Il libro della natura è scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezzi è impossibile a intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro laberinto.--Galileo Galilei, Il saggiatore (1623).
"The book of nature is written in the language of mathematics, and its symbols are triangles, circles, and other geometric figures. Without these means it is impossible to understand a single word; without them there is only a vain wandering through a dark labyrinth."
--Galileo Galilei, The Assayer (adapted).
Ngwerr-Qsimb was the nineteenth master of the pyramid and would likeliest die the last, for the city of Jmorsuu had been emptied by plague, famine, and civil war seven years before. Her deserted homes and temples had swiftly fallen to the encircling army of jungle that besieged them, and now even the ceremonial square at her heart, presided by the sky-shouldering bulk of the pyramid, was thick with sun-greedy saplings. From atop the pyramid at twilight, the saplings seemed to fill the square as the dwindling folk of Jmorsuu had in the city's last days, standing thin and silent in final supplication of the indifferent gods. Ngwerr-Qsimb might have fled the city with his folk, as the other priests had done, but he was already old when the first and uncanniest of the plagues began to tredecimate the city, drifting on unseasonal winds from the north, and saw no hope of establishing himself anew elsewhere, even had he been able to survive the journey down-river or through the jungle.
So at least he had argued to those urging his departure, but in truth he was convinced that the fall of Jmorsuu was owed to the malice of a long-forgotten neophyte, Gmurr-Tsvolg, who had been arrested and arraigned thirty years before on a capital charge of cryomancy. Hunters had been reporting for some weeks the mysterious blackening and death of swathes of jungle along the river, and Ngwerr-Qsimb, then the inquisitor general of the pyramid, had ordered a trap set in the pyramidal scrollery, with the pollen of a certain epiphytic orchid sprinkled on the leaves of three texts forbidden to any below the rank of deputy step-master. Having allowed a week to pass, he had then had the neophytes paraded before him, that their fingertips might be dipped in the juice of the same orchid. The purple stains that appeared on those of Gmurr-Tsvolg were proof against his stammered exculpations, and the neophyte was charged with the summoning of septentrional dæmons of cold. The penalty was automatic death, and after the formality of the trial he was laid under a geas of northering, whereby he would be drawn irresistibly to the arctic pole, to die there of frostbite or starvation.
Ngwerr-Qsimb had himself argued against the geas, recommending instead that the malefactor be executed in Jmorsuu herself, for none could tell how far Gmurr-Tsvolg had progressed on the forbidden paths detailed in the three texts, and it was possible he would survive his journey even to its extreme limit. He was overruled by the then master of the pyramid, Dulak-Lohh, and Gmurr-Tsvolg, gagged but with eyes eloquent with chilly threat, had been escorted into the jungle and laid under the geas with all due ceremony. Ngwerr-Qsimb, with the other chief officers of the pyramid, had watched him stumbling north, beating and clutching futilely at his ensorceled legs; but unlike them he had had no confidence that the neophyte was being dispatched to certain death. When, twenty-three years later, the first of the plagues had drifted southward on those unseasonal winds, his old doubts had re-awoken, and he watched the subsequent fall of Jmorsuu saddened but unsurprised. Somewhere far to the north, he believed, the former neophyte Gmurr-Tsvolg, risen high in the service of his cryocratic masters, cast spells against the city of his abjured nativity, and laughed to see her fall.
Accordingly, Ngwerr-Qsimb had refused to be driven forth, continuing to tend the rich blossoms of the pyramid and ward the sacred animals that dwelt thereon, representative of the three planes of earthly existence: the needle-crested lizards that basked and scuttered everywhere on the pyramid's steps; the ganoid fish that hung in the green water of the summit's rectangular pool, eight strides wide by thirteen long; and the gem-feathered hummingbirds that visited the summit's blossoms daily at dawn, waking him in his tetrahedral stone hut with the singing of their wings. When the city had been in her prime it had been his task to watch the lizards, fish, and birds for omens, but now his zoömancy was bootless and he watched mostly the birds, and only for the guerdon of their beauty. At dawn they hovered before him in their scores, nectaring with slender beaks in the slanting sunlight, their glittering heads and breasts dusted with the gold of a hundred pollens. Their numbers had swelled as the years of the city's desertion lengthened, and once-rare varieties – the emerald comet-tail, the rufous day-star, the amethyst sun-angel – had become more common, so that Ngwerr-Qsimb's faith in the eventual restoration of Jmorsuu, fallen almost to nothing with the departure of even his own priests, began slowly to revive.
But the malice and power of Gmurr-Tsvolg, it seemed, were unexhausted. The seasons were barely distinguishable at the latitude of Jmorsuu, which had known autumn and winter only by a slight lessening in warmth and slight increase in rainfall, but now, in the eighth year of the city's desertion, the heat of summer began to fail early and Ngwerr-Qsimb remarked a tarnishing in the gold of the solar disk. Soon, as the days of premature autumn advanced, the seasonal river-mists, which hitherto had been few and exiguous, thickened to palls that wrapped the crumbling city till noon, so that Ngwerr-Qsimb woke shivering on his pallet beneath his blankets of thread-bare cotton. When the avicidal mists subsided the few trees that had habitually marked autumn with leaf-shedding were joined by many hundred others, and the deserted avenues and squares of Jmorsuu swirled with the combat of a thousand leaf-armies, vivid in heraldries of bronze and scarlet, and seeming to rustle a repeated r'qet'lë, r'qet'lë, "I triumph, I triumph", in the uncouth suburban dialect of Gmurr-Tsvolg. Atop the pyramid, the lizards and fish grew sluggish and the blossoms began to fail, and the dwindling hummingbirds flew and nectared with an increasing desperation.
