The universe (which others call the Library) is composed of an indefinite, perhaps infinite number of hexagonal galleries. (1)
From the very first sentence of this story, it's clear that there's going to be an emphasis on the structural. How the universe is constructed and what it is composed of is going to be a really important theme.
The arrangement of the galleries is always the same: Twenty bookshelves, five to each side, line four of the hexagon's six sides; the height of the bookshelves, floor to ceiling, is hardly greater than the height of a normal librarian. (1)
The fact that every single room is exactly the same makes us think that everything is very, very orderly in this universe.
One of the hexagon's free sides opens onto a narrow sort of vestibule, which in turn opens onto another gallery, identical to the first – identical in fact to all. (1)
Are you getting the picture? Everything is THE SAME. It almost makes us want to scream.
Light is provided by certain spherical fruits that bear the name "bulbs." There are two of these bulbs in each hexagon, set crosswise. The light they give is insufficient, and unceasing. (1)
Since there's not much to do around here besides read, we imagine the insufficient light is a total bummer.
Idealists argue that the hexagonal rooms are the necessary shape of absolute space, or at least of our <em>perception</em> of space. They argue that a triangular or pentagonal chamber is inconceivable. (2)
Inconceivable! https://www.youtube.com/watch?v=D58LpHBnvsI&feature=youtube_gdata_player We do not think it means what they think it means. (We've always wanted to say that.) Idealism is a philosophical theory that says that what we experience is ultimately based on mental activity, and not on the external world. So these idealists are arguing that the librarians experience rooms with six sides because it's the only kind of room they can conceive of.
We think Borges is making a little philosophical joke here about idealism. The funny thing is, his whole story is one big abstraction – that is to say, it only exists thanks to our mental activity. And, well, to us it seems possible to conceive of a Library made up of triangles or pentagons.
Each wall of each hexagon is furnished with five bookshelves; each bookshelf holds thirty-two books identical in format; each book contains four hundred ten pages; each page, forty lines; each line, approximately eighty black letters. (3)
The regimented order of the Library even extends to the number of letters in each book. Are we surprised? No, no we're not.
There are also letters on the front cover of each book; those letters neither indicate nor prefigure what the pages inside will say. (3)
Okay, <em>this</em> comes as a bit of a surprise. What's the use of a cover if not to tell you the title of the book? This problem provokes a huge exercise in reason and logic on the part of the librarians.
First: <em>The Library has existed</em> ab aeternitate. That truth, whose immediate corollary is the future eternity of the world, no rational mind can doubt. (4)
Not only does the Library follow strict structural rules, but so does the way in which the librarian makes his argument. In giving us rules (axioms) and using those rules to deduce other truths (corollaries) about the Library, he's taking a very reasoned and logical approach.
Second: There are twenty-five orthographic symbols. That discovery enabled mankind, three hundred years ago, to formulate a general theory of the Library and thereby satisfactorily solve the riddle that no conjecture had been able to divine – the formless and chaotic nature of virtually all books. (5)
The inhabitants of the Library proceed from the strictly regimented order of the books to a general theory of the Library, using the strictly regimented method of logical deduction. Rules, rules, rules... they're everywhere in this story!
From those incontrovertible premises, the librarian deduced that the Library is "total" – perfect, complete, and whole – and that its bookshelves contain all possible combinations of the twenty-two orthographic symbols (a number which, though unimaginably vast, is not infinite) – that is, all that is able to be expressed, in every language. (7)
This conclusion turns out to be the most important rule in the entire Library. It's the key to understanding the way the entire universe works.
Infidels claim that the rule in the Library is not "sense," but "non-sense," and that "rationality" (even humble, pure coherence) is an almost miraculous exception. They speak, I know, of "the feverish Library"...Those words, which not only proclaim disorder but exemplify it as well, prove, as all can see, the infidels' deplorable taste and desperate ignorance. (13)
Here we see a conflict between the narrator's perspective and that of those he calls the "infidels." The narrator believes – he really <em>wants</em> to believe – in an elegantly ordered universe that follows all the rules he just explained to us. He criticizes the "infidels" for not having faith in order, and for thinking that the universe is chaotic.
If an eternal traveler should journey in any direction, he would find after untold centuries that the same volumes are repeated in the same disorder – which, repeated, becomes order: the Order. (15)
This is the narrator's personal theory and his closing argument as to why we should believe that the universe is ordered. The universe, he says, is <em>periodic</em> (it might be round, or it might just repeat itself in some way). The infinite repetition of what looks like disorder creates its own pattern, which he calls "the Order" with a super-important capital "O."