The Library of Babel
Encyclopedia
"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
translation
s 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
.
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 language
s. 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 behaviour, 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. Another is the belief 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.
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"):
Many of Borges's signature themes are featured in the story, including infinity
, reality
, cabalistic reasoning
, and labyrinth
s. 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.
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
.
books. (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 Library of Congress
, 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.
The number of different ways in which the books could be arranged is
.
, others phonetically, some in made-up languages, etc. Every book in the library is intelligible, 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 catalog 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. 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. One can consider 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.
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.
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 at random by the bearer, who would be able to read the resulting text in Morse code
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.
Related Links and Commentary
Other such simulations also exist
Short story
A short story is a work of fiction that is usually written in prose, often in narrative format. This format tends to be more pointed than longer works of fiction, such as novellas and novels. Short story definitions based on length differ somewhat, even among professional writers, in part because...
by Argentine
Argentina
Argentina , officially the Argentine Republic , is the second largest country in South America by land area, after Brazil. It is constituted as a federation of 23 provinces and an autonomous city, Buenos Aires...
author and librarian
Librarian
A librarian is an information professional trained in library and information science, which is the organization and management of information services or materials for those with information needs...
Jorge Luis Borges
Jorge Luis Borges
Jorge Francisco Isidoro Luis Borges Acevedo , known as Jorge Luis Borges , was an Argentine writer, essayist, poet and translator born in Buenos Aires. In 1914 his family moved to Switzerland where he attended school, receiving his baccalauréat from the Collège de Genève in 1918. The family...
(1899–1986), conceiving of a universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
in the form of a vast library containing all possible 410-page books of a certain format.
The story originally appeared in Spanish
Spanish language
Spanish , also known as Castilian , is a Romance language in the Ibero-Romance group that evolved from several languages and dialects in central-northern Iberia around the 9th century and gradually spread with the expansion of the Kingdom of Castile into central and southern Iberia during the...
in Borges's 1941
1941 in literature
The year 1941 in literature involved some significant events and new books.-Events:*Frank Herbert marries Flora Parkinson.*F. Scott Fitzgerald's unfinished work, The Last Tycoon, is edited and published by Edmund Wilson.-New books:...
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
Ficciones
Ficciones is the most popular anthology of short stories by Argentine writer and poet Jorge Luis Borges, often considered the best introduction to his work. Ficciones should not be confused with Labyrinths, although they have much in common. Labyrinths is a separate translation of Borges' material,...
(1944
1944 in literature
The year 1944 in literature involved some significant new books.-New books:*Samuel Hopkins Adams – Canal Town*Jorge Amado – Terras do Sem Fim *Saul Bellow – Dangling Man*Jorge Luis Borges – Fictions...
). Two English-language
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
translation
Translation
Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. Whereas interpreting undoubtedly antedates writing, translation began only after the appearance of written literature; there exist partial translations of the Sumerian Epic of...
s appeared approximately simultaneously in 1962
1962 in literature
The year 1962 in literature involved some significant events and new books.-Events:*January 7 - In an article in the New York Times Book Review, Gore Vidal calls Evelyn Waugh "our time's first satirist."...
, one by James E. Irby in a diverse collection of Borges's works entitled Labyrinths
Labyrinths
Labyrinths is an English-language collection of short stories and essays by Jorge Luis Borges.It includes "Tlön, Uqbar, Orbis Tertius", "The Garden of Forking Paths", and "The Library of Babel", three of Borges' most famous stories. Many of the stories are from the collections Ficciones and El...
and the other by Anthony Kerrigan as part of a collaborative translation of the entirety of Ficciones
Ficciones
Ficciones is the most popular anthology of short stories by Argentine writer and poet Jorge Luis Borges, often considered the best introduction to his work. Ficciones should not be confused with Labyrinths, although they have much in common. Labyrinths is a separate translation of Borges' material,...
.
Plot summary
Borges's narrator describes how his universe consists of an enormous 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 punctuationPunctuation
Punctuation marks are symbols that indicate the structure and organization of written language, as well as intonation and pauses to be observed when reading aloud.In written English, punctuation is vital to disambiguate the meaning of sentences...
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 language
Language
Language may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...
s. 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 behaviour, 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. Another is the belief 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
The story repeats the theme of Borges's 19391939 in literature
The year 1939 in literature involved some significant events and new books.-Events:*December 25 - A Christmas Carol is read before a radio audience for the first time....
essay "The Total Library" ("La biblioteca total"), which in turn acknowledges the earlier development of this theme by Kurd Lasswitz in his 1901
1901 in literature
The year 1901 in literature involved some significant new books.-Events:* First Nobel Prize for Literature awarded, to French poet Sully Prudhomme; many are outraged when Leo Tolstoy does not win...
story "The Universal Library" ("Die Universalbibliotek"):
- Certain examples that AristotleAristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
attributes to DemocritusDemocritusDemocritus was an Ancient Greek philosopher born in Abdera, Thrace, Greece. He was an influential pre-Socratic philosopher and pupil of Leucippus, who formulated an atomic theory for the cosmos....
and LeucippusLeucippusLeucippus or Leukippos was one of the earliest Greeks to develop the theory of atomism — the idea that everything is composed entirely of various imperishable, indivisible elements called atoms — which was elaborated in greater detail by his pupil and successor, Democritus...
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 LlullRamon LlullRamon Llull was a Majorcan writer and philosopher, logician and tertiary Franciscan. He wrote the first major work of Catalan literature. Recently-surfaced manuscripts show him to have anticipated by several centuries prominent work on elections theory...
'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
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
, reality
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
, cabalistic reasoning
Kabbalah
Kabbalah/Kabala is a discipline and school of thought concerned with the esoteric aspect of Rabbinic Judaism. It was systematized in 11th-13th century Hachmei Provence and Spain, and again after the Expulsion from Spain, in 16th century Ottoman Palestine...
, and labyrinth
Labyrinth
In Greek mythology, the Labyrinth was an elaborate structure designed and built by the legendary artificer Daedalus for King Minos of Crete at Knossos...
s. The concept of the library is often compared to Borel's dactylographic monkey theorem
Infinite monkey theorem
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 a given text, such as the complete works of William Shakespeare....
. 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
The Book of Sand
"The Book of Sand" is a 1975 short story by Jorge Luis Borges. It has parallels to "The Zahir", continuing the theme of self-reference and attempting to abandon the terribly infinite....
"; 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
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
having its center everywhere and its circumference
Circumference
The circumference is the distance around a closed curve. Circumference is a special perimeter.-Circumference of a circle:The circumference of a circle is the length around it....
nowhere. The mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and philosopher Blaise Pascal
Blaise Pascal
Blaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...
employed this metaphor
Metaphor
A metaphor is a literary figure of speech that uses an image, story or tangible thing to represent a less tangible thing or some intangible quality or idea; e.g., "Her eyes were glistening jewels." Metaphor may also be used for any rhetorical figures of speech that achieve their effects via...
, 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.
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
Robert Burton (scholar)
Robert Burton was an English scholar at Oxford University, best known for the classic The Anatomy of Melancholy. He was also the incumbent of St Thomas the Martyr, Oxford, and of Segrave in Leicestershire.-Life:...
's 1621 The Anatomy of Melancholy
The Anatomy of Melancholy
The Anatomy of Melancholy The Anatomy of Melancholy The Anatomy of Melancholy (Full title: The Anatomy of Melancholy, What it is: With all the Kinds, Causes, Symptomes, Prognostickes, and Several Cures of it. In Three Maine Partitions with their several Sections, Members, and Subsections...
.
Influence on later writers
- In "The Net of Babel", published in InterzoneInterzone (magazine)Interzone is an award-winning British fantasy and science fiction magazine. Published since 1982, Interzone is the eighth longest-running science fiction magazine in history and the longest-running British SF magazine...
in 1995, David LangfordDavid LangfordDavid Rowland Langford is a British author, editor and critic, largely active within the science fiction field. He publishes the science fiction fanzine and newsletter Ansible.-Personal background:...
imagines the Library becoming computerComputerA computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
ized 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 dataDataThe term data refers to qualitative or quantitative attributes of a variable or set of variables. Data are typically the results of measurements and can be the basis of graphs, images, or observations of a set of variables. Data are often viewed as the lowest level of abstraction from which...
and informationInformationInformation in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
, and satirizingSatireSatire is primarily a literary genre or form, although in practice it can also be found in the graphic and performing arts. In satire, vices, follies, abuses, and shortcomings are held up to ridicule, ideally with the intent of shaming individuals, and society itself, into improvement...
the InternetInternetThe Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...
. - Daniel DennettDaniel DennettDaniel Clement Dennett is an American philosopher, writer and cognitive scientist whose research centers on the philosophy of mind, philosophy of science and philosophy of biology, particularly as those fields relate to evolutionary biology and cognitive science. He is currently the Co-director of...
's 1995 book Darwin's Dangerous IdeaDarwin's Dangerous IdeaDarwin's Dangerous Idea: Evolution and the Meanings of Life is a book by Daniel Dennett which argues that Darwinian processes are the central organizing force that gives rise to complexity...
includes an elaboration of the Library of Babel concept to illustrate the mathematics of genetic variation. It is called the Library of Mendel. - Russell StandishRussell K. StandishRussell K. Standish is a computational scientist based in Sydney, Australia. He was the founding director of UNSW's from 1997-2005. In 2005 he established a computational science consultancy called . Since 2002, he has held an adjunct associate professorship with UNSW's . He grew up in Western...
's Theory of Nothing uses the concept of the Library of Babel to illustrate how an ultimate ensembleUltimate ensembleIn physics and cosmology, the mathematical universe hypothesis , also known as the Ultimate Ensemble, is a speculative "theory of everything" proposed by the theoretical physicist, Max Tegmark.-Description:...
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 EcoUmberto EcoUmberto Eco Knight Grand Cross is an Italian semiotician, essayist, philosopher, literary critic, and novelist, best known for his novel The Name of the Rose , an intellectual mystery combining semiotics in fiction, biblical analysis, medieval studies and literary theory...
's postmodern novel The Name of the RoseThe Name of the RoseThe Name of the Rose is the first novel by Italian author Umberto Eco. It is a historical murder mystery set in an Italian monastery in the year 1327, an intellectual mystery combining semiotics in fiction, biblical analysis, medieval studies and literary theory...
features a labyrinthine library, presided over by a blind monk named Jorge of Burgos. - Terry PratchettTerry PratchettSir Terence David John "Terry" Pratchett, OBE is an English novelist, known for his frequently comical work in the fantasy genre. He is best known for his popular and long-running Discworld series of comic fantasy novels...
uses the concept of the infinite library in his DiscworldDiscworldDiscworld is a comic fantasy book series by English author Sir Terry Pratchett, set on the Discworld, a flat world balanced on the backs of four elephants which, in turn, stand on the back of a giant turtle, Great A'Tuin. The books frequently parody, or at least take inspiration from, J. R. R....
novels. The knowledgeable librarian is a human wizard transformed into an orangutan. - William Goldbloom Bloch wrote the non-fiction work The Unimaginable Mathematics of Borges' Library of Babel exploring the short story from a mathematical perspective. He analyzes the hypothetical library presented by Borges using the ideas of topology, information theory, and geometry.
Value as a mathematical thought experiment
The Library contains at least books. (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 Library of CongressLibrary of Congress
The Library of Congress is the research library of the United States Congress, de facto national library of the United States, and the oldest federal cultural institution in the United States. Located in three buildings in Washington, D.C., it is the largest library in the world by shelf space and...
, 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.
- 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 is
.Philosophical implications
There are numerous philosophical implications within the idea of the infinite library. One of these is 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 cipherSubstitution cipher
In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters , pairs of letters, triplets of letters, mixtures of the above, and so forth...
, others phonetically, some in made-up languages, etc. Every book in the library is intelligible, if one decodes it right. This lends itself to the philosophical idea proposed by Immanuel Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....
, 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 catalog 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. 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. One can consider 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.
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.
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 at random by the bearer, who would be able to read the resulting text in Morse code
Morse code
Morse code is a method of transmitting textual information as a series of on-off tones, lights, or clicks that can be directly understood by a skilled listener or observer without special equipment...
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.
External links
- St. Jerome and the Library of Babel
- The James Irby translation of the "Library of Babel".
- dicelog.com digital access to the Library of Babel – a Library of Babel simulation
- Reduced Library of Babel – a Library of Babel simulation reduced to English and French
- How Big is the Library of Babel?
Related Links and Commentary
Other such simulations also exist