Authors: Michael Flynn
Joachim’s prayers cut off abruptly. After a moment, the man rose to his knees, crossed himself, and turned around. “Is that what you think?”
“In Galatia, those Jews who had not accepted Christ criticized those who had, because the Galatian pagans who had also been saved did not follow the Law of Moses. So, the Jewish Christians urged the Galatian Christians to become circumcised, hoping to use that outward sign to mollify their accusers. But the Galatians had a horror of bodily mutilation; so much turmoil resulted. Paul wrote to remind everyone that outward signs no longer mattered.”
Joachim pressed his lips together and Dietrich thought he would launch some retort; but after a moment, he rose to his feet and straightened his robe. “I wasn’t praying for that.”
“What, then?”
“For you.”
“Me!”
“Yes. You are a goodly man, I think; but you are a cold one. You would rather think about the good than do it, and you find it more congenial to debate angels and pinheads
than to live the true life of poverty of the companions of the Lord—which you would know, if you thought about what Paul meant in his letter.”
“Are you so holy, then?” Dietrich said with some heat.
“That men’s hearts do not hold always what their lips proclaim, I am heartily aware—ja, from childhood! Many a whitened sepulcher proclaims Jesus with his tongue, and crucifies Him with hands and body! But in the New Age, the Holy Spirit will guide the New Man to perfect himself in love and spirit.”
“Ja doch,” said Dietrich. “‘The New Age.’ Was it Charles of Anjou or Pedro of Aragon who was to have started it? I’ve forgotten.” The New Age had been prophesied by another Joachim—he of Flora. Paris had reckoned him a fraud and “a dabbler in the future,” for his followers had prophesied that the New Age would begin in 1260, then in 1300, as political winds in the Two Sicilies shifted. Flora’s teaching that St. Francis had been a reincarnation of Christ Himself struck Dietrich as both impious and logically flawed.
“‘The man of the flesh persecutes those born of the spirit,’ “Joachim quoted. “Oh, we have many enemies: the Pope, the Emperor, the Dominicans …”
“I should think Popes and Emperors enemies enough without taking on the Dominicans.”
Joachim threw his head back. “Mock on. The visible church, so corrupted by Peter with Jewish falsifications, has always persecuted the pure church of the spirit. But
Peter
fades, and beloved
John
appears! Death stalks the land;
martyrs burn!
The world of fathers will be replaced by a world of brothers! Already, the Pope is overthrown, and Emperors rule in name alone!”
“Which still leaves the Dominicans to deal with,” Dietrich said dryly.
Joachim lowered his arms. “Words hang like a veil before your understanding. You subordinate spirit to nature,
and God Himself to reason
, and so cannot see. God is not being, but
above
being. He is in all places at all times, in
times and places we cannot know save by looking within ourselves. He is all things because he combines all perfections, in a way past all understanding. But when we see past the limitations of such creaturely perfections as ‘life’ and ‘wisdom,’ that which remains is God.”
“Which does not seem beyond understanding, at all, and reduces God to a mere
residuum
. You preach Platonism warmed over like yesterday’s porridge.”
The young man’s face closed. “I am a sinful man. But if I pray that God will forgive my sins, is it so terrible that I include yours, too?” He bent and rose again with a sprig of hazel in his fingers that had fallen from Theresia’s herb basket. The two parted with no further words.
D
IETRICH ALWAYS
found his meetings with the Krenken unnerving. “It is the fixity of their features,” he had told Manfred. “They lack the capacity for smiles or frowns, let alone expressions more subtle; nor are they given to much display or gesture, and that bestows on them a menacing mien. They seem like statues come to life.” That had been a special terror of his from boyhood. He remembered sitting beside his mother in the cathedral church at Köln, staring at the statues in their niches, and he remembered how the flickering candlelight made them seem to move. He had thought that if he stared at them too long, they would become angry and step down from their niches and come for him.
Dietrich had concluded that it was not the
Heinzelmännchen
that spoke, but the Kratzer who spoke through him, and he had learned the difficult trick of perceiving the words of the talking head as coming from the giant grasshopper instead—although whether boxes or grasshoppers spoke was in either case wonderful. He said as much to the Kratzer, who explained that the box remembered words as numbers.
“A number may be expressed as a word,” Dietrich responded. “We have the word
eins
to signify the number one. But how can a
word
be expressed as a
number?
Ach … You mean a code. Merchants and imperial agents use such methods to keep their messages secret.”
