14
The Sealed Stones

I was hauled off to the Boot and Thorn. I’d meant to leave quiet and get home but the forces were too great. The mass of my fellows, students I knew and had lectures with, manhandled me through the streets and into the Common Room. I’d have sooner settled in at the other side of the Square. Staehelin was brought, too. He wasn’t pulled as hard by the students but he was a bachelor with no family at home, so he didn’t resist, either. And Daniel took no pulling or hauling at all; he was the motive force.

The room was uncommon raucous. I was toasted and celebrated, though Daniel was given far more acclaim. And I was a leaf in the wind, in a narrow street of hard walls. I couldn’t tell if I or anyone was surprised. Only the tankards on the shelves seemed to be thoughtful at it, staring in every direction to see what it might all mean. And the oddest was that Charon the cat settled into my lap and purred. His weight alone was too great for me to stand or leave.

All things must end, though. All things human, at least. The room thinned and the smoke thickened. It was after two o’clock, hours since the casket had been closed with my stone in it. But Charon still held me prisoner.

Then Daniel was with me. The melee of the celebration had swept him past several times but we hadn’t talked. Now he was ready to speak. He sat across the table, deliberately, and I saw that, for all the jubilance in his laughs and grins, there was a calculation in his stare that contradicted all his jollity. He took a breath and his firm set jaw and bright eyes were like a duelist examining his opponent.

“Then Leonhard,” he said. “I should have known. That’s all right. We’ll have the best man win, then?”

“The best lot chosen,” I said. “I hope it’s yours.”

“I’ll see that it is. The best man will win.”

“Of us two, you’re the best. That won’t help with choice of the stone.”

“I don’t mean the best between us,” he said. “It’s the best between Brutus and me. That’s the game.”

“What do you mean, Daniel? You’ve said this over and over. What is it, really? Explain this plot that your father has, and how you’ll beat it, and what the game even is.”

He had a cup of dice in his hand, still there from some other table. “What’s your reason for asking?” he asked. He rolled the cup around and around and the dice tumbled inside it.

“I’d like to know. All this you have been saying for days!”

He shook his head. “No, that’s not the right answer. There are two reasons you might ask, and that’s what you’d say either way.”

“What reason would I have beside that you’re maddening with all your hints and threats?”

“What other reason? I’ll tell you. That you’re in the game, too, and wanting to know my next play.”

“What game, Daniel?”

“Take care, friend. Be a piece on the board, and defeat is only a disappointment. Make yourself a player, though, and the stakes are higher.”

“The stakes are to have the Chair, or to not,” I said firmly, not driven quite to anger. “The game is just chance, one chance in three. That’s all.”

“I’ll let you think that, if you really do. But I’ll give you this, Leonhard. If Brutus is under force to give the Chair to one particular man, and he doesn’t want to, what’s his move? He puts up another who might put the first out of the way. But how could that be done? That’s the question.”

“What force, anyway?” I said. “That’s my question.”

He only shook his head. “And,” he said, “to make that other glitter, he sends letters extolling him to Paris! He says he will, anyway. That’s all he needs to do to get you past his committee. I wonder if he’ll waste the paper and ink. He’s even stingier with his reputation, to spend it on recommendations.”

“Daniel.” They were harsh words. “The day has overwhelmed you.” Indeed, it had. His color was pale and his breath short.

“Your proof, though, that’s the nut of it. That’s elegant. Where did it come from, Leonhard?”

“Not from anyone.”

“It came at an opportune time. Almost as if it was for the moment of the Election. It certainly put you in the thick, didn’t it.”

“Daniel, I forgive you for what you’ve said about your father, and about me, and everyone else. You’re conquered by the day and your nerves. Go home, have some food that’s more wholesome than what you’ve had here, then sleep, and find your senses.”

“You’re a good man,” he said and laughed. “I’ll do that. I’m raving and you’re gracious in return.”

It was well into the afternoon. We left together and parted in the Square. I still had the letter from Russia in my pocket, but it still didn’t seem a right time to give it to him.

