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

by Barrington J. Bayley

  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.*

  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.

  There was, for in
stance, a space that, though continuous, was not symmetrical in all directions but was hung between two great poles like a magnetic field. Motion along the direction of the axis between the poles was as easy as it is for us, but transverse movement was an altogether different phenomenon that required a different type of energy and a different name. This polarisation continued down into every event and structure, which was invariably positioned between two opposing poles of one kind or another. There was stereo space with great cracks of nullity running all through it, chasms of zero-existence which were impossible to cross and had to be gone round. There was space where an entity could travel in a straight line without incident, but where on changing direction he shed similar, though not identical, duplicates of himself which continued to accompany him thereafter. Prior to their rescue by me the Knight and his crew had believed themselves to be in such a space, for they had chanced to catch a glimpse of a woman accompanied by several daughters of various ages who closely resembled her. Also along these lines, there was a space where the image of an object or entity had the same powers and qualities as the original. This space abounded in mirrors and reflecting surfaces, and an entity was liable to project himself in all directions like a volley of arrows.

  When you think about it, the necessity to be in only one place at a time is a pretty severe restriction. Many are the spaces where this law has never been heard of, and where an entity may multiply himself simultaneously into disparate situations without prejudice to his psychic integrity, roaming over the world in a number of bodies yet remaining a single individual. Chameleons have caused some puzzlement among biologists because their eyes operate independently of one another; the right eye knoweth not what the left eye is doing but each scans separately for prey or enemies. Does the consciousness of the chameleon give its full attention to both eyes simultaneously? If so, the chameleon is a mental giant which no human being can equal. This feat is a natural function, however, in the space of ‘multiple individuality’ I have described.

  The Knight warned me against a restrictive concept of motion. It was not, he said, an idea of universal validity, but what we understood by motion could be subsumed under a more generalised concept he called ‘transformation’, a much larger class of phenomena. Thus there were spaces where to go was to come, where to approach was to recede, where to say goodbye was to say hello. In short, my maxim which says that to approach one point is to recede from another is not a universal law but a local case. Inversely, there were types of transformation that no mangling of the English language could succeed in hinting at. Once again the Knight suggested that I waste none of our precious time in trying to understand these inconceivable variations.

  He spent some words in describing spaces that were not totally homogeneous. The space with cracks was one of these; another was ‘sheaving space’ with a quite odd quirk: the space split itself up into branches not all of which had any possible communication or influence with one another, even though they might all communicate with some common branch. Thus both A and B might communicate with C, but it would still be impossible for any message or particle to pass from A to B even via C. The separate branches usually contained innumerable worlds, with bizarre results.

  Space can also vary in the quality of time it contains. (The Knight was quite firm in asserting that time is a subsidiary feature of space.) Time is not always irreversible, but in some spaces can be revisited by retracing one’s steps. The Knight fascinated me by telling of one space which he called ‘a space of forking time’ where every incident had not one but several possible outcomes, all equally real. Thus space branches continually in this continuum to develop alternate histories; where this space differs from the stock science-fiction notion, however, is that every past event is recoverable, and hence all possible histories communicate. By retracing his steps in a certain manner a man (or entity) can go back to the crucial moment that determined the shape of events and take a different path. When I reflected on how the fate and happiness of men is tyrannised over in our space by the singleness of time and the cruel dice-throwing of fleeting happenstance, this realm appeared to me to be a perfect abode of happiness.

  It will be obvious that causality is governed by the type of space in which it takes place. The Knight mentioned that our space contains the principle of ‘single-instance causality’, which is also the principle obtaining in most space-times, and means that prolonged and complex processes can come to completion only with difficulty. The reason is thus: if A causes B, and B causes C, it still does not follow that A will lead to C because in the interim B might be modified by interceding influences and fail to cause C. There are, claimed the Knight, space-times of extended causality where every process or project reaches completion and no tendency is ever interrupted. As the realising of ambitions is automatic any ‘effort to succeed’ is quite redundant in this space-time. The struggle and drama of life consists not of trying to actualise intentions but of the struggle to form intentions in the first place.

