Los libros y la noche

“The universe, (which others call the Library), is made up of an indefinite, and perhaps infinite, number of hexagonal corridors, with shafts of ventilation in the center enclosed by very low rails. From any corridor, one can see the floors above and below, interminably…

Like all men in the Library, I’ve traveled in my youth; I’ve made pilgrimages in search of a book, perhaps from catalogue to catalogue; now that my eyes can hardly decipher what I write, I prepare myself to die only a few leagues from the hexagon where I was born.”

In honor of the 25th anniversary of the death of Jorge Luis Borges, the Casa de América will be screening “Los libros y la noche,” a documentary/fictional movie based on the works of the Argentinian writer.

I watched this little clip of the film, a reenactment of one of his most famous stories, “The Library of Babel”, in which Borges creates an elaborate and chilling metaphor for the universe. I had only ever imagined in my head those hexagons, which contain 20 bookshelves, 5 on each side, each shelf containing 32 books exactly, each book enclosing 410 pages, each page with 40 lines, and each line containing 80 black letters… The film creates well that atmosphere of horror and wonder that I always feel reading his stories.

My relationship with Borges began last summer in Vermont on the island campus of Middlebury, where I was ushered into his world of labyrinths, infinite structures, vertigo, dreams within dreams… His stories are akin to those feverish dreams and hallucinations you have while tossing in bed, whose extremity and element of infinite-ness makes them so horrifying, whose sudden moment of heightened consciousness makes it seem as if you have accessed another dimension too fleeting to grasp.

Borges’ infinite Library not only contains all the possible (even uninteligible) combinations of all the “25 orthographic symbols” but also all the misprints possible varying by one or two letters. Some fun facts from Wikipedia about the Library as a mathematical thought experiment:

The Library contains at least 25^{1,312,000} \approx 1.956 \times 10^{1,834,097} books.(That is, 25 orthographic symbols and 1,312,000 letters in each book…then the use of logarithms which beats me.)  

(The average large library on Earth at the present time typically contains only several million volumes, i.e. on the order of about  7\times 10^{6} books. The world’s largest library, the Library of Congress, has  2.18\times 10^{7} books.)

Just one “authentic” volume, together with all those variants containing only a handful of misprints, would occupy so much space that they would fill the known universe.

  • Authentic volume: 1
  • Variants with one misprint: 24 \times 1,312,000 = 31,488,000
  • Variants with exactly two misprints: 24^{2}\tbinom{1,312,000}{2} = 495,746,694,144,000
  • Variants with exactly three misprints: 24^{3}\tbinom{1,312,000}{3} = 5,203,349,369,788,317,696,000
  • Variants with exactly four misprints: 24^{4}\tbinom{1,312,000}{4} = 40,960,672,578,684,980,713,193,472,000

The number of different ways in which the books could be arranged is 10^{10^{33,013,740}}.

What an awful beast of a library…shudder. Okay, that’s enough nerdity and numbers for the day. Go read Borges! He’s good for the soul and for some boggling of the mind.

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