After twenty or thirty minutes the giant slowly begins to sink, occasionally first leaning between eight and twelve degrees in the vertical axis. There are larger and smaller symmetriads, but even the dwarves rise a good two and a half thousand feet over the horizon after they begin to submerge, and can be seen from miles away. It’s safest to enter their interior immediately after they reach stability, since the whole ceases to drop into the ocean, and at the same time it returns to the perfectly perpendicular. The best point of entry is the area just below the summit. In this place the relatively smooth polar “cap” is encircled by an area honeycombed with funnel-shaped openings to inner chambers and channels. This configuration constitutes, as a whole, a three-dimensional solution to a higher-order equation.
It’s common knowledge that any equation can be expressed in the figural language of higher geometry, and a solid can be constructed that is its equivalent. In this understanding, a symmetriad is a relative of Lobachevsky’s cones and Riemann’s negative curvatures, but a very distant relative, due to its unimaginable complexity. Occupying an area of several cubic miles, it constitutes the solution to an entire mathematical system; this solution, furthermore, is four-dimensional, since certain essential coefficients in the equation are also expressed in time, that is to say, in the changes brought about by its passing.
Naturally, the simplest conception was that this was no more and no less than a “mathematical machine” of the living ocean, a model created on its own scale for calculations it needed for some unknown purpose; but this idea, the Fermont Hypothesis, is no longer credited. It was tempting, to be sure; but the claim that these titanic eruptions, every tiny particle of which was constantly subject to the complicating formulas of the overall analysis, were being used by the living ocean to examine questions of matter, space, existence — this notion proved untenable. Too many phenomena were to be found in the giant’s innards that could not be reconciled with such a simple (some said childishly naive) depiction.
There was no lack of attempts to come up with an intelligible model of a symmetriad, a visualization of it. One popular explanation was offered by Averian, who presented the matter as follows. Imagine an ancient terrestrial building from Babylonian times. Let it be built out of a living, responsive, evolving substance. Its design proceeds fluidly through a series of phases, taking on, as we watch, the forms of Greek and Roman architecture. Then the columns begin to grow narrow as stalks, the ceiling loses its weight; it rises, sharpens, the arches turn into steep parabolas and eventually fold and soar. The Gothic that has appeared in this way begins to mature and age; it dissolves into late forms, its former precipitous severity replaced with eruptions of orgiastic exuberance. Before our eyes Baroque excess proliferates; and if we continue this sequence — all the time regarding our changing formation as if it were the successive stages of a living being — we’ll finally arrive at the architecture of the space center era, at the same time perhaps getting closer to understanding the nature of the symmetriad.
Yet this analogy, however it may be expanded and enriched (in fact, there were efforts to show it visually using special models and films), remains at best weak, at worst an evasion, if not a downright falsehood, for a symmetriad is unlike anything on Earth…
A human being is capable of taking in very few things at one time; we see only what is happening in front of us, here and now. Visualizing a simultaneous multiplicity of processes, however they may be interconnected, however they may complement one another, is beyond us. We experience this even with relatively simple phenomena. The fate of a single person can mean many things, the fate of several hundred is hard to encompass; but the history of thousands, millions, means essentially nothing at all. A symmetriad is millions, no, billions, to the nth power; it is unimaginability itself. What of it if, in the recesses of one of its aisles that is a ten-fold version of a Kronecker space, we stand like ants holding onto the folds of a breathing vault, that we watch the rise of vast planes grayly opalescent in the light of our flares, their interpenetration, the softness and infallible perfection of their resolution, which only lasts a moment, for everything here is fluid — the content of this architecture is motion, intent and purposive. We observe a fragment of the process, the trembling of a single string in a symphonic orchestra of supergiants, and on top of that we know — we only know, without comprehending — that at the same time, above us and beneath us, in the plunging deep, beyond the limits of sight and imagination there are multiple, million fold simultaneous transformations connected to one another like the notes of musical counterpoint. For this reason someone gave them the name of geometric symphony, but if this is the case, we are its unhearing audience.
Here, in order to truly see anything at all, one would have to draw back rapidly, retreat to an immense distance; yet in a symmetriad all is internal, all is propagation, surging avalanches of births, endless shaping. At the same time each shaped thing is itself in the business of shaping other things, and no mimosa is as sensitive to a single touch, to the changes taking place where we stand, as the distant other pole of the symmetriad, miles away and separated by hundreds of stories. Here every momentary structure, with a beauty that attains its fulfillment beyond the limits of sight, is a co-creator and conductor of all the others that occur at the same time, and they in turn have a modeling influence on it. A symphony — very well, but a kind that writes itself and drowns itself out. Terrible is the end of the symmetriad. No one who sees it can resist the impression of witnessing a tragedy, if not a murder. After two, at the most three hours — this explosive growth, multiplication of itself, self-reproduction, never lasts longer — the living ocean goes on the offensive. It looks as follows: the smooth surface wrinkles over; the surf, calm now and covered with dried foam, starts to seethe; concentric series of waves rush in from the horizons. They form the same kind of muscle-bound craters as those that assist at the birth of a mimoid, though these ones are incomparably huger. The submerged part of the symmetriad is compressed and the colossus rises slowly upwards as if it were about to be flung from the planet; the upper layers of the ocean’s glial matter move into action, they creep higher and higher up the symmetriad’s side walls, covering them over, hardening, blocking up the passageways. But all this is nothing in comparison with what’s taking place at the same time within. To begin with, the formative processes — the making of successive architectures — pause for a brief moment, then suddenly accelerate; movements that up till now have been fluid, interpenetrations, foldings, the addition of foundations and ceilings, all of which has proceeded thus far smoothly and as surely as if it were to endure for centuries, begins to rush. There’s an overwhelming sense that faced with imminent danger, the colossus is hurriedly moving towards some kind of consummation. Yet the greater the speed of the transformations, the more glaring the terrible, horrific metamorphosis of the material itself and its dynamics. All the soaring, magically curving planes soften, grow flaccid, droop; there begin to appear lapses, unfinished forms, grotesque, misshapen. A gathering roar rises from the unseen depths; air, expelled as if in death throes and rubbing against the narrowing channels, wheezing and thundering in the passageways, stimulates the collapsing ceilings to a wail as if from lifeless vocal cords or monstrous throats overgrown with stalactites of slime, and despite the furious movement that has been unleashed — it is, after all, the movement of destruction — the spectator is immediately overcome by a sense of utter deadness. By this point the towering construction is supported only by the gale howling from the abyss, passing through it via a thousand shafts, inflating the structure, which begins to slide downwards, collapse like a plaster statue caught in the flames, though here and there the last twitchings can still be seen, incoherent movements disconnected from the rest, blind, ever weaker, till the huge mass, undermined and exposed to constant attack from outside, collapses with the slowness of a mountain and vanishes in a confusion of foam like that which accompanied its titanic appearance.