The Kratzer leaned forward. “You have this species of knowledge?”
“The signs we use to signify beings and relations are arbitrary. The French and the Italians use different word-signs than we do, for example; so to assign a number is not in principle different. Yet, how does the
Heinzelmännchen
… Ach, I see. He performs an
al-jabr
of some sort on the code.” Then he had to explain what
al-jabr
was—and then who the Saracens were.
“So,” the Kratzer said finally. “But these numbers use only two signs:
null
and
one.”
“What a poor sort of number! There gives often more than one of a species.”
The Kratzer rasped his forearms. “Attend! The … essence-that-flows … Fluid? Many thank. The fluid that drives the talking head flows through innumerable small mill races.
One
tells the
Heinzelmännchen
to open a sluice gate so the fluid may run down a particular race.
Null
tells him to leave the gate closed.” The creature drummed rapidly on the desktop, but Dietrich was unsure what mood this represented. In a man, it might signify impatience or frustration. It was clear that the Kratzer sought to communicate certain thoughts that fit poorly within the vocabulary that his talking head had thus far provided, and so Dietrich must tease the meaning from the words much as thread is teased from wool.
The Herr Gschert had been listening to the byplay from his usual position, leaning casually against the far wall. Now he buzzed and clacked and the talking head picked up some of what he said through the “small-sound” automaton to which Dietrich had given the Greek name
mikrofoneh
. “How does this discussion use?”
The Kratzer said, “Each knowledge uses always.” Dietrich did not think the utterance was meant for him and kept a blank face—although blank faces might convey weighty matters to such an expressionless folk as the Krenk. The
servant who groomed the talking head turned a little and, while his great faceted eyes never looked on anything squarely, Dietrich had the uncanny feeling that the servant had glanced his way to gauge his reaction. The servant’s soft upper and lower lips came together and parted in a slow, silent version of what the priest had come to consider Krenkish laughter.
I do believe that I have seen one of them smile
. The thought came unbidden, and left him with a curious sense of comfort.
“The twofold number is the smallest piece of knowledge,” the Kratzer instructed him.
“I disagree,” said Dietrich. “It is not knowledge at all. A sentence may impart knowledge; even a word may. But not a number that represents a mere sound.”
The Kratzer rubbed his forearms together in what appeared an absentminded fashion, and Dietrich thought that the act signified something like what a man would mean by scratching his head or rubbing his chin. “The fluid that drives the talking head,” the Kratzer said after a moment, “differs from that which drives your mill, but we may know something of the one by a study of the other. Do you have a word that signifies this? Analogy? Many thank. Hear this analogy, then. You may break a pot into shards, and these shards into fragments, and the fragments into dust. But even the dust can be broken into the smallest possible pieces.”
“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 in his posture save the slow rhythmic scissoring of his horny side-lips.
Dietrich had grown accustomed to these wild arguments, although they unnerved him with their sudden vehemence. They were like thunder-weather, blowing up from nowhere, and passing just as quickly. The Krenken were a choleric race, like the Italians, or they were under some great strain.
When the Kratzer had reachieved his balance, he said, “This has been said by another.” Dietrich knew he meant the servant. “‘You speak a word. The
Heinzelmännchen
repeats it in our tongue. But has it spoken what has been said?’”
“That is a great problem in philosophy,” Dietrich admitted. “The sign is not the signified, nor may it convey the entire significance.”
The Kratzer threw his head back briefly in a gesture whose meaning Dietrich had not yet plumbed. “Now we hear it,” the Krenk complained. “The poor
Heinzelmännchen
is speechless. What is a ‘problem’? What is a ‘philosophy’? How can the ripening of a fruit or your ‘holy breath’ be like the speed of a falling body?”
The servant spoke again, and this time the box translated his words: “The box-that-speaks stands the word ‘philosophy’ not in the German tongue.”
“Philosophy,” Dietrich explained, “is a Greek word. The Greeks are another people, like the Germans, but more ancient and learned, save that their great days were long ago. The word means ‘love of wisdom’.”
“And ‘wisdom’ is what meaning?”
All at once Dietrich felt pity for Zeno’s Achilles, running forever after the tortoise, coming always incrementally closer, yet never in fact reaching it. “‘Wisdom’ is … perhaps, having the answers to a great many questions. Our ‘philosophers’ are those who seek answers to such questions. And a ‘problem’ is a question to which no one yet knows an answer.”