The effects of light on a symmetriad are especially striking during the blue day and the red sunset. The planet appears to be giving birth to a twin that increases in volume from one moment to the next. The immense flaming globe has scarcely reached its maximum expansion above the ocean when it bursts at the summit and cracks vertically. It is not breaking up; this is the second phase, which goes under the clumsy name of the ‘floral calyx phase’ and lasts only a few seconds. The membranous arches soaring into the sky now fold inwards and merge to produce a thick-set trunk enclosing a scene of teeming activity. At the center of the trunk, which was explored for the first time by the seventy-man Hamalei expedition, a process of polycrystallization on a giant scale erects an axis commonly referred to as the ‘backbone,’ a term which I consider ill-chosen. The mind-bending architecture of this central pillar is held in place by vertical shafts of a gelatinous, almost liquid consistency, constantly gushing upwards out of wide crevasses. Meanwhile, the entire trunk is surrounded by a belt of snow foam, seething with great bubbles of gas, and the whole process is accompanied by a perpetual dull roar of sound. From the center towards the periphery, powerful buttresses spin out and are coated with streams of ductile matter rising out of the ocean depths Simultaneously the gelatinous geysers are converted into mobile columns that proceed to extrude tendrils that reach out in clusters towards points rigorously predetermined by the over-all dynamics of the entire structure: they call to mind the gills of an embryo, except that they are revolving at fantastic speed and ooze trickles of pinkish ‘blood’ and a dark green secretion.
The symmetriad now begins to display its most exotic characteristic – the property of ‘illustrating,’ sometimes contradicting, various laws of physics. (Bear in mind that no two symmetriads are alike, and that the geometry of each one is a unique ‘invention’ of the living ocean.) The interior of the symmetriad becomes a factory for the production of ‘monumental machines,’ as these constructs are sometimes called, although they resemble no machine which it is within the power of mankind to build: the designation is applied because all this activity has finite ends, and is therefore in some sense ‘mechanical.’
When the geysers of oceanic matter have solidified into pillars or into three-dimensional networks of galleries and passages, and the ‘membranes’ are set into an inextricable pattern of storeys, panels and vaults, the symmetriad justifies its name, for the entire structure is divided into two segments, each mirroring the other to the most infinitesimal detail.
After twenty or thirty minutes, when the axis may have tilted as much as eight to ten degrees from the horizontal, the giant begins slowly to subside. (Symmetriads vary in size, but as the base begins to submerge even the smallest reach a height of half a mile, and are visible from miles away.) At last, the structure stabilizes itself, and the partly submerged symmetriad ceases its activity. It is now possible to explore it in complete safety by making an entry near the summit, through one of the many syphons which emerge from the dome. The completed symmetriad represents a spatial analogue of some transcendental equation.
It is a commonplace that any equation can be expressed in the figurative language of non-Euclidean geometry and represented in three dimensions. This interpretation relates the symmetriad to Lobachevsky’s cones and Riemann’s negative curves, although its unimaginable complexity makes the relationship highly tenuous. The eventual form occupies an area of several cubic miles and extends far beyond our whole system of mathematics. In addition, this extension is four-dimensional, for the fundamental terms of the equations use a temporal symbolism expressed in the internal changes over a given period.
It would be only natural, clearly, to suppose that the symmetriad is a ‘computer’ of the living ocean, performing calculations for a purpose that we are not able to grasp. This was Fremont’s theory, now generally discounted. The hypothesis was a tempting one, but it proved impossible to sustain the concept that the living ocean examined problems of matter, the cosmos and existence through the medium of titanic eruptions, in which every particle had an indispensable function as a controlled element in an analytical system of infinite purity. In fact, numerous phenomena contradict this over-simplified (some say childishly naïve) concept.
