Order and Disorder
The last, albeit long, line of The Library of Babel struck me as particularly interesting.
"If an eternal voyager were to traverse it in any direction, he would find, after many centuries, that the same volumes are repeated in the same disorder (which, repeated, would constitute an order: Order itself). My solitude rejoices in this elegant hope."
The Library of Babel, Ficciones Page 87-88
However, the eternal voyager takes advantage of a usable infinities to explore a portion of this larger infinity. As finite creatures (unless some of you are immortal vampires, but we reserve judgements here at Cornell), we can only dream of this elegant hope. Yet, I can't help but think (both because we're studying entropy and because I am slightly obsessed with The Crying of Lot 49) that it's slightly unreasonable to find order in disorder.
The universe prefers macrostates of higher multiplicity, and our world trends towards that. Not that macrostates of small multiplicity are impossible, but rather, are highly improbable. What qualities, in the context of the library, gives us macrostates of higher multiplicity if every book is unique? Is there no semblance of order to begin with, or does "the same volumes are repeated in the same disorder" imply that there is an order to the Library in the same way that the oscillations of a sine wave is infinite?
I think that the narrator's theory is that the books, which are seemingly random within the section of the library he exists in, are repeated in the same order throughout sections of equal size. His theory does not necessarily promise any truths, but only that some kind of order could be found if they discovered this pattern. I'm not quite sure what you mean by 'what qualities give us macrostates of higher multiplicity if every book is unique?' it seems that every book can take on any of these numerous values through the many permutations of letters, which gives rise to a nearly continuous spectrum of possibilities for any given book. Also, the library seems to follow many different rules than our own universe so it is possible they simply are not the same in this aspect.
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