7
The Outer Wall
They’ve buried him already,” I told Grandmother. Lunch waited on our kitchen table but I wouldn’t eat it. “It was to get him away, out of the Walls. They don’t want it to spread. They carried him straight out from the Council Room.”
“What did each one in the room do?” she asked.
“There was fear,” I said. “Like smoke and it hid everything. The mayor called the Watch to take him out, and Gustavus went with them. Everyone was frightened, and Daniel most. And Master Johann only sat and watched. He was still there when I left. Mistress Dorothea hurried Little Johann out, but then she was back right away. Nicolaus wasn’t scared, but he left quickly. I didn’t see him go.”
“And Caiaphas?”
“He just stood and walked out as if it was nothing, but kept his gendarme close with him.”
“What did you do, Leonhard?”
“And now?”
I still was.
Later I went out of the city, looking for respite. Huldrych was old and to my discredit, I’d known impatience with him. But I’d been so fond of him, too. He’d been always patient with me, even when he’d doubted my ideas. I wasn’t ready for him to die. I wished at least he’d lived until I was older.
I had my place on the hill, and my sky and warm low sun. All that was, was at peace. I waited, wanting peace for myself. But for all the calm that was around, none came to me. Instead, my own disquiet spread out from me, running down the hill and on wing to the sky, until I saw what was really surrounding me: a foaming, blowing turmoil, and nothing at rest. There was no hourglass pivoting to stay still. Nothing was still. Where could the storm reach? The far mountains were so distant that they should have been invisible.
The dust, when I saw it, floated thick above the trees that hid the road. I hadn’t even thought of the coach returning. I held my hillside. Inside the Walls they’d be waiting for it. The Day Watch would have orders about it, though I didn’t know what they would be. I didn’t want to be any part of the coach and the crowds, so I walked around the Walls away from the Ash Gate, and to the Stone Gate. I wanted stone permanence, stone hardness.
Still, I came to the Barefoot Square only as the coach did, led by two officers of the Day Watch, and heard the tale the crowd was gossiping, that the coachman Abel had refused to come in to a plague city and the Watch had taken him under guard. Even as I stood with the gawkers I saw them escorting him into the inn. The coach was brought round to the front door and met by Gustavus and Fritz.
Fritz tossed down baggage from the rack as if it were rocks, then dropped like a stone himself to the ground. Gustavus caught the pieces as he opened the coach door. Abel gave no thought to the sweating, gasping horses or the tumbled, bruised passengers. He pushed ahead of his guards and into the inn and anyone could hear him bellowing for his supper. Gustavus said nothing. He unhitched the horses and handed them to Fritz, then he pulled the coach by his own hand to its place in the front of the stable tunnel.
Abel had entered Basel again under protest and by threat of harm. He’d known of the plague because black pennants were already flying above the gates, and I saw the notice hammered to the troubadour pole in the Square’s center. It ordered that illness be reported, and that any sick person was to be brought to the Barefoot Church for the Physicians to see and they were empowered to put anyone out of the city who was deemed to have the contagion. I’d seen in the Council’s Law Code what would be printed in later notices, if they were needed: how corpses were to be collected, how their death-bedding was to be burned, and on, even to the laws regarding estates that were forfeit because no heirs were surviving. All those laws had been kept through centuries and called out as necessary like funeral dress.
Lieber the bookmaker hurried past me with a bundle under his arm. “What are you printing today?” I asked him.
“More of those,” he said, meaning the notice on the pole.
“But you’re a book printer.” He’d always left cheap broadsides to lesser printers.
“Plague laws,” he said. Those required that every printer produce these notices if the Council instructed. Much of common life was upended by the plague.
I left the Square. Not by a street, but through a doorway and into the Barefoot Church.
The falling sun in the west was on the face of the building. No direct light came in the high hall, just diffused glowing. My bench was still and I could feel that the church was still firmly held by heaven and wasn’t moving. It couldn’t be moved.
The Inn had its own foundation deep into the earth and couldn’t be loosed from it. Between earth and heaven, the Barefoot Square was stretched taut and Basel rocked by waves as a boat tied to two different piers. Someday the tension would become too great and the Square would tear loose from one side or the other. Or the city would tear in two between them.
I stayed a very long time there.
I rose early Friday morning; it wasn’t morning but still night. My grandmother never woke while I dressed and took my water buckets and went out. I heard a single declaration from the clock in Saint Leonhard’s, so I only knew it was half past an hour, but not the hour. There was no moon. It must have been after three. There was no dawn. It must have been before five.
I heard muffled, quietly drawn wheels and hooves. The Barefoot Square was formless and void. I waited at the edge until I could see the coach at the door of the inn. The horses somehow knew to be soundless. Their breathing was little more audible than it was visible. But one of them smelled me and whinnied. Abel, hard lout he was, still could quiet a horse with a whisper, and I heard him do it.
Voices in the door were crashing bells to the silence of the Square, but they were only murmurs. I could hear sullen displeasure from the passengers pulled early from bed and herded to the open coach, and the coach door closed but not latched. The luggage was already on the roof. I walked closer, hidden only by darkness in the openness. The horses knew I was there. I came close enough and stopped. Then we were all waiting. It was far earlier in the morning than the coach was ever readied, which showed how far more urgent was its reason to leave.
Silence and dark made time slow. The long minutes went by, but they were only minutes. Finally there were two voices and I listened. One was like coals and one like sparks. I couldn’t hear their words, only their heat.
Blacker than the night, making it light in contrast, black robes issued from the Boot and Thorn, and black boots and coat. Abel opened the coach door and the robe stood in front of it to climb in. The boots braced to help steady the high step.
“Magistrate Caiaphas,” I said. His foot had already been lifted. He set it down and very slowly turned. Gustavus beside him had his eyes on me. Then Abel unveiled a lantern and its single beam struck me and everything else was perfect black.
“Master Leonhard. What are you doing here?” Caiaphas said. Immediately he’d known me. His voice and words would have scratched rock.
“I’m getting water.” I held up my buckets.
“What do you want of me?”
“Only to wish you well,” I said.
