The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

   

The Library of Babel

 In Jorge Luis Borges's short story, "The Library of Babel," he describes a fascinating library of dubious functionality. The Library consists of nigh innumerable hexagonal rooms lined with shelves of books. Each book has a constant number of pages, filled with nonsensical combinations of characters.

In the course of the narrative it is revealed that each book is unique, and every possible book of 410 pages is represented. So the library contains "Hamlet", millions of near copies of "Hamlet" with slight errors, and countless number of texts with the "To be or not to be" soliloquy intact, but otherwise complete garbage.

At the "Grey Labyrinth" we've just gotten hold of several betas of CD ROMs purporting to be "The Library of Babel Now On CD-ROM". We haven't had time to install them, but we were wondering which could potentially be legitimate, and which were hoaxes. Apart from the distinctions listed below, they all have the following (purported) features in common, unless noted otherwise:

  • All have a virtual-reality interface allowing one to wander from room to room, shelf to shelf, book to book, and page to page.
  • Apart from the text on the pages, all books, rooms, shelves, etc. are identical. Reasonably, the CD-ROMs need only hold a relatively small number of images.
  • Each room has four bookcases.
  • Each bookcase has five shelves.
  • Each shelf has thirty-five books.
  • Each book has 410 pages.
  • Each page has forty lines of eighty characters.
  • There are fifty different symbols, including punctuation and spaces. (Borges's story had twenty-five)
  • All the CD-ROMs claim to run on an arbitrary turing machine of infinite RAM. (Talk about bloated code!)
  • The Libraries are static; two people running the same CD-ROM on different machines will be able to navigate to identical texts using the the same set of instructions, e.g., fifty rooms north of start, three floors up, bookcase one, shelf two, book twenty-three, page one hundred, starting at the beginning of line seven, might read "It was the best of times it was the blurst of times."
Having established what these CD-ROMs have in common, here's what they claim as their particular unique features:
  • CD-ROM 1 has a small repeating subset of the Library. Not all books are represented, and some repeat.
  • CD-ROM 2 claims the complete Library, with some sort of defined ordering to the texts.
  • CD-ROM 3 claims the complete Library, but the texts are arranged in a completely random fashion (no order whatsoever).
  • CD-ROM 4 claims a "more than complete Library"; in addition to all possible 410 page texts, it also boasts a reference section with a finite number of unique books of infinite length (really thin pages, you can just keep turning and turning...).
  • CD-ROM 5 allegedly offers an infinite number of unique texts- every possible text of arbitrary finite length.
  • CD-ROM 6 supposedly contains the "more complete than the more than complete Library" with all possible texts of both finite and infinite length.
No CD-ROM makes any claim about whether or not you'd ever be able to read all the books. Just the assurance that they're all there. A CD-ROM can store, say, 800 megabytes of uncompressed data.

Ignoring the general caveats regarding software manufacturers' claims, which of the above CD-ROMs are possible, at least in theory? Accept into theory the axiom which most software manufacturers now take for granted: everyone's PC is equipped with an infinite amount of RAM.


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