“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?”