Any number of attempts have been made to transpose and ‘illustrate’ the symmetriad, and Averian’s demonstration was particularly well received. Let us imagine, he said, an edifice dating from the great days of Babylon, but built of some living, sensitive substance with the capacity to evolve: the architectonics of this edifice pass through a series of phases, and we see it adopt the forms of a Greek, then of a Roman building. The columns sprout like branches and become narrower, the roof grows lighter, rises, curves, the arch describes an abrupt parabola then breaks down into an arrow shape: the Gothic is born, comes to maturity and gives way in time to new forms. Austerity of line gives way to a riot of exploding lines and shapes, and the Baroque runs wild. If the progression continues – and the successive mutations are to be seen as stages in the life of an evolving organism – we finally arrive at the architecture of the space age, and perhaps too at some understanding of the symmetriad.
Unfortunately, no matter how this demonstration may be expanded and unproved (there have been attempts to visualize it with the aid of models and films), the comparison remains superficial. It is evasive and illusory, and side-steps the central fact that the symmetriad is quite unlike anything Earth has ever produced.
The human mind is only capable of absorbing a few things at a time. We see what is taking place in front of us in the here and now, and cannot envisage simultaneously a succession of processes, no matter how integrated and complementary. Our faculties of perception are consequently limited even as regards fairly simple phenomena. The fate of a single man can be rich with significance, that of a few hundred less so, but the history of thousands and millions of men does not mean anything at all, in any adequate sense of the word. The symmetriad is a million – a billion, rather – raised to the power of _N_: it is incomprehensible. We pass through vast halls, each with a capacity of ten Kronecker units, and creep like so many ants clinging to the folds of breathing vaults and craning to watch the flight of soaring girders, opalescent in the glare of searchlights, and elastic domes which criss-cross and balance each other unerringly, the perfection of a moment, since everything here passes and fades, The essence of this architecture is movement synchronized towards a precise objective. We observe a fraction of the process, like hearing the vibration of a single string in an orchestra of supergiants. We know, but cannot grasp, that above and below, beyond the limits of perception or imagination, thousands and millions of simultaneous transformations are at work, interlinked like a musical score by mathematical counterpoint. It has been described as a symphony in geometry, but we lack the ears to hear it.
Only a long-distance view would reveal the entire process, but the outer covering of the symmetriad conceals the colossal inner matrix where creation is unceasing, the created becomes the creator, and absolutely identical ‘twins’ are born at opposite poles, separated by towering structures and miles of distance. The symphony creates itself, and writes its own conclusion, which is terrible to watch. Every observer feels like a spectator at a tragedy or a public massacre, when after two or three hours – never longer – the living ocean stages its assault. The polished surface of the ocean swirls and crumples, the desiccated foam liquefies again, begins to seethe, and legions of waves pour inwards from every point of the horizon, their gaping mouths far more massive than the greedy lips that surround the embryonic mimoid. The submerged base of the symmetriad is compressed, and the colossus rises as if on the point of being shot out of the planet’s gravitational pull. The upper layers of the ocean redouble their activity, and the waves surge higher and higher to lick against the sides of the symmetriad. They envelop it, harden and plug the orifices, but their attack is nothing compared to the scene in the interior. First the process of creation freezes momentarily; then there is ‘panic.’ The smooth interpenetration of moving forms and the harmonious play of planes and lines accelerates, and the impression is inescapable that the symmetriad is hurrying to complete some task in the face of danger. The awe inspired by the metamorphosis and dynamics of the symmetriad intensifies as the proud sweep of the domes falters, vaults sag and droop, and ‘wrong notes’ – incomplete, mangled forms – make their appearance. A powerful moaning roar issues from the invisible depths like a sigh of agony, reverberates through the narrow funnels and booms through the collapsing domes. In spite of the growing destructive violence of these convulsions, the spectator is rooted to the spot. Only the force of the hurricane streaing out of the depths and howling through the thousands of galleries keeps the great structure erect. Soon it subsides and starts to disintegrate. There are final flutterings, contortions, and blind, random spasms. Gnawed and undermined, the giant sinks slowly and disappears, and the space where it stood is covered with whirlpools of foam.