Orbit 16 - [Anthology]

by Ed By Damon Knight

  Shortly thereafter, Craig came looking for me. He stopped when he saw me and grinned. “I thought you might’ve run away.”

  Now why hadn’t I thought of that? It would not be easy, of course. There were barren mountains on three sides of the house, and no other habitations for a hundred kilometers. On the fourth side was the unplumbed, salt, estranging sea. Would it be possible to escape Craig in the mountains and stay alive there till help came? I wasn’t sure.

  Craig went and got some brandy, coming back to sit beside me.

  “How long are you planning to stay?” I asked.

  He shrugged and cupped his hands around the snifter, warming the brandy. “Are you so eager to get rid of me, Lucia?”

  I looked at his worn, weary-looking face. Poor fellow, I thought.

  There’s no more dangerous emotion than pity, except guilt, of course. Both make you put up with intolerable situations. “No. I’m not,” I said softly and took hold of his hand. He smiled and set down the brandy snifter. We kissed.

  That afternoon we walked on the beach again. At night, we slept in the crystal bedroom, which was my favorite room. The ceiling shone and shifted like a kaleidoscope. Multicolored gleams of light slid over the glassite furniture. The floor was silver. My troglodytes, calm at last, brought us glasses of cold wine and clusters of crystallized grapes. When I woke in the morning I heard Craig singing in the shower. That at least was unchanged. He couldn’t carry a tune any more now than he could before.

  I spent the morning working in my rock garden and the afternoon making an Aztec dinner. In the evening my troglodytes entertained us with music and tumbling. When they were done, Craig put a music cube into the player. I turned off the ceiling. We danced in the firelight, one of the old, slow dances that were coming back again, after I forget how many centuries. When we started to get tired, we went up to the red bedroom.

  Early the next morning the repair crew came in a fanwing that landed on the beach below the house. Neither of us woke till they rang my doorbell. That woke me. I rose and put my robe on. Craig groaned, rolled over and sat up. I kissed him good morning, then went down to let the repair crew in. They asked me what had happened to my transmitter. I told them, and they called the law service. A few minutes later the cops arrived. They found Craig in the silver bathroom, shaving in front of the mirror wall, and they arrested him and took him away.

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  * * * *

  EUCLID ALONE

  William F. Orr

  Which is more important: the truth, or an error that holds the whole world together?

  1

  The elevator was passing the tenth floor when Dr. Donald Lucus started from his reverie into the panic of embarrassment he always felt when he had passed his floor unknowingly. His mind shifted with reluctance from one program to another as it was drawn to the demand for a decision by the illusion of a sudden decrease in gravity that indicated the elevator would stop on the eleventh floor. He would have approximately ten seconds to decide. He could stay on this elevator, possibly all the way to the twenty-fifth floor, and get off at six on the way down, wasting a large but certain amount of his time, resulting in only a brief moment of embarrassment before unknown engineers on the top floor, who would realize his foolish mistake when he remained in the elevator, who would smile and wonder why this absent-minded old fellow hadn’t been retired by the Institute yet. Or he could get off now, at eleven, and wait for the next down elevator to take him to his own floor. Again, it would be apparent to the secretary at Genetics that he had gone by his floor, and he would be aware of her, sitting behind him at her desk, thinking he had been a section head much too long and ought to be replaced. As an alternative, he could resort to subterfuge and walk down the hall to knock on the door of an empty office, pretending that he had legitimate business there.

  But he had neither the will nor the energy to act out such a pantomime, when his mind needed urgently to be occupied with another problem, which it had been drawn away from by this trivial face-saving decisionmaking. In the end, he decided that getting off at eleven would waste less time than any other course of action, and that was, after all, the most important consideration.

  As it was, he made this decision too late to avoid another embarrassment, that of being hammered on both sides by the elevator doors as he stepped out, while the secretary of Genetics looked up and smiled. An automatic mumbled “Pardon me” crossed his lips as he pulled free of the gentle vise-grip and turned self-consciously to push the down button.

  Only then could he relax and let his mind sink back to the complex but ordered patterns of proof which were its true medium. And that order had form quite as real as the world of elevator buttons and social ineptitude, of old men and young men and publishing deadlines and hiring policies. There was an intricate structure made entirely of straight lines in a plane that intersected in named points and formed identifiable triangles, all related to one another by a carefully chosen pattern of congruences, similarities, and equal sides and angles.

  This structure had been built very carefully to its present state by a process of repetitive partial construction. All the way along the freeway he had occupied himself with the task of mentally rebuilding the structure which he had spent almost the whole night examining. He would begin each time at the same starting point, building one line at a time, noting each label, each equality and similarity, until the structure reached a degree of complexity, as it did each time, that exceeded his ability to assimilate new information and which became manifest in the sudden complete loss of a necessary fact. At this point the only possibility was to begin again at the foundation. Each time, he got a little farther in the proof, and while it might seem at first a most inefficient method of construction, it would eventually result, not only in a completed proof, but also, and more importantly, in a complete intuitive familiarity with that proof, both in its overall conception and in all its particulars.

  It was a learning method that Dr. Lucus could remember having employed successfully for over forty years, and even his loss of mental agility resulted only in a longer amount of time spent with any one proof and not in any loss of total comprehension once the process was completed.

