Borges Math, with bonus probability
Pretty sure I mentioned in passing that I'd been working on this, and I've finally gotten around to typing it up.
I apologize in advance for any overly flowery language, but that's kind of how I think when it comes to academic writing.
(Once I get my paper graded for my Sci-Fi class, I'll put a few of the less-flowery but still mildly humorous bits from it up.)
In Jorge Luis Borges' "The Library of Babel," there is a curious conception of the universe (which, in this story, is simply the Library) as an infinite construction. In his desire to impress upon us the vastness of the Library, however, Borges imposes limits upon his world by using exact figures.
We are led to believe that no two books in the Library are identical in content. (The titles are random combinations of letters that have nothing to do with anything and don't really factor into this.)
The Library is made up of a network of hexagons. Each hexagon is joined to exactly one other hexagon by a hallway leading out of an open side of the hexagon. In this hallway, there is a spiral stair that continues up and down to other tiers of hexagons. Somewhat like this:
Borges tells us that four of the remaining five walls of each hexagon are populated with shelves of books. This means that each tier has eight walls with shelves. Borges also tells us that each shelved side of a hexagon has five shelves.
8 Shelved Walls per Tier * 5 Shelves per Shelved Wall = 40 Shelves per Tier
Later, Borges tells us that there are thirty-five books per shelf.
40 Shelves per Tier * 35 Books per Shelf = 1400 Books per Tier
Keep that figure in mind for later.
Each book is comprised of 410 pages. Each page contains 40 lines of text.
410 Pages per Book * 40 Lines per Page = 16400 Lines per Book
Each line is comprised of approximately 80 characters (which is the number we will be using, for simplicity's sake).
16400 Lines per Book * 80 Characters per Line = 1312000 Characters per Book
We assume that every book in the Library is of this specific format.
The Alphabet of this world is comprised of 22 letters, along with a comma, a period, and a space. this leaves us with 25 possibilities for each character slot.
1312000 Characters per Book * 25 Character Possibilities = 32800000 Possible Configurations of Characters [Books]
This means that there are 32800000 possible books in the Library.
Given our earlier determination that there are 1400 books per tier (700 books per hexagon), we can calculate the exact amount of tiers of hexagons in the Library.
32800000 Books / 1400 Books per Tier = 23428 Tiers (with a remainder of 800 Books)
Thus, the Library is not, in fact, an infinite space, but a finite space composed of 23429 tiers of two hexagons, each containing 1400 books (save one which contains only one hexagon full of books and one hexagon containing only three shelves populated with books, one of which has room for five more volumes).
This is why I am seriously debating just taking more math classes.
BONUS:
I took the time to figure out the probability for the coin tosses in the first act of Rosencrantz & Guildenstern Are Dead. As a direct response to a remark made by my professor. ("Please don't tell me you took the time to figure out the probability." "...no, but now that you've said it I have to. Thanks.")
Each coin toss has a 50% chance of landing on heads. If you toss two coins, the chance that both will be heads drops to 25%. Three, 12.5%. Et cetera.
A total of 101 coins are tossed that come out heads. Essentially, that means we're looking at this:
100% / (2^101)
In other words:
100% / 235301200456458802993406410752 = (4.2498720706061358028603920326842 * 10^-30)%
Remove the decimal point from the answer, put 29 zeroes in front of it, and then put the decimal in front of the first zero.
Using numbers to make a point:
Stoppard: 1
Borges: 0
I apologize in advance for any overly flowery language, but that's kind of how I think when it comes to academic writing.
(Once I get my paper graded for my Sci-Fi class, I'll put a few of the less-flowery but still mildly humorous bits from it up.)
In Jorge Luis Borges' "The Library of Babel," there is a curious conception of the universe (which, in this story, is simply the Library) as an infinite construction. In his desire to impress upon us the vastness of the Library, however, Borges imposes limits upon his world by using exact figures.
We are led to believe that no two books in the Library are identical in content. (The titles are random combinations of letters that have nothing to do with anything and don't really factor into this.)
The Library is made up of a network of hexagons. Each hexagon is joined to exactly one other hexagon by a hallway leading out of an open side of the hexagon. In this hallway, there is a spiral stair that continues up and down to other tiers of hexagons. Somewhat like this:
Borges tells us that four of the remaining five walls of each hexagon are populated with shelves of books. This means that each tier has eight walls with shelves. Borges also tells us that each shelved side of a hexagon has five shelves.
8 Shelved Walls per Tier * 5 Shelves per Shelved Wall = 40 Shelves per Tier
Later, Borges tells us that there are thirty-five books per shelf.
40 Shelves per Tier * 35 Books per Shelf = 1400 Books per Tier
Keep that figure in mind for later.
Each book is comprised of 410 pages. Each page contains 40 lines of text.
410 Pages per Book * 40 Lines per Page = 16400 Lines per Book
Each line is comprised of approximately 80 characters (which is the number we will be using, for simplicity's sake).
16400 Lines per Book * 80 Characters per Line = 1312000 Characters per Book
We assume that every book in the Library is of this specific format.
The Alphabet of this world is comprised of 22 letters, along with a comma, a period, and a space. this leaves us with 25 possibilities for each character slot.
1312000 Characters per Book * 25 Character Possibilities = 32800000 Possible Configurations of Characters [Books]
This means that there are 32800000 possible books in the Library.
Given our earlier determination that there are 1400 books per tier (700 books per hexagon), we can calculate the exact amount of tiers of hexagons in the Library.
32800000 Books / 1400 Books per Tier = 23428 Tiers (with a remainder of 800 Books)
Thus, the Library is not, in fact, an infinite space, but a finite space composed of 23429 tiers of two hexagons, each containing 1400 books (save one which contains only one hexagon full of books and one hexagon containing only three shelves populated with books, one of which has room for five more volumes).
This is why I am seriously debating just taking more math classes.
BONUS:
I took the time to figure out the probability for the coin tosses in the first act of Rosencrantz & Guildenstern Are Dead. As a direct response to a remark made by my professor. ("Please don't tell me you took the time to figure out the probability." "...no, but now that you've said it I have to. Thanks.")
Each coin toss has a 50% chance of landing on heads. If you toss two coins, the chance that both will be heads drops to 25%. Three, 12.5%. Et cetera.
A total of 101 coins are tossed that come out heads. Essentially, that means we're looking at this:
100% / (2^101)
In other words:
100% / 235301200456458802993406410752 = (4.2498720706061358028603920326842 * 10^-30)%
Remove the decimal point from the answer, put 29 zeroes in front of it, and then put the decimal in front of the first zero.
Using numbers to make a point:
Stoppard: 1
Borges: 0