Eifelheim - Michael Flynn [51]
“Ah, you must mean the atoms of Demokritos.”
“You have a word for this?” The Kratzer turned to Herr Gschert and, in another aside, translated by the talking head, said, “If they know such matters, there may yet give help.” But the Herr replied, “Say nothing of it.” On hearing this, Dietrich glanced curiously at the servant.
“The analogy,” said the Kratzer, “is that the twofold number is the ‘atom’ of knowledge, for the least you can say about a thing is that it is—which is one—or it is not—which is null.”
Dietrich was unconvinced. That a thing existed might well be the most one could say of it, since there was no reason save God’s grace for anything to exist at all. But he said nothing of these doubts. “Let us then use the term bißchen for this twofold number of yours. It means a ‘little bite’ or a ‘very small amount,’ so it may as well mean a small bite of knowledge. No one has ever seen Demokritos’s atoms, either.” The metaphor of a “bit” amused him. He had always thought of knowledge as something to drink—the springs of knowledge—but it could as well be something to be nibbled.
“Tell me more,” said the Kratzer, “about your numbers. Do you apply them to the world?”
“If appropriate. Astronomers calculate the positions of the heavenly spheres. And William of Heytesbury, a Merton calculator, applied numbers to the study of local motion and showed that, commencing from zero degree, every latitude, so long as it terminates finitely, and so long as it is acquired or lost uniformly, will correspond to its mean degree of velocity.” Dietrich had spent many hours reading Heytesbury’s Rules for Solving Sophismas, which Manfred had presented him, and had found the proof from Euclid very satisfying.
The Kratzer rubbed his forearms together. “Explain what means that.”
“Simply said, a moving body, acquiring or losing latitude uniformly during some assigned period of time, will traverse a distance exactly equal to what it would have traversed in an equal period of time if it were moved uniformly at its mean degree.” Dietrich hesitated, then added, “So wrote Heytesbury, so nearly as I recollect his words.”
Finally, the Kratzer said, “It must be this: distance is half the final speed by the time.” He wrote on a slate and Dietrich saw symbols appear on the Heinzelmännchen’s screen. His heart thudded as the Kratzer assigned to each symbol distance, speed, and time. Here was Fibonacci’s idea, letters used to state the propositions of al-jabr so succinctly that entire paragraphs could be said in one short line. He pulled a palimpsest from his scrip and wrote with a charcoal, using German letters and the Arab numbers. Ach, how much more clearly it could be said! His vision blurred, and he wiped his eye. Thank you, O God, for this gift.
“So, we see the fruits of the Holy Ghost,” he said at last.
“The Heinzelmännchen is unsure. ‘Ghost’ is when you breathe out, and what has this to do with motion?”
“There was a great question for us: Does a man participate in unchanging Spirit more or less, or does Spirit itself increase or decrease in a man? We call that ‘the intension and remission of forms,’ which, by analogy, we may apply to other motions. Just as a succession of forms of different intensities explains an increase or decrease in the intensity of color, so the succession of new positions acquired by a motion may be considered as a succession of forms representing new degrees of that motion’s intensity. The intensity of a velocity increases with speed, no less than the redness of an apple increases with ripening.”
The giant grasshopper shifted in his seat and exchanged looks with the servant, saying something which the mikrofoneh did not this time translate. An exchange between the two escalated, growing louder, with the servant half-rising from his seat and the Kratzer smacking his forearm against the desktop, while Herr Gschert looked on with no change