OT: Another math problem

The Library of Babel is a library which contains an infinite number of hexagonal rooms, each with four exits and four walls containing bookshelves full of 410 page books, each page with 40 lines of 80 characters. These books contain random permutations of the 25 basic characters.

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Suppose the number of books in all rooms of the library is the same and is N. One starts in a random room in the library, and selects X books at random from a uniform distribution on N, i.e. X

Reply to
bitrex
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Who cares? Some math problems are entertaining, and some are entertaining o nly for mathematicians.

I had a mathematical friend once, and learned that when he got onto "intere sting" math problems, all one could do was nod from time to time, to give t he impression of paying attention, and wait until he said "and it generalis es" after which intelligible communication would resume.

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Bill Sloman, Sydney
Reply to
Bill Sloman

only for mathematicians.

resting" math problems, all one could do was nod from time to time, to give the impression of paying attention, and wait until he said "and it general ises" after which intelligible communication would resume.

Sounds like something from some recreational math puzzle book for people to waste their lives on.

Reply to
bloggs.fredbloggs.fred

Why do some people watch two teams of guys throw a ball back and forth? Why do some people spend thousands of dollars to construct an HO scale version of the Baltimore and Ohio railroad circa 1936 in their basement? Why do anything?

Reply to
bitrex

Because you get paid for doing some things?

If I'm going to think hard, I prefer to be paid for it.

Reply to
John Larkin

** Nevertheless, the Wiki on the " Infinite Monkey Theorem" is entertaining:

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.... Phil

Reply to
Phil Allison

On Sat, 5 Sep 2015 08:00:13 -0700 (PDT), Phil Allison Gave us:

Use a computer to do it at GHz or even THz rates and you will still very likely get not even a single sentence properly generated.

The probability number is as near zero as it can get.

BOOM! Shaka laka laka.

Reply to
DecadentLinuxUserNumeroUno

You could think of it as training with a weighted bat.

Reply to
bitrex

I enjoy thinking about and working on mathematical problems, but unfortunately I'm nowhere near talented enough to make a living at it.

If someone wanted to pay me to be a "so-so mathematical problem solver" I'd jump on it. But no such opportunities immediately spring to mind.

Reply to
bitrex

Maybe, but you succeeded in typing that post...

Reply to
bloggs.fredbloggs.fred

You can shorten this to "randomly draw a book from an infinite library of books." All the other furniture in the description is just noise.

This implies that there is a one-to-one and onto map from each book to the natural numbers.

The probabiliity of drawing at random a number from an infinite set is still zero - lim(p(x)) at p(x)=1/N as N->infinity.

So the number of moves is - surprise! - N.

"Infinity is just a mechanism for reasoning about limits." - Euler.

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Les Cargill
Reply to
Les Cargill

I know it was meant to be snarky, but that was actually pretty funny given the context. lol

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Rick
Reply to
rickman

Really? The probability has nothing to do with the number of values in the character set or the length of the text being matched? N is just the number of books in each room. Your mapping is wrong BTW. The library of books may be infinite, but they are not all unique. There are 25^(410*40*80) possible unique books.

BTW, did no one notice there are hexagonal rooms with only four exits and only four walls of books? How does that work exactly? Not your typical XY grid. Maybe they are the kind of libraries with bookshelves built into the doors?

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Rick
Reply to
rickman

I don't know the arrangement exactly as I haven't read the original novella. You could call it octagonal if you want - the four exits were just such that it's an equal graph in two dimensions.

Yes, the solution is not so simple. As you say, while the number of books is infinite there is a finite number of _unique_ books. Also, it can be shown from the theory of random walks that a random walk on Z^2 will "almost certainly" self intersect itself at some point, so there's the problem that the walker will eventually come across rooms where he has already selected some books and discarded them.

Reply to
bitrex

This reminds me of a scene from a game:

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As you explore this area, you find floors containing books relating to objects and environments of the game itself. Which you can read, and rewrite (in a very limited way), modifying the game from within.

(And yes, it's easy to make it crash, if you know what you're doing. :-p )

Tim

--
Seven Transistor Labs, LLC 
Electrical Engineering Consultation and Contract Design 
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Reply to
Tim Williams

On Sat, 5 Sep 2015 09:27:45 -0700 (PDT), snipped-for-privacy@gmail.com Gave us:

Nice try, punk.

Reply to
DecadentLinuxUserNumeroUno

I'll keep that in mind. I may have a numerical problem coming up. In the foolishness of youth, I used to enjoy solving puzzles and playing chess and such; now I'm more willing to delegate.

Reply to
John Larkin

The full short story (it was anthologized in _Labyrinths_ by Jorge Borges) goes into more detail. There are stairs to other floors, and water fountains, and restrooms. Alas, no provision is made to resupply the premises with toilet paper... no entrances, no exits.

Reply to
whit3rd

And then my trick is when I get stuck, to outsource the part I'm stuck on to mathematics stack exchange and get the _real_ nerds to work on it for free...:)

Reply to
bitrex

Actually, neither you nor Borges says this directly. But it can be inferred in that "... the library also must contain, somewhere, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books" that the books are indeed unique.

This does not form a constraint on the number of books nor whether they are unique or not.

--
Les Cargill
Reply to
Les Cargill

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