In Light of Everything: Möbius Strips
Photo by David Benbennick / CC BY-SA 3.0
December 15, 2020 at 11:18 am
You already know what it is, baby: Möbius strips! Don’t tell me you forgot about these things, man.
Now, I know what you’re thinking: “on top of everything else that’s going on in the world right now, we really have to deal with these little pieces of shit?” First of all, language. Second of all, calm down! They actually aren’t that bad, okay? They’re the simplest non-orientable surface, and they love you dearly.
Möbius strips, or as I like to call them, “Euler’s Revenge,” are unique in a couple of ways. They have only one side. They are made of paper. They are always watching over us from a safe place. Talk about tried and true topology!
What’s that? Okay, hold on — there’s someone knocking at your door. Who could it be? Oh, it’s just a Möbius strip. Now what? Better let it in. Where’s it going? I don’t know. Why’s it digging around in the pantry? Once again, I’m not sure. I don’t think Möbius strips require sustenance, but then again, I wouldn’t be surprised if they did.
Open your eyes. It was all a dream. You’re sitting on a gigantic manifold. Looking around, you observe that the platform beneath you actually twists in on itself, running along the horizon until it eventually circles back to form a complete and perfect loop. “How bizarre and subversive,” you remark aloud.
Your eyes return to the glistening, immaculate spectacle of the manifold itself. You run your hands across its sleek, Mercurian surface. It feels like home. Can you trust it? Can it trust you? Would Ferdinand Möbius be proud of what his creation had become, or would he cower in fear?
With a shrug, you start walking. You walk, and walk, and walk, and seconds become minutes, and those minutes meld together to become the drippings of time we call “days,” and those “days” stretch out to infinity and back to become what might be recognized as a “week,” or perhaps even a “month,” because at this point there’s really no way of telling how long you’ve been walking, or when the path will finally end.
You reason that there is no choice but to walk forward. Surely, forward was better than backward, which was the dastardly direction of tail lights and politicians. But, of course, this begs the question: what is direction in a world without a start or an end, without an origin or a termination? With no place to walk back to, and no place to walk forward to either? After spending a period of time pondering, you figured that such distinctions of direction were meaningless. With a deep breath, you decide to quit walking forward, and to simply walk instead.
What would you make of a world like that? A world atop a Möbius strip, so to speak. A world where no matter how far we traveled, we would always end up retracing our steps. A world where we could always remember, but could never, ever forget. A one-sided world where everything would be known, leaving nothing left for the hounds of ignorance. Lost in your own thoughts, you end up walking for a very, very long time.
What is this? A love letter to an oft-forgotten mathematical entity? A philosophical inquiry? An exercise in post-ironic satire? Puerile rubbish? I suppose it’s not really my place to say.
Good luck on finals and I’ll catch you guys on the flip side.