More remotely, other worlds model themselves on Three, Four, Five, and so on up the scale of integers to infinity. In addition there is a corresponding scale of negative integers, as also of worlds modelled on every possible fraction, on irrational numbers, on imaginary numbers, and on groups, sets and series of numbers, such as on all the primes, all the odd integers, all the even integers, and on arithmetic and geometric progressions. Beyond even these abstruse factualities are the ranges of worlds, centred on numbers and number systems not possible or conceivable to us. The only truly symmetrical, non-centred, relativistic space-time, said the Knight, is one giving equal weight to all numbers.
Georg Cantor, wrestling with the enigma of the infinite, discovered a branch of mathematics called transfinite arithmetic, in which he developed a progression of numbers analogous to the positive integers but whose first term was infinity and whose succeeding terms were as qualitatively different from and beyond infinity as are Two, Three, Four, etc., beyond One. In short, he found that there are numbers larger than infinity. As might be expected, the Knight confirmed the reality of this number system and of the transfinite space that goes with it. There is a whole range of transfinite spaces, probably even larger than the range of finite and infinite spaces (since the number of total spaces is both finite, infinite and transfinite). At this point the Knight seemed to think that we were wandering from the type of description from which I might be expected to profit, and proposed to resume, expatiating on those nearer to familiarity. I objected; it was diverting, but less challenging, to be presented with nothing but modifications of an existence I already knew. In a sense I could almost have invented these modifications myself. Would not the Knight consent to offer me, or at least attempt to make me understand, worlds having no common ground with my own – for even the Knight’s own locational-transitional space-time, I reminded him, was not hard to describe. I longed to hear something so original as to blow my mind free of all its preconceptions. After some hesitation and muttering as to the perplexities engendered by my request, the Knight agreed to make the effort and favoured me with the following amazing descriptions:*
Suddenly the Knight broke off to warn me that the power drain was now significantly close to tolerable limits and that he would not be able to linger much longer. A brief feeling of panic assailed me. There must be one question that above all others needed to be asked – yes! The choice was obvious, and I did not delay in putting it. Did the chess-people have any single, particular purpose in undertaking their admirable explorations of space?
The instinct of exploration, said the Knight, is a natural one. There was a central quest, however: to try to determine whether, in the multiplicity of space-times, there is a common universal law or principle, and thereby to discover how existence originates and is maintained.
I cursed myself for not having broached this subject sooner, instead of leaving it until it was almost too late. I had given much thought to this Basic Question myself, I tendered. And, if it was of any interest, I had once come to a tentative conclusion, that there was a basic law of existence. It is simply: ‘A thing is identical to itself.’ This principle explained the operation of cause and effect, I claimed. The universe being a unity, it is also identical to itself, and an effect only appears to follow a cause. In actuality they are part of the same thing, opposite sides of the same coin.
Once again the Knight had cause to chide me for my lack of imagination. This axiom certainly held in my own space, he conceded, but I shouldn’t suppose because of that that it was a universal law. There were numerous space-times where things were not equal to themselves. In fact even in my own space the principle adhered only approximately, because things were in motion and motion involved a marginal blurring of self-identity. My axiom held as an absolute law only in those spaces where motion was impossible.
Unabashed, I offered my second contribution, this one concerning the maintenance of existence. There was a theory, I told him, that used an electronic analogy and likened existence to a television screen and a camera. The camera scanned the image on the screen, and fed it back to the screen’s input, so maintaining the image perpetually. Thuswise existence was maintained: if the feedback from the camera to the screen should be interrupted, even for a split second, existence would vanish and could never be reconstituted.
A pre-electronic version of the theory replaces the screen and camera by two mirrors, each reflecting the image of existence into the other. It is my belief that this is the meaning of the ancient alchemical aphorism ‘As above, so below’ found on the Emerald Table of Hermes Trismegistus, it being imagined that the mirrors are placed one above the other. Other authorities unanimously assert that it refers to the supposed similarity between the macrocosm and the microcosm; but I consider that this, besides being of doubtful veridity, is a crude, pedestrian interpretation unworthy of the thought of the Great Master. The full text of the saying runs:
That which is above is like to that which is below, and that which is below is like to that which is above, to accomplish the miracles of one thing.
It has to be understood that the mirrors themselves are part of the image, of course, just as the screen and camera are part of the scanning pattern – if it is asked how this could possibly be, I would refer the enquirer to that other Alchemical symbol, the Worm Ouroboros, who is shown with his tail in his mouth, eating himself.
The Knight appeared to look on this exposition with some approval. Hermes Trismegistus, he said, was certainly a king among men of science. I asked what theories or discoveries the chess-people had on the subject; but, the Knight announced, time had run out and he could delay departure no longer. The few seconds remaining would not suffice to tell what he otherwise might have to say; but, he added, he had not so far revealed that the question of space was also intimately bound up with that of consciousness, and that it was towards consciousness that the chess-people were now directing their researches. He mentioned a space where an entity, as it might be a man, was forced to enjoy a double consciousness – not only was he conscious in himself, but he was also conscious at every moment of his appearance to the physical world around him, which was also conscious. The Knight invited me to ponder on what existence would be like in such a state – but his words now came in haste and he bade me goodbye.
