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

My reader, still suspicious of my truthfulness, will also want to know how it was that the Knight spoke to me in English. The appalling difficulties offered by any other explanation have tempted me to decide that we did not really speak at all, but only telepathically from mind to mind. And yet my grosser, more stubborn recollection belies this evasion: we did speak, the air vibrated and brought to me the thin, resinous tones of the Knight’s voice. His own remarks on the matter were off-hand and baffling. There was scarcely a language in the universe that could not be mastered in less than a minute, he said, provided it was of the relational type, which they nearly all were. He seemed to find my own mystification slightly disconcerting. The only comment I can contribute, after much reflection, is that for a locational-transitional being what he says may well be the case. Language, as he pointed out, largely concerns relations between things and concepts. To the Knight relations are the stuff of life, and he would find our own comprehension of them far below the level of imbecility. In our world to have but one fraction of his appreciation of relations, which to us are so important but so difficult to manage, would make us past masters of strategy and I believe no power would be able to withstand such knowledge.

But here lies the antinomy: the Knight and his crew were coming to me for help. They found the conditions of four three-dimensional continuum as incomprehensible and chaotic as we would find their realm. They had not even been able to ascertain what manner of space it was, and begged me to explain its laws to them in order that they might be able to find their way out of it.

There was a certain irony in being asked to describe the world I knew when I yearned to question the Knight as to his world. (Indeed my imagination was exploding – were there galaxies, stars and planets in the locational-transitional space? No, of course there could not be: such things were products of continuous space. What, then, was there? Some parallel to our phenomena there must be, but try as I might I could not picture what.) However, a cry of distress cannot go unanswered and I launched into an exposition.

It was quite a test of the intellect to have to describe the utterly familiar to a being whose conceptions are absolutely different from one’s own. At first I had great difficulty in explaining the rules and limitations by which we stereo beings (that is the phrase I have decided upon to describe our spatial characteristics) are obliged to order our lives. In particular it was hard to convey to the Knight that to get from point A to point B the basic strategy is to proceed in a straight line. To give them credit, the chessman crew had already experimented with the idea that continuous motion of some kind might be needed, but they had conceived the natural form of motion to be in a circle. When sighting my chessboard they had proceeded in the opposite direction and approached it by executing a perfect circle of a diameter several times that of the galaxy. I could not help but admire the mathematical expertise that had put both their starting point and their destination on the circumference of this circle.

After a number of false starts the Knight successfully mastered the necessary concepts and was able to identify the class of spaces to which ours belongs, a class some other members of which had been explored previously. They were regarded as dangerous but none, he informed me, had so far proved as hazardous and weird as our own, nor so difficult to move in. He still could not visualise our space, but I had apparently given him enough information for the ship’s computer to chart a course homeward (computers, theirs as well as ours, are notoriously untroubled by the limitations of imagination).

During the conversation I had naturally enough sought his opinion on various contemporary theories of the space we inhabit: on Riemannian space, Poincaré space, special and general relativity. Is our space positively or negatively curved? Spherical, parabolic or saddle-shaped – or is it curved at all? Is it finite or infinite? I acquainted him with the equation for the general theory of gravitation and invited his comments:

R1k – 1/2g1k R = T1k

His reply to all this was discouraging. The only definitive datum he would give me was that our space is infinite. As for Einstein’s equation, he said that it merely gave an approximate, superficial description of behaviour and did not uncover any law. He told me that in our continuum motion depends on a set of expansion.^*