The Unimaginable Mathematics of Borges' Library of Babel
Jorge Luis Borges, a Spanish writer of the 20th century, wrote a short story, really a description, in 1941 of an imaginary library with books 410 pages long, each page filled with forty lines of 80 letters each. He goes on to describe in detail the structure of a library that has all the books of all the combinations of the 25 character lexicon in those books. Logically, by the completeness of combinations, there will be every possible readable book ever written or to be written hidden in amongst the many more books of gibberish. And so begins the mathematical adventure for William Goldbloom Bloch. The author asks and answers questions like how big is the library? Will it even fit in our universe? What is the overall shape of the library? How long would it take to traverse the library? Bloch attacks these and other problems using a variety of mathematical approaches, including combinatorics, information theory, geometry and graph theory, topology, and others. If you like math and thinking about things that are just shy of the infinite, then this will be a fun read.