I did not denounce these Certifications, but concurred with Dr. Eierkopf’s sentiments regarding the Certifier. Croaker’s incisions certainly did look tender; however, I could discern no subscription of any sort on Eierkopf’s Scapulist motto, which hung over a worktable littered with files, lenses, grindstones, calipers, micrometers, high-intensity lamps, and cartons of eggs.
“I don’t see those initials you mentioned,” I said.
His head lolled, apparently in amusement. “I can’t see them either! Except through this glass.” He pointed to a thick-ringed lens on the table and explained that Bray—whose ingenuity he
did
have to admire—had thought it appropriate to inscribe his Certification in letters of a sort and size that only an Eierkopfian Lens (a mated pair of lenses, actually,
the one “synthetic,” or panoramical, the other “analytic,” or microscopical) could resolve and focus—and that inconsistently, so it seemed, for when he held the device for me I could see nothing.
“Oh well,” Eierkopf said; “at least my Certification makes sense, even if not everybody sees it all the time. Croaker is seeing his, but nobody understands it!”
I was about to reply that Croaker could at least
feel
his. But as Eierkopf made a gesture of contempt with the hand that held the lens, I thought I glimpsed the missing initials on its objective face. I pointed them out to him, a bit triumphantly it may be, as further evidence of Bray’s deceitfulness; but although Dr. Eierkopf himself could not see the reversed letters
on the glass (owing to some feature of his spectacles), he was undisturbed by the disclosure.
“The point’s the same,” he said. “Anyhow, I told you I don’t believe in Grand Tutors till I see once a miracle.” He was pleased, however, to clear up the somewhat puzzling detail of the image’s inconstancy, as he was convinced that for better or worse all phenomena were ultimately intelligible. Contrary to what one might suppose, he said, an image twice refracted in certain complementary ways was not always thereby restored to its original state, any more than a cat dissected and reassembled in the zoology laboratories was the same cat afterwards: sometimes it came out doubly distorted (as it always was in theory); sometimes it seemed to vanish altogether, especially when the characteristics of his own extraordinary eyeglasses and the astigmatism they compensated for were added to the optical equation, or the light was wrong.
“But,” he smiled, “take away my lenses, I’m blind as Dean Taliped.” However, I was not to infer that because all lenses distorted (“Your own included,” he said, perhaps unable to see that I wore none), nothing could be truly seen; all that was necessary was to compensate for optical error, and for this he relied, in his own work, on the lens in his hand, which he knew to be accurate.
I asked him how he knew. His round eyes twinkled.
“I like you, Goat-Boy! Croaker fixes you a lunch, you can eat it around behind the clockworks.” But my question, which I’d thought to be serious and difficult as well as perceptive, he disposed of lightly, perhaps facetiously. The lens affirmed his Graduatehood, did it not? And since he was in fact a Graduate, he affirmed the accuracy of the lens.
“Wait a minute!” I protested. “Bray Certified your Candidacy, but you don’t believe in him.”
He wagged a hairless little digit at me. “I won’t affirm Dr. Bray, but I
can’t deny him, because it must be the same with Grand Tutors, if they really exist, as it is with Graduates: it takes one to know one, not so?”
I readily agreed.
“And a Grand Tutor would know Graduates from non-Graduates,
ja?
But not vice-versa. Well, just so with this lens: I know it’s correct because a Graduate like me can tell correct lenses from incorrect ones.” The case was analogous, he argued, to the interdependent relation between WESCAC and the Tower Hall Clock, which he had explained to me in the Observatory, and was reflected also in the problem of the clock’s accuracy, which, like all problems involving final standards and first principles, could be only academic.
“You claim you’re the Grand Tutor yourself, and Bray’s not,” he said, “but you can’t prove it—without a miracle. You can only know it, just as I know I’m a Graduate.”
