Who Would Survey the Library of Babel?

The Library of Babel was conceived by the inimitable Jorge Luis Borges and stands as one of the greatest metaphors for combinatorial potential ever penned.

A brief excerpt from the unnamed narrator, a native of the library:

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. From any of the hexagons one can see, interminably, the upper and lower floors. 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. One of the free sides leads to a narrow hallway which opens onto another gallery, identical to the first and to all the rest...

...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.

Based on this description, it is possible to calculate the size of the Library of Babel, presuming that it is a finite universe containing every possible book.

410 pages/book x 40 lines/page x 80 letters/line = 1312000 letters per book

There are 25 different letters.

This means that there are:

251312000 = 101834097 possible books.

4 walls/room x 5 shelves/wall x 35 books/shelf = 700 books/room

Implying that there are 101834094 hexagonal rooms in the Library. If we assume each room to measure some 80 cubic meters, then one expects the approximate linear extent of the universe to be:

(80 x 101834094)1/3 = 10611365 meters

Compare it to the size of the known, visible universe: a mere 1027 meters.

101834014 of our visible universes could fit into the Library of Babel.

This is the nature of our Reality. It is but a tiny mote couched inside a sea of potentiality of mathematical vastness.

blog comments powered by Disqus