Grandmother was in the kitchen, sitting at the table, which I saw was set for lunch. Soup was in a pot hung near the fire, and bread with butter was on the sideboard; they were covered with a white cloth, but I knew what they were.

“I’m sorry to be late,” I said. “I didn’t mean to be taken to the inn.”

“Be taken?” she asked.

I corrected myself. “I didn’t mean to go to the inn. But they wanted me and I went.”

“You had reason to be with friends.” That meant she knew, though of course she would have known. I expected that.

“I wanted to come here first,” I said, and though she knew, I still had to say it. “I’ve been nominated, Grandmother. For the Chair in Physics.”

“That’s well done, Leonhard. I’m very pleased for you.”

“Thank you. And Master Johann nominated me.”

“He would only nominate a candidate he thought highly of.”

“And Daniel’s also a candidate. It’s he who should win.”

“It’s in God’s hands.”

“I hope so much that it is.”

We talked awhile more. She said nothing condemning or accusatory; I felt those myself and wasn’t sure why. But as I was there in her kitchen and she served the soup and bread, the smoke of the Common Room dwindled. I finally began to feel a good joy and a decent pleasure. I’d been nominated for a prestigious Chair by a committee of intelligent and accomplished men. Knowing that I didn’t deserve the honor let me more freely accept their knowledge that I did.

“Are you able enough for this Chair?” she asked.

“It would be prideful to say yes.”

“Would it be pride or truth?”

This was the difficult question. “I would learn, and work very hard, and I would become able.”

“Do you want this Chair?”

This was the more difficult question. “It would be a wondrous life, I think. To devote my time and effort to writing, and reading, and thinking, and teaching.”

“That would be a noble life.”

“And devoted to God, too,” I said. “All devotion is to God. I think it would be a way to serve.” She’d always had a keen sense of my heart, more than I did. She must have known whether I was truthful in my humility. I didn’t know.

“And all three candidates were from Basel?”

“It was Daniel who was the foreign candidate. They decided he was coming from Padua.”

“Which symbol did you choose?” she asked.

“The symbols were the seven days of creation. A candle for light, a raindrop for the separation of waters, a tree for living plants, a sun for the lights of heaven, a fish for creatures of the sea and air, a lamb for the beasts of the field, and a throne for God at rest. At the first of creation God created the laws to govern the rest. So I chose the light.”

“That was a wise choice,” she said.

“I’ll need greater wisdom than that,” I said. “I’ll go to my room now and think. I need to think.”

Was anything still in the storm? When waves were taller than mountains and ships in them were leaves and splinters? My thoughts were raindrops in a gale. And on my desk was the package Gustavus had given me. It was a rocky island that might be a haven or might shipwreck me.

I opened the wrapping and it was just as I’d known, Master Jacob’s papers. I’d never seen the handwriting but I knew the words, even from the first sentence. There were a dozen sheaves, each tied with ribbon, each a hundred or so sheets. I untied one and sifted through it. Near the top was a careful sketch of a Logarithmic spiral.

I studied it awhile. I felt drawn to it, as if this was the first step I was to take into those many pages. Then I saw a description beneath it, in the same Latin that filled all the sheets.

“The Logarithmic Spiral may be used as a symbol, either of fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self.”

When I’d accepted that as the premise of all the writing, I began to read.

It would have been impossible to read every word in one afternoon and evening. It wasn’t necessary. Many pages I immediately knew from the Ars Conjectandi. Others I knew from Master Johann’s lectures, though the comparison of what in my room I was reading and what in lectures I’d heard seemed to draw an edge between what the two brothers each knew himself and what each had learned from the other.

There were other pages that I recognized from a score of books, most by men I knew had corresponded with Jacob. There were his solutions to the brachistochrone and tautochrone, and even his attempt of the Reciprocal Squares. As I read, more and faster, there were only a few pages I’d never seen before.

Then also, there were the letters he’d received. The pages were without envelopes, all smoothed flat like the other papers. On many, only the signature showed who’d written them. These I would have studied carefully, but I saw that many were questions and comments on his own work. Few of his correspondents had had greater understanding than Jacob himself.

