An Elegant Solution

by Paul Robertson

  The lecture that day was on a very basic principle of Calculus, the statement that if a function has a certain value, then increases or decreases in any way while staying continuous, and at a later time returns to that same first value, then there is at least one point in between where the function must have been level. Monsieur Rolle of Paris, and who was a member of the Academy there, first stated this principle.

  Of course, Master Johann’s description was far more clear and more easily understood than I could have attempted. He smiled, gestured, was even humorous. He gave examples, that there must always be a top to a hill and a bottom to a valley, to make his audience understand.

  The lecture hall was filled with Basel’s gentility. The Chairs’ lectures were a powerful bond between the City and the University, allowing each to be acquainted and improved by the other.

  And not only the City attended, but several students, also. There were a few new to the University taking the opportunity to first see the famed Master Johann; there were a few who had a sincere interest in the Calculus, though this was a very few; and there was an occasional unfortunate who had fallen under the cloud of Master Johann’s disapproval and was trying to regain favor. I remembered Gottlieb’s appointment concerning a student who’d shown disrespect to a Master; and I saw a student I knew, named Gluck, in the second row, who was usually proud and joyful but was now desperate, eager, and ignored.

  That night Grandmother asked about Master Johann’s Theology and Philosophy. “Leonhard, you’ve said that Master Johann was accused of being a Cartesian. Tell me how it was heresy.”

  “The Mathematician Descartes a hundred years ago said that only what was sensed or touched was real. So he determined to reason, from only his own senses, what he believed.”

  “Then does he say that God is not real?”

  “No, the Monsieur claimed that he was able to reason that God was real.”

  “Is it heresy?”

  “Some people say it is, because they say God’s word makes a thing real, not a man’s reason. But Descartes said he didn’t know God’s thoughts, that he only knew his own thoughts, and he would have to decide for himself what was true.”

  “What does Master Johann say?”

  “I think he is very thoroughly a Calvinist. But for him, there’s a world of Theology, and a separate world of Mathematics.”

  “For you?”

  “They aren’t separate. One is the rain and one is the river.”

  10

  The Remembered Meteor

  Thursday morning Nicolaus tapped my shoulder as I was carrying a sack of flour into Mistress Dorothea’s kitchen from her cellar. “I think we’ll talk today,” he said.

  Then later when I, in black and white and beneath my tricorne, left my house for a lecture with Master Desiderius, Nicolaus was beside me in the street. I knew better than to wait for Nicolaus to start a conversation. “I tried to talk with Daniel about Master Jacob,” I said. “And he doesn’t want to hear a word.”

  “He’s done with that.”

  “I’m not.”

  There was never any menace to Nicolaus. He was only quiet and intent. I could wait silently, too. “Why?” he asked, finally.

  “It’s worth some looking.” Usually I walked a brisk pace to lectures, or anywhere, or I just ran. But I was in my tricorne and talking with a man in his. We walked deliberately. I waited again.

  “What did you see of Knipper in my mother’s kitchen?” Nicolaus asked.

  “I saw him there,” I said. “I’ll never deny that. He only asked me to fetch Willi from the inn, to carry that black trunk.”

  “It might have been made known to the Inquisitor.”

  “I thought you wouldn’t want him to know,” I said. “Did you want the Inquiry to come into your own house?”

  “The Inquiry would have found its own Inquisitor there and he could decide himself what to make of it. That might have been why he was made Inquisitor. I think it more likely that you didn’t want the Inquiry to find you in my own house.”

  “I wasn’t asked anyway.”

  “Answers needn’t have questions.”

  “Questions needn’t have answers, either,” I said, but only as it seemed a properly ambiguous remark to make.

  “Does the Reciprocal Squares have an answer?”

  “Not that I know. But it must, I think. Have you tried to solve it, Nicolaus?”

  “I have.” And he smiled. “Everyone in the family has for years.”

  “But the challenge only came from Paris this month!”

  “The problem is older than Monsieur de Molieres’ challenge. It’s older than the Monsieur himself.”

  “Has Daniel also played at it?”

