Damon Knight - Orbit 16

“Uh, yes, yes, Ruth. Uh, thank you, but I really must talk to the Director as soon as he comes in. It’s . . . it’s quite important. Would you leave a message for him to call me? It’s very high priority, Ruth.” He thought high priority sounded better than urgent, more professional. It was a term the Director would probably use.

“Yes, sir. Will that be all?” There was only a faint sign of reproach in her voice for this break with tradition.

“No, that’s all, Ruth. Thank you.”

But there was more. There was much more he had to do before lunch.

“Wait! Ruth? Ruth, would you get Publications on the phone? I want to speak to Jack Hudson. That’s right. Thank you, Ruth.”

He sat frozen behind his desk. He had to talk to Hudson and stop today’s mailing, to recall any copies that had already been sent out, to hold them until someone could make a final decision. Someone. He should run a check on the computer, and a projection too. Ordering these things in his mind was a difficult task. There were too many factors to tell what to do first. The whole pattern of his schedule was torn, and he had left his damn briefcase with that damn paper in the car. Construct angle F’G’H = angle GG’B. Then, if AJ is dropped perpendicular to BG from A, BJ = AJ and BG = F’H. Thus triangle ABG is congruent to . . . is congruent to . . . He rose, rushed to the blackboard, and began drawing furiously, attacking that hideous proof directly, headlong. He must find a fallacy. It must be false. He drew in three colors of chalk, erasing and redrawing segments in new proportions, stepping back across the room to view his diagram from a distance, making quick notations on the back of the piece of yellow paper on his desk, pacing the room jerkily and returning to the board to scowl, erase, and redraw. He hardly noticed it when Ruth buzzed to tell him Hudson was on the line. He strode to the desk, one eye on the board, and surprised himself by his handling of the situation.

Was the autumn number of the Quarterly Mathematics Publications of the Federal Basic Research Institute ready for mailing? Good, hold it until further notice. No, no serious problem. A rather important error that would have to be corrected. A paper might have to be removed. Had any copies been sent out? Five review copies had gone out earlier. Please have them recalled. As soon as possible, yes. Lucus himself would write to the American Mathematical Monthly. No, it wasn’t a serious problem. It would be rather difficult to explain to a nonmathematician. Thank you very much for your cooperation, Mr. Hudson. Terribly sorry to cause your department all this bother. Yes, thank you. Good-bye, Mr. Hudson.

It took only a moment at the blackboard to regain his balance, to recover his position. His construction started at the bottom, spread out on both sides, and then began climbing upward, just as it had in David’s paper. Like some sort of tower. That’s what Hans would call it, if he were here. A tower of matchsticks, something like that. Then he would insist that he was going to do a painting of it. And he might, in fact. It was rather attractive, quite nicely symmetric. The whole picture had a neat look of innocence about it, as if it were nothing more than a new proof of the Pythagorean Theorem, for example. Hans would call it “The Tower That Demolished the Tower” or something like that and find the irony of it hilariously funny. The destruction of centuries of mathematical thought would mean nothing to him. It was a joke. A joke on Lucus, a confirmation of everything Hans had said over those interminable Tuesday-night games of Go.

As the tower neared its peak, it became increasingly obvious to Dr. Lucus that the proof was correct, that there was no fallacy. After six times through it, he could no longer tell himself he was not following it well enough, that he would see the obvious hole in the logic the next time through. David had been meticulous, he had left out no steps. His paper was densely written and quite thorough. Euclidean geometry was not Donald Lucus’ field. He was not used to its methods of proof. But by now he could feel each lemma and corollary of David’s Theorem in his guts. He knew it was true. Only a computer confirmation remained.

He called the computer office and arranged for some time that evening, asked for three tapes to be sent to his office: first, CONPROOF 2: Confirmation of the consistency of a proof in a mathematical axiom system given as a subroutine; second, EUBERT: Hilbert’s axioms for Euclidean geometry, subroutine for CONPROOF 2; and finally, LOBACHEVMANN: Lobachevskian and Riemannian geometries, subroutine for use with CONPROOF 2.

Then he called the head of the computer division and explained that he wanted to run a social projection later in the week. The man was incredulous—and amused.

“In Math?” he asked.

“Yes,” replied Lucus. “And I want the problem and the output to be considered Limited Interest.”

The man paused only a second at the other end of the line, his mouth hanging open an inch from the receiver.

“I . . . I’ll have to have an okay from the Director on that first, but all right, I’ll see what I can keep open for you Friday night.”

Lucus thanked him and hung up. His palms were covered with sweat. The use of the term “Limited Interest” had frightened him and impressed on him the seriousness of the thing he was doing. There was no classified research at the FBRI; its fundamental philosophy was one of “basic research in a free and open environment.” All the work done in the building or under FBRI grants was published and widely disseminated. However, it occasionally became clear to the Institute officials that certain results could prove dangerous in one way or another if prematurely released to the public or to the scientific community at large. Therefore the code “Limited Interest” had been developed to refer to such work: unclassified, but kept strictly under wraps.

It was nine thirty, and he had done all he could until he talked to the Director. The tower stood flat against the blackboard, a dead, crystalline, cutting blade of red and blue and orange. Outside the window, a squirrel darted along a branch and vanished down one of its countless customary routes in the maze of almost leafless branches. The Institute was built into the side of a hill, so that Dr. Lucus’ office, which was on the sixth floor if seen from the front, actually appeared to be no higher than the third floor. He had a peaceful view of grass and sky, held fast by the swift, layered lattice of branches. Often he felt that he did his best thinking while he was standing here, running his eyes peacefully along the branching lines, like one of Kaufmann’s illustrations in Graphs, Dynamic Programming, and Finite Games. But today he could not think in leisure. The soap-white walls that rose to enfold his world were too close now, and he was trapped, trapped and falling.

He did have one thing left to do, although he did not feel like seeing Ruth. It must be done, and it would give his mind something to grasp until he could talk to the Director. He had her come in, and he dictated a polite letter, a bit too long, to the editor of the AMM, explaining that an embarrassing error had crept into the fall Quarterly and asking that it be returned, so that it could be replaced by a corrected copy.

As Ruth got up to go, her steno pad pushed the yellow paper off his desk to the floor. He bent to pick it up and smoothed it on his desk, staring blankly at the calculations on the back. His watch said 10:05.

At ten fifteen he still sat, frozen, his eyes open and filled with the erected sword shape plastered flat against the blackboard. It was cutting deep into his retinas, but his mind was suspended in dreamless waking sleep that numbed the wound and held him in inanimate rigid repose. Solidity of metal and wood near him and touching him melted, and only the neat impersonal sword hung above, simple, clear, no longer threatening, neutral now as all things were within the asbestos web which held him.