by Brooks Riley

MobiusLogoRemember the winter scarf? A long strip of knitted wool, the two ends knotted, crossed, or wrapped around the neck. I’ve worn them all my life, struggling to keep the ends from unwinding in a cold wind, or retrieving a loose end from my latte as I reach across a table to shake someone’s hand. A shroud would be an improvement, long and fulsome, but it too comes with loose ends, to be saved for later.

Loose ends, the obvious metaphor for a life in limbo, is simplistic. And just what are those ends anyway? Bookends to the main event, the Alpha and Omega of existence, birth and death—useless but inevitable.

Recently, in search of a new scarf, I came across a woolen loop, slightly elasticized so that it could be wrapped twice around my neck. Look, Ma, no ends! It’s nothing special these days, but for me it was a revelation: I was liberated from the struggle to make ends meet or stay put. Now I felt safe, in more ways than one: A woven furnace caressing my carotid arteries, I was wrapped in a security blanket without issues, clearing the way for worries of the endogenous sort, the kind that don’t come bundled with small physical irritations.

Delighted with this new-millennial improvement on age-old warmers, I shopped for another one. My second scarf went the first one even better: a brilliant woolen Möbius strip that didn’t even have to be doubled—a fat Möbius which sits firmly on the shoulders, its twist neatly snuggled at the nape of the neck, allowing the fullness of the rest to fortify the shoulders and throat. While others might be drooling over the latest wearable tech, my needs were answered by a 5 € purchase, made possible by two 19th century mathematicians, August Ferdinand Möbius and Johann Benedict Listing, who came to the same conclusion simultaneously in 1858 in their land of Zeitgeist or the zeitgleich. (Poor Herr Doktor Listing: Möbius won the posterity game.)

Why had it taken them so long to provide the ultimate verification of the infinity symbol, which John Wallis had promoted in two-dimensional form two centuries earlier? Why had it taken so long for their discovery to find such an ingenious practical application as a scarf? And why was it called a Möbius strip when it is no longer a strip, but a loop with a twist?

As I get older, I care less about the great social upheavals in which we all are imbedded. I’ve withdrawn from social activity or interaction, politics, or even discourse. Instead, I’ve become more fixated on the marvel of things. Slouching toward a borrowed autism that keeps people at arm’s length, I wonder about abstractions, discoveries and phenomena, enigmas and conundrums, puzzles and elegant solutions. I no longer ask ‘What is the meaning of life?’ I ask, ‘Do birds appreciate a good sunset?’ Or why symmetry, the two of everything, is so fundamental in nature. Two hands, two eyes, two ears, mostly two genders—the answer is obvious. But the double helix, the symmetrical markings on a cat, the two sides of a surface, or the two ends of a scarf?

And what is it about the Möbius loop that makes it so intriguing? Like the basic loop, you can travel along its surface and end up where you began. But there’s a difference: On the loop you’ve travelled only one side of the surface, like a rat on a treadmill. You’re either outside or inside. With the Möbius loop, however, as M.C. Escher so charmingly illustrated, you cover both sides of that surface before you end up where you started. The Möbius loop defies logic with an astonishing, pregnant paradox. It’s difficult not to think analogously, of how this mathematical truth applies to other, intangible aspects of life.

I think of Wagner’s Ring of the Nibelung, a cycle that ends where it began, in the Rhine—or as Anna Russell so aptly put it: “You’re exactly where you started 20 hours ago!” Why that cycle compares to a Möbius loop instead of a basic loop is this: You’ve travelled the Valhalla and the Nibelheim sides of the cycle, those yin and yang surfaces, without interruption, seamlessly. When you arrive back to where you started, nearly all the protagonists are dead. The Rhine Maidens become the seam that allows the story to continue, but a different cycle would begin, with a different dramatis personae (and a different composer). Wagner was alive when Möbius made his discovery. Had he known of it, might not the Norns have taken advantage of the circularity of fate? It wouldn’t have changed the ultimate Riss, that shocking moment when the rope they are weaving snaps. (Es riss! It’s snapped!) A snapped Möbius loop would also have put those Norns out of business.

In the Möbius life, where birth and death are conjoined to form a single band of existence to be travelled but once, its continuum covers the fortunes and misfortunes (the two antagonistic surfaces) of a single destiny without interruption or divergence from the path. At the seam where birth and death meet, a new individual takes up the inevitable, idiosyncratic journey. The loop remains the same, but the twist, ah the twist: It alone defines a finite experience within infinity. Unless you believe in reincarnation. Then you merely step across the seam and keep going.

It’s no wonder that the Möbius loop appealed to rollercoaster designers. There are three in the world, but only one that sounds like a true Möbius loop, the Montaña Rusa in Mexico City. Rollercoasters themselves are worn-out carriers of metaphoric weight, especially where lives are concerned. Who can say that they’ve never taken a joy ride on one of those contraptions, at least metaphorically, braving the ups and downs of destiny?

The more I ponder the Möbius loop, the more I see it in other constructions, for instance Jan Potocki’s masterpiece The Manuscript Found in Saragossa, written in the early 1800’s, its multifarious trails always leading back to the hanging tree. Or any number of endeavors which end where they began, for better or worse. Or history, the great repeatable, but that’s another story, another scale.

I’m still wending my way along a Möbius loop, traversing the lightness and darkness of being, without a detour. And just in case, I’ll keep wearing my Möbius scarf.