A Klein bottle is a twisty, self-intersecting three-dimensional representation of a two-dimensional manifold embedded in four dimensions. A Klein bottle is also a bottle in the fist of a young man named Klein, who is sitting on the carpet of the lounge in his university dorm building.
This bottle is not self-intersecting in any mathematical way, but it intersects with Klein’s mouth, and Klein often feels that the bottle is a part of himself, a snakelike extension, so perhaps it is self-intersecting. Klein himself is a mostly closed surface, and therefore qualifies as a two-dimensional manifold. His skin locally resembles a Euclidean plane. There are anomalies in his smoothness, of course. Latent cystic acne sprung up from nowhere at the age of fifteen and has refused to let him go, even so far into sophomore year of college.
He is concentrating loosely on swallowing cheap beer, Busch Light, which falls down his esophagus and doesn’t tempt comfort so much as a lecture on fluid mechanics. He can hear a scratching on the window. The rhododendrons in the courtyard have stretched up so high that they can just reach the second floor. The buds sound like witch fingers, tapping to be let in. Klein doesn’t dislike the sound -- he doesn’t know if he is capable of disliking a sound, only feeling it rattle through him as if he were an expanse of space.
He pries the window open. The opening is only wide enough to squeeze his head and shoulders out of. He swats the rhododendron buds out of the way and curses meaninglessly at them. The lawn of his college campus stretches out before him. The surface of the earth itself is a two-dimensional manifold. Walking across it, it seems to stretch only forward. Humans operate on too small a scale to see Earth’s curves on their own, resorting to airplanes and rockets to lift them up on the third axis. Klein squints to see the curve of the earth in the lawn of the campus green but there is flatness all the way from the library to the student union building. Lecture halls and laboratories are in the way, as are distant trees and mountains.
Klein’s attention is attracted by movement in the grass. A couple is staggering across it, a blonde girl wearing layers of coats and a boy with a hat and long dark hair. The hems of their pants are each stained dark from nighttime dew. They are wandering in inebriated circles, their bodies visible and invisible and visible again and they cross in and out of the shadow of the library clock tower.
If there was a fifth dimension, or a sixth or a seventh, the couple might be moving through them without knowing. They might be tossed and whisked away suddenly only to return in what felt like an instant, and as flatlanders, as three-dimensional bodies staggering across a two-dimensional manifold while the fourth and fifth and sixth dimensions of time and space and more space trickled out from Klein’s very eyes, they would not and could not know what was happening to them.
Klein wonders how, if at all, it would be possible to tell them. Whether it is his responsibility to let them know that they might very well be travelling inter-dimensionally.
Klein’s bottle intersects with his mouth again. The rounding edge falls against a budding zit on his lip and a subtle bump of pain rings through him like a sound ricocheting. Klein routinely buys beer he doesn’t like from his roommate’s girlfriend’s friend and then he drinks it in the lounge of his dorm on days and at hours when he is sure no one else will be there.
He watches the couple hawk-like. They appear to be dancing to music that is coming from one of their cellphones, though Klein can’t hear it. He can only see their bodies jerking back and forth as if they had fishhooks in them and were being whipped around by some invisible string. Their whispers and laughs are chewed up and rereleased by the campus’s architecture, bouncing, bouncing, landing like mangled throat-noises in Klein’s ears.
And all at once, they turn sideways, and disappear into quicksilver.
Klein is not drunk enough to second-guess himself. He doesn’t even blink. His skinny acne-blessed face hangs out of the high-up window and contorts indignantly, mouth open, eyes bugged, until he says, just for posterity:
“I saw that.”
The rhododendrons change ways in the wind and smack at his lip. He shoos them away, his concentration broken. The hole where the couple had been dancing bleeds a smoky cross-dimensional receipt.
He doesn’t move. He doesn’t drink. He holds the menace-plants out of the way with his elbow and scans the lawn, hunting for slivers of the couple, evidence that they had been there, a hint of their eventual return. After seconds that feel like chronons of stillness, something between light and pure color sprinkles itself over the grass. Little rips in a blanket, grains of rice. All bewilderingly chromatic and quite possibly unreal.
As if the couple was both back and gone forever, and as if they had been there since the beginning of never and would continue forever in streaks like sunlight and spider’s web.
Klein’s fingers cannot not keep up with his eyes which cannot not keep up with his brain nor his face, and so he feels his beer bottle slipping from his fingers, the body giving way to the neck giving way to thin air, and it falls through an eternity before hitting the bricks two stories beneath him. But it doesn’t make a sound, and there is no feeling of the hit against the world. It just slips away and keeps falling.
The couple is undergoing an extraordinary transformation and Klein is the only one watching. They are dancing still. They return from the rain of chromatic rice into just feet, just little feet stamping away on the wet grass, before the feet fall away to just lines, vertical slices of the couple as if they were paper dolls being viewed from the side. Then they are polygons ballooning and shrinking, then they are concave in a way that makes Klein begin to feel sick, and although he feels like he might vomit if he continues to watch, he keeps watching because he is the only one.
Before Klein’s brain catches up to his eyes, the couple looks the way they looked at the beginning. The girl’s layers of coats billow while she twirls and the boy’s cap falls off onto the grass and he puts it back on his head like nothing happened. Klein is surprised that whatever has just begun is now over. He can still taste the declaration of seeing on his tongue. He can still feel the echo of where the bottle's lip met his zit and it stung faintly.
He is hawk-like again, looking for the broken pieces of the bottle, but the bricks beneath him are undisturbed.
The couple runs away. A campus security vehicle drives through a nearby parking lot and the headlights are ripe and bright, unequivocally there. Klein forgets to notice which direction they go. He thinks for a moment they have run straight up, or straight down, through the surface of the earth or into the air which is not nothing but is often called nothing. He noisily pulls his head and arm back inside the window. The rhododendrons spring into place.
Klein forms the words “I saw” in his mouth again and again without saying them until the syllables feel like pudding. His hand wraps around a bottle that’s not there, not the way it was five minutes ago. His brain sews itself back together. He runs his thumb over the swelling bump on his lip where the zit will soon emerge. He begins the processing of relocating what he has seen, the chromatic rice, the quicksilver, the spiderwebs, the polygons, the paper dolls, the bottle.
He sits very still and he takes it all and he places it somewhere safe, and he drops it out the window and into a funnel where it is taken away to a place that people, such as Klein is, can only imagine.