from?”
“Where?” He hadn’t thought that question before. “It would always have been. The world we see is created on it.”
“But could it have always been? Even the invisible world must have been created, also.”
“The created world is as it was chosen to be,” he said. “Mountains and rivers are where they are, but they could have been otherwise. Mathematics can only be as it is. There is no other possibility. So, was it created?”
I tried to think of a Mathematics different from the one I knew. Could one and two add to something other than three? Or did they only because that was how they were created to be?
“That would mean they are beyond the Creator.”
“We will keep our discussion on Mathematics and Mathematicians.”
“Yes, Master. But then I have another question. What makes a Mathematician great?”
“If he discovers great things. Then he is known.” He looked at me a moment. “Is that what you mean?”
“No, sir. What would make him able to discover great things?”
“What are his qualities? Is that what you mean?”
“Yes, sir.”
He sat back into the silence of the room. “He sees.”
“Into the invisible.”
“Yes.” Then Master Johann laughed. “But then he must also publish and he must become known. A great Mathematician who is unknown is not great.”
So I plunged forward. “Then I wish to send my proof to Paris.”
“To Paris? Monsieur Fontenelle will deride and dismiss the work of a young student. Monsieur Molieres would glance through it and find every fault that I do.”
“It would be treated respectfully if you wrote a letter of recommendation for it.”
“Yes, it would.” He did not deride me. He even seemed unsurprised that I had asked. “But should I? I am not fully convinced of it myself.” The one word though, fully, showed that he might soon be. He considered me, his young supplicant, in the same way he had the last Saturday, and it seemed that he was seeing something new.
My mother’s father was pastor of Saint Leonhard’s for three decades. He died before I was born. My grandmother didn’t speak often of him, as she was not given to reminiscing. Mostly she used him as an example to me of a sound, pious, dedicated, and competent man. Everyone else who remembered him spoke more highly even than she did.
This pastor’s daughter, my mother, married a pastor. He was a young man of good family and humble means, unshakable in his faith and in every part of his life. Beneath his calm demeanor, though, his heart burned with a slow, steady fire so hot that all the flames of the Boot and Thorn would be just a sputtering candle beside it.
For several years he had the pulpit at Saint Leonhard’s. It was even now still warm from him. When his son was born, the child was named for his father’s parish. Then, instead of taking a higher perch at the Munster or beyond, this man took his wife and child out of Basel to pastor a village in the hills north of the city and settled into its smallness. Whether the cottages of Riehen ever knew what great spirit they had, I would not be certain. He was certain of the choice he was making. He was my father. I learned from him that God was not served by our greatness but by our humbleness.
On Sunday morning I took my grandmother to church, and in the preaching we were instructed on the very greatness of God: his righteousness, his love, and his sacrifice. I would never tire of that lesson.
Monday morning, Mistress Dorothea poured words as a fountain pours water. Basel’s fountains provided a greater flow than the citizens need, so that a great deal simply flowed over the basin and into the streets; and Mistress Dorothea had more to say than there were ears to hear.
But as I was finishing, the fountain stopped. “Leonhard.”
“Yes, Mistress Dorothea?” I said.
“Master Johann has instructed me that you are no longer to be obliged to perform chores in this house.”
“Not obliged?” I was dumbfounded.
“From this moment on.”
“But . . . Mistress Dorothea . . . why not?”
“I don’t question the Master’s reasons.”
I was trying to understand, and reeling, though I also did notice that she’d let me put in my full morning’s labor before she’d said this. “Then . . . am I no longer to come on Saturdays?”
“You’ll need to discuss this with Master Johann. He is expecting you upstairs.”
“Come.” This was the third Monday Master Johann had answered my knock on his door.
It seemed more difficult each time to concentrate on speaking. The room was too marvelous. “Mistress Dorothea said I was no longer obliged to do chores for her in the mornings.”
“That is true.” From where I stood and how he was seated, I couldn’t see his desk well. There were just a few papers visible at the edge.
“Then I’ll no longer come on Saturdays?”
“You will still come.”
“But, Master, how will I pay you for the time?”
“I’ve written a letter to your father. From the present, your lessons will be at my pleasure. They will not be in exchange for tuition or service.”
“Thank you, sir . . . but I can’t. It would be unearned. An imposition.”
He shook his head. “It is my decision.”
“Yes, sir. Master Johann?”
“Yes?”