I very much wanted to pursue the matter of the clock, my reason for being there, but I could not resist declaring to him that his position seemed to me not only circularly reasoned (which might indeed, as his analogies showed, be strictly a logical problem, not a practical one), but inconsistent with itself: he had deduced his Graduateship, on his own admission, by an operation of formal logic, and denied Croaker’s by the same procedure; yet when the logic led him into a bind he waved it away, freely interchanging conclusions and premises.
“Is that a fact,
Geissbübchen!
” he said indulgently. “Then please Grand-Tutor me while Croaker and I do our work. You still don’t think I’m a Graduate?”
Croaker all this while had been hanging by one hand from a steel rafter near the machinery of the clock, with a light attached to his forehead and what looked like a whetstone in his other hand. Before him rocked an anchor-shaped escapement several meters tall, which served in turn to actuate the great pendulum, or be actuated by it; its impulse- and locking-pallets engaged and released the teeth of the last gear in the train, and the escapement itself rocked on a knife-edged bright steel bar that ran through a ring in the top of its shaft. Between
tick
and
tock
Croaker dextrously would swipe one side of this bar’s edge with his stone, between
tock
and
tick
the other; then without ever touching the escapement itself he’d make some sort of measurement through a lens fixed onto the bar, and croak the reading down to Dr. Eierkopf. His noises were unintelligible to me, but Dr. Eierkopf would jot figures in a notebook, say
“Ja ja”
or
“Pfui,”
and return to measurements of his own, which he seemed to be
taking with great delicacy from a white hen’s-egg mounted in a nest of elaborate apparatus.
“May I speak frankly, sir?” I asked. “Presumptuous as it may seem to you, I
do
have a suggestion to make, and then I’d like to ask your advice about repairing this clock …”
His pink eyes rolled behind the glasses. “You lost your mind, Goat-Boy?”
I showed him my Assignment and told him how I’d come by it. “If it says to fix the clock, then the clock must be broken, mustn’t it? I believe you told me WESCAC always reasons correctly.”
Very much concerned, Dr. Eierkopf affirmed that the computer was normally incapable of faulty reasoning; he pointed out, however, that in the absence of any actual malfunction in the works, to speak of Tower Clock’s being inaccurate was to speak unintelligibly, as who should accuse the Standard Meter of being too short.
“But you told me yourself last night that the clock needed working on,” I reminded him, adding that my own self-winding watch (by which term I meant, innocently, that I wound it myself) showed a different hour, whereto with his permission and Croaker’s help I’d thought to make Tower Clock conform.
“Don’t talk so!” Eierkopf cried. “You don’t touch anything! It’s bad enough Croaker, he’s such a clumsy!” He squinted at my Assignment-list again, this time through his lens, and suddenly clapped his hands. “I got it, Goat-Boy!” Croaker dropped from the rafter at once, mistaking the signal, and lifted Dr. Eierkopf onto his shoulders; the scientist was too pleased with his new idea to protest.
“It says
Complete in no time, ja?
So: the clock’s not
kaput
, it takes you no time to fix it! You’re done already.”
This reasoning, though I could not refute it, satisfied me less completely than it did Dr. Eierkopf, who declared it at once a fulfillment of my task, an explanation of the troublesome due-date of my Assignment, and a vindication of WESCAC’s “malistic” dependability. To my inquiry, Why was he himself tinkering with the clockworks if no repairs were needed? he replied that standards of reference were sometimes improvable though never logically subject to challenge; thus the University Standard Meter, for example, was originally one ten-millionth of the campus’s quadrant, later the distance at o° Centigrade between two particular scratches on a platinum-iridium bar in the Intercollegiate Department of Standards, and presently one million five hundred fifty-three thousand one hundred sixty-four and thirteen one-hundredths wave-lengths of red light
from the element cadmium. In like manner the accuracy of Tower Clock was from time to time improved—though only by comparison to its own past accuracy, never (“…
Q.E.D
., Goat-Boy …”) by comparison to the accuracy of other timepieces. Current work in the field, I was told, centered around escapement-theory, and had led to opposing points of view. One group of researchers (whom Eierkopf referred to contemptuously as “Everlasting Now-niks”) would abolish all forms of escapement in favor of what they—or their detractors—called “tickless time”; the other, led by Dr. Eierkopf, hoped with the aid of special lenses and micromilling techniques to perfect the edge on which the present escapement pivoted—or the theory, I was not sure which.
