The terms Möbius strip, Möbius band and Möbius surface designate a surface having only one side and one edge, formed by twisting one end of a rectangular strip through 180 degrees and joining it to the other end. (The first element also appears as Mobius, Moebius, and with lower-case initial.)
Named after the German mathematician August Ferdinand Möbius (1790-1868), who described it, the surface was also discovered independently by another German mathematician, Johann Benedict Listing (1808-82).
The following appeared in Our New Age, published in several U.S. newspapers on Thursday 1st November 1962, for example in The Arizona Republic (Phoenix, Arizona)—a cartoon panel intended to make advances in science easy to understand, Our New Age was created by Dr. Athelstan F. Spilhaus, dean of the University of Minnesota Institute of Technology, and Ray Evans, cartoonist and science writer:
THE AMAZING MOEBIUS STRIP!
Put a half-twist in a paper strip and paste the ends together. Cut it down the middle. Instead of two bands, you will still have one continuous strip!
See what happens if you make two cuts!
The earliest figurative use of Möbius strip that I have found is from It’s Only a Portrait, But It’s Exceptional, the review by Betty McNabb of Julie (New York: Simon & Schuster, 1960), a novel by Bernard Frizell. In this review, published in The American-Statesman (Austin, Texas) of Sunday 14th February 1960, Möbius strip
– first characterises Julie in the sense that only one aspect of her personality is revealed;
– then denotes the fact that Julie’s personality remains a perpetual mystery:
Bernard Grizell [sic] has made a masterful try at dissecting this Moebius-strip of a woman, whose inner self is forever exposed and whose outer surface must perforce remain hidden. […]
[…] Taken at self-value, or at any rate at publisher-value, the book can be read and enjoyed solely as entertainment […].
But taken as an author’s honest attempt to grasp the entity, the being of Julie Jones, it is even more enjoyable—at least to the female of the species. He fails, of course, to achieve the dimension he seeks—he has only painted a portrait where he hoped to sculpt a bust. The Moebius strip never ends.
The second-earliest figurative use of Möbius strip that I have found is from the column Of Smith and Men, by Jack Smith, published in the Oakland Tribune (Oakland, California) of Tuesday 16th May 1961—the title of this column is of course a pun on the phrase of mice and men:
“I’ve finally figured it out, Pa,” my older boy said the other morning. “Life is a Mobius strip.”
[…]
“What do you mean a Mobius strip?” I asked.
“It’s where you take a strip of something—like a ribbon or some Scotch tape—and give it half a twist and then glue it together at the ends.”
“I don’t get it,” I said.
“Well,” he explained, “you find out that it never ends and you can’t paint it on one side. It doesn’t have one side and it doesn’t have two sides. I read about it in mathematics.”
“I think I get the picture,” I said. “But what brings this observation at 6 o’clock in the morning?”
“Life is like a Mobius strip,” he explained. “I empty the waste baskets twice a week and every time I look at the waste baskets they’re full.”
“I see,” I said. “It’s the kind of situation you can’t paint on one side, eh?”
“That’s it,” he said. “And it never ends.”
The term Möbius strip occurs in the sense of an interrupted musical interpretation in Christian Directs Fine Tribute to President, by Jeanne Suhrheinrich, published in The Evansville Courier (Evansville, Indiana) of Tuesday 26th November 1963—John Fitzgerald Kennedy (1917-63), 35th President of the United States (1961-63), had been assassinated four days earlier:
Music also soothes the saddest breast.
A beautiful tribute to end four days of sorrow and painful soul-searching and an inspiring communion with dedicated artists giving their best was presented by conductor Minas Christian and the Evansville Philharmonic Orchestra Monday night at the Coliseum.
[…]
[…] It was with Brahms’ Double Concerto for Violin and Cello that conductor, soloists, and orchestra caught fire. Intimations of the excitement to come were brilliantly apparent in the first movement, with cellist Leslie Parnas (who seems to have grown in confidence and glowing tone power ever since he played here with the orchestra in February) and violinist Hyman Bress, guest artists, alternately presenting themes, one lovely line following the other, to be taken up later by the orchestra.
Gathering momentum and building inspiration in a Mobius strip of interpretative fire from Parnas to Christian to orchestra to Bress to Parnas, and so on, the vibrant performance of the sweet but majestic music soon drew the audience, too, into the welded rapport, always the goal but not often the prize of a conductor or a performer.
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