“May I still be allowed to do chores here nonetheless?”
I saw no reaction. He just said, “You may request that of Mistress Dorothea.”
“Yes, yes, Leonhard,” was Mistress Dorothea’s answer to that request. “I’ll keep you for my kitchen, for the present. But there’s a time coming when it won’t be fitting.”
“At least a little longer,” I said.
And when she was out of the room, Little Johann came in to ask, “You’ll keep coming?”
“As long as I can.”
“Why?”
“It’s right to do. I shouldn’t take lessons without paying.”
“That’s all?”
“It would be an exile to not come.” Of all the family, I was least sure of Little Johann’s thoughts, and all the family was an opaque set. I didn’t know if he was glad or thought me a fool. He took a covered basket from beside the hearth, opened it, and took out a plump, risen ball of dough. “I’m not gentleman enough yet to be above work.” I sighed a wistful sigh. “But I’m not sure I’ll ever wear my old hat again, even if I did have it. It might be only tricornes for me now.”
As he began working his dough, Little Johann seemed grieved as I was. He squeezed the dough. He had such strong hands.
Then I said, “What became of my hat, Johann? Did you lose it?”
He stared at the dough, kneading and pressing it so hard. Then he nodded.
“It’s all right,” I said. “I have it back.”
“You do?”
“Yes. I just wonder how it came to be where I found it.”
“Where did you find it?”
“Where did you lose it?” I asked.
“I had it from Cousin Gottlieb. I took it to the Barefoot Square to find you in the inn or the church.”
“What happened?”
“A gust blew it out of my hand. It was away too quick. I didn’t see where.”
“I found it in the Square,” I said. “So it’s all right. And Johann, on your father’s desk. There’s only one letter for Daniel. The letter from Paris. The other, from Russia, is gone.”
I stayed home that afternoon and evening. Sometimes I was driven so strongly to write that everything else fled aside, as if an angry bull were let loose in the market square. That evening my thoughts had piled so high from Saturday morning that they were riotous as the bull and the scrambling market-goers together. The quill in my hand flew tempest and my pages drifted into deep snowbanks against my books. It was a blizzard! Once I noticed a plate of supper had alit at my side, and another time I noticed it was empty, and some other moment I saw that I’d lit a candle. Or it might have spontaneously lit itself.
And finally I dimly perceived that I was in bed and the candle was out. Saint Leonhard’s bell sounded three times. But all of that was only the visible world. In the invisible, I was still writing and every word was exact and clear.
As I was in Mistress Dorothea’s kitchen Tueday morning, scrubbing an iron skillet, I was called upon. It was a student, Heidelmann, who clerked for the Provost, and he watched me work my elbow.
“Your grandmother said you’d be here. That’s nothing for a student or even any man to be doing,” he said, but in friendship.
“It’s rusted. It needs a hard hand.”
“I have man’s work for you. I have a task from my Master, and you know who he is.”
“I know.”
“He wants you for an errand.”
“I don’t know that. So make yourself look like a young gentleman, if you can, and get over to Master Provost, and he’ll tell you what to do.”
I could make myself look like a young gentleman, though looks were deceiving, and I could do it fast. Grandmother was curious over my summons but there was little I could tell her.
“What would the Master Provost want with a student?” she asked.
“To learn his lessons, pay his tuitions, and comport himself decently.”
“Oh, Leonhard! What does he want of you?”
“I pay my tuitions,” I said, “so it must be I’m lacking the others.”
But I did know a few reasons the Provost might have to call a single student, and one was to be a messenger. When just the Senior members of the University met for a routine matter, they were simply sent a message the day before. It was much less picturesque a gathering than the Convention, and a single student was given the task. He was given a day for it: some score of Chairs and Deans and Officials took a few hours at least.
So I called on the Provost at his home as soon as I was presentable. He lived not far from Magistrate Faulkner and in a similar house, though Faulkner’s had more pleasant trees and gardens. I was shown in to the front parlor and soon greeted by the Provost himself.
He was a bit of a jovial man, once a Chair of Law, comfortable in his office, unafraid of it, and placid in its exercise. It was the Deans who saw to the affairs of their Colleges, and the Chairs who were the affairs of the Colleges. A Provost held a high position that depended on his wisdom and light touch. But there was a weight on his shoulders and duties to be performed. So he wanted me for a messenger.