Ngwerr-Qsimb lay now on his pallet beneath moth-eaten ceremonial cloaks of rhea-feather and sloth-fur, salvaged from store-rooms delved in the pyramid's core, and composed himself to sleep each night with the prayer that the cold had reached its limit. But his prayers went unheard and when the cold on a sudden tightened on the city like a fist, for the space of three mornings he found hummingbirds lying dead beneath his shriveled blossoms: many on the first day, lying in glittering drifts; fewer on the second; a mere handful on the third. Thereafter, the hummingbirds came no more to the pyramid of Jmorsuu and the lizards basked and scuttered no more on its lichened steps, and Ngwerr-Qsimb knew that he must soon join them in death: the snares he laid through Jmorsuu were catching fewer and fewer prey of smaller and smaller size, and he knew that the creatures of the jungle were fleeing south from the cold. Soon he was living solely from his fishing, forced to spend hours blue-lipped and shivering on the river-bank, and barely able to re-climb the pyramid with his meagre catch to the work he had set himself in his final days.
The trees that had claimed the city were now quite bare of leaves, and Jmorsuu had re-emerged through them in a final commemoration of her former glory. Genuine winter was almost upon him, and the fishpool atop the pyramid was matutinally filmed with a delicate layer of that once nigh-mythical substance known as ice. Then, as though a final sentence had been passed upon him by the malice of Gmurr-Tsvolg, he rose one morning to find the city flooded: the river, which had been rising for days, had overflowed its banks and the avenues and squares of Jmorsuu glittered pale silver in the bleak light of the rising sun. The cold now was carnivorous, seizing on any patch of exposed flesh with teeth as slender and piercing as needles, and no fish responded to the line he cast into the ice-crusted water level with what had once been the nineteenth of the pyramid's steps. He abandoned his fishing in mid-morning and re-climbed the steps, breath labored and flocculent on his lips, to return to the summit and the hut in which he dwelt. Even now he could not bring himself finally to adjure the gods and cast his line into the fishpool on the pyramid's summit; but whether he fished or no, without warmth he would be dead by nightfall. One course alone remained to him, and he saw in it a final ironic jest of his hidden enemy.
The pyramidal scrollery, abandoned with all else by the city's fleeing priesthood, had succumbed to moulds engendered by the damp of departed autumn, and most of the texts Ngwerr-Qsimb now began to burn in his hut, postponing his death a few futile hours, were illegible save for phrases here and there that stuck in his mind like burrs, uselessly clinging as irreplaceable manuscripts crackled and burned with the light and heat of a vanished sun. When he had exhausted the nearer shelves of the scrollery, he resorted to the further, and came across texts he knew either by repute alone or not at all, including a few by his ancient predecessor Lomm-Tsyalk, about whose name an odor of unsanctity still clung for the heterodoxy and even heresy of his theological speculations. One of these texts, gnomically entitled The Way Unto the Plane of the Fourth, had been left by chance almost untouched by mould, and before he burnt it Ngwerr-Qsimb turned its pages and read passages at hazard. His eyes were blurred with dizziness as he read, for he was almost at the end of his bodily tether and the cold seemed to be deepening round him till his ears hissed and pattered with it, as though grains of wind-driven sand were swirling on the walls of his hut.
When we can move not, we can mark but a point, which we might call the cube of the noughth, so named for that it extendeth in no dimension of space. Extending the point, whether left or right, up or down, forward or back, we make a line, or cube of the first, so named for that it extendeth in but one dimension. When the line is thereafter extended at right angle to itself for its own length, we make a square, or cube of the second, and next proceeding to extend the square at right angle to itself, we make a true cube, or cube of the third. Hereupon we reach, at first appearance, the limit of our extensions, ¿for what remaineth to the geometrician when he hath moved up-down, left-right, and forward-back? But it is not so: it is our imaginings alone that are limited, for Nature is unexhausted and She offereth a further dimension to him of true wisdom, wherein he might extend his cube of the third to a cube of the fourth, exploiting the dimension of chelp and nang, hath he but the understanding and courage to summon the elementals who inhabit this further plane, and who will refashion his eyes and limbs that he might move within it and see its hidden glories.
In the morning the roofs of the abandoned city of Jmorsuu were blanketed in white, for snow had fallen and claimed her early for the glaciers even then grinding their way south. But nothing stirred on the summit of the great central pyramid: Ngwerr-Qsimb's hut was empty and the footprints that marked the snow for eight or nine paces from its ash-smirched threshold ended abruptly, as though the priest had taken flight somehow, to wing his way belatedly south to lands where gem-like hummingbirds still nectared in the bright light of early morning.