Definitions

# The Library of Babel

"The Library of Babel" is a short story by Argentine author and librarian Jorge Luis Borges (1899-1986), conceiving of a universe in the form of a vast library containing all possible 410-page books of a certain format.

The story originally appeared in Spanish in Borges's 1941 collection of stories El Jardín de senderos que se bifurcan (The Garden of Forking Paths). That entire book was, in turn, included within his much-reprinted Ficciones (1944). Two English-language translations appeared approximately simultaneously in 1962, one by James E. Irby in a diverse collection of Borges's works entitled Labyrinths and the other by Anthony Kerrigan as part of a collaborative translation of the entirety of Ficciones.

## Plot summary

Borges's narrator describes how his universe consists of an endless expanse of interlocking hexagonal rooms, each of which contains the bare necessities for human survival—and four walls of bookshelves. Though the order and content of the books is random and apparently completely meaningless, the inhabitants believe that the books contain every possible ordering of just a few basic characters (letters, spaces and punctuation marks). Though the majority of the books in this universe are pure gibberish, the library also must contain, somewhere, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books. The narrator notes that the library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages. Conversely, for many of the texts some language could be devised that would make it readable with any of a vast number of different contents. (Of course text consisting of all the same letter 'aaaaa' would not have any content by any scheme of interpretation).

Despite — indeed, because of — this glut of information, all books are totally useless to the reader, leaving the librarians in a state of suicidal despair. However, Borges speculates on the existence of the "Crimson Hexagon", containing a book that contains the log of all the other books; the librarian who reads it is akin to God.

## Themes

The story repeats the theme of Borges's 1939 essay "The Total Library" ("La biblioteca total"), which in turn acknowledges the earlier development of this theme by Kurd Lasswitz in his 1901 story "The Universal Library" ("Die Universalbibliotek"):

Certain examples that Aristotle attributes to Democritus and Leucippus clearly prefigure it, but its belated inventor is Gustav Theodor Fechner, and its first exponent, Kurd Lasswitz. [...] In his book The Race with the Tortoise (Berlin, 1919), Dr Theodor Wolff suggests that it is a derivation from, or a parody of, Ramón Llull's thinking machine [...T]he elements of his game are the universal orthographic symbols, not the words of a language [...] Lasswitz arrives at twenty-five symbols (twenty-two letters, the space, the period, the comma), whose recombinations and repetitions encompass everything possible to express in all languages. The totality of such variations would form a Total Library of astronomical size. Lasswitz urges mankind to construct that inhuman library, which chance would organize and which would eliminate intelligence. (Wolff's The Race with the Tortoise expounds the execution and the dimensions of that impossible enterprise.)

Many of Borges's signature themes are featured in the story, including infinity, reality, cabalistic reasoning, and labyrinths. The concept of the library is often compared to Borel's dactylographic monkey theorem. There is no reference to monkeys or typewriters in the The Library of Babel story; Borges had mentioned that analogy in his earlier 1939 essay The Total Library: "[a] half-dozen monkeys provided with typewriters would, in a few eternities, produce all the books in the British Museum". In this story, the closest equivalent is the line: "A blasphemous sect suggested [...] that all men should juggle letters and symbols until they constructed, by an improbable gift of chance, these canonical books".

Borges would examine a similar idea with his later story, "The Book of Sand"; in the later story, there is an infinite book (or book with an indefinite number of pages) rather than an infinite library. In addition, the Book of Sand is written in an unknown alphabet and its content is not obviously random.

The concept of the library is also overtly analogous to the view of the universe as a sphere having its center everywhere and its circumference nowhere. The mathematician and philosopher Blaise Pascal employed this metaphor, and in an earlier essay Borges noted that Pascal's manuscript called the sphere effroyable, or "frightful".

In any case, it is clear that a library containing all possible books, arranged at random, is equivalent (as a source of information) to a library containing zero books.

