An Elegant Solution

by Paul Robertson

  But as my feet descended the stairs, another pair were ascending. As I passed Little Johann on his way up, I said, “The letters are still on his desk. Both from Paris and from Russia.”

  By a narrow passage between two houses I came to the stone yard. It was bare of grass or any green, part dirt and part stone flags, and dizzy of worked, unworked and part-worked stone. There were keystones, cornices and corners, and other architecture, but really the yard looked most like a churchyard for the monuments and figures and angels. And everywhere, there was dust. It was very fine and gray.

  The man was there, too, his hammer hanging in his hand, staring very thoughtfully at a gray veined square. “Lithicus,” I said. “who’s that for?”

  “Oh, is it you? It’s not for you.” In his yard he was a gray man. His hair was, his dust covered skin was, and his loose smudged shirt. But the veins in his arms were as stark as the veins in his marble, and I wondered what flowed in either.

  “I hope not!”

  “No, a fish merchant. He choked on a fishbone.”

  “It’s a pretty piece. What will you put on it?”

  “A long life and much to say about it. It won’t fit on this. So this one’s not for him. I’ll want a bigger slab.”

  “Oh, I think I know who it was,” I said. “Reinkarper?”

  “That’s him.”

  “He wasn’t rich. It would be a big stone for a middle merchant.”

  “There’s three kinds that take a big stone,” Lithicus said. “The rich, the pious, and the sinful.”

  “The sinful? For atonement?”

  “For their side of the argument.”

  “I have a job for you,” I said. “It’s a memorial, too, and not for any of your three kinds.”

  “What family of yours is dying? Or are they already?”

  “He isn’t and he is. It’s Master Huldrych.”

  “Huldrych. Yes. That’ll take a good stone. But what are you to him to be here?”

  “I was sent.”

  “Sent.” His eyes narrowed beneath his dusty brow. “Sent, are you? Who by?”

  “Master Johann.”

  He dropped his hammer and the yard rang. “I would have known,” he muttered. “And he’s paying for it?”

  “He said to tell you. Will you do it?”

  “He knows all well that I will. What’s it to say?”

  I read the paper to him. “It lists when he died, and that he was Chair of Physics. It’s for the church wall.”

  He stared at the words. “They’ll balance right.”

  “What do you mean?”

  “Can’t have short lines then long lines. Those’ll split.” He pointed to spots on the paper between the words. “Plain words,” he said.

  “He wasn’t a plain man.”

  “He is now, plain as any of them.”

  “It says what he was,” I said, “not who he was.”

  “When a man dies he should die and be done with it. Not keep a hold on his place and people. Take a broom to his house and sweep it clean.” It seemed an odd philosophy for a monumentalist. Lithicus’s trade was memorializing in stone. A good portion of Basel’s past would be remembered mostly by his chiseling. “Now, any border on this? Any decorations?”

  “You’re to make it whatever the current style is. And draw it first and send it to Master Johann with the cost.”

  “I’ll do it. And when he says it’s right, I’ll carve it the same as it’s drawn, to the scratch. I won’t have any trouble with this one. Not like the other.”

  “Which one?”

  “For his brother. Jacob. He didn’t like what I did. If I’d seen what he wanted before, instead of after, I would have made what he wanted.”

  I didn’t even say the word, spiral.

  Master Vanitas lived on the Peter Square, which was wide and tree-filled, near Saint Peter’s church. The Square was bounded on one side by the Grace Cloister, whose original monks were no longer present in Basel. Now the cloister was part of the city Armory. On the other side of the Square was a row of comfortable houses which, not content with the trees in front of them, also had large gardens behind.

  Master Vanitas held the Chair of Theology. He seemed to be an old man, but was actually only aged beyond his years. He had a sprightly, devoted wife and a cherubic young child. In fact, he was surrounded by all the vanities of life. His best known lecture was on the certainty of death.

