The Library of Babel is a short story by Borges about a structure that held every possible 410-page book composed of 25 characters. "For every rational line or forthright statement there [were] leagues of senseless cacophony, verbal nonsense, and incoherency..." The Library was an endless number of hexangonal galleries lined with bookshelves. The only occupants were the librarians, a race of humans with nothing to do but endlessly wander the galleries. After much examination of its contents, they came to understand the nature of the Library and realized the implications it held:
"The Library is 'total'—perfect, complete, and whole—and that its bookshelves contain all possible combinations of the twenty-two orthographic symbols (a number which, though unimaginably vast, is not infinite)—that is, all that is able to be expressed, in every language. The detailed history of the future, the autobiographies of the archangels, the faithful catalog of the Library, thousands and thousands of false catalogs, the proof of the falsity of those false catalogs, a proof of the falsity of the true catalog... the true story of your death, the translation of every book into every language, the interpolations of every book into all books..."
At first, the librarians were overjoyed. "There was no personal problem, no world problem, whose eloquent solution did not exist—somewhere in some hexagon." Even books previously thought unintelligible could be deciphered, if one were just able to locate the key that inevitably had to exist, somewhere...
Various sects arose among the occupants of the library in wake of the revelation. There were the hopefuls who wished to find their Vindication, a prophetical work that held their futures. "Inquisitors" came and went, searching for the books that contained the origin of the Library and time itself. There was the legend of the "Book-man," a librarian that had examined "the cipher and perfect compendium of all other books." None ever found what they were looking for. Enthusiasm degenerated into chaos and despair as the Library refused to yield its treasures. Many were driven to insanity and suicide. Some librarians still search, but their numbers dwindle.
A few people have tried their hand at visualizations of the library. This one is probably my favorite. There's also a partial simulation of the Library. It doesn't actually store all information, (it's physically impossible, as discussed later) but it does suggest the experience of wandering through endless galleries and looking at volumes of nonsense. Just don't stay too long...
The concept of virtual infinity is a common theme in Borges's work. Other short stories of his such as The Aleph and The Book of Sand have similar premises.
Grains of Sand...
Borges's Library contains 1.9560399...×101834097 books. It turns out the total permutations of a book with 25 possible characters, ~80 characters per line, 40 lines per page, and 410 pages is a lot. The number of atoms in the observable universe is inexpressibly miniscule in comparison.
A drop of water in the ocean doesn't come remotely close to being able to compare the two. If each atom were to be replaced with the entirety of the universe, the total count of atoms still wouldn't be any closer. What if you did that a total-number-of-atoms-in-the-universe number of times? What I mean by that is if each atom in the universe were replaced by an a copy of the universe, then each atom in each of those universes were replaced by a copy of the universe, that would be a depth of 2. We'd want a depth equal to the number of atoms in the observable universe. And if you were to do that, it wouldn't be enough. And it still wouldn't even be a drop in the ocean. The count of atoms in the universe is already a concept out of reach of human imagination.
Quotations are from Andrew Hurley's translation of Borges's Collected Fictions.