“You know the names, Leonhard,” he said. “Tell them, the faculty will come together tomorrow morning at ten.”
“Yes, sir. For what, should I tell them?”
“The reports of the committees. The nominations.”
“I’ll tell them all, sir.”
I started my door-to-door. But I couldn’t run, which was a pity, as young gentlemen didn’t, at least not when they were seen, and there were only a few streets and alleys that were empty. And I came to each door, and knocked, and said I must speak to the Master himself, and when the Master was produced, gave him the message. It wouldn’t usually be proper to demand the sight of the mighty men, but they knew that the day would have been coming soon and were expecting it. A few weren’t home so I asked when they would be, and rounded on them again. The people of Basel were in their homes much more than anywhere else, and the Masters of the houses really had little reason to leave besides church.
The only door that worried me was my own Master’s. I could have easily come in the back and sent Little Johann up for his father, but the University had to be served in its own way. So I knocked, and Little Johann answered, and I told him I had an important message for Master Johann. Then I was let in. A gentleman wasn’t kept waiting outside, even if it was me.
I took a seat in the front parlor, where more often I was cleaning or tending the fireplace. As always the room was in twilight. Then with no warning the door opened. I was up on my feet like a rabbit.
Master Johann regarded me. “Sit down,” he said. His near-round face was caught somehow in a shaft of light; I hadn’t seen the light before he came in. His wig was bright white in it. “You have a message for me?”
“Yes, sir.” I jerked up again. “The Provost requests that the faculty attend to important business at the University tomorrow morning at ten o’clock.”
“Sit down.” He stood watching me. I sat down. Then he sat down. When I came on Saturday afternoons we both sat, but the table was between us, and he was already sitting. That was very different. Here, he was sitting to converse, with me. “Leonhard,” he said. “I have written a letter to Paris. It is to Monsieur Frontenelle of the Academy, to tell him that I have seen a solution of the Reciprocal Squares problem by my student, and that he should await a letter from Master Leonhard.”
“Master Johann . . . thank you . . . thank you! I don’t how to thank you!”
He dismissed my amazement. “The Monsieur is also an editor of the Acta Eruditorum, and I have suggested that the proof should be published.”
I nearly fell from my seat. The Acta was the journal to which Master Johann submitted his own most important papers! It was incredible that he would consider promoting me this way.
“I . . . but Master Johann . . .”
“I believe your proof is worthwhile. Leonhard, you have great potential. It is time to consider plans for your future.”
This was all beyond my greatest hopes. I’d had so many small evidences that Master Johann was favorable toward me, but many others that contradicted those. And I knew well how little he was given to selfless generosity. Yet here we sat, almost as equals, and he, the truly famed Master Johann of Basel, was advising me for my future.
“I’ve thought of the future,” I said, “but not of plans.”
“Then listen to this counsel.” Oh, of course I would! “Should the Academy accept your proof,” and of course, with his recommendation they would! “or the Acta Eruditorum publish it,” and with his suggestion, how could they not? “then you will find many opportunities open to you.” Many? All! Any door would open! “I would advise you,” he said, “to choose carefully.”
“Yes, sir,” I said. “Of course I would want to.”
“There are numerous positions that seem significant but great men aren’t found in them.”
I nodded.
“And there are other positions,” he said, “which are fewer, which great men do hold.”
“I wouldn’t know which was which,” I said.
“And the men in these positions recognize each other.”
“I’m sure you must,” I said.
“Even great ability will only raise a man to a certain level. Occupying one of these highest Chairs, holding office in one of these exceptional Academies, or attending one of these erudite Courts, is just as necessary.”
“I’d aspire to such a position,” I said.
“These positions are never simply given.”
“They must be achieved?” I asked.
“They must be negotiated.”
“But . . . with whom?”
He had leaned forward, slowly, as he talked. Now he leaned back and his manner changed from conspiratorial to magnanimous. “An introduction to the Royal Academy in Paris will be a step forward, and I have every hope the Secretary will receive it graciously. Now, Leonhard, the Provost and I both thank you for your service today.”
All the bells of Basel tolled three o’clock as I walked back to my grandmother’s house. They were a cacophony but pleasant and grand and noble. I felt them calling me to noble and grand places. Then they fell silent, and their echoes circling the city dwindled. From far off, I heard the single bell of Riehen answer two o’clock, quietly.