  He hadn’t many friends, and very few of his students admired him, but I did. His history was that he’d also come to Basel as a young man to study Mathematics, and he’d studied at the feet of Master Jacob.

  No one else knew this. Daniel didn’t, nor Nicolaus. Vanitas was a student in the years before they returned to Basel. I had even asked Gottlieb once if he’d known how Vanitas came to his Chair, and Gottlieb had told me a few normal details but not that there was Mathematics involved, and it seemed he would have told me if he’d known. I only came to know myself because of an odd moment in a Theology lecture.

  It had been in just my first or second year as a student. I was listening very attentively, not realizing how stultifying it was. In the course of a discourse on the inviolability and invisibility of heavenly truths, he’d made a statement: “It is no more possible for man to see or feel God’s law than to see a trigonometric identity.” That, of course, had roused my interest, both that his point was so intriguing, and also that he was aware that trigonometry had identities.

  We had talked a few times since. He had lost interest in Mathematics because of what he called its arrogance, that it brooked only one correct answer to a question, and within its own rules. He preferred questions that couldn’t be answered, and answers that didn’t satisfy. But I’d thought deeply myself about the similarities between Mathematics and Theology, how they were both invisible, unchangeable, and seemingly unfathomable. Both ruled us, and we could struggle and challenge them, but finally, we were bound by them.

  He let me in and took me through his house to his garden. His wife was at play there with their daughter, who had only lately discovered walking and the possibilities of self-locomotion. We watched her explore. A soap bubble from some neighbor house settled lightly on a blade of grass beside her and a butterfly settled as lightly beside it. A clock inside sounded solemnly. The bubble popped, the butterfly soared from it into the sky, and the child, amused and bemused, turned away. These were reminders to me of ephemeral life.

  “Master,” I said. “I’d like you to tell me about Master Jacob.”

  “Master Jacob,” he said. “Well, then, Leonhard, please sit and I will tell you.”

  Master Vanitas was a man who spoke carefully, slowly, and long. There had always been a tinge of sadness in his voice. Whenever he spoke, and whatever he spoke of, he seemed always aware of the weight and implication of humanity. This gave his lectures on Theology a meaning, a purpose, and a depth in which his students quickly drowned. Those who remained awake felt that they were hearing things that must be understood but were not understandable. I was always fascinated by his teaching, though I was careful to have a full night’s sleep beforehand.

  When he conversed on subjects more mundane, he wasn’t abandoned by that weight of thought he always carried, and so if he was asking Lieber for a book or his wife for a plate of fish, or just considering the chance of rain, his listener felt that nothing was trivial, nothing was answerable, and nothing was even visible. It was so much like Mathematics!

  Therefore, as Master Vanitas told me his thoughts and impressions of Master Jacob, it was as if that Master was an Old Testament Prophet translated via Latin from the original Hebrew. I interpreted the verses and imagined him.

  Jacob had been like his brother Johann. He was brilliant, sullen, far-seeing, narrow, vengeful, could think like lightning . . . but there was a trait that the older brother didn’t have which the younger did, the ability to control the men around him. And, he’d been very suspicious of Master Johann, especially because he’d known
his younger brother had that great advantage and was honing it in Holland. In the ten years they were apart, they fought constantly and with only a little mercy. Their letters and publications were full of vitriol for each other, but they had respect.

  And when Jacob had learned that Johann was returning, he fell into a thick, bitter, angry sadness. Vanitas had already stepped away from Mathematics toward Theology but he still called on his old teacher, and he’d seen that something final was occurring in his Master’s thoughts.

  “What do you mean by final?” I asked.

  “Something that was an end and irretrievable.”

  “How did he die?”

  “Of an illness. He was in poor health but I hadn’t expected it. When I was young, death was still a surprise to me.”

  “Did he die before or after Master Johann arrived in Basel?”

  “At just about the same time,” Master Vanitas said. “There was a grievous elegance to it. That the Chair should pass from one brother to another. Death brought about change that in some ways was no change.”