  “Dearly.”

  I knew enough about my Master’s family and their Mathematics to make a guess. “Nicolaus,” I said. “Would it be that Daniel wrote to the Paris Academy and pressed them to make the challenge?”

  “Why would you think that?” So of course I was right.

  “Because Daniel couldn’t solve it, and was afraid his father might. Now all Europe will try. Daniel would rather anyone else solved the problem than his father.”

  “You know the lion by his paw.”

  “But Daniel wouldn’t have solved it anyway,” I said. “It’s not the kind of Mathematics he’s genius at. It’s too . . . invisible.”

  “Nor I,” Nicolaus said. “It’s too invisible for me, as well.”

  We’d reached the house of Desiderius. “Master Desiderius came from Strasbourg.”

  “Many of us have come through Strasbourg. The trunk has now, also.”

  “What do you know about the black trunk?” I asked.

  “Everything.”

  “It was Master Jacob’s. It had been in Huldrych’s laboratory and then in your father’s house. And Jacob’s papers were in it.”

  “And then Knipper was. This is what I want of you, Leonhard. Come with me tonight to ask Willi what he found in the kitchen.”

  So now, I was Nicolaus’ clerk. “I was wanting to. Nicolaus, should I tell Gottlieb that Knipper was in the kitchen? Should I tell the Council, or Magistrate Faulkner?”

  “Whether only a few know that, or everyone does, it will still mean the same thing.” And he tipped his hat. I did the same.

  After his Greek lecture, I asked Master Desiderius about the Faustbook. “If a bargain is made with mere men instead of Mephistopheles, what is at stake? Can a man wager his soul?”

  “I hope he can’t,” Desiderius said.

  “What else would he wager?”

  “In truth, all a man has is his soul.”

  “So there isn’t any wager, then,” I said.

  “I hope there isn’t. In your Mathematics, are there problems without a solution?”

  “There are some. And there are some that might, but the solution hasn’t been found yet. Last Saturday Master Johann gave me a problem just like that. Either there is no solution, or it will be very elegant.”

  “An elegant solution.” He was wistful. “Yes, that’s what’s needed.” He smiled. “Leonhard, I have a bargain for you.”

  “You’ll give me fame and knowledge?” I asked and we laughed.

  “No, you’ll do something very small for me, and get nothing out of it in return.”

  “I’d want nothing anyway. What may I do?”

  “You’ll know soon.”

  On that Thursday it had been one week from Huldrych’s death, and there had been no other deaths. The Council ordered that the black flags be taken down, and commerce be resumed. Commerce hadn’t been embargoed, as it would have been in earlier years, but it had slowed. In just the course of the day it quickly revived. The piers were busy with boats coming and going, the gates were thick with carts, and the Market and Barefoot Squares were bustling to make up what had been missed.

  In the Market Square I saw all the people of Basel. Wives with their baskets, kitchen girls on errands from their mistresses, booths of leather,
cloth, ironmongery, and pottery and the craftsmen who’d made them, fish and fishermen, bread and bakers, farmers and all that their fields made, butchers and meat, and passing through the Square was a pastor one moment and a lawyer the next, a scholar of the University herding a flock of flapping black and white students, then a troop of the Watch.

  All the Death Dance was there, but Death himself. Or, he was invisible.

  Thursday evening came, and among all the men affected by Knipper’s death, finally one of them had reason for real joy. Beside Willi in the box was planted a booted and weathered man of goodly girth and mirthful visage, though Willi’s smile was wider by far. This was Knipper’s replacement, a man from Bern who’d been recruited by the innkeeper of the Roaring Lion. And Gustavus seemed to be expecting him and went in with him to the stables once he’d unloaded the passengers and luggage.

  “That one’s a coach driver for any road,” Willi said as the horses disappeared into the tunnel. “See that smile? Oh, and do you think he’s just fat and pleased? There was a highwayman blocking the road on the pass over Solothurn, and his partner on a horse right out from the trees behind us, and fat old Rupert shot them both dead, one pistol shot each. And he never slowed down, and he never stopped smiling.”

