They had been advancing in the hallway for a few minutes now. Their steps resonated under the curved ceiling, and the strangely sweet, sickly smell of subway grease had almost faded from their perception.
Coupled with the background noise of trains and subway, they were expecting at any point to stumble upon stairs to the surface, or onto a train station. And yet, behind every turn, only red tiles, only black ceiling, only smooth stone.
As they walked, their morale fell.
"How long is this going to go on ?" said Feaser, breaking the silence. "I mean. Shouldn't we have found at least something ?"
Nobody answered. "Where are we anyway ?"
The million dollar question. Finally, Esgol spoke. "You know, earlier. You said... maybe this was a studio set or something. I'm not so sure.
-What do you mean ? This could be between the sets."
"Let's say it is. Then there would be different sets, linked together by this... hallway. First of all, there would be doors to other sets. That much is obvious." Feaser nodded, not seeing where Esgol was going. "So the fact we wouldn't have doors in a while is because, simply, we would be between to large sets. Right ? Two really big sets, and they each have a door."
"That makes sense." "Except it doesn't. We've already had a few turns. These two sets have a really fucked up shape. And, also,these would be really, really big sets. Like, we've been walking for nearly half an hour now, and still we haven't seen a door."
Everyone was silent. "And, finally, if that didn't convince you. We just turned left for the fifth time. We should have made a full turn. But we haven't."
Yedor spoke up. "Are we in a... a non-euclidian space ," "Explain. I'm afraid flamingo boy here is lost."
"The space we exist in normally is called euclidian space. You can visualize it as a flat piece of paper. If you draw a shape with right angles on that space, it will need 4 angles before it is closed. This is due to one of Euclid's law. This law, known as the parallel postulate, states that two parallel lines will be perpendicular to another line. If one of the lines is perpendicular, then the other is. Imagine it like traintracks, or a ladder. They continue in infinity, always at the same distance from each other.
"However, this kind of space isn't the only one. There are, basically, two other spaces. The first one is called elliptic space. You can see this space as the outside of a ballon. On this balloon, if you draw two lines so that both of them are perpendicular to a third one, these two lines will be parallel. And, despite that, they will intersect, as they will slightly curve toward each other.
"The third space is hyperbolic space. This space is like the inside of a bowl. It's different in that it is both finite and infinite. If you draw a railway on that space, the two line will divert from each other, and drift apart forever."
She made a pause. Esgol asked Feaser if he was following, and he answered a weak yes.
"Ok. This is fascinating but what does it mean ?" finally said Esgol.
"Right, right. Basically : in our space - euclidian space - a square will need four right angles to be closed. On the ball - elliptic space - a square will need three right angles to be closed. And, in the bowl - hyperbolic space - a square would need at least five right angles to be complete."
"I see. So... are we no longer on earth ?
-Maybe. Maybe we are no longer in our universe.
-No longer... In our universe ?
-It's impossible to modify space like that on our own universe. But at the same time... Something is weird. This is the first sign we see of no longer being in euclidian space.
-And with a circle ?
-With circles ? Hmm... It's complicated. There were multiple tests. In the end, it was possible to recreate elliptic space on a small area, but not hyperbolic space.
-What size ? What was the size of the area ?
-About... a few centimeters."
They were silent for some time, continuing to advance.
Again and again, the walls gave way to more walls. Red tiles and black ceilings and swmooth floors, forever.