The Library of Babel | |
---|---|

by Jorge Luis Borges | |

Original title | La biblioteca de Babel |

Translator | numerous |

Country | Argentina |

Language | Spanish |

Genre(s) | Fantasy |

Published in | El Jardín de senderos que se bifurcan |

Publisher | Editorial Sur |

Publication date | 1941 |

Published in English | 1962 |

"**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.

- Plot
- Themes
- Philosophical implications
- Infinite extent
- Quine's reduction
- Comparison with biology
- Influence on later writers
- See also
- References

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*.

Borges' narrator describes how his universe consists of an enormous expanse of adjacent hexagonal rooms. In each room, there is an entrance on one wall, the bare necessities for human survival on another wall, and four walls of bookshelves. Though the order and content of the books are 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 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 superstitious and cult-like behaviors, 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.

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 [...] The 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'sThe Race with the Tortoiseexpounds 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 makes an oblique reference to reproducing Shakespeare, as the only decipherable sentence in the library "O time thy pyramids" is surely taken from Shakespeare's Sonnet 123 which opens with the lines "No Time, thou shalt not boast that I do change, Thy pyramids...".

Borges would examine a similar idea in his 1976 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 you may contemplate the variation of the twenty-four letters," is from Robert Burton's 1621 * The Anatomy of Melancholy *.

In mainstream theories of natural language syntax, every syntactically-valid utterance can be extended to produce a new, longer one, because of recursion.^{ [3] } However, the books in the Library of Babel are of bounded length ("each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters"), so the Library can only contain a finite number of distinct strings. Borges' narrator notes this fact, but believes that the Library is nevertheless infinite; he speculates that it repeats itself periodically, giving an eventual "order" to the "disorder" of the seemingly random arrangement of books. Mathematics professor William Goldbloom Bloch confirms the narrator's intuition, deducing in his popular mathematics book * The Unimaginable Mathematics of Borges' Library of Babel * that the library's structure necessarily has at least one room whose shelves are not full (because the number of books per room does not divide the total number of books evenly), and the rooms on each floor of the library must either be connected into a single Hamiltonian cycle, or possibly be disconnected into subsets that cannot reach each other.^{ [4] }

W. V. O. Quine notes that the Library of Babel is finite, and that any text that does not fit in a single book can be reconstructed by finding a second book with the continuation. The size of the alphabet can be reduced by using Morse code even though it makes the books more verbose; the size of the books can also be reduced by splitting each into multiple volumes and discarding the duplicates. 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 are 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."^{ [5] }

The full possible set of protein sequences (protein sequence space) has been compared to the Library of Babel.^{ [6] }^{ [7] } In the *Library of Babel*, finding any book that made sense was almost 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 picked out only protein sequences that make sense. Additionally, each protein sequence is surrounded by a set of neighbors (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.

- 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. The room is, however, octagonal in shape. - Russell Standish's
*Theory of Nothing*^{ [8] }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. *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.^{ [9] }^{ [10] }- 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*.^{[ citation needed ]} - The Library of Babel, a website created by Jonathan Basile, emulates an English-language version of Borges' library. An algorithm he created generates a "book" by iterating every permutation of 29 characters: the 26 English letters, space, comma, and period. Each book is marked by a coordinate, corresponding to its place on the hexagonal library (hexagon name, wall number, shelf number, and book name) so that every book can be found at the same place every time. The website is said to contain "all possible pages of 3200 characters, about 10
^{4677}books".^{ [11] } - In Steven L. Peck's novella
*A Short Stay In Hell*(2009), the protagonist must find the book of his life's story in a library containing every possible book. Borges' story is mentioned directly, although the library is structured very differently.

In logic, mathematics, computer science, and linguistics, a **formal language** consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.

**Jorge Francisco Isidoro Luis Borges Acevedo** was an Argentine short-story writer, essayist, poet and translator, as well as a key figure in Spanish-language and international literature. His best-known books, *Ficciones* (*Fictions*) and *El Aleph*, published in the 1940s, are collections of short stories exploring themes of dreams, labyrinths, chance, infinity, archives, mirrors, fictional writers and mythology. Borges's works have contributed to philosophical literature and the fantasy genre, and have had a major influence on the magic realist movement in 20th century Latin American literature.

The **infinite monkey theorem** states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible finite text an infinite number of times. However, the probability that monkeys filling the entire observable universe would type a single complete work, such as Shakespeare's *Hamlet*, is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is *extremely* low. The theorem can be generalized to state that any sequence of events which has a non-zero probability of happening will almost certainly eventually occur, given enough time.

"**Tlön, Uqbar, Orbis Tertius**" is a short story by the 20th-century Argentinian writer Jorge Luis Borges. The story was first published in the Argentinian journal *Sur*, May 1940. The "postscript" dated 1947 is intended to be anachronistic, set seven years in the future. The first English-language translation of the story was published in 1961.

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantities and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language.

"**Pierre Menard, Author of the Quixote**" is a short story by Argentine writer Jorge Luis Borges.

**Kurd Lasswitz** was a German author, scientist, and philosopher. He has been called "the father of German science fiction". He sometimes used the pseudonym *Velatus*.

* Labyrinths* is a collection of short stories and essays by Argentine writer and poet Jorge Luis Borges. It was translated into English, published soon after Borges won the International Publishers' Prize with Samuel Beckett.