“That?” he said. “What, nothing more?”
“Not for myself, sir. Will Willi be allowed back?”
“I’ve no use for him. But you, in poor peasant clothes. Is there nothing you want from me?” The words were bent up at the end like a hook.
“Soon you will.”
“Only for now, sir, that you have a safe journey and Godspeed.”
“Speed from here!” he answered in his sudden screech. “I leave my curse on this city! Curse it to the desolation of plague, and speed on its journey there.” He took hold of Gustavus’s arm and entered into the coach. The door closed on him. Abel climbed to the box and held his lantern out and whipped the horses. They leapt from statues to gales, and sparks shot from the stones under their shoes. The coach pitched and almost fell. Then it flew across the Square fast and loud as cannon shot.
The words had struck hardest. I’d taken them full force. But they’d been blocked and captured and exhausted, kept from reaching the Square and the city, and that had been my intent. The Church of Bare Feet behind me had held me firm, I’d felt it.
So the day had started, I alone in the Square, and through the dark, Abel driving like a mad bull and the roads forsaken before him.
At home, my grandmother said nothing, and only watched me do my chores as she did hers.
With such little sleep, my arrival in Master Johann’s kitchen was subdued and my appearance depressed. But I thought I’d had more rest than Mistress Dorothea. She had even less of her usual manner, and an odd stare at me, too.
She was only sitting at the table. She had a knife in her hand and potatoes in a bowl, but they were waiting. There was no motion.
“Good morning,” I said.
“Oh, Leonhard. Yes, good morning.”
My first job is always to tend to the fire and the wood settle, and I saw the hearth was cold. “Should I start the fire?”
“Yes. Thank you. I see that I haven’t.”
There was no kindling brought in. I went to the yard to bring some sticks and then set to igniting. The wood was dry and there were still a few embers. I had a flame quickly, and two split logs against it to catch, and when I turned back, Mistress Dorothea was still in her chair, still holding her knife, and still. So I went up to her and set my knee on the floor to lower myself to her height, and asked her, “Are you well, Mistress?”
“I’m not ill,” she said.
“You’re not well,” I was bold to say.
“There’s little well.”
“There’s plague in the city.”
“I don’t fear that, Leonhard.”
“You don’t? Everyone does.”
“Master Johann says it’s not to be feared, not yet. If it should be then we’ll leave Basel.”
“Is there something else, then?” I asked.
“The hub and the spokes,” she said.
This was a proverb in Basel. It meant, a family was like a wheel. The children were the spokes and the mother was the center. She held them in place, and felt the ruts and stones that any of them struck. The father wasn’t mentioned but I thought he was the axle, and all the weight he carried was also pressed onto her. So, she was admitting to me that it was her family that was not well. I waited and the kitchen was the most quiet I’d ever known it with its Mistress present. “If you see regret,” she said, finally. “Or grief, Leonhard. If you see remorse or regret, I’d like to know that you have.”
I nodded.
“And if it’s penitence or repentance, even more I’d like to know. Anywhere you see it.”
“I’ll tell you. I think there’s much I regret myself.”
But later, when Mistress Dorothea was upstairs, Little Johann came into the kitchen. “What did you mean?” he asked, kneading his dough. “What do you regret?”
I made light of it. “Where were you listening from?” He hadn’t been in the kitchen when I’d said it.
“You said you had regrets.”
“For my hat,” I said, just jesting.
“Your hat?” He squeezed the dough and it bulged out between his fingers.
“Cousin Gottlieb took it and I regret I don’t have it back. It was from my father.”
At Gottlieb’s name he pressed the dough all the harder. And I realized I did regret that I’d lost the hat.
I walked from Mistress Dorothea’s kitchen slowly, not toward home. There were odd creatures in the streets: wolves and vultures and half-beast minotaurs. But they left the people alone, for the moment, slinking in shadows and growling low. I walked out on the bridge to look at the Rhine. It was calm. But somewhere underneath something stirred and touched the surface and a ripple appeared, a perfect circle. It spread out, just the one circle on the smooth water, its radius growing, and finally fading.
That circle was like so many other circles. Usually I would be reminded of how sound travelled that way through the air, but that morning my thoughts were on other circles. Plague spread like a circle. Fear did. I saw a man crossing the bridge, pulling a bag-laden cart, and with a wife and children walking behind him. It was a sight that had instant meaning. He was fleeing the city. But so far, he was the only one I’d seen. He reached the far end of the bridge in Small Basel and turned toward the Blaise Gate.
So Basel had lost Huldrych besides Knipper, and now it was losing others. It was all loss, and I felt it.
The bell of the Munster clock rang ten, all melancholy and pleading, as if calling out. I found myself counting as it ended, not at first even remembering why. Then I knew. Just at thirty seconds, I heard a far off clock in Riehen, from my father’s church, that bell ringing nine. It was an answer, louder than I’d ever heard in the middle of the city.
“There’ve been no other reports of plague,” I told my grandmother at lunch. She knew that, of course. She never gossiped or rumored, and wouldn’t abide anyone else telling tales. Yet she always knew important news.
“You said Master Huldrych spoke of Black Death?” she asked.
“When we came to his door, Gottlieb and I. He asked if there was another Black Death. And Gottlieb was angered by it. Grandmother? Would you know? When did Gottlieb first wear a tricorne hat?”
“He had it when he came from Holland.”
“When he came back with Master Johann?”
“The first I saw him when he came back, he was wearing his tricorne.”
“He was younger then than I am now!” That was hard to imagine. “Or at least as young.”
“He was a serious youth.”
“I’m not very serious,” I said.
“Yes, Grandmother. Have there been any other deaths in Basel of plague?”
“If there have, it’s not been announced. What happens inside a family’s house isn’t always known.”
“But to not tell is against laws.”
“Some are below the law, and some are above.”
“Huldrych saw Gottlieb, and a tricorne worn for the first time, and he thought of plague. It persuades me that Jacob died of plague. Gottlieb didn’t want that memory revived.”
“Those of us who are old don’t always remember well,” she said. “The University will meet soon. They’ll choose a new Chair to replace Master Huldrych.”