Finally I heard Saint Leonhard’s bell strike six and I realized I was hungry for supper. I stretched and went down to the kitchen but the room was empty, the table clear, and the fire nearly spent. Then I saw there was no light in the window, and then I saw the sky was gray, but in the east.

So, it was time not for evening meal but for morning chores. And when I reached the Barefoot Square to draw water, the fountain was low and slow filling. The dry days had taken a hard toll on the Birsig.

I was weary as I approached my Master’s house. But that was no excuse. I had work to do.

Mistress Dorothea’s most amazing quality of her speech, even more than its quantity, was that she never spoke ill of anyone. She spoke truth, which was a close neighbor, but never spite. And there was wisdom in what she said, if a listener was willing to pick through the wide field for the single blade among the grass.

Her words were spilling out the kitchen door when I reached it. She was discoursing to her girl about the morning’s eggs and the dry weather and cabbages in the market and her cousin’s gout. It took effort to open the door against the stream. But when she saw me she paused a long pause. And then she just said, “You’ll still do kitchen work, Leonhard?”

“I will,” I said. “And I hope to always.” It wasn’t only kitchen work, though, that I had to do.

“I’ve no allowance to spare for a man who’s a Chair,” she answered. “There’s one already in this house.” But she said it graciously.

“I want no allowance, and I’m not yet a Chair. It’s twice as like as not that I’ll still be a poor student a week from now.”

She approved. “You’re a credit to your father and mother, and to your grandmother.” And that was more praise than I deserved.

I set to work as hard as I could and kept my jaw as firm as I could against yawning. And when I finished, as I’d known he would be, Little Johann was waiting.

“You’re near to be a Chair,” he said.

“Near’s not in,” I said. “And I’d rather Daniel had it. I have a question.”

He knew, and he nodded. “Come and I’ll show you,” he said. But reluctantly.

He led me out the back door, which seemed strange; but then he went immediately to the cellar door, and I understood. The top of this door was set against the back of the house, and its base, though angled up and out, was still beneath the level of the ground. Two steps led down to it. It was kept locked, and the key was in on Mistress Dorothea’s key ring, but Little Johann had already asked for it and had it in his hand. So, like mice, down we went into the foundation of the house.

It was dark and cool and moist, which was its purpose. We took no candle, as the morning light came plenty in the door. It wasn’t a large room, only the space beneath the kitchen. I’d been there many times. There were old tools and kitchen ware, useless enough that they wouldn’t be missed, but useful enough to not yet discard. Some meat was kept, though not much. Mostly the room was piled with root vegetables in wood bins. And even in the dark, I could see what Little Johann had to show me: one of the bins had been pulled out and pushed back in place. The tracks in the earth floor were obvious.

“I’ll pull it out,” I said. Little Johann said nothing.

I moved the bin forward. It wasn’t heavy. Behind it was the foundation wall. It was easy enough to find that one large stone was loose, and was only a thin flagstone fit in place. It would have been hard to find if I hadn’t been led to it.

“Have you ever looked in it?” I asked. He shook his head, no.

I lifted the stone away and behind it was a niche, about sixteen inches high and deep, by twenty-four wide. I put the stone back in place. It was shaped perfectly and showed no sign of the space behind it.

It was skilled stonemasonry that had made that hiding place.

Back in the kitchen, just us two, Little Johann was still anxious.

“Are you bothered that you’ve shown a secret?” I asked, and he nodded. “I’m sorry. But I think I know what was in that place. I’ll never tell anyone what I’ve seen, ever.”

I was still weary but there was no use to sleep. The mountain on my desk was not nearly climbed.

What I’d read, hundreds of pages and scores of letters, had all been of Mathematics. Most I knew. Most I recognized, and of most I knew how they had travelled from those pages to others’ book and articles. A few pages were new, though not profound.

