What is the significance/symbolism of the hexagon in "The Library of Babel"?

Question

In *The Library of Babel* by Jorge Luis Borges, the speaker describes the Library, as the universe, as > The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings. This explains how the universe in which the story occurs is made up of hexagons. However, there is also a group of people who believe that the rooms may also be circular as we learn when the speaker says, > The idealists argue that the hexagonal rooms are a necessary from of absolute space or, at least, of our intuition of space. They reason that a triangular or pentagonal room is inconceivable. (The mystics claim that their ecstasy reveals to them a circular chamber containing a great circular book, whose spine is continuous and which follows the complete circle of the walls; but their testimony is suspect; their words, obscure. This cyclical book is God.) Given that the organization of the library could most likely work with pentagonal rooms, given the vagouness of the specifications. This suggests to me that there is a non-mechanical reason for the choice of the hexagon. So, what is the significance/symbolism of the hexagon?

Answer 1

First, a fact-check. Pentagons would not work, or at least not work in the way Borges describes. The internal angle of a regular pentagon is 108 deg., which doesn't divide evenly into 360, which means they won't align perfectly. A cluster of regular pentagons would have gaps between them, and since Borges is describing a universe, we can't allow for gaps. Gaps in the universe are, to use Borges's word, inconceivable. Hexagons don't have this problem--they fit perfectly.

As for significance, the only true answer is that there is no "right" answer. But here are two things to think about to get you started.

1. You might argue that squares or triangles would also fit perfectly, and they do. However, if you look at a hexagonal grid versus a triangular or rectangular / square grid, what differences do you notice? The main one I notice is that triangles and rectangles divide the grid into "strips." There are single lines that go all the way across the grid, so you could make divisions between one side of a dividing line and another. Hexagons fit together perfectly, but there are no straight lines that go across them. Maybe this suggests that Borges's universe, while marked off by rooms, is, as a whole, indivisible. There are no single axes (plural of axis) in a hexagonal grid, which means there is no absolute frame of reference. If you're with me so far, what does that mean to you?
2. If you're looking for a non-mechanical answer, the number 6 by itself may be significant. The Ancient Greek mathematicians were really into 6, because it is the first "perfect" number. That is, the lowest number that is the sum of its own factors not including itself. In other words, the factors of 6 are 1, 2, and 3; 1 x 2 x 3 = 6. But also, 1 +2 + 3 = 6. So if Borges is describing the universe in an extended metaphor that also includes more than a little religious vocabulary, ancient ideas of perfection are pretty relevant.

That's what occurs to me on the significance of hexagons, but I'm sure that's not all there is to say. Please hit me up with any more Borges questions--he's one of my all-time favorites!