  “And he left them?”

  “He never slowed down. He just told sheriff in Solothurn they were there.” Willi shook his head. “Knipper would at least have been put in bad humor by it. This new driver, Rupert, never stopped smiling.”

  There was evening and morning in each day of Genesis, and Master Desiderius read the Hebrew this way: a twilight of turning and twisting, to a dark night of dark things, then a breakthrough dawn to the age of day. The earth turned from the sun as I walked Basel’s streets, and though Basel was not too tightly a part of the earth it rested on, it turned from the sun, as well. I passed a Night Watch on his way to his post and he greeted me. Basel had watchers in the night, some visible. Charon the cat was watching, also. I didn’t see Nicolaus.

  Daniel was in the Common Room, and I stayed away from him and his dice and cards. He was too boisterous, and still off balance. His voice rose and swayed like a pass through the Alps, and he sounded in danger of falling off its edge. And he laughed, and no one else was yet. But his rough humor served us when he chided Willi too hard for his failings as a coach driver and drove Willi to leave the Common for his own room.

  And as I stepped back into the hall outside the Common Room a shadow came beside me. Nicolaus had been watching for me.

  I took Nicolaus to the hall, and up the stairs toward the living, moist smell of horses. Below us we heard neighs and shuffles, and Knipper’s niche was in an invisible corner. The door was poorly fit and glow of a candle leaked through and around it. I held up my own candle and knocked. “Be away, and if it’s food leave it.”

  “It’s not food,” I said. “It’s just Leonhard.”

  “Then just be away.”

  “No, Willi, I won’t bother you.” I pushed on the door, which had no latch, and Willi was hunched sitting on the straw pallet. The room might have been any size, a closet or a cathedral, beyond the meager part that the candle lit. Likely Knipper had never seen it except at night. “And it’s Master Nicolaus, too.” As little light as Willi’s candle gave, nearly as much seemed reflected from his face. Or maybe it was his own glowing anger that we saw in his eyes and cheeks and chin.

  “I’m weary,” he said.

  “Weary of talk,” I answered. “I know you are. But you won’t drive the coach anymore, will you? That Rupert has it now.”

  “No, I won’t drive it. I won’t ever drive it. I’ll throw myself into the River rather than drive.”

  “Will Rupert have this room?”

  “He’ll have to find it first, and get me out of it when he does.”

  “He won’t find it if he hasn’t already,” I said. “Can I ask your help, Willi? I want to know who killed Knipper.”

  “I don’t know. I didn’t.”

  “I know that. Nobody knows but one man, the man who killed him, and I want to know who it was. That’s the one who’ll be thrown into the River. So I just want to ask you a few questions and they’re not hard.”

  “I don’t know anything.”

  “You know if Knipper was there in Master Johann’s house in the kitchen when you fetched the trunk.”

  “Oh, you! You sent me after that trunk! That’s what started it!”

  “I did,” I said. “Knipper sent me for you. He said it’d been brought from the coach by mistake.”

  “I didn’t take it there. It was never on the coach.”

  “Was Knipper there in the kitchen with the trunk?”

  “I already said he wasn’t! I had to lift that myself.”

  “Was it heavy?” Nicolaus asked. It was always startling when he spoke and Willi shrank back from the question. “About the weight of a man. Was Knipper in it, do you think?”

  “Aye, yes, he was.” All the light in Willi’s face faded. It was as if the candle had been blown out, though it burned unchanged. “He rolled around in it, and I could feel it. I thought it was poor packed, and whatever it held would be bad broken by Strasbourg.”

  “How did you know it was going all the way to Strasbourg?”

  “The label on it said so.”

  “How much can you read?” Nicolaus asked. It was a surprise that he could any.

  “I know that word, Strasbourg.”

  “What else did the label say?”

  “That’s all I knew. It wasn’t till Freiburg that the innkeeper read it to me. The trunk was for Magistrate Caiaphas in Strasbourg.”

  “For him?” I asked. “Then it was being sent to him! When was the label put on it?”