Before I started again, I tried a different sieve. On a page of my own, I began a catalog of my own Master’s writing that was not just a reflection of his brother’s. It was a long list. Master Johann’s discoveries were at least as great and numerous as Master Jacob’s. Oh, what would their sum have been if they had partnered, not just in Johann’s early years, but on, into his tenure in Holland! Yet they’d been enemies by then. And if Jacob had lived longer; if he’d still held the Chair of Mathematics while Johann had been Greek. That would have taken a humble man, but the two together in Basel, cooperating, sharpening, consorting . . .

But Jacob, already estranged from Johann, had died before they laid eyes. Or within a day after: Which had it been?

One package was left of all Jacob’s papers, and I turned to it.

It was the first I’d seen, topped by the spiral, and by other indications appeared to be the last. The other reams had been in order by subject, more or less, but this was from just one period, the final year of his life. So I steadied myself and started reading.

The Mathematics of the later pages was mostly the same. There was less new and more repetition of the earlier work, though purer. That one ream of paper might almost have replaced all the others. It was the elegant restatement of the rest.

But there were notes and whole pages that went beyond the Mathematics, and these arrested my quick reading. In his last months, Jacob had bared his soul.

He’d written of his disputes with Newton and the English. He listed his enemies, which was a long list, and his friends, which was short.

He’d written of his weakness and age. There were several pages of his plans to confront his brother when they met. And he feared the meeting. He knew that Johann was a stronger, more forceful opponent.

The last pages were in a hand that was still his but crabbed and shaken. He knew he was dying. He’d written that Gottlieb was with him, and he’d given him instruction to keep his papers from Johann.

Finally I came to the last page, which was the first sheet I’d seen, with the spiral, and Resurgo Eadem Mutata. On its back were his last notes, nearly illegible. I read them, then again as their importance struck me, then again and again. This last sheet I took out from the others and set on my dresser to keep.

Thursday afternoon, very weary, I greeted Charon the cat and asked him to find his Master. And when Gustavus came to me in the Common Room, I only had enough strength to hand him the wrapped bundle of pages and stumble back toward the door to the Square.

But he stopped me.

“There is payment due for these.”

“Who wants it?” I said.

“You’ll be called for it.”

“Why were these pages given to me? Who told you to put them in my hands?”

“You must know, Master.”

I nodded. “Yes, I know.”

The Barefoot Church was at peace that evening, as it most often was, whatever raged outside it. It was as separate from Basel as Basel was from its own outside. But Basel was Basel only with the church. I sat long enough on the bench to see the cast light move across the floor from side to front, and sanctify the altar, and rise. The air was moist. Even the world’s drought seemed stopped at the church door.

Fortified, I entered the Barefoot Square which seemed, more than it most often was, to be a bridge between two sides. I felt the invisible chasm that it crossed and heard roaring depths beneath me. Part way across I saw both Daniel and Nicolaus enter the Boot and Thorn. As I came to the door of the inn, the coach from Bern arrived.

Rupert brought the horses to their stop at the door, and one passenger, from the look of him perhaps a new student, emerged with shudders and relief and backward glances. A medium trunk was lowered to the ground for him but two other trunks, heavy and black, were left in the rack. Willi had come out, but Rupert kept the reins and led the horses and coach, all still harnessed, into the stables tunnel and out of the Square.

I looked into the Common Room, but neither Daniel nor Nicolaus was there.

As I had before, I called on Magistrate Faulkner later than was polite. He answered the door himself and took me into the parlor and had me sit beside him.

“I can only tell you that he was in the coach from Bern,” I said.

“I knew he would be.”

“Then I shouldn’t take more of your time.”

“I will take your time, Leonhard.”

I suddenly thought of Jacob’s papers and wondered if I was to be asked for my payment. “Yes, sir?”

But not. “You are a candidate now for the Physics Chair.” A lion would regard its cub with mercy but its prey with none, and each knew which it was. But I wasn’t sure.

“I am, sir, yes.”

“The University is a power in Basel. You may attain an authority you aren’t expecting.”

“If I am chosen—”

“Or, if you are not. I will not yield my own prerogatives in either case.”

“And I would ever yield to you! Magistrate Faulkner, it’s a terrible thought to me that I would consider a challenge to anyone of your position, or at all to you. I—”

“You may have no choice.” He sighed. “But, nor may I. What will come, will come.”

