What is more delightful than beholding an image wherein opposites have been artfully merged? What is more fascinating than an impossible object, like the ones appearing in Escher paintings, wherein two contraries come to be combined or even identified.
Fish are “opposites” of birds—they move in “opposite” realms. Escher plays on this opposition and renders it as the complementarity of shapes in a geometrical lattice—that is, as another kind of opposite. Here we find a translation of difference from one domain to another. In this case, the source idiom is the vertical opposition of sea and sky. Like all oppositions, it is false—the artifact of referring two things to some arbitrary context, framework, or dimension-of-variation. In this case, the opposition is doubly dependent—first, on the vertical difference “above horizon” and “below horizon”; second, on the force of gravity. Force of attraction (downwardness) is proportional to mass, so nitrogen gas weighs less than dihydrogen monoxide, and so there is a horizon line—the interface of two opposites.
Any mote-sized (or larger) solid object that you place between the two will run automatically to the sea. Unless it is a balloon, rocket, lightweight thing in a thermal or wind gust … or a bird. Birds move in the sky; fish move under the sea; land animals move on the horizon line between the two.
So birds and fish are opposed by habitat. But here they are opposed by being perfectly contiguous boundaries of each other in two-dimensional space. Escher accomplishes a spatialized pun, something that had never been seen before.
Here’s another in the same vein:
Not only are the figures complementary, they also shift their boundaries in a way reminiscent of the zoetrope and also come out of the planar world and into our own, which reminds us (today) of the shocking emergence from the TV screen in Ringu:
The geometrically impossible
These tower stairs go up and up clockwise, according to how things look at each vertex. Through what dark magick, then, is this infinite non-ascending ascent made possible? The trick is to take advantage of how depth, for bifocal humans, is conveyed through horizontal and vertical position. (The only time we intuit the z-axis directly is when we extend our limbs or locomote.) Everyone knows (from 3-D goggles and posters) that z-axis position can be faked from x- and y-axis position. And by conforming objects to one, two, or three vanishing points, we can make fully convincing illusory 3-D drawings and trompe l'oeil. As is done here, but with angles that cheat just enough to make impossible objects.
This is a monument of effrontery and cognitive strain. The third floor is the chief cheater (and enabler of the paradox), but knowing this does not lessen the pain.
The possible but uncanny
The indoor stairs are a double-trick. The felt weirdness appears to be due to being grafted onto an impossible object. But the object is normal, only the orientation of the stairs is useless for down-aiming gravity.
Here it the possible-but-uncanny drawing from above, animated. I would love to visit this place. I’d move there if I could, keep a mundane journal, and sell it to the current universe as an anthology of experimental poetry:
Even though the geometry is totally ortho-Euclidean, it is thie piece the reminds me of the four famous geometry passages from Lovecraft. For those to don’t know, Lovecraft was a great writer beloved by high school punk-intellectuals in the 80s. The most hardcore punk I’d even met—dyed mohawk, ears pierced, anarchy black leather jacket with spike studs, spike studded leather bracelets, combat boots (surely the best part). He carried one, and only one, book on his at all times. It was some tore-up Lovecraft paperback best-of anthology. He let me borrow his book, and told me:
He’s the most important writer in English. The most psychedelic. Read him, my son. Read him—and your soul will be enriched. Bring a dictionary.
He was right. It was painful for my young, stupid brain. But I learned to read. Building images from Lovecraft sentences isn’t easy. None of the familiar Lego pieces would work. I had to go to Home Depot for each piece of the construction.
I wasn’t amazed or scared, but I admired the garden-like quality of the meandering adjective clusters. The story ideas were OK. “The Outsider” is actually fun—and has a super fun ending. And “Memory” is also cute. It was actually the inspiration for Pierre Boulle’s Planet of the Apes. Anyway, the (uniquely Lovecraftian) trope I loved most was the enticing promise that the attempt to grok impossible, wrong, or peculiar geometry could be mind-blowing or even insanity-producing.
Lovecraft brings weird to the metaphysical and presentable
Lovecraft—who was born two years, two months, and two days after Escher—made Escher-eqsue geometrical weirdness a key element of his weird fiction. For me, it was also the most exciting element—because it brought weirdness to the deepest possible level that is still quasi-graspable. He thus avoids the two pitfalls of weird evocation:
- Saying that the thing is so weird that it is beyond description. Talking about totally transcendent weirdness that cannot be imagined in any way fails. It fails because it fails to present anything at all.
