On 15 November 2014 16:46, meekerdb <[email protected]> wrote: > > And since the books are limited to 400 pages the catalogue must consist of > different volumes, one for each book catalogued. >
Yes, Russell got that right (and Borges got it wrong). But I think the idea is that each book is unique, although the characters in the story have no way to prove this. So in fact there is no index. > 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? > No. Each book is all possible combinations of symbols, and in the story the main character has only seen one book which contains a short fragment of intelligible text. Wikipedia's plot summary... Borges' narrator describes how his universe consists of an enormous expanse > of adjacent hexagonal <http://en.wikipedia.org/wiki/Hexagon> rooms, each > of which contains the bare necessities for human survival—and four walls of > bookshelves. Though the order and content of the books is random and > apparently completely meaningless, the inhabitants believe that the books > contain every possible ordering of just 25 basic characters > <http://en.wikipedia.org/wiki/Grapheme> (22 letters, the period, the > comma, and the space). Though the vast majority of the books in this > universe are pure gibberish, 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. The narrator notes that the library must contain all useful > information, including predictions of the future, biographies of any > person, and translations of every book in all languages > <http://en.wikipedia.org/wiki/Language>. Conversely, for many of the > texts some language could be devised that would make it readable with any > of a vast number of different contents. Despite — indeed, because of — this glut of information, all books are > totally useless to the reader, leaving the librarians in a state of > suicidal despair. This leads some librarians to superstitions > <http://en.wikipedia.org/wiki/Superstitions> and cult > <http://en.wikipedia.org/wiki/Cult>-like behaviours, such as the > "Purifiers", who arbitrarily destroy books they deem nonsense as they scour > through the library seeking the "Crimson Hexagon" and its illustrated, > magical books. Others believe that since all books exist in the library, > somewhere one of the books must be a perfect index of the library's > contents; some even believe that a messianic figure known as the "Man of > the Book" has read it, and they travel through the library seeking him. 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. Yes (or rather it wouldn't because they are hypothesisted to be unique). > > (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 100 books with that "title". > Not 25? Actually the hash function (itself contained in some books) would be longer than the books in question because if it accurately gives the position of the book in the library (to be a catalogue it should, I assume) that position will be in some huge coordinates - distances far larger than the size of the visible universe! So 1594 as mentioned in this quote is shall we say a little ... low. One which my father saw in a hexagon on circuit fifteen ninety-four was > made up of the letters MCV, perversely repeated from the first line to the > last. Another (very much consulted in this area) is a mere labyrinth of > letters, but the next-to-last page says "Oh time thy pyramids". And here is the bit I was talking about originally :-) Everything: the minutely detailed history of the future, the archangels’ > autobiographies, the faithful catalogues of the Library, thousands and > thousands of false catalogues, the demonstration of the fallacy of those > catalogues, the demonstration of the fallacy of the true catalogue, the > Gnostic gospel of Basilides, the commentary on that gospel, the commentary > on the commentary on that gospel, the true story of your death, the > translation of every book in all languages, the interpolations of every > book in all books. And here is a comment on the size of the LOB Consider: according to Borges’ description, each book in the Library is 410 > pages; each page is made up of 40 lines each consisting of 80 positions, > and there are 25 possible alphabetic symbols that can fill any of these > positions. This works out to 410 x 40 x 80 = 1,312,000 positions per book, > each of which can be filled in 25 distinct ways: 25 x 25 x 25… and so on, > 1,312,000 times. In other terms, the Library of Babel contains 25^1,312,000 > books. This is a number compared to which the number of atoms in our > universe is infinitesimal. You may think it's a long way down the road to the chemist, but that's just peanuts compared to space. And space is peanuts compared to the library of Babel... > Brent > “Siempre imaginé que el Paraíso sería algún tipo de biblioteca.” > --― Jorge Luis Borges > > Yes, me too. My mother was a librarian, and I have an inordinate number of books. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
