The Gaming Den

You wake up on the marble floor of a vast lobby, lit by hundreds of chandeliers overhead. As you stand up and get your bearings, you see that this place is empty except for rows and rows of shelves, extending as far as the eye can see. Books of every shape, size, and color sit stacked tightly on the shelves, in no discernable order, with ladders included on every row for your convenience. Down by your feet you see a single, very thin softcover book, with the title "Welcome". You open it up to discover that it has only one page, and written on this page, in flowing script is as follows:

"Welcome to the Library of Conundrums! This is an infinite, ageless space, where both space and time are boundless. You will be here until you can figure a way out. This place contains more books than anyone could read in a lifetime - luckily, you shall never grow old or die here. Every possible combination of letters, characters, and spaces can be found in one of the books somewhere in this library. Good luck!"


I forget where I saw this idea - possibly here on the Den, actually, but I was wondering: since every possible combination of letters and so forth is somewhere within this library, which of the following can be found here if you simply search long enough?

1) A description of the library and how to use the randomly assorted books to escape.
2) A description of why it is impossible to use the randomly assorted books to escape.
3) Both.
4) Neither.

Also, neat place to include in a D&D game maybe, yes/no?

Screw escaping the library. Somewhere is the formula for godhood.

Sounds like L-Space.

It's 1 or 2, can't tell, as well as an infinite number of books with flawed methodologies for getting out and an infinite number of flawed proofs for how to get out.

Since every book in here is random and error-prone, reading the books in hopes of discovering anything useful is actually a waste of time.

And yes, the formula for godhood, if it exists, is in there; regardless, there's also an infinite number of flawed formulae for godhood.

IGTN wrote:It's 1 or 2, can't tell, as well as an infinite number of books with flawed methodologies for getting out and an infinite number of flawed proofs for how to get out.

Since every book in here is random and error-prone, reading the books in hopes of discovering anything useful is actually a waste of time.

And yes, the formula for godhood, if it exists, is in there; regardless, there's also an infinite number of flawed formulae for godhood.

Correct, but you have infinite time. You can test indefinitely.

But reading the books is a waste of time regardless. Even though you can succeed at any task possible with the tools at your disposal given truly infinite time and completely random trial and error - you can achieve any of those tasks much more quickly if you apply directed, systematic methods to the problem.

As to whether there is a method for escape or ascendance anywhere in the library, there may or may not be. But also, the fact that it exists does not mean that doing all of the possible methods will get you out. Everything you do adds something to the set of things that you have done, but it also permanently removes things from the set of things you have not done. Once you eat the pomegranate seeds, there is no escape plan possible based on never having eaten anything in the library.

-Username17

I think that Borges dreamed up a universe similar to this, though he gave it people and a history.

Not good for DnD (due to planar travel, etc), but excellent for Call of Cthulhu.

Narcissus wrote:Not good for DnD (due to planar travel, etc), but excellent for Call of Cthulhu.

I was thinking of fleshing out and populating it a bit more, maybe introduce people who knew part of how to get useful information but not the whole thing. Planar travel would, of course, be blocked until the PCs figure out whatever puzzle I wanted to give them in there.

I would seriously advise reading Jorge Borges' "The Library" (pretty sure that's the title.

Also, planar travel takes a while to get, so this would be a good low-ish level setting.

As an aside, I always liked the idea that the library is only one part of an extra-planar museum.

Narcissus wrote:As an aside, I always liked the idea that the library is only one part of an extra-planar museum.

What else could one find in this museum? A menagerie of creatures born from every conceivable DNA sequence? Something else?

EDIT: Yeah, the Library of Babel, by that dude! That's where I've heard this from.

EDITEDIT: Actually, what prompted me to make this thread was this:

Wikipedia wrote:Borges speculates on the existence of the "Crimson Hexagon", containing a book that contains the log of all the other books; the librarian who reads it is akin to God.

I wasn't convinced that this book would actually exist, so I was curious to hear what you all thought.

Gelare wrote:I wasn't convinced that this book would actually exist, so I was curious to hear what you all thought.

It exists, as do an immense number of copies of it with varying degrees of inaccuracy (everything from misplaced punctuation to complete falsehood)

Gelare wrote:

Wikipedia wrote:Borges speculates on the existence of the "Crimson Hexagon", containing a book that contains the log of all the other books; the librarian who reads it is akin to God.

I wasn't convinced that this book would actually exist, so I was curious to hear what you all thought.

I wonder if it contains the log of itself. </Russell>

IGTN wrote:

Gelare wrote:I wasn't convinced that this book would actually exist, so I was curious to hear what you all thought.

It exists, as do an immense number of copies of it with varying degrees of inaccuracy (everything from misplaced punctuation to complete falsehood)

Perhaps I read "log of all the other books" as "guide to how to use the library", in which case such a book would only exist if there is a way to use the library.