## Influence on later writers

• In "The Net of Babel", published in Interzone in 1995, David Langford imagines the Library becoming computerized for easy access. This aids the librarians in searching for specific text while also highlighting the futility of such searches as they can find anything, but nothing of meaning as such. The sequel continues many of Borges's themes, while also highlighting the difference between data and information, and satirizing the Internet.
• Daniel Dennett's 1995 book Darwin's Dangerous Idea includes an elaboration of the Library of Babel concept to illustrate the mathematics of genetic variation.
• Russell Standish's uses the concept of the Library of Babel to illustrate how an ultimate ensemble containing all possible descriptions would in sum contain zero information and would thus be the simplest possible explanation for the existence of the universe. This theory therefore implies the reality of all universes.
• Umberto Eco's postmodern novel The Name of the Rose features a labyrinthine library, presided over by a monk named Jorge of Burgos.

## Value as a thought experiment

The Library contains $25^\left\{1,312,000\right\} approx 1.956 times 10^\left\{1,834,097\right\}$ books. Just one "authentic" volume, together with all those variants containing only a handful of misprints, would occupy so much space that they would fill the known universe.

• Authentic volume: $1$
• Variants with one misprint: $24 times 1,312,000$ = 31,488,000
• Variants with exactly two misprints: $24^\left\{2\right\}tbinom\left\{1,312,000\right\}\left\{2\right\}$ = 495,746,694,144,000
• Variants with exactly three misprints: $24^\left\{3\right\}tbinom\left\{1,312,000\right\}\left\{3\right\}$ = 5,203,349,369,788,317,696,000
• Variants with exactly four misprints: $24^\left\{4\right\}tbinom\left\{1,312,000\right\}\left\{4\right\}$ = 40,960,672,578,684,980,713,193,472,000

Very large libraries typically contain several million volumes.

In his book Out of Control, Kevin Kelly devotes a chapter to the concept presented by Borges. Among other things, he proposes that the librarians may have been horribly mistaken about the nature of some of the books of nonsense. Some of these are assuredly copies of other books, some written in a substitution cipher, others phonetically, some in made-up languages, etc. Kelly points out the proposal that every book in the library is legible, if one decodes it right. This lends itself to the philosophical idea proposed by Immanuel Kant, that by defining rules for the universe, we create rules of the universe. Because the librarians assumed that the books of nonsense were exactly that, they may have tossed away several copies of Directions to the crimson hexagon from where you are now standing, simply because it was written in a cipher. Additionally, because there are by definition all books, there are certainly also books of lies and falsehoods. For each copy of the codex to the library, there will be many copies of false codices, claiming some false books to be true and some true books to be false. In short, any room in the library could be the crimson hexagon.

Kelly also takes a mental journey through the library, realizing that a book entitled "Out of Control, by Kevin Kelly" lies hidden somewhere in the library. This copy of this book is better than the one he is currently writing. His narrative takes a turn here, as he realizes that he would spend more time looking for such a book than he would actually writing such a book himself. He returns to the philosophical examination of the library by noting that hidden in the gibberish of the library, there are works beyond human capacity to write, simply by definition that it contains all possible books, of which these are a possibility. The library cannot be damaged by the destruction of any of its books because even though a single book is unique, there are also similar books differing by a single letter. The library is a temptation, because it offers these gems of enlightenment, and buries them in deception. He concludes by saying that one can consider any text, including his, as being pulled from the library by the act of the author defining the search letter by letter until they reach a text close enough to the one they intended to write. The text already existed theoretically, but had to be found by the act of the author's imagination.

### Quine's Reductio

In one short essay, W.V.O. Quine noted the interesting fact that the Library of Babel is finite (i.e., we will theoretically come to a point in history where everything has been written), and that the Library of Babel can be constructed in its entirety simply by writing a dot on one piece of paper and a dash on another. These two sheets of paper could then be alternated back and forth at random by the bearer, who would be able to read the resulting text in binary as he flipped them back and forth. This shows that the Library of Babel is actually quite manageable, and that everyone with paper and a pencil can create it in a couple of seconds.