Later, I made a visit to the Boot and Thorn in the chance of finding Daniel, which I did. Nicolaus was there, of course. I don’t think he enjoyed the smoky dungeon any more than I did.
“It’s all for tomorrow,” Daniel said. “Just hours.”
“It’s a Chair,” I said, “but only a Chair. Daniel, you’re nervous as a sheep that smells a wolf.”
“As a wolf that smells a sheep,” Nicolaus said.
“You’ll be nominated,” I said. “I’m certain you will. And you’re certain. Be at peace.”
“It’s a certainty that doesn’t bring peace,” Nicolaus said.
Daniel snarled at him. “What’s that?” His anger flared, but Nicolaus was still as always. “You’d take a nomination if you could! You’d give as much as I.”
“How much have you given?”
Daniel shrugged him off. “He’s just jealous,” he said to me.
“There are three nominations,” I said.
“And two are worthless.”
“Worthless after the stone’s drawn, or before?” Nicolaus said.
“After,” I said. “They’re each worth the same while they’re each still in the box.”
“Don’t under-guess Mighty Brutus,” Daniel said. “He’ll squeeze just what he wants out of that box. There’s no telling what he might do.”
“I don’t understand you,” I said. “You seem so sure that you’ll be nominated and chosen, and you’re sure your father will be sure that you aren’t. What does it mean? And your father isn’t so vengeful as you think, anyway.”
“What do you mean by that?”
“He’s conceded my proof. He’s said he accepts it and even admires it.”
“Brutus? He said that?”
“To me, this morning.”
“That’s easy enough, I suppose, when there’s no one to hear him.”
“He says he’s sending a recommendation to Paris that I’ve solved the challenge.”
Daniel leaned close, and even Nicolaus did, too. “But has he sent it?”
“It’ll be on the Post to Belfort tomorrow. It will be in Paris in a week.” I couldn’t help myself, boastful as it was to say it. “And he’s recommending it to the Acta Eruditorum, as well.”
“What? Never. It’s not the same man! You’ve been captivated by a conjurer, Leonhard. It wasn’t any member of my family who said that.”
“Or father’s been captivated,” Nicolaus said, thoughtfully.
“If he’s been,” Daniel said, “it’s worth guessing by whom. No, Leonhard’s the one captivated, and by Brutus.”
“Would you want a nomination, Nicolaus?” I asked.
“I have my Chair already in Bern, and I’m wise enough,” he said with a nod to his brother, “to not give up my own until I have something better.”
“The nothing I have now is better than that Chair was. And you’ve neglected your Chair this past month.”
“It will stand a rest when I have more urgent business here.”
I asked Daniel a question. “Which part is Gottlieb of the schemes? Is he of yours or your father’s?”
“That’s a question,” Nicolaus said. “Which is he, Daniel?”
“We’re fire and stone,” Daniel answered. “Enemies that can’t help or hinder.”
“And cousins, too,” I said, “who’ve been friends before.”
“And aren’t now. Brutus won that match. But he can’t win this one. Watch, Leonhard. The committees he’s put together so carefully, he can only use to nominate me. He’s forced into it.”
“Then when you’re nominated, you’ll be sure it’s your scheming. Oh, Daniel. I think the only man caught in your nets is yourself.”
He laughed. “Then you’ll believe it when the lot is cast.”
“If you win the Chair, will you take it?” Nicolaus asked.
“What? Why wouldn’t I?”
“Something better might come.”
Daniel laughed again. “That would be a trick. What card might Brutus pull from his sleeve? I’ll accept he’s clever enough at the game that he might.”
At that I left.
I crossed the Barefoot Square, to the Barefoot Church, and sat in the back corner I preferred. I even took off my shoes; it seemed right to do so. At times the light through the windows was straight as taut string, which reminded me of the weight of the whole city which the church held up. Where the light struck was lit, and where it did not, was not.
But other times, and this was one, the light was diffuse. It reflected and spread, seeping and merging until every spot was some mixture of glow and shadow. When I would see this, I wondered whether there was light and dark, or only lighter and darker.
Shod, and in the Square, I stopped at the Coal Arch. The rubble was cleared all away, and the good, formed stones of the old arch were piled to be repaired and replaced. I lifted one. They were all the same, the same size and the same shape, a proper trapezoid front to back, and square on the sides where the stones rested against each other. The stone in my hands was almost as much as I could lift. A good arch would stand by just friction. There’d been mortar between these stones, but not enough to hold the arch from falling. I wondered who’d finish the stonework. Then I wondered who would make a stone for Lithicus.
