Jose Luis Borge’s Library of Babel

Source: The Conversation, Feb 2016

In “The Library of Babel,” the fascinating short story by Jorge Luis Borges, we learn about a certain library in which each book has 410 pages, and each page has 40 lines of 80 characters. The alphabet in use has 22 letters and three punctuation marks, making a total of 25 orthographic characters. We are told that every possible book is somewhere in this imagined library. So, how many books are there? First note that there are 410 x 40 x 80 = 1,312,000 characters in each book and since we have 25 choices for each character, there are 25¹³¹²⁰⁰⁰ possible books. As a power of 10, that’s roughly 10¹⁸³⁴⁰⁹⁷.

While we can’t possibly enumerate a catalog of all the books, we can imagine any book we like. There is a completely blank book. There is a book with a single comma in the middle of page 204 and nothing else. There are actually 1,312,000 books with a single comma and nothing else (just in each of the possible locations). There is a book with only the letter y in every spot. This article you’re reading right now appears exactly as it is written (by spelling out the numbers and ignoring extraneous punctuation) in an enormous number of books in the library (10 to a very large power, certainly more than 1.7 million). It appears in every language on the planet (suitably translated into the alphabet).