"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.
"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 short.
"But you told me yourself last night that the clock needed working on," I reminded him, adding that my own selfwinding 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 0 °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.