Years ago, I read The Library of Babel in a volume of collected short
stories by [Argentinian] Jorge Luis Borges, published under the title,
Labyrinths and translated from the [Spanish]. Like many of the mystic
Borges's works, it has staying power. Get past the religious metaphors,
you'll find bare-knuckle mathematics, e.g., `The Library is a sphere whose
exact center is any one of its hexagons and whose circumference is
inaccessible.' Sure to warm the prefrontal cortex of anyone who's ever
pondered measurement demarcation problems in extrinsic and intrinsic
geometry. Forget about plot -- I would think that those who enjoy books on
infinity, such as the classic nonfiction of Roscza Peter, Playing with
Infinity, would also enjoy this very short but dense tale.
This story has recently been reprinted in the mathematical collection Imaginary Numbers.
Although there is not a word of explicit mathematics in this short story, I consider it as deeply mathematical; there is of course combinatorics (the number of books that can be written), but more than that, there is deep topology! the last sentence reads "the library is illimited and periodic": but this exactly means that the library is a three dimensional torus! It is a perfect illustration of the notion of universal covering of the torus, and I have always been tempted to continue: of course, if it is illimited, every book appears an infinite number of times, and the destruction of a particular copy of a book is unimportant. However, if it is truly periodic, people living in it are also periodic, and each time somebody destroys a book, all his copies in the library destroy at the same time alle the copies of this book, so it really exists only once! Is not this a perfect illustration of a covering? If you imagine being in the libray, you would of course be very interested to discover if you are alone of your kind, or if you have an infinite number of clones distinct from you; but you will soon understand that there is no way to know that, and that there is in fact no meaningful distinction between the 3-torus and the 3 dimensional euclidian space
where everything conceivable is periodic by a 3-dimensional lattice.
I look at this story as one a reader an MA in English, so pardon my downgrading the relevance of the mathematics. Math, philosophy, and theology are all of equal importance in the story, and any reader may understand it without knowing any of the relevant mathematical concepts. Indeed, the mathematical foundation for the story is, as Borges notes in other works, older than the author. Having said all of that, I am working on a scholarly article that deals with higher level mathematiics than anyone else has yet ascribed to the story—concepts I can understand if not express in mathematical terms—so by way of academic secrecy (I must protect my work, after all), I will say only this for now: There is more going on here than I have ever seen anyone suggest.
I double majored in Math and Spanish. This was my favorite reading of my college career as it was a beautiful blend of both.