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In The Library of Babel by Jorge Luis Borges, the speaker tells us about the library with the following specification,

The distribution of the galleries is invariable. Twenty shelves, five long shelves per side, cover all the sides except two; their height, which is the distance from floor to ceiling, scarcely exceeds that of a normal bookcase.

This specifies the organization of each hexagonal room.

I say that the Library is unending.

The above quote specifies that the library is infinite

There are five shelves for each of the hexagon's walls; each shelf contains thirty-five books of uniform format; each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters which are black in color.

This final quote describes what each book wall is like. We learn from all of this information that there are 25^1312000 individual books within the library. However, this is a finite number and the speaker has already told us that the library is infinite. This leads us to one of two conclusions, that there are multiple copies of each book or there are some empty rooms. However, the second is already disproven by the third quote, which is a universal description and the first can not be true because the speaker says,

One: the Library is so enormous that any reduction of human origin is infinitesimal. The other: every copy is unique, irreplaceable, but (since the Library is total) there are always several hundred thousand imperfect facsimiles: works which differ only in a letter or a comma.

The above quote makes it clear that every book is individual and irreplaceable. So, given that the library is not infinite in the normal sense, what does the author mean by the library being infinite?

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There are several options -- which makes sense, as this is a story which explores the idea of infinity.

The Library is spherical

Immediately following the line "I say that the Library is unending", the narrator says:

Let it suffice now for me to repeat the classic dictum: The Library is a sphere whose exact center is any one of its hexagons and whose circumference is inaccessible.

This is one way the Library can be infinite -- if the Library wraps around and re-connects to itself, it is infinite, in the sense that you can walk in a single direction forever. The number of hexagons and books are finite, but the Library itself has no beginning and no end.

The Library repeats infinitely

The story concludes with this thesis:

I say that it is not illogical to think that the world is infinite. Those who judge it to be limited postulate that in remote places the corridors and stairways and hexagons can conceivably come to an end -- which is absurd. Those who imagine it to be without limit forget that the possible number of books does have such a limit. I venture to suggest this solution to the ancient problem: The Library is unlimited and cyclical. If an eternal traveler were to cross it in any direction, after centuries he would see that the same volumes were repeated in the same disorder (which, thus repeated, would be an order: the Order). My solitude is gladdened by this elegant hope.

In other words, he posits that the Library is literally infinite; that the 25^1312000 individual books repeat over and over.

He calls this "elegant," as yet another hope for order in random chaos -- here is suggesting, not only that there are infinite copies of all books, but that the arrangement of those books is preserved. This is an order that cannot be perceived, tested, or comprehended by any mortal, but its (hypothetical) existence is a comfort to the narrator.

Another variation arises naturally -- that the Library does extend infinitely, but with different arrangements of the books. Eventually, of course, you would exhaust the possible arrangements of books -- but you could create new configurations of those arrangements, and their location respective to one another.

However you look at this, Borges is demonstrating the idea of magnitudes of infinity - e.g. the idea of an infinity of infinities.

The Library is metaphorically infinite

Part of the point here is that the narrator has no idea what the structure of the universe is. He has no way to discover it. He can guess and conjecture, but is overwhelmed by the ungraspable nature of the Library, and of infinity.

The thing is, infinity is not a concept the human mind can grasp easily. In many ways, it is easier for us to understand something finite but whose immensity presses upon us (i.e., a finite Borgesian Library), than the infinity of our own universe (where it is so easy to focus on our own planet, country, home).

Understanding true infinity is very difficult; creating an example of true infinity might have resulted in less powerful imagery. But Borges's Library is immense in a way we can grasp intuitively. It gives you a sense of scale -- the difficulty of finding a single comprehensible word in a book generated from random characters; the existence of books that are works of truth and art, as the product of randomly combining characters until one forms. This is not literally infinite, but it feels so near the real thing, as to be metaphorically infinite, to demonstrate the sense of infinity even if it isn't the real thing.

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It's periodic.

This is directly answered in the text, at the very end of the story:

I have just written the word "infinite". I have not included that adjective out of mere rhetorical habit; I hereby state that it is not illogical to think that the world is infinite. Those who believe it to have limits hypothesise that in some remote place or places the corridors and staircases and hexagons may, inconceivably, end - which is absurd. And yet those who picture the world as unlimited forget that the number of possible books is not. I will be bold enough to suggest this solution to the ancient problem: The Library is unlimited but periodic. If an eternal traveller 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. My solitude is cheered by that elegant hope.

  • Oh man, I have read the story over and over trying to answer this question myself, but I can't believe I missed this. – Benjamin Jan 27 '17 at 2:28
  • Maybe you didn't read quite far enough? :-) It's literally the final paragraph of the story. – Rand al'Thor Jan 27 '17 at 2:29
  • Well, once I started reading it, I vaguely remembered that from one of my first read-throughs, but it is quite possible I missed it in later ones. – Benjamin Jan 27 '17 at 2:33

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