Again I begged him to stay, just for a little while. But he turned and looked commandingly around him over the chessboard. The pieces began to move and to execute their flickering dance pattern around the board. The Knight joined them, gyrating around the board like a dance master directing the others. As the invisible ship lifted away the pieces surged round the board in a circular movement as if caught in a vortex; then they were still. The Knight could no longer speak to me in his resinous, friendly voice: he was only a chiselled piece of dead wood.
I came out of my shocked reverie with a start. On the disappearance of the alien influence the pieces had reverted to their original positions, ready to resume the game. There would be no need, I thought blankly, for me to write to my partner for the details.
I pushed myself away from the table. The sweet opium smell still hung on the air. The breeze from the garden was only marginally cooler. The far-off, sun was still in the act of descending to the horizon through an elegant Technicolor sky.
It was hard for me to admit that only a minute or two could have passed, when I was sure that I had been talking and listening for hours. I will never be able to know absolutely, and certainly never be able to prove, that what I say took place really did take place. I can only speak of the compelling veridity of my recollection. But whatever the truth, it has at least brought to my notice that for all our knowledge of the universe, even when we project our giant rockets into space and imagine that at last we are penetrating the basic void that holds all things, we still have not touched or even suspected the immensities and the mysteries that existence contains.
THE BEES OF KNOWLEDGE
It scarcely seems necessary to re
late how I first came to be cast on to Handrea, like a man thrown up on a strange shore. To the Bees of Handrea these details, though possibly known to them, are of negligible interest since in their regard I rate as no more than an unremarkable piece of flotsam that chanced to drift into their domain. Let it suffice, then, that I had paused to say a prayer at the shrine of Saint Hysastum, the patron saint of interstellar travellers, when an explosion in the region of the engine-room wrecked the entire liner. The cause of the catastrophe remains a mystery to me. Such accidents are far from common aboard passenger ships, though when they do occur subsequent rescue is an uncertain hope, owing to the great choice of routes open to interstellar navigators and to their habit of changing course in mid-flight to provide additional sightseeing.
My timely devotions saved my life, though reserving me for a weirder fate. Within seconds I was able to gain a lifeboat, which was stationed thoughtfully adjacent to the shrine, and, amid flame and buckling metal, I was ejected into space. After the explosion, picking my way through the scattered debris, I learned that no one but myself had escaped.
The crushing sense of desolation that comes over one at such a moment cannot adequately be described. Nothing brings one so thoroughly face to face with blind, uncaring Nature as this sudden, utter remoteness from one’s fellow human beings. Here I was, surrounded by vast light years of space, with probably not another human soul within hundreds of parsecs, totally alone and very nearly helpless.
My feeling of isolation mounted to a state of terror when I discovered that the rescue beacon was not operating. Once again I had recourse to prayer, which calmed me a little and brought me to a more hopeful appraisal of my situation. The lifeboat, I reminded myself, could keep me alive for up to a year if all went well. There would have been little point in activating the beacon immediately in any case. The star liner would not be reported missing for several weeks, and taking into account the delay before a search was organised, and the dozens of possible routes to be surveyed, a sweep within range of the beacon might not occur for months, if at all. During that time its repair seemed a feasible project, or at any rate not a hopeless one.
But it could not be done conveniently in space, and I peered again through the lifeboat’s portholes. On one side glimmered a reddish-yellow sun. Close by on the other side hung a big murky globe resembling an overripe fruit – the planet Handrea, to provide a view of which the star liner had been slowing down at the time of the explosion. It had received its name but an hour previously from one of the passengers (the privilege of naming newly sighted worlds being another of the minor perquisites of interstellar travel) and had already been ascertained as being tolerable as regards chemistry, and geology. So, heartened by having at least some course of action to pursue, I turned my small lifeboat towards it.
As I passed through them I made a careful recording of the bands of magnetism and radiation that planets of this type usually possess, noting as I did so that they were uncommonly strong and complicated. I was perturbed to find that the atmosphere was a deep one, descending nearly seven hundred miles. Upon my entering its outer fringes the sky turned from jet black to dark brown and the stars quickly vanished from sight. A hundred miles further down I entered a sphere of electrical storms and was buffeted about by powerful gusts. It had been my intention, had Handrea looked unduly inhospitable, to fly straight out again, but before long it was all I could do to keep on an even keel, not being an expert pilot. Eventually, much relieved after a harrowing passage, I entered the layer of calm air that lies close to the surface and accomplished a landing amid large tufts of a plant which, though maroon in colour, could fairly be described as grass-like.
