"So: der Ziegenbübe." Eierkopf squinted through his eyeglasses; Croaker grinned and grunted. "Step here then. Look sharp." As I made my way to them between the wall and the pendulum-slot, Dr. Eierkopf had Croaker place him on a high stool. The great Frumentian then bounced up and down, fetched up his shirt (he was dressed now in his usual garb, the gray cotton sweatsuit worn by varsity athletes, with NTC across chest and shoulders) and pointed happily to his belly, where I saw a livid pattern of fresh-looking scars below his navel.
"He wants you to congratulate him on his Certification," Dr. Eierkopf mocked. "You want evidence that Dr. Bray's a faker? There you are." Bray it seemed had left the Belfry not a quarter-hour past, having visited it to make an official inspection of the clockworks, and before proceeding to the Chancellor's mansion had Certified both Croaker and Dr. Eierkopf.
"Both of you?" I could not conceal my incredulity. Dr. Eierkopf agreed that Commencement Gate, whatever and wherever it might be, could not imaginably be wide enough to admit contraries: Entelechus's Second and Third Logical Laws forbade the possibility. That he himself was a Candidate, if not indeed a Graduate, he needed no Grand Tutor to tell him: Scapulas's motto Graduation is a state of mind had long hung on the walls of Observatory and Belfry; it was a conclusion he had reached, like Scapulas, by inexorable logic, and confirmed to his satisfaction on WESCAC. He had explained it politely to Bray out of deference to the administration in which he hoped to recoup his former high position, not out of any reverence for the man himself; and the self-styled Grand Tutor had had the good sense merely to write Q.E.D. under that motto, making it a certificate of Eierkopf's Candidacy.
"What else could he do?" Dr. Eierkopf smiled over his gums. "Even Scapulas was a brute compared to me." Which made it the more absurd, he scoffed, that Bray should also Certify the shoulders, so to speak, on which the head perched. Scornfully he quoted Bray's quotation from the Founder's Scroll: "Consider the beasts of the woods, that never fail." Whatever Enos Enoch might have meant by that advice, He surely wouldn't have Certified an animal who couldn't even read the Certification. But Bray, apparently determined to pass absolutely everyone, had first translated the Certificate of Candidacy into a Frumentian pictogram (a matriculation and procreation symbol, so he'd claimed) and then, somehow gaining Croaker's confidence, had engraved it on the black man's belly. Eierkopf himself was unfamiliar with the emblem; whether the bearer understood its significance was questionable, but he was most pathetically proud to display it in spite of the discomfort he no doubt suffered.
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.D.E.Q 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.
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