An Elegant Solution

by Paul Robertson

  “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.

  “Was it plague?” I asked.

  “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 somethi
ng 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.

  8

  The Eadem Medallion

  Sunday morning I escorted my grandmother to Saint Leonhard’s, and I had to do it as a gentleman and not as a humble grandchild; I still only had one hat. The service calmed and comforted us both greatly. Three days after the Inquiry there had been no other indications of plague, and the city was whispering what Daniel had announced, that Huldrych had died of a common cause. Yet there were those who still held with Gustavus. That morning on our benches we were reminded that the truth was that we were in God’s hands. If there was judgment, we would not escape it; if there was mercy, we would receive it. That was an essence of the Reformation.

  Two hundred years ago, in the years that Holbein’s art came to Basel, and Paracelsus’ darker art came to Basel, the Reformation also came to Basel. It came in a man. His name was Hausschein, which meant HouseLamp; for his scholarly name he took Oecolampadius, which was Greek for that same HouseLamp. And he was a very bright lamp in Basel. He came when he was thirty from Heidelburg, at the very moment that Luther was nailing his theses to the Wittenburg door, and that was the flame that lit Oecolampadius’s wick.

  He preached atonement at Saint Martin’s Church and was the Reader of scripture at the University. He assisted Erasmus in that scholar’s translation of the New Testament, and disputed that scholar’s interpretation of it. Erasmus was finally bested; he admitted it himself, and Oecolampadius carried the city. Erasmus, near twenty years older, outlived him, though not for long. They’re both buried in the Munster.

  Zwingli was a student in Basel when Oecolampadius was in Heidelberg, and they became friends even as one had left Basel before the other arrived. They were partners in the disputations that ranged through Switzerland those years, arguing for Luther against Rome, arguing for Anabaptism against Luther, arguing for Luther against Anabaptism, arguing against anything, against each other if there was nothing else, and fracturing Catholicism in Switzerland forever, taking the land city by city and canton by canton into the Reformation.

  Oecolampadius and Paracelsus were contemporaries. I could imagine the dispute those two would have had. And if Mephisto, on leaving the Alchemist’s door, had, in the streets of Basel encountered the Reformer, that dispute would have been the greatest of all. And I’m sure who would have bested the other.

  Within twelve years of Luther’s nailing, the University in Catholic Basel was so engulfed in the Reformation’s fire that the Pope suspended his charter of the school and took its scepter, its seal, its statutes, certificates, privileges, and its cash assets. Three years later, Protestant Basel reopened the school. Oecolampadius had died the year before. The University had lost its seal, but the Pope had lost his University. It had risen, the same University, but altogether changed.

  My grandmother and I then walked back through Basel’s same streets to our own home and were offered no disputes or bargains. I preferred disputes in Mathematics, where ultimately a correct statement was irrefutable and an incorrect statement was indefensible. A dispute of Theology must also have truth and error, just as in Mathematics, but it seemed every man still chose for himself which was which.

  And this was why there were both judgment and mercy, and why sacrifice made it possible for there to be both.

  We ate in humble righteousness, which was the only kind.

  “Grandmother,” I said. “I was speaking with Master Nicolaus last night.”

  “Were you?” she said, nodding. “Yes, I spoke with him yesterday, also.”

  “I thought you might have.”

  “He called on me. He’s a very gentleman.”

  “You must have had a pleasant conversation,” I said.

  “He thought that you hadn’t been able to answer a question that was put to you at the Inquiry.”

  “I hadn’t been able,” I said. “It was just then that Master Huldrych became ill.”

  “He asked me if I knew the answer to the question you’d been asked. I told him that in his mother’s kitchen, you spoke with Knipper, and were sent to the inn for help with the black trunk.”

  “Thank you,” I said. My grandmother was the wisest of women and always knew what was right and proper.

  On the next, rain-soaked Monday morning, I opened the kitchen door as I always did and wondered how I’d find Mistress Dorothea. She might have been as slow as she’d been on Friday or she might have been returned to her normal whirling state. But she was neither, nor in between. She was in her normal household attire, except that she had on a black housecoat, and she was standing in the center of the room, stiff, waiting. For me. “Leonhard.”

  “Yes, Ma’am,” I said.

  “Master Johann wishes to see you.”

  I looked down at my mud-splashed self. “But Mistress Dorothea,” I started.

  “He said as soon as you arrived.”

  “Then, please,” I answered, and followed, all brown. We went to the hall, and to the stairs, but up only one floor. The door we came to was one I’d seen only once before, when my father brought me to Master Johann at my matriculation, to discuss my Saturday afternoons. Dorothea knocked and the voice answered, but it was different, as different as brown was from black and white, as different as Monday morning was from Saturday afternoon.

  The room behind the door was as different and more. The Saturday room upstairs was sparse and dark hollow. Now I stood on the threshold of a chamber dense and bright. I’d never seen so bright a room in Basel. There was the usual curtained window, but the true light was from a dozen candles. And what they lit! A desk, a chair, a cabinet, a case of shelves; and papers. Thousands of pages. It was surely thousands! And all of them crossed like a market square with lines of text and diagrams and equations.

  “Leonhard.” He looked up and perceived me.

  “Yes, Master Johann,” I said. “I apologize for how I look . . . I wasn’t expecting to see you.”

  He continued his stare. I stood in silence as the rain was still dripping from my hair, to my forehead, and one great drop splashed off my nose. Then he rubbed his hands and glanced back at his desk, and my apology had been accepted. “You said that you have been upset by Master Huldrych’s death?”

  “Yes. I have.”

  “As I said, I also. It was grievous and unfortunate. He wasn’t always obsolete in his lectures. He was once advanced in his field. The University will choose a Chair who is
more modern, but he is still a loss. Were you attending his lectures?”

  “Yes, sir. His advanced class.”

  I was first fooled that the papers were in disorder, but I knew they couldn’t have been. In an instant, I saw that there was an order, an order that I knew perfectly. To compare my own books and papers with this room would have been to match an acorn to an oak, but I was bold enough to call my desk an acorn at least. “I have a task for you.”

  “Yes, Master Johann.”

  He lifted a single sheet from all the papers. “It may help you in your grief. Do you know the stonecutter on the White street?”

  “Lithicus? Yes, sir, I know him.”

  “Good. Go to him. I want a memorial made for Master Huldrych. Take this.” He held out the paper, and I took it. “That is what it’s to say.” I looked at the page and read the words.

  “How should the stone be made?” I asked.

  “A wall piece. I want it a modest size and it will be placed in the Preacher’s Church, which was his parish. Modest but well made. He was a modest man. Make it whatever shape is the current style. Let the stonecutter decide, or you. But bring me a drawing before he starts, and his price. Tell him I’ll pay. He’ll know what that means.”

  “Yes, sir.”

  “A new Chair of Physics will be chosen. And Leonhard, as for the coach driver. The Inquiry is closed.”

  I dared to ask. “Was any answer found?”

  He looked at me, considering his answer. “Perhaps if I had completed my interview with Magistrate Caiaphas, there would have been an answer.”

  “Yes, sir.”

  That was all. I left the room both dimmed and dazzled. I was nearly desperate to see it again, to see in detail the books and papers I’d had only a few seconds to study.