Tuesday evening I felt an odd chill in my room where I was writing. It was penetrating enough that I set down my quill, and once I had, my line of thought was broken.
To find it I stepped out of my house. It was twilight. As I seemed to always do in these recent weeks, I walked toward the Barefoot Square, and there, took a place in the door of the church. But the chill just wrapped me more and I shivered. I heard horses and wheels. The clatter seemed more real than the actual appearance of the coach from Freiberg. Rupert the driver, always grinning, brought the carriage to a hard stop at the door of the inn, almost against it, blocking it from my view. But I was hearing, not seeing, and I heard the coach door open and I heard black robes and black boots pass through the brief air into the inn.
Faint as it was, I even heard the fires’ greetings inside.
From the Barefoot Square I went on further. The chill was gone, replaced by a heat in the air like a fever. I followed through evening streets beneath the stars and past closed windows with lights like stars. In a while it led me to a garden beneath trees and a door that was closed but hospitable anyway. I knocked. It was soon answered.
“I’m sorry for the late call,” I said. “Might I speak with Magistrate Faulkner?”
“Come in,” I was requested, and I did. I didn’t wait long. I’d been in the room a few other times. Even in a great man’s house, in Basel the rooms are quiet and simple. But there were portraits on the wall and upholstered chairs and flowers.
“Leonhard?” Faulkner smiled and greeted me. He was in his black coat and breeches, as I was. But his black was the purest in Basel.
“Good evening, sir. When we met on the Wall, some days ago, you had asked me to come.”
“It’s Tuesday night, isn’t it.” His voice was like black ink on white paper. “Did you speak to him?”
“I only heard him get off the coach. I knew it was him. I didn’t see him.”
“I don’t doubt you.”
“Do you know why he is here, sir?” I asked.
“Yes, I do. Were you born in Basel, Leonhard?”
“Yes, sir. Though my father took me to Riehen soon after.”
“I remember when your father left the city. I hope someday he would return.”
“I don’t know if he ever will. He visits, of course.”
“Yes, he’s close. But outside. Basel is separate from Riehen and from everywhere else.” He was musing, and I’d never before known him to be indirect or to wander. “But the outside is very close. Riehen is close, and the Empire is close, and France is close.”
“Yes, sir,” I said, and stood. He opened the door for me.
“Thank you, Leonhard. He may leave on the morning coach, but he will soon return. Tell me what you see of him.”
“I will, sir.” So, then I understood the danger to Basel. At least, I understood what Magistrate Faulkner and Master Gottlieb believed was the danger to Basel. I’d already known the true danger, which they didn’t know.
Grandmother met me at my door and I knew at once I had a visitor. Her palms were pressed together as they had been when Daniel had come, but her expression was very different. Instead of that knot of disapproval, the cord was more a tangle of impropriety and aversion and surprise, all of them mild and polite as befitting her.
I entered the parlor and found a rotund guest, hat not on bald head but clenched in hand, a hand that usually clenched reins. Rupert the coach driver stood in the middle of the room, nodded his head, aware and unbothered that he was in a house above his own station. “Master Leonhard,” he said, “good evening,” and I nodded, too.
“Good evening, Rupert,” I said. “Welcome.”
“Thank you, sir. I do feel so. I’ll only take a short minute of your time, if you don’t mind.”
“Not at all. Go ahead.”
“I’ve only just taken the coach,” he said. “I’m not accustomed to your city yet, and its ways. I hope you’ll forgive my familiarity.” He didn’t seem at all uncertain.
“Of course.”
“Yes, sir. And as I’ve taken the coach, I’ve looked through it to know it, and what I’ve found I’m not sure what’s to be done with.”
“What have you found?”
“This, sir. It was in the post box.”
He handed me a letter which I had seen before. Daniel’s name was in the most beautiful script, covering much of the front, and the wax seal covering much of the back of the envelope had the Tsar’s own double Eagle. “And I’m not sure how long it’s been there.” I knew it couldn’t have been long, as I’d last seen it in Master Johann’s office only a week before.
“It was in the postbox?” I asked.
“There’s an edge to the box, you see, and a bit of a place a letter could be caught and hid.”
I handed it back to him. “Why did you bring it to me?”