I peered at the landscape. Vision was limited to about a hundred yards, and within this span I saw only the mild undulations of the ground, the drab coloration of the vegetation, the dull grey air. Instruments told me that the air was dense, but not of the intolerable pressure suggested by the depth of the atmosphere, consisting of light inert gases and about five per cent oxygen. The temperature, at twenty degrees, was comfortable enough to require no special protective clothing.
After a while I put on an oxygen mask – not trusting myself to the outside’s natural mix – and equalised pressures before opening the hatch. Taking with me the lifeboat’s tool-kit, I stepped outside to remove the beacon’s service plate.
Underfoot the maroon grass had a thick-piled springy texture. As I moved the air felt thick, almost like water, and perfect silence prevailed. I tried to close my mind to the fact that I stood on an alien and unknown planet, and concentrated on the task in hand.
I worked thus for perhaps twenty minutes before becoming aware of a low-pitched droning or burring sound, which, almost before I could react to it, swelled in volume until it made the air vibrate all about me. Like the parting of a curtain the opaque atmosphere suddenly disgorged two huge flying shapes. And so I saw them for the first time: the Bees of Handrea.
Describing them offers no particular difficulties, since unlike many alien forms of life they can be compared with a terrestrial species. They are, of course, vast if measured alongside our earthly bees, and the resemblance is in some respects a superficial one. The body, in two segments, is three or four times the size of a man, the abdomen being very large and round so as to make the creature closest in appearance, perhaps, to our bumble bee. As in the terrestrial bee the fur is striped but only slightly so – a relic, I would guess, from some previous evolutionary period the Bees have passed through – the stripes being fuzzy fawn and soft gold, so that the Bees seemed almost to shine in their monotonous environment.
On Earth this great mass could never take to the air at all, but the density of Handrea’s atmosphere enables such a creature to be supported by two pairs of surprisingly small wings which vibrate rapidly, giving off the pronounced drone I had first noticed. The Bees move, moreover, with all the speed and agility of their earthly counterparts. Their arrival occasioned me some alarm, naturally, and I attempted to make a hasty retreat into the lifeboat, but I had time to take only a couple of steps before one of the huge creatures had darted to me and lifted me up with its frontward limbs which ended in tangles of hooks and pincers.
The desperation of my initial struggles may be imagined. From acquaintance with earthly insects I had expected instantly to receive some dreadful sting which would paralyse me or kill me outright, and I fought with all my might to free myself from the monster. In the struggle my oxygen mask was torn loose and fell to the ground, so that for the first time, with a cold shock, I drew Handrea’s air into my lungs. All my efforts were to no avail; no sting was forthcoming, and the Bee merely modified its powerful grip so as to leave me completely helpless, and I was borne off into the mists, leaving the lifeboat far behind.
The two Bees flew, as near as I could tell, in a straight line, keeping abreast of one another. The narrow patch of landscape in my view at any one time presented no change of aspect, but we travelled through the foggy, impenetrable air at what seemed to me a prodigious speed. Unhindered now by my oxygen mask, the world of Handrea met my senses with a new immediacy. The breath that coursed through my nostrils smelled damp, bearing hints of dank vegetable fragrance. Quite separate from this, I was aware of the much stronger smell of the Bee that carried me – a sharp, oddly sweet smell that could not be ignored.
Reminding myself of insect habits, I was fearful now of a much worse fate than being stung to death. My imagination worked apace: these Bees would hardly have seized me for nothing, I told myself, and in all probability their intention was to use me as a body in which to lay eggs, so that the larvae could feed off my live flesh. In my despair I even contemplated the sin of suicide, wondering how I might kill myself before the worst happened. When I remember these fears now, my present circumstances seem relatively good.
On and on we droned, the increasing distance between myself and the lifeboat, and the virtual impossibility of my ever returning to it, causing me no small agony of mind. A
t least an hour, and possibly several, passed in this fashion before the Bees’ destination came looming out of the fog.
At first I took the shape ahead to be an oddly-formed mountain until its artificial nature became apparent. Then it emerged as an uneven, elongated dome whose limits passed entirely out of sight in the dimness: a stupendous beehive. I now know its height to attain several thousand feet, with nearly the same proportions at the base. As we came closer a generalised humming could be heard emanating from the huge edifice. At the same time I saw giant bees flitting hither and thither, coming and going from the great hive.
We approached an entrance set about a hundred feet from ground level and without pause passed through to the interior. I observed a number of Bees stationed just within the opening, some apparently standing guard, others vibrating their wings rapidly, presumably to ventilate the hive as bees do on Earth. Indeed, their work set up such a wind that the clothes were nearly torn from my back as my captors alighted on the floor of the vestibule. From this chamber several passages radiated – that, at least, was my first impression. As my captors set off down one of these. I realised that in fact the openings all connected up with one another; the internal structure of the hive was largely an open one, the space of any level being divided by the pillars which supported the next.
Barrington Bayley SF Gateway Omnibus: The Soul of the Robot, The Knights of the Limits, The Fall of Chronopolis Page 26