I paused, thinking very hard, and he waited.

“Sir,” I said.

“Yes, Leonhard?”

“I understand what Master Gottllieb meant was the danger to Basel.”

“Then you also understand why Magistrate Caiaphas is here and why this Election is important to him.”

“Yes, sir. But . . .” And I wasn’t sure how I was regarding him. “I will do what I must do. Because it is more than just Basel.”

He didn’t understand. He frowned, and I didn’t know if he was disturbed or disappointed. He nodded and we stood, and I left.

At home Grandmother had supper for me. I hadn’t seen her in the morning, or the evening before. We didn’t speak much, but I saw that neither had she slept the night before.

I was so, so tired! Yet I still had more to do. I took my black cloak from its hook in the closet and wrapped it on.

“Is the night cold?” Grandmother asked. She knew it wasn’t.

“No, but I’ll wear it.”

I went out. It was nights like this one when I saw so many things in the streets. Slow, heavy, unshod footsteps were behind every corner. The shadows of strange beasts were ahead of every turn. I wondered, when I was invisible, would invisible things more easily see me? But I didn’t have far to go. I came to my Master’s house, in the back alley. I chose the very darkest place. Then I stood and waited.

I didn’t know how long I’d wait.

I didn’t know how long I did wait.

Finally the back door of the house opened and Master Johann came out with a small, dim candle. He went to the cellar door and opened it, and set the candle on the steps. Then he went back up into the house.

Just a moment later he came out again, with a heavy bag in both hands. I couldn’t see just what size it was. He went down the steps into the cellar and another moment later took the candle in with him and shut the door.

I waited, not long.

The cellar door opened and he came out with just the candle. He closed and locked the door and went back into his house. I heard the bolt on that door turn.

And then, I could finally be done with the day. I went home and to my room and threw myself into the bed.

Water, water. It had not been long since the last rain, but all Basel seemed to be drying out. The fountains were all pinched. The streets were lethargic and filled with dust.

Yet the fountains still brought out their stream, reduced but valiant. I filled my buckets, and as always on Fridays the coach’s preparation for departure was a performance for me to watch. I did watch and I saw no black, cloaked passengers.

I would always hurry through my chores. Time was far too valuable to waste. Yet I paused there in the Barefoot Square for twice or three times the minutes it would usually take to get my water and leave. And finally, with the gray dawn light just at its last edge with morning, I saw a tall young man, black cloaked and crowned with wig and tricorne, slip quietly into the inn.

I lifted my buckets but only carried them as far as the inn’s Common Room window. Then I stood still again. It was dark looking in and I didn’t try. I didn’t want to be seen through the window anyway.

A property of the morning air was that it would often be very still. The Riehen church bell would sound as close as Saint Leonhard’s. The Rhine’s murmuring was like the streets speaking. I waited and finally I heard the voices I knew I would.

“Why will you not come to my room?” which was Magistrate Caiaphas. “This is a poor place to talk.”

“Negotiations must be neutral,” which was Nicolaus. “Not in father’s room, and not in yours.”

“It’s no negotiation. It’s only a message. What is the message?”

“That it’s been done.”

“That’s what I want.”

“Do you have a reply?” Nicolaus asked.

“There’s no reply.”

“There is a second message.”

“What message?” Caiaphas’s voice was suspicious.

“That there be a different choice.”

“What use would that be to me?” He was speaking quietly, but there was no difficulty hearing him. Something was torn with every word. “My reply is, I’ll have the choice I’ve made and the bargain I’ve made, and it’s no matter to me that he detests it. Give him that reply.” It was a challenge, not a refusal.

“There is a third message, then.”

“Then tell me the third message.” Caiaphas was intrigued, and even pleased, as if he’d expected it.

“That it will be to your profit.”

“That’s the message?”

“That’s all of it. There are no other messages.”

“My profit? That’s no matter to him! He’d care more for a gnat than he’d care that I’d profit.”

“But he says, that it will be to your profit.”

