Words with a Twist

Long trips often give me a chance to catch up with my reading. I spent much of my journey home from the 2011 Joint Mathematics Meetings (JMM) in New Orleans reading the Dec. 13, 2010, issue of The New Yorker. The issue proved a winner, with several interesting articles and, best of all, two mentions of Möbius strips.

I have been collecting references to Möbius strips in articles, stories, and other venues for many years, and I'm particularly interested in examples in which the term is used without further explanation. In other words, the reader is expected to understand the reference and all that it stands for.

In "A Widow’s Story," Joyce Carol Oates describes the final week before her husband’s death in 2008. In the entry for February 14-16, she writes:

"Those days—nights—a Möbius strip continuously winding, unwinding.

This nightmare week of my life—and yet during this week Ray is still alive."

Her allusion draws on a particular characteristic of a Möbius strip, without burdening the reader with a detailed explanation. But the allusion is that much richer for readers already familiar with the surprising topology of this mathematical object.

The second mention is in a listing of reviewers’ favorite books from 2010, where Mr. Peanut by Adam Ross is simply described as "the novel as Möbius strip."

Indeed, the original review by Daniel Mendelsohn, which was published in the July 12&19 issue of The New Yorker, remarked on the novel's convoluted, twisting, self-referential structure and its explicit references to M.C. Escher and Möbius. The book's chief character is a successful videogame designer, who is working on a project titled Escher Exit, in which an avatar moves through cunningly designed environments before finally confronting an evil archenemy—named Mobius.

"If 'Mr. Peanut' is something of a Möbius strip, Ross seems to be saying, then so is a marriage: in both fiction and relationships one 'side' can turn out to be the same as the other—love and hate, form and content, art and life, past and present," Mendelsohn writes.

Finding references to Möbius strips at the JMM is probably much less surprising. Indeed, one entry in the exhibition of mathematical art at the 2011 meeting was a Möbius band on which was printed the words of a story. Created by Barry Cipra and titled Loopy Love, the paper sculpture incorporated a story written for a workshop on creative writing in mathematics and science, held in 2010 at the Banff International Research Station.

The story is "a dialog presenting both sides (or is there only one side?) of a twisting love/hate relationship between two characters named Daniel and Danielle," Cipra writes in the exhibition catalog.

Barry Cipra.

"Assembled by hand with tape, the resulting scrollable sculpture retains its shape yet remains flexible, so that the reader can easily read the story without ever having to turn the page," he continues. "Viewers are invited to pick it up, play with the paper, and read the story from start to finish—except there is no start nor any finish!"

Photos by I. Peterson