  He had taken temporary comfortable refuge in the beauty and symmetry of this proof, which he could do now, shutting out all thought of the threat, the horror of its ultimate implications. The four cups of coffee kept him awake and uncomfortably numb to the eventual attack on his one sure foothold on reality. He stepped into the elevator and forcibly turned his thoughts from what he must do in the next few hours. For he was not certain what he must, could, or wanted to do. Too many roads were open to him, and they all seemed to lead to eventual dead ends. But that was only, as Hans used to tell him, his own lack of imagination, his lack of initiative to build his own road. So be it. As he began once more to piece together his elusive triangles, he was aware more than anything of the face of the secretary of Genetics, frozen in the last narrow inch between the closing elevator doors, smiling at an old, absentminded man who held in his mind the cursed flame of destruction of this whole temple of reason.

  If Ruth was aware of the worn, drugged look of his eyes and face when he entered the Math office, she did not betray this. She turned from her typing, pulled her glasses down on her nose, and regarded him with what she supposed was a friendly smile, as she always did. After the obligatory good-mornings, he paused, trying to force efficiency into his reflexes, confused over what were to be his instructions to her.

  “Uh, Ruth,” he began at length, “Ruth, would you get the Director on the line for me?”

  “The Director, sir?”

  She was not, in fact, asking for confirmation, only registering surprise. Dr. Lucus seldom had any contact with the Director, except at executive board meetings. When he did contact the Director, it was always through interoffice memo, and Ruth had shown her surprise at this breach of tradition before she had a chance to check herself. One telephoned subordin
ates and colleagues. One wrote to superiors.

  “Uh, yes, Ruth, it’s rather important.”

  Was there something else to say to Ruth? He had to call Publications, but that could wait until after he got the go-ahead from the Director.

  “Oh, uh, Ruth, is the mail in yet?”

  “No, sir, but there was a telegram. It’s on your desk.” She was impatient to get back to her typing, impatient with his slow talk and his hesitation. But she would not return to work until he left the room. Office etiquette was her one comfort in this job.

  “Oh, uh, thank you, Ruth.” He turned to his office. At the door he paused a moment, as she said, in accordance with custom, “Would you like me to bring you a cup of coffee?”

  He had anticipated the question, so his answer was immediate —in fact, clumsily abrupt. “No, thank you, Ruth.”

  As the door swung shut, the steady patter of her machine resumed. She would type one page to allow him time to take off his coat and get settled. She would sip her own lukewarm cup of coffee, which she nursed for three hours every morning, and then turn to the telephone. Her wrinkled face would show no sign of the joy she felt at hearing her own crisp, stiff voice conducting business efficiently and properly.

  His hand was strangely empty as he took off his coat. He had left his briefcase in the car.

  “Damn,” he muttered. That meant he would have to go back for it during his lunch hour. He would definitely need to have the papers in it before he saw the Director. In fact, he had wanted to review Professor David’s paper this morning and to check the mental construction he had prepared in the car. In any case, he would need the paper itself before he could run a computer check on the validity of the proof.

  All these trivial irritations made it even more difficult to see through the haze of a sleepless night that he was caught up in something historic, in something frightening. He was not made for scrapping a lifetime of firmly held beliefs in a day, as Hans was. He was not made to be forced suddenly and rudely into a crucial position of responsibility. Hans could handle that sort of thing; he could not. Hans could submerge himself in madness and come up smiling, happy and sane. But for Donald Lucus madness, if it came, would be the end. He rested a hand on Hans’s sculpture as he sat at the desk. In the outer office, the sound of typing stopped.

  There was a thin wire human figure suspended inside a cage, which was formed by the edges of an irregular icosahedron, slightly skewed on its axis. Two edges of the polyhedron were broken, and the figure was falling, one hand stretched out vainly toward an edge, a bar of the cage. Its mouth was open.

  “This,” the artist had said to him years before over a game of Go, “this is you, Don. Not now. This is you at sixty-five. This is you and your twenty-faced monster and your quintic equation. I want you to save it for your old age and then tell me if I’m right.”

  He had clicked the cigarette holder between his teeth and grinned that diabolical smile that always dared you to guess whether he was joking or serious.

  “Look at it, Don. And when you finally recognize yourself, write and let me know.”

  The telegram was brief and clear.

  DON.

  HANS DIED OF A STROKE FRIDAY. BETH ASKED ME TO LET YOU KNOW. FUNERAL WEDNESDAY AT ONE ST. PAULS, CINCINNATI. WILL NOT BE THERE AS THINK THAT WOULD BE BETTER FOR BETH. HOPE YOU CAN THOUGH. MUCH LOVE.

  MARY

  “Dr. Lucus, I have the Director’s secretary on the line. The Director will not be in until ten this morning. His schedule is full today, but I can make an appointment for you Tuesday afternoon.”

  Tuesday afternoon. He set the telegram down and covered his eyes to think. Tuesday afternoon. He could make an appointment for Tuesday afternoon, and that would give him another day to relax, another day before he really had to do anything about the situation. But no, that was impossible. He couldn’t put it off, and he couldn’t be put off. Of course, he must see the Director immediately.

  “Dr. Lucus?”

  “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.”