Never the Final Word (Vol. 2)

by FanOfMostEverything

chris the cynic's As Below, So Above (Rambling Writer's "Best Hell Ever")

Author's Note:

[Slice of Life]

This is a continuation of Rambling Writer's Best Hell Ever (2,191 words [Comedy])

BEST HELL EVER SPOILERS: Due to a clerical error, Twilight is sent to Hell before she dies. Specifically, the Library of Babel, which contains every book that can exist. Twilight is tasked with sorting it. Naturally, she does, to the demons' distress. They boot her out, to her distress.

*much later*

Twilight looked at the monoceros --it seemed nice to the point that it practically exuded visible kindness-- and tried to feel good about being in Heaven. She couldn't shake the despair that filled her.

"It's been a long time since we last had an alicorn die," the monoceros said. "Died in some war, did you?"

"No," Twilight said. "My friends --all mortal-- had died, I'd set my affairs in order, I had adequate replacements for all of my roles. I just felt like time."

"Well, we'll certainly be sure you're reunited with your friends," the monoceros said.

"That's good," Twilight said, and she meant it. Yet somehow she couldn't seem to feel it.

"Perhaps you could tell me why you're feeling so down," the monoceros said.

"I know it's silly, and I know things don't work that way," Twilight said, "but I was really hoping to be sent back to Hell."

The monoceros gave a confused, "Hmmm," and brought a clipboard into its field of view. A moment later its eyes opened wide and it said, "Oh! Twilight Sparkle. I've heard about you." It turned around and gestured for Twilight to follow. "I think I know just how to cheer you up."

"I doubt you can make me happy," Twilight said, but she followed, even though her head was low.

"I think I can, you see," the monoceros said, reaching the end of the Hall, "We have a better library here."

When the monoceros opened the door, Twilight's head shot up. She hadn't been this happy since Hell.

"It has, however, been some time since it was last organized."

Twilight made sounds of joy so pure it could only be expressed in Heaven, as no mortal utterances could contain such meaning.

Comments

[horizon]

The idea of a better library than the Library of Babel — which definitionally contains every book which does, or ever could, exist — is an interesting one.

If the idea of "book" requires a finite text (which I'd imagine is implied), then there's no way to add books to the Library of Babel to make it even better, because it already contains every possible book, by definition [1]. (And, as a note, is finite in size, if very very large; because there is a finite number of letters [2] that are put together in a finite combination to form a word, so there are a finite number of possible words; and there are a finite number of words in a book.)

One might argue that a library can be "better" if it is better organized — i.e., easier to find interesting content within the overwhelming piles of books consisting of "ewrmvq wrprn tmzl" nonsense — but given that that's Twilight's job, that's not the distinguishing factor here.

Therefore, having a "better" library than Hell's must require that they have removed books, and furthermore, that the books removed have actual negative utility.

It's sort of a counterintuitive idea, but makes sense on further reflection. The Hell library, for example, contains a large number of books which are nothing but graphic descriptions of Twilight Sparkle being tortured to death over and over again. Or reasons why it's a good idea to kill yourself, or to commit genocide, etc. There's whole wings of sub-libraries containing nothing but falsehoods ("The sky is green. George Washington invented the peanut. Computers don't use electricity." etc), and sub-libraries which mix truth and falsehood indistinguishably. A Library of Babel with ground rules about content is arguably better than a library which contains these things. Which rules about content is, of course, debatable; but this is Heaven here, so I'm pretty sure they could tailor it to her needs.

--
[1] On the other hand, if a "book" is defined as "any collection of words of any length", then the Library of Babel is incomplete!

This follows from the Cantor diagonalization argument, more or less. If you assume that there are a finite number of distinguishable letters [2], then each word contains at most a countably infinite number of letters (since you can do a one-to-one mapping between letter position within the word and the natural numbers), and the book contains at most a countably infinite number of words (since you can do a one-to-one mapping between word position within the book and the natural numbers). The product of countable infinities is itself countable.

So you can create a list of the Library of Babel's books — any countable infinity can be mapped to the natural numbers, and that means you can place them in order to list them out — and then artificially construct a book by doing the following: Choose a word for word #1 that is different from word #1 of book #1. Choose a word for word #2 that is different from word #2 of book #2, etc. (If the book you're comparing to ends before it reaches word n, then choose a word for your book which is not the null word.) When you're done, your book will be different by at least one word from every other book in the Library!

So Heaven's library could be better than the Library of Babel simply by including all of the Library of Babel's books, plus the one you just wrote — which the Library of Babel doesn't contain.

[2] Which is necessary unless you allow glyphs of infinite size — otherwise you can find the number of possible letters by multiplying the number of permutations of pixels at the largest letter's resolution x size. And if you have glyphs of infinite size, then the book is unreadable.

[kajisora]

8606449
Alternatively, it could contain every possible book, EXCEPT the ones that contain only random characters (at least, the ones that are not in some way interesting)

Also, the Library actually exists online for any sequence under 3200 characters.
Here's an entry of this exact story
(with some random words before and after. It also contains an exact match, but that seemed less interesting)

EDIT:
Since, as noted, we're dealing with heaven here, a perfect library could contain, not every possible book in existence, but every possible book that you, personally, would be interested in reading.

[CrystalWaters]

8606449
8828040
I can't help but think you're both missing the simpler option, perhaps intentionally because your train of thought is more interesting.

The idea of a better library than the Library of Babel — which definitionally contains every book which does, or ever could, exist — is an interesting one.

Perhaps the better library simply has the pleasant, faded scent of wood, superlatively comfortable carpet and shelves which are just the right height.

[horizon]

8902355
Good point!

[Eruantalon]

8902355 Simpler - but it's a much less interesting option! Wouldn't a truly Heavenly library both have comfortable carpet and pleasant scent, and have removed books of negative utility?

[WanderingPony]

It's worth noting there is an actual, delightful sequel to the original story as well.

https://www.fimfiction.net/story/435360/heaven-of-a-hell

[UrsaMajor]

8606449
The Library must be infinite, regardless of whether a book must be finite.
If we assume that a given book has a finite length that is defined as a non-negative integer number of words, words being collections of letters and symbols without intervening spaces, there are still an infinite number of possible book lengths — and word lengths, for that matter. Even a mini-Library of Babel (perhaps a Library of Ur?) that contained only all possible books with a given number of words assembled from the characters used in writing standard English would have to be infinitely large, because there's no upper bound on word length. And that's true even if you limit it to meaningful English (let alone German!) words, because there's no real limit on the number of prefixes that can be attached to a word, and each carries semantic weight.

[keybounce]

On the other hand, if a "book" is defined as "any collection of words of any length", then the Library of Babel is incomplete!

This follows from the Cantor diagonalization argument, more or less. If you assume that there are a finite number of distinguishable letters...

I have wondered if the diagonalization argument can survive quantum computers and qbits. Can you have a qbit that is the entangled representation of every possible letter? Then, a quantum computer with enough qbits can represent any possible book; and if you truly allow infinite length, then the universe (which is technically a finite state system) can never hold any representation of it.