Damon Knight - Orbit 16

“Of course I am. It was her idea. Or maybe it was mine. Anyway, we talked it over and thought it would be fun. But now you’ve sidetracked me. I was explaining your role in my art. Ever since I started playing Go over here, look how I’ve improved. Look at that sketch I did of your continuous function theorem. The critics love it. They think I’m a genius.”

“It’s ugly, you know. It’s really ugly.” As much as he liked Hans, Don had never been able really to appreciate any of his work. He found it childish, simple, and sometimes repulsive. Since Hans had begun basing his things on diagrams in Don’s math books, he liked them even less. They seemed to make art lifeless and mathematics unprincipled.

“Yes, it is,” agreed Hans. “Very ugly. And you see, before you inspired me I’d never been able to paint anything quite that ugly. I’d tried . . . Lord, I have as good a sense of what is offensive to the eye as any other artist, but I’d never been able to put it down on canvas. I would walk around in the slums and look at the dreck in the alleys and think it was ugly. I would eat starch sandwiches at the Automat and wipe my beard with a used napkin and think that was ugly. But then when I looked into your Hocking and Young and saw that wild sphere—I knew I had found it! I knew other men had seen the true vision, and I could learn from them.”

“You’re crazy, Kaefig,” Don intoned, shaking his head.

Hans clicked his teeth against his empty cigarette holder and drew a pack of Camels from the pocket of his Levi jacket. “You’ve said that ever since college, my dear Professor, and it hasn’t made it any less true, you smug sane bastard. Let’s put away the game and get drunk. I think I’ve done quite enough to try to save your soul for one night.”

And so it went for over seven years, from Don’s thirty-eighth birthday deep into his forties, until Hans and Mary finally split up and he moved to the Midwest.

And Don never tired of his friend’s harangues, because he knew there was something important there, something he should hear. And so he listened to all the nonsense and rambling, trying to sift out the bit of informational content, the little he could really learn from Hans.

Mary had been hired as conductor of the Denver Symphony, and Don had heard little from either of them since, except for sporadic Christmas cards. He had left teaching to come to the Institute at fifty-five, and there he had remained, sitting—how had Hans put it?—sitting on top of that pile of elephant tusks, lord of what little he surveyed.

A few years ago, a journalist had interviewed Dr. Lucus, because Hans had said he was the only man who could explain his sculpture Ragtime Band, that sprawling monstrosity that was the culmination of his fascination with the wild sphere in Hocking and Young and, according to many critics, the culmination of his career.

And now all that remained of those endless games of Go were a couple of Hans’s paintings in Donald Lucus’ house, the wire sculpture on his desk, and a telegram with few hasty calculations on the back.

He worked on the program until past his usual lunchtime, carefully cross-referencing the manuals spread out on his desk. The first step had been to write out the entire proof, as well as he could remember it, but with the diagram on the blackboard to help him. This was written in his own private notation, a hybrid of FORTRAN, mathematical symbology, and abbreviated English. The next step was to translate this into symbolic logic, using the special terms and syntax laid out by CONPROOF 2 and EUBERT. Not only was it necessary to translate from one code to another; in order to avoid an impossible mass of detail, Lucus also had to augment the Hilbert axioms for Euclidean geometry with statements of all the Euclidean propositions called upon in David’s proof. There was a list of these in the supplementary notes on EUBERT, and so he didn’t have to worry about coding them, only that he had inserted all the necessary ones and correctly labeled them.

This was only the Euclidean part. For a while, he was afraid it would be necessary to duplicate all this work to program his Lobachevskian and Riemannian checks. But then he discovered a special tie-in in LOBACHEVMANN which would allow him to use the exact same input as was used for EUBERT and have validity checked in both non-Euclidean geometries at the same time. He was familiar enough with the use of the old CONPROOF 1, but only in conjunction with such systems as TOPOSPACE and ENSN, which he used constantly in verifying topological proofs. The axiom systems for synthetic geometries had been a complete mystery to him for over thirty years, and what he had relearned in the last three days was hasty and incomplete.

So his office, normally neat to the point of sterility, took on the aspect which it had only a few days a month, those few days of feverish inspiration when he had all the business details of his position out of the way and could allow himself the luxury of creation. Directly in front of him were a programming pad, on which he was writing his final version, and a pile of scratch work. Across the upper part of the desk the three program manuals lay open; to his left was his recent reproduction of David’s proof, continuous on the back of last month’s budgetary output, and a stack of used scratch paper which contained calculations important enough to be saved; on his right, a well-worn Fortran manual on top of the three books which were almost the only customary adornment of the desk: Webster’s New Collegiate Dictionary, Whittier’s Trilingual Mathematical Encyclopedia , and a book of Go proverbs. The wire sculpture and desk calendar had been moved to the file cabinet to make room for all the necessary reference material.

By twelve thirty Ruth had gone to lunch, but the programming was not nearly completed. He had to pull himself away from the pad and pencil almost violently. His hand, his whole body, and a portion of his mind were unwilling or unable to stop writing. Once the trance was broken and he was putting on his coat, it began to frighten him. Surely he worked efficiently in such a hyperactive state, but it was dangerous. He could easily push himself too far, almost unknowingly, uncaringly, if he were allowed to give himself up to the immersing impulse too often. Even as he walked through the outer office, he noticed a stiffness in his legs and neck, an ache in his back and hand, that he had been oblivious to minutes before. Returning to awareness of his body’s torture, he found the temporary divorce from objectivity even more frightening, as though it had been imposed not by himself but from the outside, as though he had been driven too hard by some other being, with little or no concern for his complaints or his safety. He had been abused. And he was tired, very, very tired.

His stomach was feeling upset—from the two cups of coffee he had had with lunch, he supposed—when he returned with his briefcase and David’s paper at one fifteen. He found that once he lowered himself into the swivel chair it was necessary to sit still for several minutes to catch his breath. He knew he needed rest, but there was much more to do before he saw the Director. He tried to weigh the priorities in his mind, to reach a reasonable plan of action, but it was difficult to pin down ideas, and his thoughts were constantly intruded upon by images of congruent triangles and hyperbolic planes. Each attempt to list the tasks of the afternoon and assign time estimates to them was met with frustration, and his ears rang with the faint sound of laughing voices chattering in FORTRAN.

Finally he decided that the only really necessary task was to finish the programming foe CONPROOF 2 and have it sent to the computer division.