“I asked Gustavus, the keeper at the inn, if the man was known in the city here, and he said he was.”
“He’s at the Inn under Gustavus’s own nose near every day.”
“Yes, sir, he has been shown to me. But there’s a saying, I’m told, to treat all that family with great care, and it might even go ill with the one who brings him a letter that’s been delayed such. It seems an important letter.”
“I think it is,” I said.
“And there’s another saying, that you’re a friend to most, sir, and you might hand it to him on my behalf and with my regrets.” And he held the letter back to me.
I stared at it. The story was implausible in every detail, but most of all in this last statement. If Rupert were to walk direct back to the Inn, Daniel would surely be there even at that moment, and Gustavus could hand the letter to him without any fear.
“All right,” I said. I took the letter. He bowed and smiled and I let him out.
I went to the kitchen where my grandmother was waiting. “He’s gone away,” I said.
“Was there anything he wanted?”
“He had a question for Daniel, but was told to be cautious of all Master Johann’s family, so he wanted some counsel first.”
“It’s not well to speak of a man behind his back to a stranger.”
“I only told him he had nothing to fear.” I thought that to tell her about the letter would only be a confusion should Nicolaus stop in again with questions. “And Grandmother. Master Johann said he’d write a letter to Paris for me. He’s accepted my proof. And now, I must write a letter to the Academy myself, to explain the proof.”
She was astonished as I’d been. I told her everything about it, and even Mistress Dorothea couldn’t have spoken as much in an hour.
I sat at my desk and took my pen and ink and poised myself for the words to come. For the moment, though, they did not. This would happen, though rarely, and I’d never found a solution for it but to wait.
So I stood and went to my dresser. I felt the curve of my bowls, and ran my finger through the conch’s spiral, and finally took my hat and tried a little to soothe it again into better shape, and to smooth out the marks of its crushing.
It seemed evident that the hat had been lodged in the arch after escaping Little Johann’s hand. The peculiarity of its return to me was remarkable, greatly.
I looked more closely at the marks on it. They made most of a square. The square was just the size of the stone I’d held that day in the Barefoot Square.
I held it to different angles, and close to my candle light. Then I saw that my hat’s journey had been even more astonishing than I’d realized.
It had been crushed between two arch stones, and not just in the falling of the arch. It had been placed between the stones.
And if it had only been the hat between the stone, and not any mortar, then the arch would have been weakened. When Lithicus had loosened some other stone close by, there would have been no friction where this hat had been.
The arch would have fallen because my hat had been set in it.
I still believed Little Johann’s word of how the hat had been accidentally lost. So the peculiarity remained, but it was not only remarkable. It was wicked. And it was a challenge. And there was an enemy.
I was staggered by it.
Though a restless sleep on my bed intervened, the next morning found me again in the door of the Barefoot Church. Willi didn’t know I was watching as he led the horses and carriage out into the Square and put piled baggage that had two black trunks into the rack, and neither did Rupert even know me at all as he came out of the inn with his face bright with firelight and conspired with Gustavus, who also knew nothing of my observing.
But Caiaphas knew I was there as the coach door was held for him and he climbed in, pausing and knowing and staring straight into the shadow that hid me. He seemed satisfied that I was there.
The carriage crossed the Square to the Coal Gate and I felt pulled after it. When it was gone I was somehow out in the middle of the Square. I crossed on to the Boot and Thorn and looked in. There was a yellow light from a lantern down the hall and from the Common Room the red fire glare was both intense and dim. I stood looking in. It was empty, I thought, but then on a near table was a bundle, the size of a footstool. I looked at it closely. It was rectangular like a small trunk, wrapped in heavy cloth, and tied with string.
“That is for you,” Gustavus said. Of course he was there, also.
“What is it?”
“Take it.”
“Is it to be returned?”
“Tomorrow evening it is to be returned.”
The parcel was heavy as wood for its size but not solid. Its shape shifted in my hands as I struggled home with it. So I knew what it was, and I feared what it might be. I left it on my desk as I did my grandmother’s chores, then Mistress Dorothea’s chores.
I finished in Mistress Dorothea’s kitchen, under the eye of Little Johann with his bread dough. “This is a big house,” I said. “How well do you know it?”
“I know it,” he said.
“Do you know its hiding places?”
“I know them.”
“There’s one I want to see, if I can. It would hold a good-sized box, so big.” I measured for him with my hands, that size of a footstool.