  “I never saw it put on. When I got to the kitchen where I picked it up, the label was on.”

  “How long did it take you to get to Master Johann’s house from the Inn?”

  “I was pounding horseshoes that were bent; Gustavus had told me to do it. I wasn’t going to go help Knipper before I finished what my own Master had told me to do. I won’t cross Gustavus.”

  “Then ten minutes or more.” I asked Nicolaus, “How long was the family together? Who would have left or gone to the kitchen?”

  “We were together long enough.”

  I didn’t ask more. Willi wasn’t understanding what I was asking Nicolaus, but he might start if I asked anything else. So I asked Willi, “Do you think anyone could have opened the trunk that night after you’d put it on the coach?”

  “They’d have had to tie it up again just as I had, and I tied it fast.”

  “Did you take the trunk to Caiaphas?” Nicolaus asked.

  “No, that was for Dundrach to do. That evil—that evil, evil bat came to me. From Hades he came.”

  “What did Caiaphas want?”

  “He wanted to know how I came by the trunk, and what had happened to Knipper. He threatened me with torture if I didn’t answer him.”

  “He didn’t tell you that Knipper was in the trunk?”

  “Never! He never did.”

  “Did they say you’d been arrested for bringing a corpse into the city?” I asked.

  “They said that, and I called them evil liars for it. They didn’t say it was Knipper.”

  “Did Caiaphas ever ask you anything else?”

  “Only about the trunk. I told them I’d just been told to put it on the carriage, and I never knew who tagged it. And I told him where I’d got it, from the Master’s kitchen, and I told him it was you who came for me to get it.” And he pointed at me.

  “You told him by name?” Nicolaus asked.

  “I said, The student, young Master Leonhard, who’s servant to Master Johann’s house. And he screamed at that, that you’d be a Master or a servant, but you couldn’t be both.”

  “I am both,” I said. “You were right. And Magistrate Caiaphas remembered my name. Willi, tell me about Strasbourg.”

  “That city’s all evil. All the pe
ople, down to the dirt in the streets.”

  “They’d have good people there, too,” I said.

  “They’ve like been cast out. The city’s evil.”

  “I don’t remember it that way,” Nicolaus said. “We stopped there for some time, a month, when we were coming to Basel.” Nicolaus would have been ten years old then. And his impression, even from twenty years ago, might have been more accurate than Willi’s. But Willi’s impression was as black and evil as a place could be. It made me think of the courtyard outside Caiaphas’s window at the inn. “And Gottlieb went on to Basel before we did.” He nodded to Willi. “Then that’s enough. You’ve been a help.”

  “I’ll want to know who killed the old man,” Willi said. “I’ll throw him in the river myself, for the trouble he’s caused me.”

  Nicolaus and I stood outside in the dark Square, at first saying nothing. But he had something to say and I waited.

  “A hand brought that pan down on his head,” he said, finally. “A hand in my father’s house.”

  “And a hand put Knipper in the trunk,” I said. “And took out Master Jacob’s papers that had been in it.”

  “There could have been space for Knipper and the papers both. They could have gone to Strasbourg together. Or the papers might have been taken out years ago. You’d want those papers, wouldn’t you, Leonhard?”

  “I would. And they were in the trunk.”

  “You know they were?”

  “I do, though I didn’t see them. Had you ever seen them?”

  “No. Gottlieb had.”

  “Nicolaus,” I said, “who killed Knipper? Who came into the kitchen?”

  “You came into the kitchen,” Nicolaus said.

  “I did no harm to Knipper.” And at that we parted.

  Sometimes I doubted my own memory.

  Once I saw a meteor. I had been walking back to Basel from an evening with my parents in Riehen. The sky was clear, with no moon and many stars, and it was very quiet. It was in the winter. I’d been thinking of how, if some action occurred, it would be by sight that we knew where; but it was more often by hearing that we would know that it had occurred at all. I considered the Cartesian implication that only by sensing did we know what was true. But something noteworthy could have been happening just behind me, and if it made no sound, I might never have known of it.