Not every important discovery is made in a vacuum. Many are made in the comfort of Euclidean space, where common household pets often contribute more than their so-called owners are willing to admit. For example, while Möbius' dog is generally thought to have inspired his human's august mathematical epiphany, it was his neighbor's cat, Johann, who solved the problem of a one-sided, two-dimensional object while observing the dog's tail-chasing behavior at a local pub.
From Johann's vantage point—above and slightly east of the Möbius dog—the solution came during the second, fourth, sixth and eighth passes of the evening, after which the bouncer threatened to remove the dog from the premises. Johann noted that Möbius' dog seemed particularly shallow during odd-numbered passes, while those with even numbers made him seem almost interesting by comparison. Johann concluded that, while the dog could scarcely be considered sophisticated, his flat, one-sided personality had everything to do with how many twists his leash had undergone during the course of the evening. Though he mistakenly attributed this paradromic phenomenon to Möbius' obsessive leash-laundering, Johann's observations would later become a cornerstone of postmodern psychology.
I must, again, tip my wig to the illustrious Craig Conley, who provided the inspiration—as he so often has in the past—for this monologue by way of a graphic, which is slated to appear on his site during the month of October.
Editor's note: And now we are here, and now here it is!