Barrington Bayley SF Gateway Omnibus: The Soul of the Robot, The Knights of the Limits, The Fall of Chronopolis

Our whole idea of analysing space by means of dimensions is inadequate and artificial, the Knight advised. The notion is an internally generated side-effect, and to anyone from outside, e.g. from another kind of space, it is neither meaningful nor descriptive. The essence of a spatial structure is more often expressed by a plain maxim that might appear to be ad hoc and rule-of-thumb, but that actually contains the nub of its specific law. At this I could not refrain from interrupting with the boast that privately I had once reached the same conclusion; and that if I had to state the basic physical law of our space (which I then thought of as the universe) it would be that in moving towards any one thing one is necessarily moving away from some other thing. The Knight complimented me on my insight; his ship’s computer was at that very moment grinding out the implications of a formulation quite close to the one I had come up with.

Following this, the Knight expressed his gratitude and announced his intention to leave. I begged him to stay a while; but he replied that to continue meshing the spatial laws of the ship (i.e: locational-transitional laws) with the pieces on the chessboard was proving to be a drain on the power unit. Guiltily, I confess that I allowed selfishness to come to the fore here. Did he not owe me something for the help I had given him, I argued? Could he and his crew not spend a little more energy, and would it truly endanger their lives? My unethical blackmail was prompted solely by my burning desire to learn as much as I could while the opportunity remained. I think he understood my feelings for, after a brief hesitation, he agreed to remain and discourse with me for a short time, or at least until the power drain approached a critical level.

Eagerly I besought him to tell me as much as he could of this vast universe of divers space-times to which he had access but I had not. To begin with, where did the Knight’s own spatial realm lie? Was it beyond the boundaries of our own space (beyond infinity!) or was it at right angles to it in another dimension? (I babbled carelessly, forgetting his former objection to the term.) Or was it, perhaps, co-extensive with our continuum, passing unnoticed because its own mode of existence is so unutterably different from it? To all these hasty suggestions the Knight replied by chiding me gently for my naivety. I would never know the answer while I persisted in thinking in a such a way, he said, for the simple reason that there was no answer and no question. While I was still capable of asking this non-existent question the non-answer would never be apparent to me.

Somewhat abashed, I asked a more pertinent question: was each space-time unique, or was each type duplicated over and over? As far as was known, the Knight said, each was unique, but they were classified by similarities and some differed only in details or in the quantitative value of some physical constant. It was to be expected, for instance, that there would be a range of stereo space-times resembling our own but with different values on the velocity of light. To my next request, that he describe some alien space-times to me, he explained that many would be totally inconceivable to me and that there was no way to express them in my language, mathematical or spoken. The majority of the spaces that were known to the chess-people were variations on the locational-transitional theme. There was a theory in his home world that locational-transitional (or chessboard) space was the basic kind of space in the universe and that all others were permutations and variants of it; but he agreed with me that this theory could be suspected of special pleading and that deeper penetration into the universe by the chess-people’s spaceships might well bring home a different story. He would not bore me, he added, by describing meaningless variations on locational-transitional space, but felt that I would be more entertained by those spaces whose qualities made striking comparisons with the qualities of my own realm.