“Then take this reply. I’ll account to myself what’s to my own profit and what isn’t.”

Nicolaus was silent, then, as he always was when he had more to hear. And Caiaphas finally said, “I will account which is to my profit. Make that the reply. And I’ll tell him if I account any difference.”

“I’ll tell him.” But Nicolaus stayed, and still waited. He would wait when he knew there was something else to be said, and he waited, and it became impossible for it not to be said.

“I know the choice he wants,” Caiaphas said, “and I have already begun that accounting.”

“Good day, then,” Nicolaus said, and stood.

I was gone out from the Square before anyone else came out into it.

I hurried through every chore my grandmother had for me, and then all that Mistress Dorothea had. But as I finished there, I was thinking all the more of the papers I’d read of Master Jacob, and I said to her, “Mistress.”

“Yes, Leonhard?”

“I want to tell you that I have seen repentance.”

She stopped to give me close attention. Then she said, “Thank you.”

Then I heard Daniel’s laugh in the hall as he was coming toward the kitchen. I didn’t want to talk with him. As I had already done once that morning, I left before I was seen.

That Friday ran long and hard. I had my lecture to write but I held myself away from it. I had my letter to Paris to write, but I restrained from that, also.

Instead I gave time to thought. I sat in the Barefoot Church from before noon to long after sunset.

At home, at night, no book on my shelf seemed fit for reading. I put myself in my bed and eventually slept.

The quality of early light was thin, clean, sinless, and Adam-like innocent. I’d seen many dawns. The gray and the quiet were one mixed thing and I walked the morning like an ash mote floating from a fire; we were only ashes. Or like a raindrop in the river, traveler on the road and part of it. I came in solitude through air like water to the Barefoot Square and filled my pails with water clear as air. Then I set them by the door and went in to the Boot and Thorn.

The Common Room was empty but for Charon the cat half sleeping on a shelf of tankards, who were all half sleeping, as well. I sat at a table to think and wait. A very thin pall from the near dormant hearth and even from the last night’s candles just turned the air from pure to impure, though the difference was so fine. I knew I wasn’t undetected though I’d been silent. A few of the tankards were alert enough to call their Master. And in only a minute there was a tread in the hall and shadow in the door. Old Gustavus looked in on me. The only light was from the windows, and it was absorbed in vacant space before it reached the far wall. Gustavus watched in silence. Then he came closer.

“How can I serve you, young Master?” I was in black and white, as fine as I could make them without my grandmother’s touch. And they were fine enough. The ambivalence I’d kept was lost and I would only wear brown a few more times. It was strange that it was with Gustavus that the change seemed most significant.

“May I ask about a day twenty years ago?”

“Twenty years. Yes.”

“The day that my Master Johann returned to Basel. Do you remember?”

“Yes. I remember.” His arms were folded and he waited for me. I’d never seen him impatient. I thought his servants were too afraid to have ever kept him waiting. And for all his strength and fearsomeness, he was always greatly respectful to his customers. But this was a different waiting, as if he were in a place he knew I would come to, and he had been waiting for me to arrive.

“Was it Knipper driving?”

“There was no driver but Knipper.”

“Do you remember,” I asked, “the day ten years before that, when Master Johann left Basel for Holland?”

“Yes. I remember.”

“Was that also Knipper?”

“There was no driver but Knipper.”

I didn’t doubt that he remembered, but I wanted assurance. “What time of year was it?”

“It was an April day. The coach left in a thunderstorm.”

“And the day they returned?”

“In August, and also in a storm.”

“It was near the day that Master Jacob died.”

“It was that day,” Gustavus said.

“The day itself?”

“It was that day.”

“Gustavus,” I said, “do you know how Master Jacob died?”

“I know all of how he died.”

“I guess that he was ill.”

“He was.”

“And he died of his illness.”

“He did.”

“Was Black Death his illness?”

For every question I’d asked, he’d only paused a moment to answer. Again, with his dark eyes intent on me, he answered immediately. “His family has held that as secret.”

“It was Black Death,” I said. “I know it was. And he died before Master Johann arrived? By hours? By minutes?”

