# The Library of Discord

## by Chinchillax

### Mathematical Notes

The idea from this fanfiction is strongly based on the ideas presented in Steven L. Peck’s novella “A Short Stay in Hell.” If this book intrigued you in any way. Please check out his book. According to Peck in the appendix of his book, the library presented there had books that were 410 pages long, with 40 lines of 80 characters on each page. There were a possible 1,312,000 characters in each book with 95 characters on a possible keyboard. Resulting in a library with 95^1,312,000 number of books. Or a library 7.16^1,297,369 light years wide and deep.
The Library of Discord is based off of the question, “How many books would exist in the Library of Babel if someone were to simply spell check all of the books before adding them to the library?” The eventuality of such a task would be that all combinations of all the words in the provided dictionary would have to exist somewhere in the library. Given a dictionary of 200,003 words (estimates of how large the English language is is actually around 250,000 words. The 3 is there because a prime number was easier to deal with when creating the library). Dividing the number of characters in a 410 page book (1,312,000) by five (5.1 being the average number of letters per word in the English language) produces 262,400 number of words in each book. This results in a library with 200,003^262,400 number of books.
To put this number in perspective, according to Wolfram Alpha the number of books in the Library of Babel in “A Short Stay in Hell” is 2.45*10^1203781 times more than the number of books in the Library of Discord. (Spell checking is a wonderful thing).

Books were calculated as being 3 cm thick each, 40 cm to shelve vertically. Each shelf can fit 2000 books on each 60 meter long shelf. Each side has 8 shelves each containing 2000 books each. Or 32000 books in a cubic area of 4*3*60 (4 meters- height of the hallway, 3 meters width of hallway, 60 length of bookcase) or 720 cubic meters.

The number of books in the Library of Discord is 200003^262400 number of books. That number divided by 32000 would be the number of 720 cubic meter spaces that the library would need to have.
1.33 x10^1390989 number of 720 cubic meter blocks.
At this scale, only the number of digits matter.
10^463663 meter wide and deep library
Divide by the number of meters in a light year (9.46 x10^15 meters)
Resulting in a library 10^463647 light years wide and deep.
The universe is estimated to be 91 billion light years wide. So divide 10^463647 by 91 billion.
So in total size, the vertical, hexagonal shaft of the library of Discord is approximately 10^463636 number of universes tall.