The Library of Babel

"The Library of Babel" (Spanish: La biblioteca de 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 and character set.

The story was originally published in Spanish in Borges' 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 titled Labyrinths and the other by Anthony Kerrigan as part of a collaborative translation of the entirety of Ficciones.

Plot summary

Borges' narrator describes how his universe consists of an enormous expanse of adjacent 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 25 basic characters (22 letters, the period, the comma, and the space). Though the vast 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.

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. This leads some librarians to superstitions and cult-like behaviours, such as the "Purifiers", who arbitrarily destroy books they deem nonsense as they scour through the library seeking the "Crimson Hexagon" and its illustrated, magical books. Others believe that since all books exist in the library, somewhere one of the books must be a perfect index of the library's contents; some even believe that a messianic figure known as the "Man of the Book" has read it, and they travel through the library seeking him.

Themes

Borges in 1976

The story repeats the theme of Borges' 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 Universalbibliothek"):

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.)^[1]

Many of Borges' signature motifs 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 Library of Babel", although Borges had mentioned that analogy in "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 in his 1975 story, "The Book of Sand" in which there is an infinite book (or book with an indefinite number of pages) rather than an infinite library. Moreover, the story's Book of Sand is said to be written in an unknown alphabet and its content is not obviously random. In The Library of Babel, Borges interpolates Italian mathematician Bonaventura Cavalieri's suggestion that any solid body could be conceptualized as the superimposition of an infinite number of planes.

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, a library containing all possible books, arranged at random, might as well be a library containing zero books, as any true information would be buried in, and rendered indistinguishable from, all possible forms of false information; the experience of opening to any page of any of the library's books has been simulated by websites which create screenfuls of random letters.^[2]

The quote at the beginning of the story, "By this art you may contemplate the variation of the twenty-three letters," is from Robert Burton's 1621 The Anatomy of Melancholy.

Value as a mathematical thought experiment

The Library contains at least books.^[3] (The average large library on Earth at the present time typically contains only several million volumes, i.e., on the order of about books. The world's largest library, the British Library,^[4] has 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. Each volume is 410 pages by 40 lines by 80 characters, or 410 x 40 x 80 = 1,312,000 characters. There are 25 different characters (including punctuation), so 24 ways of misprinting each of the 1,312,000 characters in a volume, ignoring the possibility of swapping two adjacent characters. Therefore, for each "authentic" volume:

• Authentic volume:
• Variants with one misprint: = 31,488,000
• Variants with exactly two misprints: = 495,746,694,144,000
• Variants with exactly three misprints: = 5,203,349,369,788,317,696,000
• Variants with exactly four misprints: = 40,960,672,578,684,980,713,193,472,000

The number of different ways in which the books could be arranged in the library is , the factorial of the number of books, and a number which is so unimaginably huge that when written down it would have roughly digits. In other words, even writing down the full length of this number, without using exponentiation, would take more digits than there are atoms in the observable universe.

(For comparison, there are only thought to be roughly atoms in our entire observable universe.)

Philosophical implications

There are numerous philosophical implications within the idea of the infinite library. Every book in the library is "intelligible" if one decodes it correctly, simply because it can be decoded from any other book in the library using a third book as a one-time pad. This lends itself to the philosophical idea proposed by Immanuel Kant, that our mind helps to structure our experience of reality; thus the rules of reality (as we know it) are intrinsic to the mind. So if we identify these rules, we can better decode 'reality'. One might speculate that these rules are contained in the crimson hexagon room which is the key to decoding the others. The library becomes a temptation, even an obsession, because it contains these gems of enlightenment while also burying them in deception. On a psychological level, the infinite storehouse of information is a hindrance and a distraction, because it lures one away from writing one's own book (i.e., living one's own life). Anything one might write would of course already exist. One can see any text 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.^[5] Another implication is an argument against certain proofs of the existence of God, as it is carried out by David Hume using the thought experiment of a similar library of books generated not by human mind, but by nature.^[6]

Quine's reduction

In a short essay, W. V. O. Quine noted the interesting fact that the Library of Babel is finite (that is, 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 at random to produce every possible text, in Morse code or equivalently binary. Writes Quine, "The ultimate absurdity is now staring us in the face: a universal library of two volumes, one containing a single dot and the other a dash. Persistent repetition and alternation of the two is sufficient, we well know, for spelling out any and every truth. The miracle of the finite but universal library is a mere inflation of the miracle of binary notation: everything worth saying, and everything else as well, can be said with two characters."^[7]

Comparison with biology

The full possible set of protein sequences (Protein sequence space) has been compared to the Library of Babel.^[8][9] In the Library of Babel, finding any book that made sense was impossible due to the sheer number and lack of order. The same would be true of protein sequences if it were not for natural selection, which has selected out only protein sequences that make sense. Additionally, each protein sequence is surrounded by a set of neighbours (point mutants) that are likely to have at least some function. Daniel Dennett's 1995 book Darwin's Dangerous Idea includes an elaboration of the Library of Babel concept to imagine the set of all possible genetic sequences, which he calls the Library of Mendel, in order to illustrate the mathematics of genetic variation. Dennett uses this concept again later in the book to imagine all possible algorithms that can be included in his Toshiba computer, which he calls the Library of Toshiba. He describes the Library of Mendel and the Library of Toshiba as subsets within the Library of Babel.

Influence on later writers

• Umberto Eco's postmodern novel The Name of the Rose (1980) features a labyrinthine library, presided over by a blind monk named Jorge of Burgos.
• 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.
• Russell Standish's Theory of Nothing^[10] 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.
• Michael Ende reused the idea of a universe of hexagonal rooms in the Temple of a Thousand Doors from The Neverending Story , which contained all the possible characteristics of doors in the fantastic realm. A later chapter features the infinite monkey theorem.
• Terry Pratchett uses the concept of the infinite library in his Discworld novels. The knowledgeable librarian is a human wizard transformed into an orangutan.
• The Unimaginable Mathematics of Borges' Library of Babel (2008) by William Goldbloom Bloch explores the short story from a mathematical perspective. Bloch analyzes the hypothetical library presented by Borges using the ideas of topology, information theory, and geometry.^[11][12]
• In Greg Bear's novel City at the End of Time (2008), the sum-runners carried by the protagonists are intended by their creator to be combined to form a 'Babel', an infinite library containing every possible permutation of every possible character in every possible language. Bear has stated that this was inspired by Borges, who is also namechecked in the novel. Borges is described as an unknown Argentinian who commissioned an encyclopedia of impossible things, a reference to either "Tlön, Uqbar, Orbis Tertius" or the Book of Imaginary Beings.
• Fone, a short comic novel drawn by Milo Manara, features a human astronaut and his alien partner stranded on a planet named Borges Profeta. The planet is overflowed by books containing all the possible permutations of letters.
• Steven L. Peck wrote a novella entitled A Short Stay in Hell (2012) in which the protagonist must find the book containing his life story in an afterlife replica of Borges' Library of Babel.^[13]

See also

• Encyclopedia Galactica
• Hilbert's paradox of the Grand Hotel
• Universal library
• World Brain
• Akashic Records
• Tupper's self-referential formula
• Infinite monkey theorem

References