The Library of Babel

The Library of Babel is a short story by Jorge Luis Borges that postulates a universe made up of a library with books exactly 410 pages in length, each page forty lines long with eighty characters per line.  No two book s are alike, though they may be separated by one character difference.  The library is formed from hexagonal cells connected via spiral stairs and a short hallway.  The narrator of the story is a librarian, one of many who live within the library.  The narrator explains some of the history of the library as well as some philosophy.

The Near Infinite Library

I was first introduced to this story as a freshman in High School.  I was in a class for advanced students, just six of us, three freshmen and three seniors, and a wonderful teacher.  We read the story of the library after watching The Name of the Rose, which remains a favorite movie of mine to this day.

What we discussed about the story was how the library was almost, but not quite, infinite.  Because the makeup of the books are a set limit, there is a total number of ways the characters can be arranged (the story indicates a total of “twenty-odd” number of unique characters, which are the standard Latin alphabet plus a few punctuation marks).  Therefore the library should have a “center”, which some in the story believe is the “Crimson Hexagon” that contains books with all the knowledge of the library.  The narrator insists that the library is actually cyclical, and if you went far enough in one direction you’d return to where you began.

This is remarkably similar to astrophysics and Einstein’s curved space and time concepts.  We discussed this in my class, and how perhaps the library is nothing more than an analogy for the real world, with packets of information instead of books.

After reading this remarkable story, we moved on the Carl Sagan’s Contact (long before the horrible movie) and we discussed the concept of messages within π.  The fact that π is an infinite, non-repeating number means that, in theory, somewhere within π is the answer to every question in the universe.  Of course, every wrong answer is contained within those numbers as well!  And that is the problem with the library; there is a book that will tell you everything you want to know, and billions more that will be a lie.

It’s a fascinating, mind-bending concept to think about the near-infinite.  It opens up the wide vistas of imagination that Lovecraft preyed upon oh so well.

For  your reading pleasure, here’s a PDF copy of the story, first published in 1941: The Library of Babel by Jorge Luis Borges

Edit: For those interested how many books the library would likely hold:

For perspective, from WikipediaJust one “authentic” volume, together with all those variants containing only a handful of misprints, would occupy so much space that they would fill the known universe.

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5 thoughts on “The Library of Babel

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  1. Hey there, interesting review of this story. Having read the story itself, I was browsing for reviews when I stumbled across yours. Here’s some food for thought.

    Sorry in advance because I’ll sound overly technical after this, but don’t you think your statement here:

    “he fact that π is an infinite, non-repeating number means that, in theory, somewhere within π is the answer to every question in the universe….”

    is somewhat vague? The thing is, since all that’s special about pi that has to do with the infinite is the fact that it’s an irrational number, having non-repeating digits, so that any sequence of numbers of any length will almost certainly (using the term “almost certainly” in the strict mathematical sense) be bound to appear somewhere in the decimal representation of it, any other randomly generated string of numbers representing some real number will do too. Just saying that it doesn’t have to be pi, because the way you phrased it seemed to imply that you attached some special significance to pi.

    Secondly, what exactly do you mean by “the answer to every question in the universe?” Doesn’t that in a sense imply a need to interpret strings of numbers? It still makes sense though if you represent pi in base 26 and used alphabets in place of numerals, so that actual sentences and answers would appear.

    Just saying. Please don’t think of it as an insult or whatever; I just like to engage in conversations with intellectual people 🙂

    1. The concept of “every answer to every question” existing within Pi or any other mathematical infinite constant was a topic I first read about in Carl Sagan’s novel, Contact. Please ignore the awful movie version. The actual novel is much better and has quite a bit of mathematics and science built in. In it, Sagan posits that if this isn’t the “real” universe, or wasn’t the first universe to exist, an advanced race might be able to place a message in a universal constant, like Pi. However, the contrast to that is Borges’ Library of Babel, which points out that while a message COULD be buried in any random limited infinite series (like Pi, which, while infinite, also has limits, i.e., 3 < Pi < 4), the signal to noise ratio makes it impossible to decode.

      Unless, of course, you had a key. In Borges work, that's represented by the red cell at the "center" of the labyrinth. In Contact, it's represented by finding the first repeating sequence within a constant, which could only be found once a society had developed computing powerful enough to find it.

      The whole thing is just a theoretical mind game, but an interesting idea.

  2. Hate to be a math nerd, but just because a number is infinite and non-repeating doesn’t mean that it contains every possible string of numbers. Here’s an example of a boring infinite non-repeating number:

    0.3030030003000030000030000003….

    where the # of zeroes between the 3s goes up by one each time. This number is clearly irrational (it never repeats), but if you interpret pairs of numbers as letters, its never going to be interesting.

    Here’s a pretty easy number to construct that *does* contain every possible substring of digits:

    0.0123456789010203040506070809101112131415161718192021222324…

    i.e. first you write down all the 1 digit numbers, then all the 2 digit numbers, then all the 3 digit numbers, ad infinitum. There are obviously lots of numbers that do contain all possible substrings.

    I have no idea whether pi is one of them. As of 2009, at least, I was in good company 🙂

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