  There was a growing risk that the entire Lecture on the Certainty of Death would proceed. I quickly asked a question on a different subject. “I was speaking with Master Desiderius. He said that it was you who nominated him to his Chair.”

  “Greek? Yes, I did. I’d not met him, but I’d known of him.”

  “Then you knew he’d be qualified for the Chair.”

  “Yes, I knew. But it was Master Johann who reminded me of him. I’m not sure who our committee might have nominated otherwise.”

  “Thank you very much, sir,” I said.

  Past seeing Lithicus and Master Vanitas, it seemed fit to walk to the Death Dance, which was nearby. That dance was certainly the most universal of all human gambols. No face in the mural was anyway joyful except for death’s. While Death Dances dated from the years of the Black Death, the dance would be true even without a plague. In the most peaceful, healthful land, Death would still take every man and woman by hand. But when he did for any reason other than age, he was being more inevitable than he needed be. I wanted to look again at Master Jacob’s epitaph.

  Through Vanitas, I’d come from the stonecutter to the stone. I stood a long while in the Munster cloister, considering Uncle Jacob’s memorial, considering the medallion, and thinking of what Lithicus the stonecutter had said.

  To most people, a spiral was the Archimedean. It would begin at a center and circle out. Mathematically, it was a polar graph with the radius at every point equal to the angle from an axis. As the angle increased and reached the full circle and increased on, over and over, the arm of the spiral would increase outward. Every point of the arm was an equal distance from the circle inside and the circle outside. There was a satisfaction to it. It had its single beginning and continued growing forever. But it was the spira mundanus, the mundane spiral, and it had this failing: that as a viewer stood back from it, it would shrink as everything would with distance. The revolutions, always equidistant, would vanish into indistinction.

  To Mathematicians, a spiral was the Logarithmic. This was a spiral like the other, but with a crucial difference: The space between the circles of the arm widened. It was the spira mirabilis, the marvelous spiral. Each repetition increased by a constant ratio. As a viewer would step back, the center might diminish, but the outer parts would just shrink down to exactly replace them. If the line were itself also to grow thicker, the spiral would appear the same from any distance, growing larger in its circling as it grew smaller from distance. And it had no beginning, either. Stepping closer would reveal an endless circling within.

  The conch shell on my shelf was Logarithmic. I was so amazed when I first saw it, because I only had my own sketches before to imagine what the shape looked like. Then I’d seen that what I’d only known invisible existed visible, as well, at least a shadow of it. It may have been that everything invisible had such a shadow.

  There were many other spirals: those of Phyllotaxis and of Fermat; the Golden Spiral of Fibonacci; the hyperbolic spiral, the lituus, the Theodorian Spiral which he received from Pythagorus. I’ve even imagined a reverse spiral which started in its center with no curvature, then tightened to a point like a fern. But none of these equaled the elegance of the Logarithmic. Perhaps someday the medallion could be replaced to fulfill Jacob’s wishes.

  But the rest of the epitaph was also worth study. I noticed again the shields that top the epitaph stone. One was a lion, which I knew by its paws. The other was Master Jacob’s, and Master Johann’s, family arms: three branches of seven leaves each. Master Johann’s grandfather was a spice merchant in Bern, who left that city during a religious upheaval. The family brought its business to Basel and quickly took in the new city the place it had lost in the old. The son, Nicolaus, grew the business and had many relatives to pass it on to; these many cousins still operated it. But of Nicolaus’ three sons and seven daughters, two sons, Jacob and Johann, went against their father’s wishes into Mathematics, and now that was the business of their branch.

  There was another also quietly deliberating leaves and spirals. “Why are you here?” I asked. It was Little Johann.

  “I saw you.”

  “Have you looked at this before?”

  “I shouldn’t.”

  “No,” I said. “You can. You should. Your father doesn’t want mention of your uncle, but you can come see his place here.”

  “I do look at it some.”

  “Do you know what it means? You’ve been taught Latin.”