  In this respect the Knight included his only description of a species of locational-transitional space: a space where there was no sequential causality at all, but in which everything happened on a purely statistical basis. Wondering what it could be like on the inside of such a stochastic wonderland, I asked whether there could ever be the slightest possibility of intelligent, conscious entities arising there. To my surprise the Knight averred that it was well stocked with such entities: statistically intelligent, statistically conscious entities.

  I have touched but lightly on the role of matter in the space-times I have discussed; it would be needless to tell my intelligent reader that matter and space are inextricably entwined. He will already have guessed that besides the innumerable spaces that form a receptacle for matter, there are also those that are Aristotelian in the sense of complying with that philosopher’s erroneous theories: where matter, instead of being atomic, is continuous and identical with the space it occupies, motion being accomplished by a process of compression and attenuation. There is no empty space in these continua, exactly as Aristotle reasons. In at least one such continuum all the matter is dense and solid, so that it consists of a blocked infinity of solid rock or metal (I am not sure which). In this continuum, the Knight admitted, the possibility of conscious intelligence could be discounted. In contrast to such immobility I particularly liked what the Knight called ‘folding space’ but which I have since named ‘origami space’ (origami is the Japanese art of paper-folding). Origami space has an inner richness that makes our own space look bland. Objects can be folded so as to develop entirely new qualities. A man (or entity), by folding a piece of paper in the right way, may make of it a chair, a table, an aeroplane, a house, a fruit, a flower, a live animal, another man, a woman, or practically anything. The art of such folding, it need hardly be added, far surpasses anything to be found in our Earthly origami. Mass and size are not constants in this continuum but can be increased (or decreased) by folding, hence a square of paper a foot on the side may end up as an airliner able to carry a hundred people.

  After recounting these wonders the Knight paused to allow me to gather my mental breath. As if by way of relaxing he briefly outlined some primitive-sounding space-times that lacked our centreless relativity but were organised around a fixed centre. Remembering that earlier he had referred to our version of stereo space as a particularly rigid and restricted variety, I seized on this latest exposition to remark that at least the world I inhabited had the dignity of being infinite, symmetrical and unconstricted by having a centre. The Knight’s amusement was genuine, if gentle. With a dry laugh he instructed me that my mistake was a classic of unsophisticated presumption, and he regretted to have to inform me that my world did not have relativistic symmetry but that it had a centre.

  Where was this centre? I asked. Once more came the Knight’s mocking chuckle. He had neglected to mention so far, he said, that also intimately related to the question of space is the question of numbers. Our space migh
t have no identifiable centre in terms of motion and direction, but in its regard to number it was very strongly centred.

  At first his meaning escaped me. Number was another way of classifying the innumerable kinds of space in the universe, he explained. There was at least one space for every possible number (a theorem stated that there were more spaces than one for every possible number), and they were arranged in an ascending series, each space having its ‘centre of gravity’ about a particular number. We are near to the bottom of the scale as our ‘centre of gravity’ is the number One (there are spaces preferring fractions and at least one preferring Zero). The consequences are immediate and self-evident: singleness is what signifies a complete object in our world; integral unity is all, and the state of there being two of a thing is incidental – a thing comes into its own when it is one. We all accept this innately. Every entity and thing is itself by assigning the number One to itself. Higher numbers introduce additional qualities, but do not carry the same weight as one.*

  In the space next above us in the scale completeness attaches to the number two. ‘Two-ness’ is ideal, and singleness is incomplete in the same way that a fraction or a part is incomplete in our world. I reflected on what a mass migration there would be if communication could be established with that world – for we also have the yearning after two in our shadowy, tantalised way. Our lives are full of complementary pairs. The tragedy of lovers is that they are thwarted by the One-ness of the spatial system: each remains alone and solitary, however much they strive and strain to be completely merged as two – for the vain yearning of lovers is not to be made One, which would negate the whole proceeding, but to be, as it were, indistinguishably blended as Two. Should a pair of Eros-struck lovers by some magic or science transpose themselves to this other realm where Two is All, then their bliss would be beyond describing.