“That takes months,” I said. “It took three months to choose Desiderius for Greek.”
“What will become of Master Huldrych’s lectures?”
“Master Staehelin is the Lecturer for Physics. He’ll take the lectures until the Chair is filled.”
Plague was bad for all business in a city. Doors were closed and locked and the streets were even emptier. That afternoon the Boot and Thorn was empty. I only saw it walking past; I didn’t go in. I was returning Boccaccio to Master Desiderius.
He wouldn’t have minded my keeping it longer, but my return of one book often led him to press another into my hands. And he might have heard, in some language only he knew, of any other news of the events of the week.
One of his children answered his door, a boy about six years old. His name was Theseus and I hoped his father’s hope in him would be achieved. “Eínai o patéras sou edó?” I said. I also hoped I had my Greek grammar correct. If I didn’t, he would correct it.
“Tha ton párei,” he answered, and I waited. And soon, his patéras arrived.
“Leonhard,” he said, as he saw me. “What? Done with it already? Of course you are. And a strange book to read, wasn’t it?”
I handed him the Boccaccio. “Very strange, sir. I’ve not read any other book like it.”
“The book itself, yes, but I meant the reading of it now. I pray we won’t see anything he describes with our own eyes.”
“There’ve been no other reports of plague,” I said.
“I think there will be none.” This was the second time that day I’d been assured of that.
“Master,” I said. “You said you came to Basel from Strasbourg?”
“Yes. Five years ago.”
“Then did you know of Magistrate Caiaphas?”
“To have lived in Strasbourg is to know of Magistrate Caiaphas.”
“Did he know of you?”
“Yes. He knew me. He knew of me.”
“Master Gottlieb knew him, and asked him why he came to Basel.”
“It is best to not know that. Leonhard, your questions are difficult.”
“I was greatly saddened by Master Huldrych’s death,” I said.
“And what does that have to do with Magistrate Caiaphas?”
“I don’t know.”
“The Inquiry is over, and also the time for questions. We’ll move to other things.”
Of course, I asked, “What is the result of the Inquiry?”
“The result is no result. The city was indulging Magistrate Caiaphas with the Inquiry, and Magistrate Caiaphas is no longer here.” Master Desiderius smiled at that, as likely most of Basel did. “And what, hasn’t Gottlieb said anything to his own clerk?”
“I’m dismissed as clerk, and anyway he’s dismissed as Inquisitor. But he said there was a result to be told, and he never told it.”
“He’ll tell the Council, and Magistrate Faulkner.”
“And he said there was a danger to Basel,” I said.
“He did, didn’t he?” Master Desiderius said. “But we don’t know what. Could it have been about the plague? No one knew that Huldrych was ill. Perhaps Gottlieb had a fear that someone might be? Did anyone say anything about plague?”
I chose my words carefully. “Gottlieb never said anything about plague. Not to me.”
“I was hoping, Leonhard, that you might have known more.”
“I wish I did, Master.”
“Anyway,” he said, “thank you for the return of the book. And I have another for you. It’s even in German.” It was odd that we didn’t spend time choosing one together; it usually took us a long time. Instead he handed me a book that seemed very new, and slender.
“Oh, yes,” I said. “I remember you said you had this for me.”
The first page showed that it was new, printed that very year, in Frankfurt by a printer named Meynenden. But the title was something of a discomfort to me, as I knew it well. This book was a new telling of an old tale, a Faustbook.
Faustbooks had been common in Europe for centuries. The story was usually short: The book in my hand had only some forty pages. The history of this story was long, from the ages of alchemy. It was, of course, about the life of Dr. Faust of Heidelberg. He was learned, terribly learned, but wanting always more knowledge, more and more. He wanted knowledge of anything, but mostly of mysteries and secrets and powers. He was greeted by Mephistopheles, a fallen angel, who offered him a bargain: all knowledge, and life as long as he wanted; but when he tired of living, he must give up his soul. There were different endings but the sum of them was he did tire finally, that his knowledge was too great to endure, and he would rather surrender to damnation than keep living.
If there was no true Dr. Faust, there have been others who might have inspired the tale.
There was a man named Philippus Aureolus Theophrastus Bombastus of Hohenheim, who took the scholarly name Paracelsus, to mean he was the equal of the great chemist Celsus of ancient times. I thought it might have been Paracelsus who was the true Faustus. He held the Chair of Medicine in Basel at the same time that Holbein was painting the Council room. He was an alchemist, when that profession was only suspect, and not sinister. So, Basel was part of the soil that the story had grown from. Its roots may still have been in the soil.
I was interested to read this new version, though I’d never enjoyed the tale. “Thank you,” I said.
“It’s only imagination,” he answered. “Such things don’t really happen. But it’s cautionary, too. A good caution to have.” I think he was emphasizing that. “Think it through well, Leonhard. It isn’t Mathematics but there’s still hard truth in it to keep in your mind. It might even be that the questions you have of the Inquiry are answered in it.”
“How could that be?” I asked.
He shook his head. “And I have a copy of Paracelsus for you, also. But not today; that is enough.”
Dr. Faust was a scholar, and that was important to the story. If a man didn’t have fame and wealth from birth, the University could be his path to those.
It was easy enough to find Basel’s wealthy men. Their houses were displays, in the subdued Basel manner. The family names of the magistrates and the council were very regular from year to year and century to century. These families had their wealth from trade and guilds, and some from land. None of this was irregular, or unique to Basel. For every Faulkner or Burckhardt in Basel, there was a Zimmerman in Zurich, a Hofburg in Frankfurt, and a Weil in Bremen. It was the University that gave Basel another class of great men.
This special parallel city was made of students as commoners; student graduates who studied toward higher degrees as the skilled tradesmen; lecturers and associate professors as wealthy younger sons; administrators and Deans and Provost as greater patricians; and at the highest level, above officials, equal with magistrates and bishops, were the Professors, the holders of Chairs. These were meant to be great men and masters in their fields. Among them were Physics, Law, Medicine, Theology, Logic, Greek, Latin, Anatomy, Rhetoric, and others. In Basel the greatest was Mathematics.
