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

As do the occupants of a chessboard, the entities of this space (which I shall term locational-transitional space) vary in the range and ingenuity of their movements. Primitive organisms can do no more than transfer themselves slowly from one location to another, without pattern or direction, like pawns, while the most evolved intelligent species, like my friend the Knight, had advanced to dizzying achievements as laid down by the possibilities of such a realm. Their most staggering achievement was that of travel to other spaces; this was accomplished by a hazardous, almost infinitely long series of locations executed at colossal speed and comprising a pattern of such subtlety and complexity that my mind could not hope to comprehend it. Indeed, few even in the Knight’s spatial realm comprehended it and for their science it constituted a triumph comparable to our release of atomic energy from matter.

The discerning reader who has followed me this far might justly wonder at the coincidence which brought these bizarre travellers to my presence at the very moment when I had been theoretically contemplating something resembling their home space. This question was uppermost in my mind, also, but there was, the Knight told me, no coincidence involved at all. On entering our continuum (which the Knight and the companions under his command did indirectly, via other realms less weird to them) the space explorers had become confused and lost their bearings, seeming to wander in a sea of primeval chaos where no laws they could hypothesise, not even those garnered in their wide experience of spatial systems, seemed to obtain. Then, like a faint beacon of light in the uncognisable limbo, they had sighted a tiny oasis of ordered space, and with great expertise and luck had managed to steer their ship towards it.

That oasis was my chessboard. Not the board alone, of course – tens of thousands of chess games in progress at the same moment failed to catch their attention – but the fact that it had been illumined and made real by the thoughts I had entertained while gazing upon it, imbuing it with conceptions that approached, however haltingly, the conditions of their home world. Hence I owed the visitation to a lesser, more credible coincidence: chess and opium. At any rate, having landed their ship upon the board and thus bringing it under the influence of that vessel’s internally maintained alien laws, they had carried out simple manipulations of the pieces in order to signal their presence and establish communication – the real ship and its occupants not being visible or even conceivable to me, since they did not have contiguous spatial extension.

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. [1] A break in the manuscript occurs here – Ed.

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.