- Saying that the thing is just a Euclidean-Newtonian object but looks extremely grotesque also fails, because it merely provides weird appearance. The objects, in their substance and being, are are still garden variety. These objects are not weird enough.
Lovecraft’s joy and goal was in producing deep weirdness—weirdness so deep that it violates not only meaning but also perception. Lovecraft’s ambition is to evoke objects that violate our normal Kantian cognition and induce genuine alarm and loss of sanity. A face with three eyes is scary; but a face that is both convex and concave is maddening. Since geometry is the basis of (and thus prior to) everything physical, putting weirdness at the level of geometry makes it metaphysical (deeper than physical objectivity) but also quasi-imaginable.
Geometry is the boundary between physics and metaphysics, so Lovecraft puts his weird-making effort there.
Here is the earliest passage, foreshadowing the more intimate first-person encounter with geometrical impossibility that is to come:
He talked of his dreams in a strangely poetic fashion; making me see with terrible vividness the damp Cyclopean city of slimy green stone—whose geometry, he oddly said, was all wrong—and hear with frightened expectancy the ceaseless, half-mental calling from underground: “Cthulhu fhtagn”, “Cthulhu fhtagn”. These words had formed part of that dread ritual which told of dead Cthulhu’s dream-vigil in his stone vault at R’lyeh, and I felt deeply moved despite my rational beliefs. Wilcox, I was sure, had heard of the cult in some casual way, and had soon forgotten it amidst the mass of his equally weird reading and imagining. Later, by virtue of its sheer impressiveness, it had found subconscious expression in dreams, in the bas-relief, and in the terrible statue I now beheld; so that his imposture upon my uncle had been a very innocent one. The youth was of a type, at once slightly affected and slightly ill-mannered, which I could never like; but I was willing enough now to admit both his genius and his honesty. I took leave of him amicably, and wish him all the success his talent promises.
Without knowing what futurism is like, Johansen achieved something very close to it when he spoke of the city; for instead of describing any definite structure or building, he dwells only on broad impressions of vast angles and stone surfaces—surfaces too great to belong to any thing right or proper for this earth, and impious with horrible images and hieroglyphs. I mention his talk about angles because it suggests something Wilcox had told me of his awful dreams. He had said that the geometry of the dream-place he saw was abnormal, non-Euclidean, and loathsomely redolent of spheres and dimensions apart from ours. Now an unlettered seaman felt the same thing whilst gazing at the terrible reality.
Johansen and his men landed at a sloping mud-bank on this monstrous Acropolis, and clambered slipperily up over titan oozy blocks which could have been no mortal staircase. The very sun of heaven seemed distorted when viewed through the polarising miasma welling out from this sea-soaked perversion, and twisted menace and suspense lurked leeringly in those crazily elusive angles of carven rock where a second glance shewed concavity after the first shewed convexity.
Something very like fright had come over all the explorers before anything more definite than rock and ooze and weed was seen. Each would have fled had he not feared the scorn of the others, and it was only half-heartedly that they searched—vainly, as it proved—for some portable souvenir to bear away.
It was Rodriguez the Portuguese who climbed up the foot of the monolith and shouted of what he had found. The rest followed him, and looked curiously at the immense carved door with the now familiar squid-dragon bas-relief. It was, Johansen said, like a great barn-door; and they all felt that it was a door because of the ornate lintel, threshold, and jambs around it, though they could not decide whether it lay flat like a trap-door or slantwise like an outside cellar-door. As Wilcox would have said, the geometry of the place was all wrong. One could not be sure that the sea and the ground were horizontal, hence the relative position of everything else seemed phantasmally variable.
As time wore along, his absorption in the irregular wall and ceiling of his room increased; for he began to read into the odd angles a mathematical significance which seemed to offer vague clues regarding their purpose. Old Keziah, he reflected, might have had excellent reasons for living in a room with peculiar angles; for was it not through certain angles that she claimed to have gone outside the boundaries of the world of space we know? His interest gradually veered away from the unplumbed voids beyond the slanting surfaces, since it now appeared that the purpose of those surfaces concerned the side he was already on.