And as the University was a parallel city, Europe’s universities were a parallel continent, and they were its kingdoms and duchies. Heidelberg was a power, Paris was a kingdom, Bologna held its independence. In the realms of Mathematics, though, Basel was Hapsburgs and Bourbons and Romanovs all in one. In the parallel continent it was unparalleled, because Master Johann was its center.
The story of Faust could only be in a place where a man could become great through knowledge, a place such as Basel. In all the Faustbooks, the story always took place in a University.
I walked Walls that Friday evening. That was common in Basel, though more often to watch the sun’s mid-morning rise, not its setting. I walked the whole Wall of Large Basel. It was near three miles long and I didn’t run any of it. I started at Saint Alban’s Gate in the late afternoon. The first stretch was the two long sides of the angle that the Ash Gate pivots. That was almost a mile. There were guard towers every few hundred yards and ramps up from the streets at every gate and barbican.
The barbicans were wide and flat, just as high as the Wall itself, protruding from it in sharp triangles to give defenders a vantage over attackers at the Wall’s base. Basel had never been taken, and rarely attacked. That could be proof that there was no need for the Wall, or proof that there was every need for it. It was an odd logic, and I wondered what Gottlieb would say about it.
As I reached the far corner past the Ash Gate and turned toward the Stone Gate, the sun was full in front of me just ready to touch the horizon. The path on the Wall was wide, twelve feet across, but all I met was the Day Watch and I greeted each man I passed. I knew many of them. I stopped to talk a few times. Then they were standing down as the Night Watch took their places. What the Watch could do against plague, I didn’t know, or they either, but the Watch had been doubled.
Just past the Stone Gate was the stream of the Birsig Flow, pouring into the moat and into its canal to the city. I walked across the arch where it entered. There was a strong portcullis there, and barbican just after, because that would always be a weak place in a Wall.
Beyond the Walls were fields. Some were farms and some were only meadows. There were no cattle or sheep in them that night, but once a black horse came out into the open from some trees, and Daniel was its rider. He lit suddenly toward the gate, whipping his black, as if racing, yet with no other horse I could see. Then I did see a white horse, without a rider, nearly beside him. Then they were hidden behind the Wall. I turned and went on with my walk.
I saw Saint Leonhard’s church spire and clock, and the Barefoot Church further in. As I passed them, the sun was just half-set and the sky an inferno. When I came to the Columned Gate the sun was gone. The moat below still was glowing red, like a candle wick’s last spark. This was the city’s largest gate, on the road from Alsace.
Then was the final long walk to Saint John’s Gate, back to the river, and it was such a long and ever darker way that I only had the stars above and the points of light from the windows, and they both seemed as far away.
The Wall was complete and unbreached. I knew it for sure now.
As I stood at the gate, I saw another watcher was also on the Walls, confirming them.
“Good evening, sir,” I said. Magistrate Faulkner recognized me in the dark.
“It’s Leonhard? Yes, good evening.”
“These Walls seem so strong.”
“They are. Despite their age.”
“They’re kept well repaired.”
I didn’t know if he would answer. He was silent for more than a minute and I wondered if I should leave him. But then he said, “Leonhard, if you see Magistrate Caiaphas return to Basel, come tell me.”
“Yes, sir. I will.” And I nodded and left him.
The return home on Saint John’s Street led by Death Dance Street where I had to stop at Master Huldrych’s house, and at the Dance that now he was partner in.
God gives all laws, as are found in books; no man may change them: hate lies, love truth. It was dark but of course I knew the Lawyer’s words, and also Death’s reply: I accept no trick or flattery, give no postponement or appeal, I overrule man’s laws and courts, both Prince and Church must yield. No prince would ever have proclaimed a law that Death must obey him. The laws of God, of nature, of Mathematics, of death: man-made laws were weak compared to those. I looked across the street to Master Huldrych’s house.
I wondered what would happen to his laboratory. It would be disturbed. Someone would sweep out that room and all the dust, carefully settled, would be dispersed. Dust to dust.
I came in my front door and Grandmother was waiting. She had a stern look.
“Leonhard,” she said. “You have a visitor.”
“Me?”
“It’s Master Daniel.”
Daniel had found me in many places in Basel: in churches, on streets, in taverns, in his own house. But in the week he’d been home, he had never sought me in my own house. “Yes, Grandmother,” I said.
Every house of any size in Basel had a sitting parlor, always with windows onto the street. My grandmother’s sitting parlor was swept every day. The floor was bare. There were three straight wood chairs and two small tables against the walls. One held a candlestand and the other a Bible. This was where we would sit on Sunday afternoons when I read to her.
Beside such, they were rarely used rooms, but Basel was a city that wasted very little and the rooms had a purpose. They were the strong wall that kept the visitor who’d breeched the door from truly being in the house, and that was important.
Now Daniel was in a chair the farthest from the Bible, and his bright silk coat was a disconcerting shock of color in a somber place, though the room managed to dim it. “Look, Leonhard!” he said, springing from his seat. “I’ve come to see you!”
“I see that,” I answered. Grandmother hadn’t come with me. She was back to the kitchen. Daniel put his arm over my shoulder. “Is there another interruption you want me to be?” I asked.
It was Daniel without Nicolaus, Daniel not cocksure, Daniel in doubt. Daniel as drained of himself as his mother had been of herself that morning.
“Leonhard,” he said, and then nothing, and I waited. “You’ll say what you think, won’t you? You always do.”
“Not always,” I said.
“But you think, whether you say what you think.”
“I do.”
“Then I want you to say what you think.”
“Tell me what to think about.”
“I will.” But he didn’t, and I waited again. “I’ve given my word on a matter, and I might want it back.”
“What matter?”
There were many pauses in the conversation. “I won’t say.”
“You gave your word in good faith? And the other person, as well?”
“That could be yes or no. I thought I did, and that the other had, as well, but now that I’ve thought more I’m not sure.”
“Well, Daniel,” I said. “I can’t say what I think if I don’t know what to think. If a man gives his word, that’s a binding to him. It’s false witness to go back on it.”