“Here you got
Tick, nicht wahr?
” he said, and pointed to one pallet-point of the anchor-shaped escapement. “Over there you got
Tock
. So pretend all the Ticks is coming and the Tocks is already gone: what I want to do is measure the point exactly between, where Tick becomes Tock. Last term we got it down past millimicroseconds; pretty soon we lick it altogether.” His labor was complicated by several factors: the two schools of thought, though not politically based, happened to divide roughly along East-West lines, the “Everlasting Now-niks” being in general associated with Sakhyanist curricula; and the political connotations which escapement-theory thus unfortunately took on were compounded—and confused—by the fact that Tower Hall Tower was a reference-point for cartographic as well as temporal measurements: that keen-edged fulcrum which Croaker had been honing happened to run north and south on the meridian of longitude which, higher up towards Founder’s Hill, divided East from West Campus, and had been used as a coordinate in laying down the Power Line; moreover, the weathercock atop the Belfry marked the center of New Tammany’s Great Mall area—a point indicated by brass discs on every floor of Tower Hall: both North-South avenues and East-West streets were numbered from the shaft whence its four arms extended. In consequence of all this it was difficult even for Eierkopf as official Clockwatcher to get permission to move or modify any part of the works, the more so as his critics (some sincerely concerned, some merely venting their anti-Bonifacism) charged that his method was self-defeating.
“I’ve gone from ticks to milliseconds to microseconds to millimicroseconds,” he said, “and the dumbsticks say I just make bigger and bigger words for smaller and smaller things, but never get to the place between Tick and Tock.” What their ignorance left out of account—and mine too, which saw no reply to their objection—was a technical breakthrough he’d recently achieved and was about to put to use: a precision honing device
he called the Infinite Divisor. Attached to one end of the fulcrum-bar, its two opposed milling-heads—tiny diamond-dust affairs—would dart along the upper knife-edge, honing it as they went; during their approach to the hole in the escapement-shaft (the point on which the whole assembly pivoted) automatic calibrators would halve and halve again,
ad infinitum
, the width of the edge, until theoretically it reached a perfect point at the center of the hole and the midpoint of the Tick-Tock swing—a point whose measurement would incidentally be recorded on the calibrator-gauges.
“One moment, sir!” I protested, dizzied by this conception. Croaker held his sweatshirt-front out from his scars and whimpered a little. “It seems to me—”
“Pretty smart,
ja?
” He may have been addressing Croaker, whose head he patted, or myself. I agreed that the idea was striking, but wondered about certain theoretical problems which I sensed more than saw articulably: a riddle Max had posed me once about Peleides and the Tortoise …
“Pfui,”
Dr. Eierkopf said. “That’s why two grinding-heads instead of one: we tackle the problem from both sides. Better hold your ears now.”
He inserted a pinky in each of Croaker’s, and Croaker clapped a giant palm over each of his, just as a new set of whirrs and clackings shot through the works. I didn’t catch his meaning until the first clapper swung against its bell, big as the lift I’d ascended in, and shuddered me to the marrow. Others followed, a tooth-jarring sequence even with ears held, until a four-phrased melody signaling the hour had been chimed: then a series of bells ascended diatonically a scale-and-a-half. The eighth brought a little cry from Dr. Eierkopf, either despite Croaker’s pressing harder or because of it; the last shivered the egg in its calipered nest.
“Durchfall und Vertreibung!”
Dr. Eierkopf squeaked, and pounded Croaker feebly on the pate. “You set the egg-clamp for high
sol
again! Put me down and clean up!” Croaker perched him obligingly back upon a stool and set to licking the apparatus.