On 11/14/2014 6:44 PM, LizR wrote:
On 15 November 2014 11:09, Russell Standish <[email protected]
<mailto:[email protected]>> wrote:
On Fri, Nov 14, 2014 at 08:46:16PM +1300, LizR wrote:
> In case anyone isn't acquainte with the library of Babel, it contains all
> possible books of a particular length (I think it's around 400 pages)
which
> use a certain number of characters, say 30. If we assume there are, say,
> 2000 characters per page, we get (I think) 30 to the power of 800,000
> books, a large but finite number of the sort I think Daniel Dennett called
> "Vast" (meaning ridiculously larger than any numbers that could be used to
> count anything in the observable universe. The LOB would dwarf the
> observable universe). It's similar to Russell's TON in that it contains
> essentially no information - or certainly no *useful* information. As
> Borges mentioned it contains the accurate catalogue of the Library
> (presumably occupying many lightyears of shelves, if assembled in one
> place) together with a "Vast" number of innaccurate catalogues. It also
Accurate? No it can't. Any complete catalogue of the library will be
vastly larger than any of the books it contains. Each book's entry
must be as large as the book itself.
And since the books are limited to 400 pages the catalogue must consist of different
volumes, one for each book catalogued.
Are you saying Borges got it wrong? It was his invention, after all!
:-)
But maybe he failed to follow the internal logic of the situation he was describing. I
assume that a catalogue has to give each book a title, which means compressing information
Do the books consist only of words - excluding undefined symbol strings? For most
languages that would allow about a 2:1 compression of the words. Then the books can be
identified by strings about half as long as the books. But otherwise, if the library has
all possible 400 page books consisting just of character strings, the titles will have to
be as long as the books to pick them out. However in this case there could not be an
inaccurate catalogue since any catalogue entry whatsoever would correspond to a book.
(e.g. there are multiple versions of many Shakespeare plays, each of which could
legitimately claim to be the "real" one). So there are, say, a googol books which start
"Colourless green ideas sleep furiously" - if we treat that as the title, then the
concept of a catalogue becomes at least meaningful, although there would have to be a
zillion light years of shelves to contain all the locations of the books in question in
the library. So maybe he had in mind a "hashing" system that would allow someone to
locate one of the googol books which start with a certain string of characters...
If you give the hash function a string that is just one character shorter than a 400 page
book, then it will return about about 100 books with that "title".
Brent
“Siempre imaginé que el Paraíso sería algún tipo de biblioteca.”
--― Jorge Luis Borges
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