Damon Knight - Orbit 16

Tuesday he worked continuously, stopping only for half an hour for lunch, fortified during the day by three cups of Ruth’s dark but tasteless coffee. He had called Bibliography as soon as he got in and had his checklist headings augmented greatly. Every month articles containing certain key words or phrases in their titles or abstracts were sent to all the department heads. The controlling program was sophisticated enough to produce some very worthwhile information and very little that did not hold at least some interest for him. Now, in addition to his standard topology codes, he added a few checks in various kinds of geometry—it was, after all, likely to be his field of specialization into the foreseeable future.

David’s proof had checked out perfectly in all situations, which did not surprise him at all. The program—which turned out to supply much more detailed output than he remembered from CONPROOF 1—even made some suggestions on simplification of certain steps in the proof. It was indeed valid. There could be no doubt of that. He began writing up a short report on the program, which he would eventually include in his report to the Executive Board.

All day Wednesday was spent in conference with the head of the computer division, explaining in detail the results of David’s proof and its connection with the rest of mathematics. They finally decided that the social projection could be done fairly easily with existing programs and data tapes, and it wouldn’t be necessary to confer with Sociology—at least not until after the initial run. Lucus found himself working especially well with the man, developing an instant rapport and communicating the details of the problem much better than he had with the Director. In fact, the entire day he felt especially energetic and happy, almost euphoric, and he finally went home after seven with a genuine sense of accomplishment, disturbed only by the itching occasional thought that there was something he had meant to do but forgotten—nothing very important, but some detail that was left out, that destroyed the symmetry of the day. But this thought was eventually buried by the mass of other details, important details, enjoyable details, that competed for his time until late Wednesday evening.

Thursday and Friday were spent shuffling between two projects: the social projection and his report to the Executive Board. The Executive Board meeting, which had been scheduled to begin at two o’clock on Tuesday, was rescheduled to the morning, and all section heads were advised that some very important business might well cause it to run into most of the afternoon. The mere fact that the nature of this business was not mentioned, of course, tipped them off that it was “Limited Interest” and probably involved the sort of executive action that the Institute was theoretically not empowered to take. Actually, the Institute did stick literally to the guidelines in the Congressional bill which had authorized its founding. It served in an advisory capacity to the agencies which carried out the occasional difficult decisions which the board was sometimes forced to reach despite the seeming incompatibility of these decisions with the supposed concerns of the Institute. And if employees of the Institute were called upon to aid these other government agencies in the regrettable but necessary enforcement of decisions made in the interest of the general good, they clearly cooperated with their government as private individuals, usually in “special consultant” positions, and not as employees of the FBRI itself.

And so by adhering to the letter of its charter, the Institute managed to stretch the spirit of the charter when that spirit became a threat to more important considerations. No one on the Executive Board took this responsibility lightly. Indeed, it was the gravity, the solemnity with which they were bound to weigh questions of ethics and then exercise their own benign power in the interests of the whole of society—it was this gravity, the awesome weight of obligation and the crucial necessity of judicious application of their superior skills which secretly thrilled many of the board members and added an unequaled zest to these meetings. There had been one department head who opposed all such actions, but he had left the Institute to return to teaching some years back. Now there was usually a broad and healthy range of opinion and discussion on questions of “interference,” as it was called, Genetics holding out against exercise of such power except in the most extreme cases, Biophysics being perhaps a bit overzealous in his enthusiasm for the Institute’s potential control of future events, and the rest of the departments arranging themselves variously between these two poles as befitted their individual politics, esthetics, professional ethics, temperaments, and digestive difficulties.

Mathematics, that is to say, Dr. Donald Lucus, was never entirely sure where he belonged in the spectrum, being, he knew, too easily swayed by each side of the debate in its turn, and most often casting his ballot with the majority. The issues were always too vague, uncontrollable, and, as he put it, “political,” and they seemed very far from his real concerns in his work. This time, however, he had no doubt which side of the issue he would take. He would have to hold the floor himself, and he knew for certain that the Institute must take appropriate measures to head off the catastrophic events that could be instigated by David’s proof.

The initial surprise of the board when they realized it was he who was going to read the report was the customary reaction he got from everybody whenever they learned that Mathematics might be involved in something important. He was the out man in the building, and he now felt a bit of pride in presenting his case, in being allowed to overshadow their scientific concerns with the problems of his field for an entire morning, perhaps for a whole workday.

He began by giving a precise and ordered account of David’s proof, its connection with the previous history of mathematics, and the interrelation of geometry with the foundations of all modern mathematical theory.

After this, and before the presentation by Computers and Sociology of the social projection, there was a period of questions directed to Lucus, as was customary, to ensure that everyone had a clear understanding of the issue. As it was, a number of them did, but the others were often reluctant to question a speaker in another field, less for fear of exposing their own ignorance than out of professional courtesy and a desire to avoid any question which might appear as a challenge to the speaker’s competence. It was usually understood that each head considered his colleagues as the final experts in their own fields, and their private terrain must be respected, as they respected his. An attempt to gain too complete an understanding of his territory was dangerously close to a takeover of his sovereign province. So the questions were only halfhearted requests for clarification about Hilbert’s axioms and the independence of the parallel postulate. Until Genetics raised a fluttering hand and asked with a Socratic smirk, “You say that the principles of Euclidean geometry can be derived from set theory, and, of course, this can be verified on the 666?”

“That’s right.”

“And so it all falls back on the principles of symbolic logic, and theoretically you could put the whole thing in terms of a proof in logic?”

“Yes, in fact, there is a program which can do just that with most mathematical proofs, and once I get around to it I intend—”

“Yes, yes. Well, very good. But isn’t it true that your whole method of proof is based on symbolic logic?”

“Yes.”

“And since you use this same method of proof in David’s Theorem—”