  “But I don’t learn it.”

  “Resurgo Eadem Mutata. It means, ‘I arise again the same though changed.’”

  “Then it’s the wrong spiral.”

  “Yes,” I said. “You’re right. The stonecutter made it wrong. It was meant it to be Logarithmic.” Arisen changed, it would remain the same.

  “What will Huldrych have for his memorial?”

  “I saw the wording,” I said. “There was no philosophy on it. Will you come with me? I’m going to the Watch Barracks.”

  “I’ll come. Why?”

  “To see the trunk again. It’s there.”

  “Then I won’t come.”

  “Do,” I said. We turned from Jacob and the Latin and the Spiral. The cloister lawn was so filled with light that it was jewels and crystal, like the green glass in Saint Leonhard’s windows with the sun full through them; there was growth and life. Little Johann followed beside.

  “I saw Daniel’s hourglass,” he said.

  “It’s sure genius,” I said. “So I think I know what the letter from Paris says.”

  “And Russia?”

  “There’s a new University. Tsar Peter has started it. He’s calling for the great scholars of Europe to be part of it.”

  “What about Poppa, then?”

  I laughed. “The young great scholars.”

  “What about you, then?”

  I laughed harder. “The young great scholars. I’m only young. I’m no great and I’m barely a scholar.”

  “They only don’t know you yet. Poppa would write a letter for you.”

  “He’d only dent his own reputation, he wouldn’t make mine.”

  Little Johann was still following and I kept him listening. I talked about Russia and Paris and Italy. I’d never been beyond Basel and Riehen and the hills around them. I talked though about Italy, which was a ruin of Renaissance times built on a ruin of ancient times, where goatherds led flocks through emperor’s palaces and the art of three centuries past was still more live and true than the superstitious villages the goatherds lived in; and I talked about Paris, which was the center of Europe and the world, all glittering and grand and rich and frightful to its neighbors, where the intellectual thought was richer and more glittering; and I talked about Russia, which was a new, exotic, mysterious land which might be barbarian but was rising and pulling and moving.

  At least, these were my imaginations of those places. I didn’t know.

 
; And Little Johann listened. I don’t know if he was as easily caught as I was, if he was with me in far-off lands, or if he only wanted someone to talk to him. He was still beside me as we came to the barracks.

  “Simeon?”

  He was there, snoring in a chair. He was Day Watch and it was Day.

  “What?” he started gently. “What is it? Oh, Leonhard. It’s not still an inquiry?”

  “No,” I said. “Except my own.”

  “What do you want?”

  “Could I see Knipper’s trunk?”

  “That he was in? Why do you want that?”

  “There was something written in it, and I wanted to see it again.”

  “What written?” Simeon’s a friendly one, but he’ll ask all the questions first. He’d want a reason to let me in.

  “I’ll show you.” That was good enough. The hall we walked had no windows, just light from the doorways on each side. It was all as it had been with Gottlieb five days earlier. We stopped a moment by the rusted armors standing guard beside the weaponry store: swords, axes, maces, bows, and guns. The room across from it stored Watchmen, some sleeping and some at tables playing and talking. Another room stored grain, potatoes, dried meat, and more foodstuffs. The last had shelves loaded with closed boxes and barrels of less obvious meaning. But here there was a change from my last visit. The floor was empty.

  “Has it been moved?” I asked.

  “It hasn’t been moved,” Simeon said. “Where would it be moved?”

  “But it isn’t here.”

  “I’m not blind.” He wasn’t, even when his eyes were closed, and now they were open, narrow, and suspicious. But not of us.

  “It’s been taken. Would the Watch have taken it?”

  “I’m the Watch for this room, and I haven’t. It must have been Night.” He stared at the space a moment, then at me, frowning. “Then do you know who might have taken it, young Master Leonhard?”

  “I’d like much to know,” I said.

  “It was taken at night, I know that. Not on my Watch.” He left us then, suspicious and grumbling threats against the Night Watch.