“I knew you’d say that, but this has a difference, and if you knew it you’d agree with me.”
I had to laugh. “Then you know what I’d think, and I don’t.”
But Daniel was so forlorn. “Tell me, then, Leonhard, when would you go back on your word? When have you?”
“I don’t think I have. I don’t remember. Daniel, I’m no one whose word anyone would want!”
“Then when would you?”
“Give my word?”
“No, take it back. Break the bargain. When would you?”
“Well . . . if I’d been deceived. I think I could then.”
“That’s what might be. You’d say I’d been deceived, I think. I’m sure you would.”
“Tell the man, then. Tell him how you think he’s misled you, and you want the bargain off. Is there one of you who acts first?”
“He already has. Part of it. But a big part. Maybe he has. I don’t know whether he has.”
“What was it, Daniel?” I asked.
“I won’t say.”
The next pause was mine. “Was it anything evil?”
“Evil . . . ?”
“That you agreed to.”
“Not that I agreed to, no. I wouldn’t have. And that’s a point, too, that I didn’t. And it’s done. Even whether he did it or not. It might not have been.” He tried to laugh. “It wasn’t anything a man would be thrown into the river for! Not what I agreed.”
“What was it?” I asked again.
He was sober again, and finished. “Leonhard, it’s best not said. There’s much to think about and I will.”
“I will, too.”
“Don’t. There’s no use.”
I think neither of us was much satisfied. Mistress Dorothea had asked me to watch for regret and remorse. I wasn’t sure yet whether I’d seen any.
I sat late, through two candles, writing in silence about sound and waves. I’d been writing this thesis for very long now: two years. The scratch of my pen came to seem like thunder to me in the quiet night. With every sentence I also heard Huldrych’s arguments against my ideas, and I wished I could answer him. Only when I could argue back did I know that there was some strength in my ideas. He was like the hammer that put force behind the chisel, forcing elegance out of my coarse and ill-formed proposals.
Finally I put the quill aside and closed the ink. I dressed for bed. I didn’t know the time. Last, I looked across my bookshelf for which volume I’d have for my Saturday. It was hard. I was still diminished. It would take time to re-grow. I picked the Ars Conjectandi and extinguished the light.
My sleep was short but restorative and I woke to my Saturday morning more at peace. I was out to the well in good time, and I chose a different fountain than the Barefoot. At home again, I felt the Saturday morning buoyancy lifting me. It was like I had hold of some hourglass that didn’t whip with the waves.
My grandmother found me more talkative, and she was, also. “What were you writing last night?” she asked, and that was a sign that she wanted to just hear me chatter. I was always writing and to her, one thing was mostly the same as another.
“I was disserting,” I said. “It’s still on sound and waves in the air.”
“And what in particular?”
“On what a wave is.”
And I said it eagerly enough that she had to ask, “And what is it, Leonhard?”
“I think it is a Mathematical equation.”
“And how can it be?”
“I don’t know if the wave is the equation or the equation is the wave. But this is what I’ve written, that the equation is the law that the wave must obey.”
“Sound must obey laws? Like men must? And who gives laws to the air?”
“I think God does.”
“And do they follow His laws?”
“Yes,” I said, and firmly. “In every circumstance they do. They aren’t unrighteous.”
“Where do they learn the laws?” She was teasing my words, but I think they were interesting to her.
“They don’t learn. They just follow. The laws are invisible.”
“You see so many invisible things, Leonhard.”
“It’s only because there are so many,” I said.
Then I was in my room and I read Uncle Jacob.
The subject was conjecture, chance, probabilities. To throw dice, what was expected? The cube would fall on one side of six, and any was as likely as any other, though only one would land upright. And throwing it again, there was still the same chance. Landing a three twice made the chance of another three no greater or less. But it was still unlikely to land threes thrice. What did chance mean? And how could chance be, when all the universe was ordered and clockwork? Did God choose which side would land?
I’d read the Ars Conjectandi a dozen times at least. I could have written out good stretches of it from memory. And now, though it’s prideful of me to say, I could place it only in the middle of Mathematical writing. Leibniz, DesCartes, Newton, and others were still above it. But it had hints. The book couldn’t have included all that Master Jacob thought, or even wrote. So I looked, as I read, for what had been written but not in these pages; I looked for the invisible writing.
Master Gottlieb had written the book from Master Jacob’s notes. Perhaps he had them still. It would have been more likely that Master Johann had those notes, but that also seemed most unlikely. It would not have been Jacob’s wish that his rival brother come into possession of them.
Instead, my thoughts turned in a spiral to another place the papers might have been. Most likely they had been gathering dust. Great amounts of dust, for many years. And then they were somewhere else.
And for a few moments, they may have been in Mistress Dorothea’s kitchen.
At the dogmatic three thirty I put my knuckles to Master Johann’s door, and it was opened by Mistress Dorothea. That sequence at least was as absolutely unchangeable as anything in Mathematics. There was no chance to it.
There was a change in me, though. I was not fearful, or not as much. But there was one obstacle between myself and my proper place, and I couldn’t overcome it. It was my hat.
I had no other hat! Gottlieb still had my humble student hat with the simple roll of the brim on either side, and I hadn’t had the opportunity or purse to buy a new one. I had only this tricorne. Would it be monstrous of me to wear it into my Master’s presence? But I couldn’t have come without a hat, either. It had to be doffed in respect and set on the table. And there it would be! As I approached the dull door, I was in a sweat and un-confident. But not fearful. How could I fear anything when I was wearing a gentleman’s hat?
What pure dilemma! And all my musings in Mathematics and Physics, Theology and Greek gave me no guidance at all for solving the problem. As the Mistress knocked on the final door, only Logic could help me. There were two choices, Hat or Not Hat, and Not Hat was impossible. So Hat had to be, so Hat was. The knock was answered, I opened the door, and not just a student but a gentleman went in.
