"I climbed these stairs for forty years," said the old mathematician, "and I've never reached the top. Nor have I descended to the bottom. The geometry won't allow it."
In the halls of the Penrose Institute, they say the architect went mad trying to draw his blueprints. Each floor was both above and below itself. The building inspectors gave up and went home.
Students still walk these corridors, forever ascending, forever arriving exactly where they started. The professors claim it teaches humility. The janitors claim it makes cleaning impossible.