"**The Garden of Forking Paths**" is a 1941 short story by Argentine writer and poet Jorge Luis Borges. It is the title story in the collection *El jardín de senderos que se bifurcan* (1941), which was republished in its entirety in *Ficciones* (*Fictions*) in 1944. It was the first of Borges's works to be translated into English by Anthony Boucher when it appeared in *Ellery Queen's Mystery Magazine* in August 1948.

**Algorithmic information theory (AIT)** is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably generated objects (as opposed to stochastically generated), such as strings or any other data structure. In other words, it is shown within algorithmic information theory that computational incompressibility "mimics" (except for a constant that only depends on the chosen universal programming language) the relations or inequalities found in information theory. According to Gregory Chaitin, it is "the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously."

In geometry, a **Cairo pentagonal tiling** is a tessellation of the Euclidean plane by congruent convex pentagons, formed by overlaying two tessellations of the plane by hexagons and named for its use as a paving design in Cairo. It is also called **MacMahon's net** after Percy Alexander MacMahon, who depicted it in his 1921 publication *New Mathematical Pastimes*. John Horton Conway called it a **4-fold pentille**.

A **universal library** is a library with universal collections. This may be expressed in terms of it containing all existing information, useful information, all books, all works or even all possible works. This ideal, although unrealizable, has influenced and continues to influence librarians and others and be a goal which is aspired to. Universal libraries are often assumed to have a complete set of useful features.

This article contains a discussion of **paradoxes of set theory**. As with most mathematical paradoxes, they generally reveal surprising and counter-intuitive mathematical results, rather than actual logical contradictions within modern axiomatic set theory.

**Temporal finitism** is the doctrine that time is finite in the past. The philosophy of Aristotle, expressed in such works as his *Physics*, held that although space was finite, with only void existing beyond the outermost sphere of the heavens, time was infinite. This caused problems for mediaeval Islamic, Jewish, and Christian philosophers who, primarily creationist, were unable to reconcile the Aristotelian conception of the eternal with the Genesis creation narrative.

**Infinity** is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .

"**The Congress**" is a 1971 short story by Argentine writer Jorge Luis Borges. The story is on an utopic universal congress and is seen by critics as a political essay.

**Jorge Luis Borges and mathematics** concerns several modern mathematical concepts found in certain essays and short stories of Argentinian author Jorge Luis Borges (1899-1986), including concepts such as set theory, recursion, chaos theory, and infinite sequences, although Borges' strongest links to mathematics are through Georg Cantor's theory of infinite sets, outlined in "The Doctrine of Cycles". Some of Borges' most popular works such as "The Library of Babel", "The Garden of Forking Paths", "The Aleph", an allusion to Cantor's use of the Hebrew letter aleph to denote cardinality of transfinite sets, and "The Approach to Al-Mu'tasim" illustrate his use of mathematics.

In evolutionary biology, **sequence space** is a way of representing all possible sequences. The sequence space has one dimension per amino acid or nucleotide in the sequence leading to highly dimensional spaces.

* The Unimaginable Mathematics of Borges' Library of Babel* is a popular mathematics book on Jorge Luis Borges and mathematics. It describes several mathematical concepts related to the short story "The Library of Babel", by Jorge Luis Borges. Written by mathematics professor William Goldbloom Bloch, and published in 2008 by the Oxford University Press, it received an honorable mention in the 2008 PROSE Awards.

**The Library of Babel** is a website created by Brooklyn author and coder Jonathan Basile, based on Jorge Luis Borges' short story "The Library of Babel" (1941). The site was launched in 2015.

- ↑ Borges, Jorge Luis.
*The Total Library: Non-Fiction 1922–1986.*Allen Lane The Penguin Press, London, 2000. Pages 214–216. Translated by Eliot Weinberger. - ↑ See https://libraryofbabel.info/
- ↑ Noam, Chomsky (1969) [1965].
*Aspects of the theory of syntax*(1st pbk. ed.). Cambridge: M.I.T. Press. ISBN 9780262030113. OCLC 12964950. - ↑ Hayes, Brian (January–February 2009), "Books-a-million (review of
*The Unimaginable Mathematics of Borges' Library of Babel*)",*American Scientist*,**97**(1): 78–79, doi:10.1511/2009.76.78, JSTOR 27859279 - ↑ W.V.O Quine. "Universal Library". Archived from the original on 2014-06-02. Retrieved May 10, 2018.
- ↑ Arnold, FH (2000). "The Library of Maynard-Smith: My Search for Meaning in the protein universe".
*Advances in Protein Chemistry*.**55**: ix–xi. doi:10.1016/s0065-3233(01)55000-7. PMID 11050930. - ↑ Ostermeier, M (March 2007). "Beyond cataloging the Library of Babel".
*Chemistry & Biology*.**14**(3): 237–8. doi: 10.1016/j.chembiol.2007.03.002 . PMID 17379136. - ↑ "Theory of Nothing". Hpcoders.com.au. May 29, 2011. Retrieved May 10, 2018.
- ↑ Bloch, William Goldbloom (2008).
*The Unimaginable Mathematics of Borges' Library of Babel*. Oxford University Press. - ↑ "William Goldbloom Bloch's home page". Faculty.wheatoncollege.edu. Retrieved May 10, 2018.
- ↑ Sturgeon, Johnathon (2015-04-23). "Brooklyn Author Recreates Borges' Library of Babel as Infinite Website".
*Flavorwire*. Retrieved 2020-11-22.

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