I had a worry, as I came into the room and studied his face and mood, that our other meeting in that place on Thursday morning would not be forgotten. But I didn’t see anything. Master Johann was seated at his table, as always, with his candle, his paper, pen and ink. His stare, as always, was just past my shoulder as if he still was in his previous thought. His wide face seemed at its least alert, which I’d learned meant just the opposite. I felt it would be a taut and grueling afternoon. He saw my hat. Surely it would only be a goad to him, to challenge me even more fiercely.
“Good afternoon,” he said, and I answered the same. “Sit down,” he said, and I did. This was the formula. I took my seat, and set my hat on the table. It was a little more between us than to the side where I would usually position it.
“Have you done your exercises?” He always asked this, and even the turmoil of the last week didn’t change what would be asked, or that I’d done the work. I handed him my papers and he looked at them critically. If there was ever an error, he would see it immediately and tell me with no attempt at gentleness. I would want no attempt; it was my fear of his rebuke that drove me to perfection. At least, that was one motive: I was driven by the rebukes I gave myself just as strongly.
“Yes, that is correct,” he said after his study. “What have you been reading this week?” It was as if he knew. To tell him Uncle Jacob had been in my hands just an hour previous would have been effrontery.
“Boccaccio. Master Desiderius lent it to me.”
“When?”
“Tuesday morning.” Before the coach arrived, and before the Town Council meeting.
“It’s satire. What did you learn from it?” He sometimes asked such questions, for him to learn about me.
“About death, sir. Black Death’s not a subject for satire this week.”
“It is not.” That was the first acknowledgment he’d given of the events of the week. “At another time you might find that the book is much about life.” He paused, and searched me. “You grieve for Master Huldrych, don’t you?”
“Yes, sir. Very much.”
“I do also,” he said, and that was the completion of our beginning. But I knew him this well, that those three words were complete truth, and his grief was as deep as mine; but he was a deeper man than me. “We will begin a new discussion today.”
Those were words that were even more wondrous than the offer of a book by Master Desiderius, or the prospect of a long, empty road begging to be run. To my great discredit, the thought of Master Huldrych stood back out of the light. But perhaps that was Master Johann’s intent, to help me with my grief.
So I set my pen at the ready. How I loved to write! White paper was a heaven for me, and the beginning of a new Mathematic subject was like angels singing. I wasn’t irreligious at all thinking this. God would be worshipped sublimely in sublime things.
“Consider a polynomial of the fifth degree.”
“Yes, sir. A specific one?”
“That it was created from five known roots.”
And we were off. He would ask questions and I would answer if I could. He would push until I could not. “In what way does it inflect? What is a description of its differential polynomial? How does Leibniz find the maximum values?” And here, already reeling and breathless, I had to also remember to use only Leibniz’s words and none of Newton’s.
“The maximum occurs where the ratio of infinitesimals is zero,” I answered.
“What is the meaning of that ratio?”
“It is how the value of the polynomial changes as the independent varies. When the ratio is zero, the polynomial is neither increasing nor decreasing, and it has reached a point between those two. If it is increasing to the point, and decreasing after it, it must be a maximum.”
“Must be? In every case?”
“It might also be a minimum.”
“Every case is one or the other?” He was like a wolf with his jaws clenched on the neck of a sheep. I was the sheep.
“Yes. It must be a maximum or minimum.” In that instant I knew I was wrong.
“What if the ratio of infinitesimals is itself at a minimum or maximum, even at zero?”
I was dizzy. “It would . . . the polynomial would increase to a point, come to level, but then increase again.” I took a deep breath. “Or decrease, and decrease,” I added hastily.
“Yes.” He nodded, and also breathed. “And there are more cases where each following differential polynomial is itself such a leveling case.”
There was a book on my shelf, Analyse des infiniment petits pour l’intelligence des lignes courbes, by Monsieur de l’Hopital of Paris, written nearly thirty years ago. Some ten years before that, the great Master Leibniz had published in the Acta Eruditorum his article Nova Methodus pro Maximis et Minimis, itemque Tangentibus, on the Calculus, the first ever published. Monsieur de l’Hopital, certainly a great Mathematician himself, failed to comprehend it and hired for himself a tutor, a young man then, my Master Johann, who began a correspondence with Paris and instructed his elder. He was likely one of only three men in the world who could have: who had both the understanding of the material, teased from Master Leibniz’s very obscure Latin, and also the ability to teach it. The other two were his brother, Master Jacob, and Mr. Newton in England.
Monsieur de l’Hopital then himself published Master Johann’s notes, with just the barest attribution to their true author, as the first textbook in the world on the Calculus. I’d read Analyse des infiniment petits and I recognized it to be thoroughly Master Johann’s own work. Only after de l’Hopital’s death did Master Johann make his claim that the book was actually his. It was Daniel’s opinion that de l’Hopital had paid Master Johann a princely sum for his silence. If that were true, Monsieur de l’Hopital at least for his own lifetime had purchased, and Master Johann sold, a very great renown. Now, though, all of that fame and prestige has returned. And Master Johann has only increased his, and all the world’s, understanding of this vast new continent of Mathematics.
And this was the man who was before me now, teaching me the Calculus. His explanations of it over the last years had always been so lucid and straight. It has all seemed so simple to me, but I knew that it was only because I had been taught so well. When I would describe the mysteries to another student, they seem to understand nothing of it. They would only shake their heads at my gibberish. I was a very poor teacher.
On we went, and on and on, and as always I’d lost all track of time: of the clock and even of the calendar. Then there was always the sudden moment when he rubbed his hands and leaned back in his chair. This was when he would give me my assignment for the following week. I was already exhausted, but now had to pay the closest attention of all. But this time he didn’t tap my papers and show me what from them I was to work on. Instead, he pulled out a paper of his own, but didn’t show it to me.
“Let us address an issue of a series of infinite numbers.”
This was quite different from what we’d been discussing. He nodded to me and I took up my pen and ink again.
“A sum,” he said. “One half, one fourth, one eighth, one sixteenth, one thirty-second, one sixty-fourth, and on. An infinite series. What is the sum?”
¹⁄₂ + ¹⁄₄ + ¹⁄₈ + ¹⁄₁₆ + ¹⁄₃₂ + ¹⁄₆₄ + . . .
“Exactly one.”