Gelare wrote:

Narcissus wrote:As an aside, I always liked the idea that the library is only one part of an extra-planar museum.

What else could one find in this museum? A menagerie of creatures born from every conceivable DNA sequence? Something else?

Whatever you want. The real trick would be avoiding Traveller silliness

EDIT: Yeah, the Library of Babel, by that dude! That's where I've heard this from.

EDITEDIT: Actually, what prompted me to make this thread was this:

Wikipedia wrote:Borges speculates on the existence of the "Crimson Hexagon", containing a book that contains the log of all the other books; the librarian who reads it is akin to God.

I wasn't convinced that this book would actually exist, so I was curious to hear what you all thought.

Borges is an excellent writer, as well as the grandfather of magic realism.

Yes, the book would exist. What really interests me is the idea of whether the infinite qualities apply to the arrangements of the books on the shelves, as well as to the arranement of the hexes. Borges doesn't say so, because he was actually envisioning a near infinity rather than actual infinity, but...meh.

Narcissus wrote:

Gelare wrote:

Narcissus wrote:As an aside, I always liked the idea that the library is only one part of an extra-planar museum.

What else could one find in this museum? A menagerie of creatures born from every conceivable DNA sequence? Something else?

Whatever you want. The real trick would be avoiding Traveller silliness

Get a hold of Warehouse 23, by GURPS. There's your "what would be in it" manual.

I'd also recommend Guards! Guards! by Terry Pratchett. It has a good long section of L-space, which...

Well, okay, it's infinite, and connected to all libraries and large-sized collections of books, at all times these exist. If one knows how, one can navigate not only through the multiverse's libraries, but through time, too.

But it's a pretty freaky place. It has its own ecology and inhabitants, some of whom have been lost in it for generations. The shelves go off into infinity, and space has gotten polyfractal--what looks like a few feet of shelving from the outside can, in fact, take you a half hour to cross at a brisk walk.

Maxus wrote:I'd also recommend Guards! Guards! by Terry Pratchett. It has a good long section of L-space, which...

Well, okay, it's infinite, and connected to all libraries and large-sized collections of books, at all times these exist. If one knows how, one can navigate not only through the multiverse's libraries, but through time, too.

But it's a pretty freaky place. It has its own ecology and inhabitants, some of whom have been lost in it for generations. The shelves go off into infinity, and space has gotten polyfractal--what looks like a few feet of shelving from the outside can, in fact, take you a half hour to cross at a brisk walk.

Thanks! I was in a library recently trying to remember the title of that one..
Got a few on file but reading DOCs for hours is a pain. Better to have the paper.
I rented Lords and Ladies. So far it's OK but Robert E. Howard has captured my interest moreso at the moment...

Talisman wrote:

Narcissus wrote:

Gelare wrote: What else could one find in this museum? A menagerie of creatures born from every conceivable DNA sequence? Something else?

Whatever you want. The real trick would be avoiding Traveller silliness

Get a hold of Warehouse 23, by GURPS. There's your "what would be in it" manual.

What does it cover, specifically?

sigma999 wrote: I rented Lords and Ladies. So far it's OK but Robert E. Howard has captured my interest moreso at the moment...

Lords and Ladies is something you have to work up to.

[Discworld Derailment]
Small Gods
Going Postal
Monstrous Regiment
Guards! Guards!
The Wee Free Men (look in the kid's section of the Library)
The Amazing Maurice and His Educated Rodents (Ditto)
[/DD]

Those are all pretty good to get your foot in the door.

A collection of observations:



As already noted, reading books at random gives you no information whatsoever; you could also just enumerate every possible string without looking at the books at all. So the only ways the books could possibly help you are:

1) If they were sorted in some useful fashion that you could figure out. For example, if all of the books that can teach you accurate things about the library are grouped together, and you successfully guess this, then looking at them might be more efficient than other possible strategies. The fact that the first book you find contains the welcome message rather than something like "Xlajioweh ;ahfwu;h;vz an;fwuh;zvu ;h o;fhweu;gh; ." suggests that the library's arrangement is probably not random.

2) If the physical process of reading the books helps you in some fashion, independent of any information actually contained in the books. For example, if one of the books turns out to be a portal like the books from Myst.



But suppose you're going to read the books for some reason. If we are pretending to cling to any vestige of reality, there will be a certain maximum size of book and minimum size of print that you are physically capable of reading.

If there are no duplicate books, then the set of books that might conceivably be usable by you is finite, and they do not contain every possible string, though they will contain every string with a length less than some constant.

Additionally, any given string (of arbitrary length) can be assembled by reading a series of those books in some particular order. So any given text that you're looking for still exists, even if it's beyond the "maximum" length, it's just in multiple volumes. One set of which will even be conveniently labeled for you, though they'll be mixed in with a bunch of other books that have the same labels but different contents.