“I only know where they are. I don’t know what’s in them or how big they are.”
“Could you see if any are empty?”
“I never look in them. I only know where they are.”
“I think one has been newly emptied,” I said.
“I’ll find which one,” he said.
And back in my room, the package was still there as I dressed, and when I left at nine thirty for the University.
Several hundreds could sit in the University lecture hall. It was filled, and more. The Professors and Deans and Officials I’d called on the day before were seated uncrowded in the front, attending each other as peers and familiars. Upward and back the lesser in rank grew greater in density. It was all very black, with wigs and collars of white, and the scarlet, azure, and other brilliant stripes on the robes of the chief birds were brighter for their contrast.
And the room was mighty. It wasn’t somber and accusatory, as the Town Council Chamber was; Master Holbein never set foot here. It wasn’t similar to any church, lofty and plain like the Barefoot Church, or grand and heavy like the Munster, or beautiful like close-by Saint Martins; no friars or almsgivers had ordained it. It was secular to itself and holy to itself, not of the Boot and Thorny earth or the Barefoot heaven. It was something in between.
Beside me was Daniel, and beside him was Nicolaus, and even Little Johann was crowded in. But not Mistress Dorothea, of course, for no woman has ever passed the portal of learning into that room. Daniel was in a froth, gibbering, then stony, then mopping sweat. It seemed hardly a reasonable time to mention to him the letter for him I now had.
“I know the nomination will come,” he said. “It’s certain. Certain, at least.”
“You’re certain?” Nicolaus asked. It might have meant that Daniel was certain of the conclusion, or that the conclusion was certain for Daniel.
“I’m certain,” Daniel said.
The Provost was seated at the front, between Deans, talking with Theology and Law. He noticed me, in the midreaches, and nodded. It was my payment for being his courier. The three committees were also represented by their leaders. Master Johann alone wasn’t leaning to his neighbor and whispering, and nodding. The bell in the Munster rang and it was time to begin.
Some things were ritual and some were not. The convening of the University was. The announcement of its candidates was not. The dignity of so many Chairs in one room made the occasion momentous, but the moment was brief. “Gentlemen!” the Provost said and the room quickly was silent. “The report of the committees appointed to nominate candidates for the vacant Chair of Physics. Master Gottlieb?”
Daniel went rigid. But I heard words escaping from his clenched teeth.
“The Brute’s outdone this time. He’ll have a taste of what it’s like. There’s no chance he’s got around me now. If only I could see his face . . .”
Gottlieb said, “We nominate Master Staehelin.”
Daniel shuddered. “What? No. Not him!” A quiet storm of murmurings rose immediately, approving and unexcited. Master Staehelin had been the lecturer in Physics for a decade and was a very competent scientist. He seemed an obvious candidate. Daniel’s reaction was mixed of contempt and suspicion. “That’s no surprise. He’s a plain choice.”
“He’s a good choice,” I said. “I’ve heard him lecture. He’s able and he’s diligent.”
“He’s a distraction, a trick. Brutus has higher plans for Physics than a plain, diligent lecturer.” Daniel was speaking to himself. “He needs two other nominees besides the man he’s picked for the Chair. That’s all Staehelin is.”
Staehelin himself had turned white. He was across the room from us in about the same row. He was a plain man, as Daniel said, about forty and probably not with the ambition to expect a Chair. But he’d take it, of course. His white turned to red and his dropped open mouth turned to a grin, and hands near him reached, discretely, to shake his. Daniel might have been right, that his candidature was only a ploy, but seeing his surprise and gratitude, I hoped for him that he’d be successful.
He made his way to the front of the room, and it was a slow journey across his row to the aisle and down the steps. He was obviously still surprised, even to stumbling as he reached the front. Then he waited, for the Provost was unlocking the casket.
Around his neck, on a long and thin but sturdy chain, the Provost had the key. The casket, resting quietly on the lectern, was a foot long, and less wide and tall, and pure black. The keyhole was the only mark on it; even the hinges were inside and unseen. The key was small, about an inch, and solid. I could tell from its weight on the chain, and how the Provost held it, that it was heavy for being small. It went into the hole and turned with effort. The lid was opened.
From the casket, the Provost lifted a wood tray.
“Master Staehelin?” the Provost said. “Please choose a stone.”
