1. "
The Case of the Missing Line - Nabokov’s Mathematics in Pale
Fire" by Jens Juhl Jensen [
http://www.lmfk.dk/artikler/data/artikler/1104/1104_39.pdf.] where
we read that " ... arithmetical entities belong to the signifiant, rather
than the signifié, and may also direct the shape of prose texts, for instance
the writings of Nabokov. Pale Fire (i.e. John Francis Shade’s poem) is a case in
point. Already in the very first pages of the Foreword Charles Kinbote asserts
that right from the start the text was intended to cover 1.000 lines, of which
only 999 have been preserved. "
The loss, however, is not
very great: ’Nay, I shall even assert (as our shadows still walk with us) that
there remained to be written only one line of the poem (namely verse 1000) which
would have been identical to line 1 and would have completed the symmetry of the
structure." Further developments carry us to ancient Persian texts and to
Vergil, with lots of surprises lying in wait.
2. As regards topology in literature, and the Moebius strip in particular,
we find in
http://www.carliner-remes.com/jacob/math/project/lit.htm
a report bringing up "several examples in literature where the
subject of the narrative is non-orientables surfaces ..., or where the narrative
itself takes the shape of a moebius strip. 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.*
"Non-Euclidean geometry often
makes appearances in works of science fiction and fantasy.
Professor James Moriarty a character in the stories written by
Sir Arthur Conan Doyle is a criminal mastermind with a PhD in
non-Euclidean geometries.
In 1895 H. G. Wells published the short
story "The Remarkable Case of Davidson’s Eyes".
The main character in Robert Pirsig's Zen and the
Art of Motorcycle Maintenance mentioned Riemannian Geometry on multiple
occasions.
In The Brothers Karamazov, Dostoevsky discusses
non-Euclidean geometry through his main character Ivan.
Christopher
Priest's novel Inverted World describes the struggle of living on a planet
with the form of a rotating pseudosphere.
Robert Heinlein's The Number
of the Beast utilizes non-Euclidean geometry to explain instantaneous transport
through space and time and between parallel and fictional universes.
Alexander Bruce's Antichamber uses non-Euclidean geometry to create a
brilliant, minimal, Escher-like world, where geometry and space follow
unfamiliar rules[ ]
In H.P Lovecraft's Cthulhu Mythos, the sunken
city of R'lyeh is characterized by its non-Euclidean geometry. It is heavily
implied this is achieved as a side effect of not following the natural laws of
this universe rather than simply using an alternate geometric model, as the
sheer innate wrongness of it is said to be capable of driving those who look
upon it insane."
obs: What I didn't find, among the cited works by the
wikipedia, was a reference to V.Nabokov's early novel, The Luzhin
Defense, with the description of young Luzhin's reaction to "the
mysteries of parallelism," when he risked an imaginary catastrophe by "forcing
the inclined line to jump off" by reconstructing the ideal parallel lines
in the Euclidean space.
"The secret for which he strove was simplicity,
harmonious simplicity, which can amaze one far more than the most intricate
magic.[ ] However, it was just at this time that he had become
extraordinarily engrossed in a collection of problems entitled 'Merry
Mathematics,' in the fantastical misbehavior of numbers and the wayward frolics
of geometric lines, in everything that the schoolbook lacked. He experienced
both bliss and horror in contemplating the way an inclined line, rotating
spokelike, slid upwards along another, vertical one — in an example illustrating
the mysteries of parallelism. The vertical one as infinite, like all lines, and
the inclined one, also infinite, sliding along it and rising ever higher as its
angle decreased, was doomed to eternal motion, for it was impossible for it to
slip off, and the point of their intersection, together with his soul, glided
upwards along an endless path. But with the aid of a ruler he forced them to
unlock: he simply redrew them, parallel to one another, and this gave him the
feeling that out there, in infinity, where he had forced the inclined line to
jump off, an unthinkable catastrophe had taken place, an inexplicable miracle,
and he lingered long, in those heavens where earthly lines go out of their
mind." The Luzhin Defense: Ch.2
...............................................................................................................................................
* Excerpts: "Nabokov’s style is incredibly rich—every single
phrase overflows with meaning, with images begging to be unloaded and
interpreted [and] 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."
In the The Gift "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.[ ] 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! "
Was Nabokov aware that his book imitated a Moebius
strip? [ ] 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 [ ] 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 [ ] 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."