“And how is that? An infinite count of numbers, and they add to a finite sum?”
“Yes, sir. Because they grow infinitely small.” This was very plain, and we had discussed it long ago. He was plotting something. He wouldn’t have asked such a simple question unless he had a difficult plan.
“Then one half,” he said, “one third, one fourth, one fifth, one sixth, one seventh, and on. An infinite series. What is the sum?”
¹⁄₂ + ¹⁄₃ + ¹⁄₄ + ¹⁄₅ + ¹⁄₆ + ¹⁄₇ + . . .
“The sum is infinite.”
“But they also grow infinitely small?”
“But for this series, not as quickly. Not as quickly as the sum grows infinite.”
“That is correct.”
Oh, he had my interest piqued entirely. I thought he might really be a show-man, the way he drew out a puzzle and pulled his student into it.
“How do you know that the first series added to exactly one?”
“There is a method,” I said. This was still all very simple. He knew the method, of course. “If the series is multiplied by two, it becomes one, one half, one fourth, one eighth, and on. If the two are subtracted, the infinity of terms is cancelled, and the remaining value is one. So, the series subtracted from twice the series is the value of the series, which is one.”
“Does this method work for any infinite series?”
“No, sir. Only for this geometric type.”
“Now write these numbers.”
Then I knew, from his voice, that this was to be the challenge. The first questions had only been to set his stage, and now he was ready to play his drama. “One, one fourth, one ninth, one sixteenth, one twenty-fifth, one thirty-sixth, and on. What are these?”
¹⁄₁ + ¹⁄₄ + ¹⁄₉ + ¹⁄₁₆ + ¹⁄₂₅ + ¹⁄₃₆ + . . .
“They are one over the square of one, one over the square of two, one over the square of three, one over the square of four, and on. They are Reciprocal Squares.”
“Yes, Reciprocal Squares.” It was roast veal and wine, exquisite, the way he said it. “They are Reciprocal Squares. Is the sum infinite? Or finite?”
“Finite,” I said, though I paused to think. “Yes. Finite. Besides the beginning one, the numbers are each smaller than the first series you listed. One fourth is smaller than one half, one ninth is smaller than one fourth, one sixteenth is smaller than one eighth, and on. So if the first sum was finite, this must be also.”
“Yes. Finite. Very good, though that was simple.” And he paused, and his pause was perfect in length and depth and width. “And what is that finite sum of the infinite Reciprocal Squares?” he asked.
“The sum . . .” I was bewildered. I stared at the numbers on my paper and tried to make sense. I looked at the pattern of them, at what they seemed to be adding to, at the other methods I knew, anything. They seemed very simple, as simple as the other sums we’d done. And finally I grasped that . . . “I don’t know.” I realized minutes had gone by. “What is the sum?”
“What is it?” He rubbed his hands. “No one knows. It is a number, somewhat larger than one and a half, and less than two. It has been calculated to a close value. But no one knows what it really is. Perhaps it’s no particular number at all, just a number. But it should be something more important than that. A squared root, a cubed root, a ratio of important numbers. No one knows.”
“It would be something . . . surprising,” I said.
“Perhaps. Perhaps. And now, the Paris Academy has issued a challenge to anyone in Europe who might discover the true value of the Reciprocal Squares.” He’d kept the paper in his hand closed from me; now he opened it. “Monsieur Fontenelle and Monsieur de Molieres of the Academy are very great Mathematicians. I have instructed them myself. Their challenge is to all Europe.”
I was reading. The page was in Latin, of course, and it was just as he’d said. The two men were members and directors of the Royal French Academy, and their announcement was as weighty as a mountain: to explain the meaning of the Sum of the Infinite Reciprocal Squares.
Master Johann was a member of the Royal Academy; if he were not, the Academy would hardly have been worth anyone else’s membership. Therefore, he had received the first copy of the challenge, and soon it would go out to all the rest of Europe. And whoever first solved it, or proved it unsolvable, would instantly leap to the highest rank of Mathematicians, if he wasn’t already there. And I was being given this glimpse into their world.
“Will you try?” I asked. I had finally returned to the dim room in Master Johann’s house. He was waiting for me.
“I have reason to believe it can be expressed in some other way than only as the sum. It has some special value as itself.”
“Why?”
I saw in his eyes a look I’d seen sometimes before, which was like the Basel Walls when their gates were closed and a banner of plague or war was flying, to tell travelers that there was no entrance to the city, and they should keep a distance if they didn’t want an arrow for warning. “I will leave you to explore that.”
“A Reciprocal Square.” Grandmother practiced the words. “Does it have use?”
“None practical.”
“But men in Paris have challenged other men to learn the answer. A wise man doesn’t answer idle dares.”
“It isn’t idle,” I said. “It’s not men in Paris who made the problem. The problem stands on it own. It’s always been. It’s men in Paris who’ve found it and asked for help.”
“Asked for help.” My grandmother understood that very well.
“No one’s been able to.”
“Would Master Daniel or Master Nicolaus know the answer? Or Master Gottlieb?”
“I don’t know if Master Johann will tell them of the challenge.” Then I thought about it longer. “Yes, he’ll tell them, I’m sure. They’ll have heard of it anyway. But Daniel studies the Mathematics of flows and pressures, and Nicolaus follows his father in the pure Calculus. Neither of them is expert in this Mathematics of infinite series. And Gottlieb studies the rules of proofs. So I think Master Johann will consider that none of his family would solve the problem, and therefore he would surely give it to them to try.”
“He would give them a problem he is sure they couldn’t solve?”
“I think that is the main reason he’d give it to them.”
“Who might know the answer?”
“There is a Mathematician in Scotland, Mr. MacLaurin, who has the Chair of Mathematics at Aberdeen. He’s a great genius in infinite series. I have his books. He should be the man to solve this problem.”
“Would that please Master Johann?”
“No,” I said. “Not at all. Master Johann has had disagreements with Mr. MacLaurin.”
“Of course,” she said, not surprised. “What kind of man is Mr. MacLaurin?”
“He is certainly a great Mathematician. I’ve read that he’s eccentric and often neglects his lectures. He has had his Chair for eight years.”
