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.