The Library of Babel¶
The story “The Library of Babel” by the Argentine writer Jorge Luis Borges first appeared in 1941 in the volume “The Garden of Forking Paths”, which was later published as the first part of the fictions. The story begins with the description of a world that has existed since the beginning of time, where all people live as librarians in a honeycombed world.
“The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings. From any of the hexagons one can see, interminably, the upper and lower floors. The distribution of the galleries is invariable. Twenty shelves, five long shelves per side, cover all the sides except two; their height, which is the distance from floor to ceiling, scarcely exceeds that of a normal bookcase. One of the free sides leads to a narrow hallway which opens onto another gallery, identical to the first and to all the rest. To the left and right of the hallway there are two very small closets. In the first, one may sleep standing up; in the other, satisfy one’s fecal necessities. A!so through here passes a spiral stairway, which sinks abysmally and soars upwards to remote distances. In the hallway there is a mirror which faithfully duplicates all appearances. Men usually infer from this mirror that the Library is not infinite (if it really were, why this Illusory duplication?); I prefer to dream that its polished surfaces represent and promise the infinite … Light is provided by some spherical fruit which bear the name of lamps. There are two, transversally placed, in each hexagon. The light they emit is insufficient, incessant.”
How big is the library?¶
Question: How big is the library if we assume that all possible books with 410 pages, 40 lines per page and 80 characters per line, and 25 possible characters are in the library?
This honeycombed world of hexagonal galleries seems to be dedicated solely to the storage and exploration of books. “Five book racks are placed on each wall of each hexagon; each rack contains thirty-two books of the same format; each book consists of 410 pages, each page of 40 lines, each line of 80 letters of black color. Letters are also found on the spine of the book; however, these letters do not designate or indicate in advance what the pages will communicate.” All texts consist of only 22 different letters and three other special characters (period, comma and space). Each book occurs only once in the library. Luis Borges describes how the librarians explore this book world and try to find meaning in the books. Finding even single coherent sentences means great happiness. Since all books are the same size and Borges describes very precisely how they are constructed, we can very easily calculate how many books there are in this library. Each book consists of 40 x 80 x 410 = 1,312,000 characters. Since there are 25 different characters, each book can be understood as a number in a base 25 place value system. If there were only 10 characters, each book would be directly interpretable as a number in our known decimal system (place value system to the base 10). In the number system to the base there are, as is easy to see, 25 to the power of 1,320,000 combinations and with it, after conversion into the ten system 10 to the power of 1,845,28 books. The number of atoms in the universe is estimated at 10 to the power 80. Even if it succeeds to store each book in an atom, the library of Babel needs a universe which must be larger than ours by one million orders of magnitude. To realize even a fraction of the books of the library on earth, i.e. to print the books and to put them in library rooms, is completely hopeless.
The Library of Babel as a counter¶
The following processing program generates all books of a certain length.
Question: Why is such a program that generates the library of Babel nothing more than a counter where you can set the maximum number of digits, that is, the number of digits?
The Library of Babel as a web application¶
However, the library of Babel can be realized as a virtual library. Jonathan Basile has written a web application that allows you to browse the library, but also to start a full-text search or to display books at random. For browsing, each room in the library is assigned a unique number. To address all rooms, the numbers can have up to 3260 digits. Once you have selected the room, you then have to select the wall, then the shelf and finally the book and can then read page by page. There are also special functions like bookmarks or the display of anglicizations.
Jonathan Basile: Tar for Mortar: The Library of Babel and the Dream of Totality
Question: Think about! Why is it possible to address any room with a combination of up to 3260 numbers and/or lower case letters? Within the room any book then is addressed by the wall (1-4), the shelf (1-5) and then the volume (1-32). Each book consists of 1,312,000 characters. All combinations occur in the library. Shouldn’t the address (or the title of the book) be as long as the book itself, i.e. 1,312,000 characters? Why is it in this case shorter?
All Books are already written!¶
So all the books we could ever write are already written, we just have to find them. They already exist in all translations, with all criticisms possible. Also all books with all variants of only possible typos, at any place, in all conceivable combinations already exist. The possibility space of the book is by no means only fictitious any more, it is algorithmically realized, only too large for the blind search and too disorganized for the superficial search. We can assume that the program of the web application of the size also fits into a book of the library. (We may have to transcode it from a 128 character system to a 25 character system.) Then all algorithms, which produce the library in many variants are likewise already part of the library. The principle described here applies not only to texts, but naturally likewise to pictures. With 1,320,000 characters, we can of course also consider each book as an image with a resolution of 1280x1025 = 1,320,000 pixels, where each pixel could be interpreted either in 25 gray value gradations or as RGB with 8 color gradations each. Also all pictures are then already produced, and all sayable is said and all music is composed and so on. Also understood as image space we could implement a search with image snippets according to the text search. The result would be similar, one would see image snippets in an otherwise completely noisy image space.
Question: Why isn’t it really a restriction that we only look at books with 410 pages? What about books with 820 pages? Well, that’s only two books with 410 pages. And we already know the possible books with 410 pages. Then where is the information? Conversely, a book with 410 pages is only a combination of two books with 205 pages, and these are only combinations of two books with 102 and 103 pages. And so on, up to two books with the length of two letters. So we always already know the all books of double length. Where is then the newness from?