Gustavas didn’t answer. He was just still and intent on me, as if he was measuring.

“Why did you come here, Master?” he asked me.

“Master Johann took the Chair of Mathematics after Jacob died,” I said.

“He did.”

“Daniel wants the Chair of Physics.”

“He does.” It was unusual for an innkeeper to admit to knowledge of University affairs or a gentleman’s desires.

“Master Johann stayed four weeks in Strasbourg on his travel to Basel. Did he send any messages while he was stopped there?”

“He sent messages.”

“Did Magistrate Caiaphas send any messages?”

“Why did you come here, Master?” he asked me again.

“Master Gottlieb was also in Strasbourg with Master Johann, though he didn’t stay as long. He came back a week earlier. And Master Desiderius came here from Strasbourg.”

“There has been coming and going between the cities for many years. The coach has been well used.”

“I’d like to speak with Magistrate Caiaphas,” I said. “I’ll come back tonight.”

“And you are welcome to come any time, Master.”

“Please tell him it will be the same conversation he had with those other gentlemen.”

“I will tell him you wish to speak with him.”

The light was still clean and innocent, and, it seemed, pure, though that was always hard to tell.

“Leonhard,” Grandmother said, even as I came in the door. “Where have you been?”

“Just walking,” I said. “It’s very dry. There hasn’t been rain.”

“You’re dressed fine.”

“It seemed proper for the early morning. The morning light was very clear.”

“Stay in it,” she said. “Stay out of the shadow.”

“But I’ll change now for my chores.”

I did my chores, though perhaps not well. Then I had a hard time reading, like pouring water into an overfull barrel. It seemed that three o’clock would never come.

Mistress Dorothea’s speech was so continuous that her silence was inscrutable. In its shadow I followed up her stairs. I saw her looking at me with eyes very narrow.

“Why did he do it?” I said, and it was like thunderbolts thrown.

“Just ask him, Leonhard.”

That was all I could muster and that was the only answer she could have made, and the worst. She knocked on his door. The “Enter” following was deeper and from deeper. The room was larger and darker and the candle on the table was far, far away and the journey to it was eternal.

Before I’d even sat, he began our lesson, and it was as if nothing had happened in all the last weeks. “Consider a simple quadratic,” Master Johann said. “But one having no intersection with the horizontal axis.”

“Yes, Master.”

“Does it have roots?”

We have discussed this before. “I believe that it does.”

“Even with no intersection?”

“They aren’t seen.” Then I knew that perhaps he was answering.

“An unseen number? Describe it to me.”

“The principle,” I said, “is that negative numbers might have square roots. If a positive number is multiplied by itself, the result is positive. If a negative number is multiplied by itself, the result is also positive. So, the root of a negative is neither positive or negative. It is something else. So it is unseen. I’ve read about these numbers since we talked about them before.”

“What did Monsieur Descartes say about such numbers?”

“He derided them and called them imaginary. He considered them foolish. But he did concede they might exist.”

“Why foolish?”

“Real numbers can be seen and counted with real objects. He said that imaginary numbers can’t be counted. There was no use for them.”

“Does that make something foolish, if it can’t be seen?”

“No, Master,” I said. “There are many things that can’t be seen, and they are more real than what can be seen. Numbers don’t need usefulness to exist. They exist on their own whether anything seen ever reaches their count or not.”

We talked longer, not about theorems or proofs, not solving problems. We didn’t write, we only talked. He questioned me, and I him, on meanings and reasons.

And at the end, after a Saturday afternoon unlike any I’d ever had, I paused and gathered my thoughts. “Master Johann, thank you for your nomination.”

“It was the committee’s nomination. Each of the members approved.”

“I don’t believe that I could be qualified.”

“You don’t believe that?”

I had to pause again. “I believe that I will become so. But Master Daniel and Master Staehelin both are, already.”

“The Chair is both for now and for the time to come.”

He gave me no exercises for the next week. When I came home, I could only tell my grandmother that we’d talked, and I wanted very much to study Mathematics for my whole life.