Does the supposition in "The Library of Babel" that, if you were immortal and went in any direction long enough, you'd eventually encounter the same books in the same disorder, which would thereby become The Order, count?
I've been doing a little meditative combinatorics. I arbitrarily assigned the length of the printing on a book's spine (which the Librarian does not tell us) to be one 80-character line. With that assumption (and ignoring the Librarian's unsupported supposition that the titles are meaningless), we find that there are approximately
1.3383768226039 x 10 ^ 1834209 books in the Library. (I've used the freely available "hypercalc" program,
http://mrob.com/pub/perl/hypercalc.txt, in this meditation.)
But of course the supposition that you'd come, when you began seeing books you had already encountered, upon the same Library in the same order, is delusionally optimistic. There are, of course, the factorial of the number of books number of orders of each book in the library. That turns out to be roughly 10 ^ ( 2.4548624015714 x 10 ^ 1834215 ) libraries before one must, perforce, begin seeing the books in an order in which one has before seen them. It is
this collection, of course, that must contain the wonders the Librarian speaks of, such as the true catalogue and all the false catalogues, because a single book is clearly far too small to contain such a thing.
But of course that, in turn, assumes that all the copies of the library are complete. If we then postulate that any iteration of the library may or may not have a copy of a particular book then the number of (complete and partial) libraries our immortal traveler must traipse through before encountering repetition becomes the power set of the number of complete libraries, or 2 ^ ( 10 ^ ( 2.4548624015714 x 10 ^ 1834215 ) ) . This, rightly, seems like a big number.
But, in fact, to an arbitrarily good approximation,
all integers are bigger than that.
Indeed, if we adopt even a naive encoding for the books of the story, "01" for the first character through "25" for the last, and simply endeavor to transcribe the set-of-all-books-in-all-libraries-in-each-possible-order as an integer encoded this way...then there is probability zero that this number does not appear somewhere in the decimal representation of pi. So all our wandering is for naught: we could just sit crosslegged and contemplate, very closely, a ring.
Adam