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We found several examples in literature where the subject of the narrative is non-orientables surfaces (mainly Moebius strips), or where the narrative itself takes the shape of a moebius strip. The most accessible are the first, and the two we chose to include in our course are “The No-sided Professor,” by Martin Gardner, and “A Subway Named Moebius,” by A.J. Deutsch. They can both be found in the collection of short stories called Fantasia Mathematica, assembled by Clifton Fadiman. We also found two examples of works where the plot resembled a Moebius strip--Ionesco’s play The Bald Soprano and Nabokov’s novel The Gift. The Bald Soprano is very accessible too--it is an easy read, and the Moebius strip analogy is straightforward. The Gift, on the other hand, is more obscure, and we suggest that only the more advanced readers try to tackle it.
We hope that the examples of Moebius strip literature we chose will inspire you to create your own short stories, poems, etc. Also, our selection is by no means exhaustive--take a minute to think of other books you have already read which remind you of non-orientable surfaces!
"A. Botts and the Moebuis Strip:"
The play is an easy read. Mr. and Mrs. Smith invite Mr. and Mrs. Martin over for dinner, and conversation gradually gets completely out of hand, until there seems to be no more logical connection between the characters’ responses, as though Ionesco were taking random phrases and placing them one after the other. " Theater of the absurd" is one of the phrases most commonly ascribed to Ionesco. We are thoroughly lost by the last pages of the play, and are unable to make any more logical links in the plot, until the concluding stage directions, which read: “Mr. and Mrs. Martin are sitting like the Smiths at the beginning of the play. The play starts again with the Martins, who are saying exactly the same words as the Smiths in the first scene.” (In fact, there have been productions in which the play has been performed for 24 hours straight, switching continuously from the Smiths to the Martins.) It’s a loop with a twist situation. The play has started over again, and the only difference is that the characters have been switched around.
Nabokov’s work is full of mathematical references. In fact, one of the first sentences of The Gift reads thus: “Running along [the van’s] entire side was the name of the moving company in yard-high blue letters, each of which (including a square dot) was shaded laterally with black paint: a dishonest attempt to climb into the next dimension.” The author alludes to geometrical configurations and to distortions of space and time throughout his book, so it is no surprise to find Moebius metaphors in it as well. I see the Moebius motif appear in two different ways, but before I develop them, let me briefly summarize the plot of the novel.
Fyodor is a young, hitherto unknown writer who has just published his first collection of poems, and Chapter One of The Gift centers around this first publication. Chapter Two then moves on to describe Fyodor’s progress as a writer, and also discusses Fyodor’s father’s zoological explorations. This chapter is largely centered around how Pushkin is reflected in Fyodor’s work, and Chapter Three concentrates on Gogol’s influence. By this time, Fyodor has met Zina, who encourages and supports him as he writes a literary biography of Chernyshevski. Chapter Four is the actual book which Fyodor writes. The last chapter comes back to an older Fyodor, who sketches out the book he wishes to write: The Gift. As you can tell from this summary, or from having read the book yourself, the narrative is very intertwined. One plot line emerges from another, until you have lost track of where to find the “true” narrative. Nabokov himself called Chapter four, the book within a book, a “spiral within a sonnet”—quite a beautiful image to portray the narrative twists in The Gift.
I suggested earlier on that if you ever got confused as to how literature could imitate a Moebius strip, you could think: “a loop with a twist”. If you extend this image, you can also think to yourself: “if you follow the Moebius strip around, what was once the inside becomes the outside, and what was once the outside becomes the inside.” This image applies directly to the narrative structure of The Gift. Fyodor is on the inside of the narrative at the beginning of the work: he is a character who Nabokov, author of The Gift, is writing about, describing his beginnings as a writer, and how he comes to meet his girlfriend Zina. Once we get to the final chapter, however, Fyodor discusses with Zina the book he wants to write: “Here is what I’d like to do,” he said. “Something similar to destiny’s work in regard to us. Think how fate started it three and a half odd years ago…” From there, Fyodor proceeds to explain that he wants to write a book about exactly what we just read: his emergence as a writer and the gradual evolution of his relationship with Zina. Fyodor is no longer the character of Nabokov’s The Gift, but the author of his own The Gift. He is now on the outside! This is really quite a remarkable yet subtle narrative twist.
Was Nabokov aware that his book imitated a Moebius strip? There is no evidence that he was—none of his comments on The Gift suggest it. In fact, the inventor of the Moebius metaphor in The Gift seems to be Omry Ronen, who used to be a literature professor at Yale and is now at University of Michigan. One of his students when he taught at Yale, Serguei Davidov, picked up on the metaphor and developed it extensively. Apparently, Ronen was very possessive of his metaphor, and one day, upon presenting his student Davidov with a present, signed it "from the author of the Moebius strip metaphor," to stress the fact that although Davidov discussed the image later, it originated from Ronen.
From a formal point of view of the narrative, therefore, The Gift imitates a Moebius strip. Furthermore, if we examine the language of The Gift, there are a number of moments which relate to Moebius strips also. The idea of flips and twists comes up often: "at the end, there is always one that does a kind of flip, and then hastily assumes its position," says the narrator about a commercial. "I turn my life inside down so that birth becomes death, I fail to see at the verge of this dying-in-reverse anything that would correspond to the boundless terror that even a centenarian is said to experience when he faces the positive end," he says further on. Or still later on in the narrative: "you look at a person and you see him as clearly as if he were fashioned of glass and you were the glass blower, while at the same time without in the least impinging upon the clarity you notice some trifle on the side--such as the similarity of the telephone receiver's shadow to a jug, slightly crushed ant, and (all this simultaneously) the convergence is joined by a third thought--the memory of a sunny evening at a Russian small railway station; ie. images having no rational connection with the conversation you are carrying on while your mind runs around the outside of our own words and along the inside of those of your interlocutor." Once again, we find the inside/outside image.
For homework, answer the questions posed to the right on the following works:
This section written by MLB.
The picture of the cover of Fantasia Mathematica is from Amazon. The Boston T map comes from the MBTA website. The picture of two people trying to paint a Moebius band is from Zbigniew Fiedorowicz's Introduction to Toplogy site. Eugene Ionesco's photograph comes from the Romanian American Forum's list of famous Romanians. The picture of Nabokov is from Corbis. Thanks to Professor Vladamir Alexandrov of the Yale Department of Slavic Language and Literature for his help with The Gift.
For further reading, look at the following books:
Fadiman, Clifton. Fantasia Mathematica. New York: Simon and Schuster, 1958. (Republished in 1997 by Springer-Verlag).
Ionesco, Eugene. "The Bald Soprano." In The Bald Soprano and Other Plays, Donald M. Allen, translator. Grove Press, 1982.
Nabokov, Vladimir. The Gift. New York: Vintage, 1991.
On the web, you can look at the following sites:
Søren Olsen's biography of Eugene Ionesco.
Zembla, a site devoted to all things Nabakov.
For more information on sources and other ideas for further reading, see the bibliography.