He looked at the offered tray. On it were the seven stones, each with its emblem. It didn’t seem that there was anything important to him in his choice, which the Ars Conjectandi, of course, said there was not. Each would be equal. He took the center.
“This one,” he said, hoarsely.
“Master Staehelin has chosen the Tree,” the Provost said. Also on the tray were three blank stones of the same sizes. He took one of these in one hand and the chosen stone from Staehelin in his other hand. Heidelmann, the Provost’s student clerk, had a bar of sealing wax and a candle, and he held them over the two stones, dripping wax on them both. The Provost pushed them together and they became a sealed cube. The wax was held entirely within the carving of the emblem and none extruded to the outside, so the cube was perfect and without blemish.
The Provost set the cube into the black casket. Staehelin clambered back to his seat. The Provost waited. Then he said, “Master Desiderius?”
“Maybe it’s Desiderius you’re waiting for,” Nicolaus said.
“No,” Daniel said. “It must be the Brute himself! Oh, that’ll be everything!”
We only saw Master Desiderius’s back. Master Johann’s face was also forward and unseen to us. Desiderius stood and just said, in a voice that was dry and carved in stone, “We have nominated Master Daniel.”
Too much happened at that for me to see it all. Of course Daniel popped like a squeezed melon. I felt him beside me. But I also tried to see any expression from his father, any motion from his shoulders or back. He did react, with a slight but sudden lean and twist of his head, like he was having trouble hearing. Or maybe it was something else. But he didn’t turn.
“So that’s what? That’s what!” Daniel said.
Then Desiderius did turn to look up at us. There was something in his expression as he looked to Daniel that seemed resignation, or worse. I don’t think Daniel even noticed, as his eyes at that moment were fixed on his father. Nicolaus stared quietly at his brother for a few seconds, then looked away. And Little Johann seemed pleased and proud.
The rest of the room reacted far more wildly than it had for Staehelin. Daniel was spice to any dish he was mixed with. Especially the older students who knew him better knew that. I shook his hand. “I know you deserve it,” I said. “You’d be an honor to the Chair.” I meant it strongly. Despite his machinations and cunning, he would be. “Go on, go choose your lot.”
He almost couldn’t stand. All his anticipation and anxiety had finally met their goal, and it was as if he had nothing left. But he did stand, and as he descended the steps his spirit ascended until he was at the front, toe to toe with his father.
Master Johann’s back was still to me. Daniel looked down on his father, and the most unfathomable expression crossed his face, between triumph and longing, and joy and grief. For an instant Johann looked back, also impenetrably, but there was at least no defeat or regret that I could see.
“If you please, Master Daniel,” the Provost said peaceably.
Daniel glanced over the stones, then delicately lifted one and handed it to the Provost. He seemed to have considered the meaning of the emblem.
“Master Daniel has chosen the Throne.”
For the second time Heidelmann performed his duty. Daniel was transfixed watching his chosen stone merge into the indiscernible cube. After one more glance at his father, and this glance also had suspicion in it, and doubt, he returned to his place beside me.
“It’s there,” Daniel said.
“And it was there for Logic two years ago,” Nicolaus said.
“But there’s a difference,” Daniel answered.
“Master Johann,” the Provost said.
“Thank you.” He stood. This was really his first motion since he’d sat, and his first words.
“This is the clever part, now,” Daniel said. “So Brutus isn’t worried? We’ll see him play his hand now. This will be the foreign candidate. What’s the trick going to be?”
And Master Johann said, gravely, “The committee nominates Master Leonhard.”
I didn’t know who it was. I’d have thought I would have heard of the man.
“It’s you,” Nicolaus said. I felt something at my hand, and I saw he was shaking it.
I looked down at the stage at Master Johann, and saw that he was also intent on me, and also the Provost and Deans. And then I knew it.
It seemed someone else, not me, who walked the steps down to the lectern. That person was greeted by the esteemed men there and returned their nods and handshakes. It was even that man who graciously and sincerely thanked Master Johann. But then, when the tray of five stones was offered, then, it was me. My question of Lithicus was answered as I saw the emblems he’d carved. The five that remained were a sun, a candle, a lamb, a raindrop, and a fish. It was my hand and no one else’s that chose the symbol and handed it to the Provost.
“Master Leonhard has chosen the Candle.” He accepted my choice pleasantly, and the wax was melted and the stone was placed into the casket with the other two.
Then the casket was locked and set on the lectern, where it was to remain until it was opened again.