Could all the monkeys in the world randomly type on a keyboard to produce a sentence from Hamlet? This question sounds like a joke, but it is a well-studied statistical problem known as the Infinite Monkey Theorem. Mathematics has inspired and influenced the arts' world since the primitive era, architecture and painting are two good examples, but this influence is a little blurry in writing. However, the Argentinian writer Jorge Luis Borges (1899 – 1986) gives rise to use of mathematical ideas in literature. For instance, Borges transformed the Monkey Theorem into a marvelous story. As Guillermo Martinez, has mentioned some Borges’ texts are little mathematical lessons (5). If we choose one of these little mathematical lectures contained in a Borges’ short story, it would be The Library of Babel.
The Library of Babel published in Spanish in 1941 and included in Borges’ book Fictions in 1944. Here, the author represents the universe as a library composed of an indefinite number of hexagonal galleries. This unlimited library contains all the possible written books including future books not written yet, and he explores all the possible meanings of these books in different languages and even non-existent ones. The librarians, the humans who live in the hexagonal galleries, one day realize that there must exist a book that justifies their existence. While keeping this idea in mind, librarians begin their pilgrimage through the library to find such book.
While reading The Library of Babel, readers plunge into the world of combinatorial analysis. As Pinker remarks, “The most vivid description of the staggering power of a combinatorial system is in Jorge Luis Borges’ story The Library of Babe”l (8). Consider the next question, how many ice cream of two scoops can we make with five different flavors? To answer this question, we need to establish some rules for counting; in this case, we can use a flavor only once, and the order of the scoops does not matter. This prior process of counting ice creams and arranging flavors is an example of combinatorial analysis. Combinatorics is a branch of mathematics devoted to solved problems related to counting, arranging, and determining all the possible configurations of a given kind. The power of combinatorics lies in being able to handle large sets with simple calculations and elegant results.
Borges describes the magnitude of the library through a combinatorial process. He explicitly establishes the rules to count how many distinct books and letters the library contains. In the short story, the author illustrates that process telling us:
… each bookshelf holds thirty-two books identical in format; each book contains four hundred ten pages; each page, forty lines; each line, approximately eighty black letters. …The Library is “total”—perfect, complete, and whole—and that its bookshelves contain all possible combinations of the twenty-two orthographic symbols.
From this information that Borges provides, Professor Bloch computed the number of different books that the library holds; thus, the number is
to be precise (17).
Another idea that Borges borrowed from the combinatorial analysis is the concept of the anagram. An anagram is a word or phrase made by transposing the order of the letters to produce other word or phrase that possess meaning. For example, it is possible to rearrange the word “Space” to produce the word “Pecas.” This word is meaningless in English, but it has in Spanish. We can see the idea of anagrams subtly suggested in the story when Borges writes:
It would be pointless to observe that the finest volume of all the many hexagons that I myself administer is titled Combed Thunder, while another is titled The Plaster Cramp, and another, Axaxaxasmio. Those phrases, at first apparently incoherent, are undoubtedly susceptible to cryptographic or allegorical "reading."
Because the Library is total, there exist millions of books that at first glance are meaningless, but readers could use the eyeglasses of anagrams to give them meanings.
The professor of mathematics Goldbloom points out that “This combinatorial process is both important and relevant for the understanding of the story” (16). First, at the beginning of the story, Borges calls the library the universe, but this use of the language is neither rhetoric nor poetic; in fact, the number of books, previously calculated, is greater than the number of atoms in the universe. Thus, the library is greater than the universe. Similarly, in the following excerpt, Borges writes in mathematical terms, not rhetoric:
...The Vindications do exist, but those who went in quest of them failed to recall that the chance of a man's finding his own Vindication, or some perfidious version of his own, can be calculated to be zero.
While keeping in mind the number of books, it is easy to compute the odds. There exist one vindication for each person, so one divided by the number of all the possible books; the result is practically zero like Borges wrote. Finally, the author says that almost all books in the library are formless and chaotic in nature, and Borges argues that they have a meaning. It seems like a contradiction, but this contradiction disappears when we acknowledge that Borges employs anagrams and permutation of letters to conceive his fiction.
It is essential for readers to be conscious of how this combinatorial process works in the story, and how it is related to linguistics issues. According to Pinker “Grammar is an example of a combinatorial system, in which a small inventory of elements can be assembled by rules into an immense set of distinct objects” (7). Because the library is immeasurable, combinatorics help readers to understand the library’s dimensions; moreover, this knowledge shed light on the cryptic language of Borges. One final example to be considered is the Borges claim “The Library is total.” The only way to reveal the meaning of this phrase is through the power of combinatorics and the rules that govern it. Otherwise, the readers have to live with the doubt or believe in Borges’ words blindly.
To sum up, Borges employs a varied of mathematical ideas in The Library of Babel such as combinatorics, cryptography, geometry, and logical reasoning. Being conscious of these ideas, readers could understand and enjoy Borges’ fictions in a more profound way, and also readers can visualize and understand abstract mathematical concepts through Borges’ stories. As the professor of mathematics, Tony Mann says “The deepest and the most influential exploration of mathematical ideas in fiction can be found in the short stories of Jorge Luis Borges” (376). The Library of Babel is not an isolated example. Many others Borges’ short stories are written in a similar way such as The Aleph or The Book of Sand. Mathematics is not the only field that that is present in Borges’ works; likewise, Scholars have suggested that quantum physics, biology, and linguistics as well.
Works Cited
Bloch, William Goldbloom. The Unimaginable Mathematics of Borges' Library of Babel.
Oxford University Press, 2008.
Borges, Jorge Luis. "Ficciones. Translated by Emecé Editores." (1962).
Mann, Tony. "From Sylvia Plath's The Bell Jar to the Bad Sex Award:
A Partial Account of the Uses of Mathematics in Fiction." BSHM Bulletin: Journal of the British Society for the History of Mathematics, vol. 25, no. 2, July 2010, pp. 58-66.
Martínez, Guillermo. Borges and Mathematics : Lectures at Malba.
Purdue University Press, 2012.
Pinker, Steven. "The ingredients of language." (1999).



