Borges' Library of Babel
During my childhood, as soon as I started delving into books, I told my parents I would like to have the Book of Why. They had never heard of such a thing, a book that has answers to all of your questions in one place, but all the adults around me had always echoed that if I wanted to know things, I should read books. This is also what the Pagemaster suggested to Richard, “Remember this: when in doubt, look to the books.” Google was not my friend at that time, and I did not know what an encyclopedia was. So how many books should I read? 21? 42? 882? I hypothesized that there should exist the book of the books, a master book that is a compendium of all the books that have ever been written, where you can find everything; an answer to every question. I named it: the Book of Why. We went to a bookshop, and I asked for this book. No one had a clue what I was talking about. The shopkeeper thought I wanted a dictionary. I left the bookshop very disappointed. Some days later, it turned out the shopkeeper was right. I realized I could extract all the information that I wanted from a dictionary by using a very simple recursive algorithm. I started with chemical compounds. Every time I looked up a compound or a mixture, I was redirected to the chemicals used to obtain it. Aware of these chemical building blocks, I consulted the dictionary again in order to find more information about them.
The library of Babel
Now, imagine instead of a dictionary you have a titanic library. This building is composed of an indefinite number of hexagonal rooms. All the hexagons are akin, and they are connected through vestibules where you can find a bed and all the necessities. In this space there is also a spiral staircase that gives access to an unknown number of floors, upwards and downwards. This design is repetitive on all the library floors. In each hexagon there are 20 bookshelves, and each bookshelf contains 32 books. Each book has 410 pages; each page contains 40 lines; each line contains 80 characters. The books contain every possible combination of 25 characters (the 22 letters of the Spanish alphabet, the period, the comma, the space). Consequently, this library is purported to contain everything! Many books are utterly indecipherable. They contain random content, gibberish. However, there will also be comprehensible and readable books. In some of them you are the protagonist. Actually, your entire life, even your future, is in some of those books. You can find all your jives, but also all other conversations and pillow talks that you have had and/or will have with your significant other. Your whole genome is also there. This very article is also there in innumerable books. If you are an avid mathematician, you may want to access the library to find the proof or disproof of Riemann's hypothesis. If you are a musician, you could find the ultimate song that no one has heard. If the information is too big to be stored in one book, then you could find it compressed with an obscure compression algorithm in another, and furthermore another book can give you instructions on how to decompress it.
This is the library of Babel. It was conceived by the Argentine author and librarian Jorge Luis Borges in his short story “The Library of Babel.” At first, you may be elated because you figured out that the library must contain all the answers to all your questions, but then you will become disconsolate. The books are randomly distributed, and you don’t know where each book is. You can easily realize that given the horrific plenitude of unreadable books, finding readable books is an absurd and literally backbreaking task. You should not even think about it.
Exactly what I was looking for
In Borges' story, the librarians believe that somewhere there must exist a catalog that is a perfect index of all the books and you can use to decipher the library and thus find all the meaningful books. If you found this catalog you would be invested with divine powers! You would be able to achieve complete knowledge. It is the sort of Book of Why that I was searching for. On the contrary, the library must also contain a huge number of false catalogs and books that contain false statements. Moreover, the title of the books are random and have nothing to do with the content inside of them.
Borges was born in one of the hexagons of the library and spent his life searching for the catalog of catalogs.
“Like all the men of the Library, in my younger days I traveled; I have journeyed in quest of a book, perhaps the catalog of catalogs. Now that my eyes can hardly make out what I myself have written, I am preparing to die, a few leagues from the hexagon where I was born. When I am dead, compassionate hands will throw me over the railing; my tomb will be the unfathomable air, my body will sink for ages, and will decay and dissolve in the wind engendered by my fall, which shall be infinite. I declare that the Library is endless.“
Knowledge is limited
Well, unfortunately (or fortunately), the Library of Babel can never exist in our observable universe.
According to Borges’ description, each book contains 410 × 40 × 80 = 1 312 000 characters. The library contains every possible combination of 25 characters, so there are 25^1312000 books. The number of baryons (subatomic particles made up of 3 quarks) in our observable universe is estimated to be “just” 10^80. We don’t have enough matter to build this library.
Jonathan Basile created a digital version of this library you can access through his website: http://libraryofbabel.info. However, that is just a computational trick that simulates the library. He developed an algorithm based on a linear congruential random number generator. I will let the nerdy readers figure out the trick as an exercise.
Let’s suppose in our universe there is enough matter to build this library, maybe it has been designed by a Demiurge; will it contain everything? Not at all. If the library contains everything, it should contain the catalog that lists all the books inside. If that is true, then there must exist another book that lists all the books including the catalog and so on, we can keep adding more and more books. Following this argumentation, you will quickly realize that in order to contain everything, the library must have an infinite number of books. Actually, you only need one book with infinite pages. However, the description that Borges gave of the library is consistent with a finite number of books. What happens if you have an infinite number of books with infinite pages? Think about it as an exercise.
You may be disheartened knowing that the Library of Babel does not exist. I’m sorry about that. However, you may draw a wise moral from the Borges' story. As Albert Einstein stated, "Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world". Reading books sparks your imagination. Have a look at our recommended Christmas books.