“How old is he?”
“Eight years older than I am.”
The Boot and Thorn had more custom that evening. Fear of the plague and thirst for news of the plague battled, and the Common Room was half empty and half full. I knew Daniel would come, so I took a bench and waited. Charon the cat sat with me. The creature had nor wanted friends, but would sometimes be a companion.
Three men were at the table: Lithicus, Lieber, and a tailor named Scheer. These three, the stonecutter, the bookbinder, and the tailor, had a game of dice they played, and had for years. I watched them. It seemed all random to me, though they claimed there was both skill and luck to it. I watched the cup twist and the dice roll, as regular as a clock but always with different results. The three shouted and hooted and swore and all the faces of the flagons on the walls each watched his own favorite of the three. Even smoke from the fire seemed less willing to travel the chimney and stayed to watch.
There had always been two uses for dice.
Sortition was the act of chance, to choose and sort with no obligation to the sorter. Gottlieb’s Ars Conjectandi was the Mathematics of this method. There was great expectation of the accumulation of results, but no expectation for any single throw. The tradesmen’s game was this use.
The second use, cleromancy, was the opposite, where some agent was thought able to control the dice. There would be few agencies that could be expected to have such a power, and cleromancy was used for fortune telling and divination. But it would also be the name for the casting of lots, the Urim and Thummim, and the choice of a new Apostle after Judas.
The selection of a new Chair, in the end, was the casting of lots. So it could have been just a choice by chance of one from three, or it could have been God’s finger pointing to the man. It was worth thinking which of these it truly was.
Usually nothing could be seen of the outside through the windows, but I saw a black horse arrive and a stable boy coming to tend it. Then a loud laugh from the hall told everyone he’d come. He’d only been back for the week but already he had his universe aligned, and other ears and heads picked up and watched his entrance. Fewer may have seen his shadow Nicolaus follow him. Nicolaus hadn’t been riding; he must have been waiting somewhere for the rider to arrive.
Daniel surveyed his duchy and chose my humble side by which to plant his flag. That meant that soon I was in the middle of everyone else, as the room coalesced around him. “Two days,” he said, “and not a signal of plague. The Council’s saying it’s a hoax.”
“Hoax?” the room said. “That old Huldrych died for a hoax?”
“No, he died for his own reasons and not for plague. It’s a hoax to call it plague. Who’s seen plague? Who’s to tell that it was?”
The black bristling center of the smoke said, “I’ve seen plague.” We hadn’t seen Gustavus but he was there, with us. “And so it was.”
The room was deadened by that. Innkeepers had special responsibilities concerning Black Death, as listed in Basel’s laws, so they were expert at recognizing it. They were responsible to send carts for corpses and collect clothing for burning.
“Jankovsky died of plague, didn’t he?” That was another voice in the dark.
“Just a chill,” another voice answered. “It’s easy to die in a winter.”
“If he did, then Desiderius has his Chair by honest death,” Nicolaus said quietly, beside me.
“Desiderius?” I asked him. “How else would he have it?”
But Nicolaus only said to Daniel, “Then what were Huldrych’s reasons for dying?”
“All the reasons that being ancient had for him. What were any reasons he had to keep living? That’s the question.”
“I’d keep living.” That was Lieber, the bookbinder. “No matter if I was ancient.”
“And you are ancient!” Daniel said. “But not as Huldrych. And you’re not in a Chair. That’s another reason Huldrych had, to be out of the way.”
“Out of your way.” That was Nicolaus. And Daniel, in his black humor, laughed at it.
They talked on, Daniel jesting and coarse, more than I thought him usually to be. It might have been that he was unsettled as the rest, or more, and that the doubt and confusion from his talk with me was still there. But he wasn’t asking for my counsel anymore. I edged back from him and his throng, into a darker place, and somehow had Nicolaus beside me. He was quiet as always. I knew he had something to say, though.
“It’s a plague.”
“But that he died of?”
“Not Knipper.”
“What killed Knipper?” I’d never been told.
“A pan, I’d say.”
The knot around Daniel laughed at something he’d said, and himself the loudest. I wasn’t following either brother well. “A kitchen pan?”
“A heavy one brought down hard.”
“He was killed in a kitchen, then?” I wasn’t sure if he was leading me, either.
“You know that, Leonhard, and the kitchen, very well.”
“Well, I do.”
“And dust, too.”
“Dust? Oh, Huldrych’s laboratory?”
He just nodded. Smoke from the fire, like dust, swirled lightly around and suddenly I choked on it.
“Huldrych breathed the dust,” I said.
“It’s not often disturbed.”
“I breathed it, also. And Gottlieb did. Or, no, we didn’t. I tried not to. Was something in it?”
“It was dust.”
“And I don’t know which pan in Mistress Dorothea’s kitchen, either,” I said.
“You don’t?”
“No,” I said and I said it firmly. But Nicolaus was hard to read in broad light and it was narrow dark in the Boot and Thorn.
“But the imperative,” Daniel said loudly across the room, “is that now there’s a Chair open. Let the bidding begin!”
Returned to my bedroom, I chose Mr. MacLaurin’s volume from my shelf. Finally, though, I put it aside.
I opened the Faustbook from Master Desiderius. The title was The World of the Black Artist and Magician Doctor Johann Faust. There might have been truth in the tale.
It had been two hundred years ago that Paracelsus held the chair of Medicine, and he held it only one year before he was thrown out for obnoxiety. He must have been exemplary in his ill-will and bad-temper. It was very rare for a man to be ejected from his Chair. I didn’t know of any other besides him, and he was very famous for it. Theophrastus Bombastus must have been an apt name.
There might have been truth of history, that a man like Paracelsus would have had pride and blindness enough to think he might get the better of bargaining with a nemesis angel. Then there might be truth of Theology, that a Mephisto would take on the bargaining. If Paracelsus had made that bargain, though, he must also have come to Faust’s end, as he lived no longer than any other man. What a terrible game it was to try, and what a fool to have tried it. I thought through all the possible outcomes, and all seemed that they would be tragic.
And finally I put my candle out.