Library the size of the Universe

Famous Argentinian writer Jorge Borges once published a very peculiar short story called The Library of Babel. It describes a Universe which consist of countless shelves filled with books. Well, that's not completely true: the number of shelves, as well as the number of books, is countable. It's just really, really, REALLY freaking big.

Fair warning: spoilers for "The Library of Babel" ahead. Although, English translation of the story is 56 years old, so I think it's a fair game for at least 6 years now.

_{Image source: Pixabay}

The Library consists of hexagonal rooms with four walls and two exits each. Exits connect each room to another indentical one. Each wall in each room contains five shelves, each shelf holds 35 books, echa book has 410 pages. There are 40 lines of 80 characters on each page.

There are people living in this strange world. After years of research they made two important observations:

• only 29 characters appear in books: letters from a to z, comma, period and space.¹
• no traveller has ever found two identical books.

Based on this knowledge they declared that the Library contains books with all possible permutation of base 25 characters on 410 pages. This means it contains all the books! Not just all the books ever written, not just all that will be written, but all books that can ever be possibly written!

If you were to pick up one random book from the shelf, you'd probably found the content to be unintelligible. Here's an example:

vtqcivdqbpkksuoybvbhcme oyaodo,npuaxqaesqrayifywqvfgmynurnaus, mkgenqlltbc (...and so on, for 410 pages)

That's because the number of "garbage" books is much greater than the number of meaningful ones. But since the library contains every possible book, it also contains, for example, Andy Weir's "The Martian" somewhere. There must exist a book with this post in it (stripped of special characters like brackets, that aren't present in the books). As well as one with previous versions of this post that were forever deleted from my laptop. And one with the comment you might leave after reading this article. Author describes it perfectly in this paragraph:

Everything: the minutely detailed history of the future, the archangels’ autobiographies, the faithful catalogues of the Library, thousands and thousands of false catalogues, the demonstration of the fallacy of those catalogues, the demonstration of the fallacy of the true catalogue, the Gnostic gospel of Basilides, the commentary on that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book in all languages, the interpolations of every book in all books, the treatise that Bede could have written (and did not) about the mythology of the Saxons, the lost works of Tacitus.

You might not believe it, but version of the Library, in full, is awailable online. Here, check it out: The Library Of Babel Website. It even provides search function. It's pretty fun to play with it.

I think this short story is a fascinating thought experiment. It shows that having all data without a simple way to distill through it is equal to having no data at all. Information which you don't have is, in a way, more important that information that you posess. The Labrary is in a state of total informational entropy, so it contains no information.

Bonus food for thought

_{Section for people who want to break their brains even more.}

Normal number is a mathematical concept of a real number that contains every possible finite number in it's digits. It's "easy", in a sense, to find a normal number - if you take one random real number from the number line - the probability of it being a normal number is 100%. It is widely believed (but not yet proven) that number 𝝿 is a normal number as well.

Now consider this:

• by definition, normal number contains every possible finite number
• every book in the Library can be "encoded" as a number (that's how your computer actually stores text, it's all digits to him)

You can find every book from the Library in any normal number. There exist infinitely many normal numbers.

_{1. In original short story there is just 22 allowed letters. I simplified it to include all letters of English alphabet.}

P.S:

this is a post in a series of posts that attempt to descibe computer science, cryptography and blockchain in simple terms. While this post is not directly related to any of those topics, it will set the stage for the upcoming fictional short story that describes the idea of hash function. Stay tuned.

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