Also, if we assume that your cognitive abilities also remain finite, then you will be incapable of remembering a string greater than a certain length, so in the process of "getting every last iota of usefulness out of the entire library," the only step that actually might take infinite time is sorting the finite number of useful books out of the infinite number of useless ones.



Regarding the original question, it's ambiguous. By the problem statement, every string exists in the library. However, the meaning that you associate with a string is arbitrary. If there exists a way to escape the library, you could define a language in which that process could not be accurately described, and you could define another language in which that process is uniquely represented by the string "xyzzy."

Perhaps a better question would be whether there exists a book which will cause you to understand how to escape the library (or why escape is impossible) if you read it. This will of course depend both on the person involved and the physical laws governing the library. Even if there is no way to escape the library, there doesn't necessarily exist a correct proof of that fact; even if a proof or a method of escape exists, it might be too complicated or nuanced for you to grasp, regardless of what you read.

Oh, another point:

Gelare wrote:EDITEDIT: Actually, what prompted me to make this thread was this:

Wikipedia wrote:Borges speculates on the existence of the "Crimson Hexagon", containing a book that contains the log of all the other books; the librarian who reads it is akin to God.

I wasn't convinced that this book would actually exist, so I was curious to hear what you all thought.

Based on the problem statement, and contrary to IGTN's remark, this actually (provably) does not exist in the library.

See, there's a countably infinite number of strings, but each individual string is of finite length (just like the set of all natural numbers is infinite, but any particular natural number is finite). So the library contains an infinite number of books, but each book is of finite length, so no book exists that individually references every other book (the book would have to be infinitely long to do so).

Even if you allowed books to be infinitely long, there still doesn't exist a list of them all, because then the set of books would be uncountably infinite. It's like going from the set of natural numbers to the set of all real numbers. You can't list all of the real numbers, even if the list is infinitely long (that is, there is no surjection from the naturals to the reals).

The Wikipedia article on the Library of Babel seems to suggest that it only contains books up to some fixed (constant) maximum length, which renders the total number of books finite. However, if it really does contain every book whose length is less than or equal to some constant, and the alphabet in question contains more than 1 character, then while an index of the books could exist, it wouldn't be one of the books in the library, because it would be too long.

Geez, people, Borge's work has been online for years:

Linky

Manxome wrote:Based on the problem statement, and contrary to IGTN's remark, this actually (provably) does not exist in the library.

See, there's a countably infinite number of strings, but each individual string is of finite length (just like the set of all natural numbers is infinite, but any particular natural number is finite). So the library contains an infinite number of books, but each book is of finite length, so no book exists that individually references every other book (the book would have to be infinitely long to do so).

Even if you allowed books to be infinitely long, there still doesn't exist a list of them all, because then the set of books would be uncountably infinite. It's like going from the set of natural numbers to the set of all real numbers. You can't list all of the real numbers, even if the list is infinitely long (that is, there is no surjection from the naturals to the reals).

That...is a good point. /sigh. Set theory.

Manxome wrote:See, there's a countably infinite number of strings, but each individual string is of finite length (just like the set of all natural numbers is infinite, but any particular natural number is finite). So the library contains an infinite number of books, but each book is of finite length, so no book exists that individually references every other book (the book would have to be infinitely long to do so).

Even if you allowed books to be infinitely long, there still doesn't exist a list of them all, because then the set of books would be uncountably infinite. It's like going from the set of natural numbers to the set of all real numbers. You can't list all of the real numbers, even if the list is infinitely long (that is, there is no surjection from the naturals to the reals).

Because there is no limit to the length of a "string" or a "book", they can be viewed as infinite sequences consisting of their total contents followed by an infinite number of null characters. Then the first case is really the second case, and there is an unenumerable quantity of books in the library (provable by diagonalization).

CatharzGodfoot wrote:Because there is no limit to the length of a "string" or a "book", they can be viewed as infinite sequences consisting of their total contents followed by an infinite number of null characters. Then the first case is really the second case, and there is an unenumerable quantity of books in the library (provable by diagonalization).

There's no limit to the magnitude of the natural numbers, either; in fact, there's a pretty trivial bijection between the set of natural numbers and the set of all strings made from an alphabet with only one symbol. (Not that it's that hard with multiple symbols: a, b, aa, ab, ba, bb, aaa, ...)

The diagonalization argument requires that the "diagonal" string be allowed to have an infinite number of non-null characters. If every individual string has finite length (before your decision to append infinite nulls), then the books are still countable, because your "diagonal" book isn't a member of the defined set, and so the fact that it's not on the list is no difficulty.

There's no reason you couldn't define the problem to include books of infinite length, but there clearly exist infinite but countable sets of strings, so there's no reason that you must define the problem that way, either.

Does that all make sense?