The touch of brain-fever and the dreams began early in February. For some time, apparently, the curious angles of Gilman’s room had been having a strange, almost hypnotic effect on him; and as the bleak winter advanced he had found himself staring more and more intently at the corner where the down-slanting ceiling met the inward-slanting wall. About this period his inability to concentrate on his formal studies worried him considerably, his apprehensions about the mid-year examinations being very acute. But the exaggerated sense of hearing was scarcely less annoying. Life had become an insistent and almost unendurable cacophony, and there was that constant, terrifying impression of other sounds—perhaps from regions beyond life—trembling on the very brink of audibility. So far as concrete noises went, the rats in the ancient partitions were the worst. Sometimes their scratching seemed not only furtive but deliberate. When it came from beyond the slanting north wall it was mixed with a sort of dry rattling—and when it came from the century-closed loft above the slanting ceiling Gilman always braced himself as if expecting some horror which only bided its time before descending to engulf him utterly.
Gilman’s dreams consisted largely in plunges through limitless abysses of inexplicably coloured twilight and bafflingly disordered sound; abysses whose material and gravitational properties, and whose relation to his own entity, he could not even begin to explain. He did not walk or climb, fly or swim, crawl or wriggle; yet always experienced a mode of motion partly voluntary and partly involuntary. Of his own condition he could not well judge, for sight of his arms, legs, and torso seemed always cut off by some odd disarrangement of perspective; but he felt that his physical organisation and faculties were somehow marvellously transmuted and obliquely projected—though not without a certain grotesque relationship to his normal proportions and properties.
The abysses were by no means vacant, being crowded with indescribably angled masses of alien-hued substance, some of which appeared to be organic while others seemed inorganic. A few of the organic objects tended to awake vague memories in the back of his mind, though he could form no conscious idea of what they mockingly resembled or suggested. In the later dreams he began to distinguish separate categories into which the organic objects appeared to be divided, and which seemed to involve in each case a radically different species of conduct-pattern and basic motivation. Of these categories one seemed to him to include objects slightly less illogical and irrelevant in their motions than the members of the other categories.
All the objects—organic and inorganic alike—were totally beyond description or even comprehension. Gilman sometimes compared the inorganic masses to prisms, labyrinths, clusters of cubes and planes, and Cyclopean buildings; and the organic things struck him variously as groups of bubbles, octopi, centipedes, living Hindoo idols, and intricate Arabesques roused into a kind of ophidian animation. Everything he saw was unspeakably menacing and horrible; and whenever one of the organic entities appeared by its motions to be noticing him, he felt a stark, hideous fright which generally jolted him awake. Of how the organic entities moved, he could tell no more than of how he moved himself. In time he observed a further mystery—the tendency of certain entities to appear suddenly out of empty space, or to disappear totally with equal suddenness. The shrieking, roaring confusion of sound which permeated the abysses was past all analysis as to pitch, timbre, or rhythm; but seemed to be synchronous with vague visual changes in all the indefinite objects, organic and inorganic alike. Gilman had a constant sense of dread that it might rise to some unbearable degree of intensity during one or another of its obscure, relentlessly inevitable fluctuations.
Real-world weird architecture
The weird architecture and bannister in “Dreams in the Witch House” (which I later found out was the basis of the first wet dream I had as a child, due to watching the BDSM scenes in The Crimson Cult) was exciting. Fruit-strip swirls of baroque, Arabic, Russian, Reims Cathedral. (I thought of because of it was the choice of The Great One in his history of man’s power over nature, called The Ascent of Man. Moulding clay is power, but too easy. To have strength, we must learn how to cut and recombine other shit—wood, rock, and then—with the “flaming sword” of fire which cuts (both smelts and alloys) chemically. And with nuclear physics and particle smashing, we cut to the core of mass and extension itself. Along the way is knowledge of support, and with this the genius of the flying buttress and the possibility of the interior luminous space, because now the walls don’t need to support anymore and so can be sheets of hanging glass.
Oh—the point. Ornate Lovecraftian objects in real life. The would be Stonehenge, Jantar Mantar, step and Egyptian pyramids, giant carvings, the Kremlin, and the Koch-curve ornaments on the Reims Cathedral spires: