The Library of Babel: a fictional library containing all possible books imagined by writer (and librarian) Jorge Luis Borges and written about by him in a story of the same name.
The Library in Borges's short story is ►eternal and ►unbounded, but not necessarily infinite. It consists of a labyrinth of hexagonal book galleries. Each gallery contains 640 books of 410 pages each, printed with words of an alphabet that consists of 25 orthographic symbols. The library contains all possible books that could be written in any combination of these symbols -- "that is," says the story's narrator,
"everything which can be expressed, in all languages. Everything is there: the minute history of the future, the autobiographies of the archangels, the faithful catalog of the library, thousands and thousands of false catalogs, a demonstration of the falsehood of these catalogs, a demonstration of the falsehood of the true catalog, the Gnostic gospel of Basilides, the commentary on this gospel, the commentary on the commentary on this gospel, the veridical account of your death, a translation of each book in all languages, the interpolations of every book in all books, the treatise that Beda could have written (but did not write), the mythology of the Saxons, the lost books of Tacitus."
Since comprehensive books can extend over several volumes, the number of pages for each volume is not a genuine limit for the length of the books. Nonetheless, the infinite amount of knowledge contained in this library is not of much use. Borges reports how the residents of the Library desperately try to discover the meanings in all those books. Some religious sects idolize the books, others call for burning them. Pilgrims explore the Library in their search for a book that may have the right answer to every question. Scientists discuss whether the Library is finite or infinite. Unfortunately, the likelihood of anyone's finding a book with even one meaningful sentence in it is rather small. For since each book contains a random order of symbols, most pages look just about like this:
How Large is the Library of Babel?
Each book contains 410 pages; each page, 40 lines; each line, 80 symbols. Thus, each book contains 1,312,000 symbols. From this, we can calculate the total number of books. That number has 1,834,098 digits. Thus, the Library is about 10611338 times* larger than the ►observable universe.
If you think that this number is exaggerated, you are probably right. In reality, the Library is much smaller than that. It conveniently fits into your pocket. This is because it actually requires only one book with one single page that contains only one symbol. If you wish to know which symbol that is you should read the article about ►Pi.
* 1,312,000 symbols from a 25-symbol alphabet yield 251312000 possible combinations. Your pocket calculator will probably refuse to yield a result during this calculation, but you can make it work by using the logarithm function. 1312000 ∙ log(25) yields 101834097.29 = 1.956 ∙ 101834097 for the number of books. Thus we need 3.056 ∙ 101834094 hexagonal book galleries. Since Borges's narrator tells us that the Library is unbounded, it must be curved on the inside; that is, it must be located on a hypersphere with a surface volume of 2π2r3. Its radius can be derived from the volume of a book gallery (c. 30 m3) as:
The radius of the ►Hubble volume, by contrast, is only about 4 ∙ 1026 m.
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