Many authors have written on implications of Borges’ Library of Babel, a fictional library which contains every possible book on a given alphabet, within a fixed format (each book 410 pages, each page 40 lines, etc.). An example of an ‘implication’ of the library is that there are numerous books that one can have conversations with. This book begins with a preface, explaining how it works, with an escape character, say ‘#’, to mark the end of each turn of dialog. Thus you can open it till you reach ‘#’, then close it and reply, then open it again. Perhaps,
Andrew– “hello book!”
Book– “hello Andrew!, thank you for reading me. #”
A– “how did you know my name?”
B– “I was written with you in mind!#”
B–“Isn’t it a bit early for those types of questions? We have 409 more pages to go. #”
A–“I don’t like your attitude, where can I find another talking book? One that is more accommodating?”
B–“surprisingly, there is one right behind you, middle of the 4th shelf up! #”
A–“Are you lying?”
B–“Yes, of course!#”
There are even books that look like this, where you can read the pages out of order, in an attempt to screw up the book, but which account for that, and still read in a linear dialog.
Of course this assumes that your conversation is essentially deterministic, and there should be ways to make this dialog fail. For example, you might ask a lot of questions about neighboring books, and even if your book maintains an English dialog, it will be forced to lie if all the possible ways to tell the truth are located in other parts of the library (where they very well might be lying). Also, it may be that whenever you encounter such a book you don’t have the ‘correct’ conversation, so that in an infinity of time one finds no meaningful conversation.
Other interesting implications: There are dense and eloquent mathematical proofs in the library which require tens of thousands of volumes to prove. Similarly there are books of cultural or psychological theory that build on tens of thousands of other volumes, these of case studies and theory development. Indeed, entire sets of volumes exist to pinpoint the meaning of individual words. It is easy to conceive of some great intelligence that can comprehend some of these books, books which must be all but gibberish to any human. What truths might they hold? Is there any limit to the level of sophistication of theories in that library? One might think so, as the library holds a finite amount of information. But as some theories take many volumes to present, we might as well consider our alphabet to consist of volumes in the library, and strings to be sequences of volumes, so by this language, any finite amount of information can be learned in an afternoon of particularly fast speed reading (say, a few trillion volumes a second, for a layman’s guide to everything). (What is called Quine’s reductio goes in the oppose direction, reminding us that the library might consist of just 2 books: all possible ‘books’ of length one character, on a binary alphabet: 0 and 1. Then any literature can be found as a specific tour through this library, stopping at each of the two books many many times).
Exercise: write a few interesting ‘implications’ about the library. Write about possible limitations, if you see any.