Talk:The Library of Babel

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Contents 1 Choral piece 2 "Mathematicians have noticed..." 3 Is "The Total Library" a story or an essay? 4 "Borel's dactylographic monkey theorem"...yeah, right 5 Quine 6 RE: Comments by Quine -- What? There ARE no symbols 1 and 0 in the library. 7 The middle page? 8 A major problem with the design of the library. 9 Influence on philosophy...

[edit] Choral piece

Is the choral piece mentioned here really notable enough to merit mention in an encyclopedia? -- Jmabel | Talk 00:31, Apr 24, 2005 (UTC)

No. Remove it. What I would like it something on the mathematics, ie. what is the 'Babel number'? ZephyrAnycon 17:33, 6 November 2005 (UTC)

Twenty-five characters, eighty characters per line, forty lines per page and four hundred ten pages per book gives a total of

books. That's a one, followed by more than 1.8 million zeroes. Compared to this, the number of atoms in the universe is a speck not worth considering. (It's still not a patch on Skewes' number, though.) And, if a number that big still can't satisfy you, one can consider the different ways the Library can be stocked: how many ways can the Babel number of books be arranged in a line? Using Stirling's approximation for the factorial operation and playing with logarithms a little, I get that the total number of ways the Infinite Librarian could arrange the Library is

So, take a 1, and after it write a million zeroes. Then take another 1 and write after it a string of zeroes whose length is given by the number written in the previous step. As Douglas Adams once said, "You won't believe just how vastly, mind-bogglingly big it is." Anville 10:02, 29 January 2006 (UTC)

[edit] "Mathematicians have noticed..."

The paragraph that begins "Mathematicians have noticed..." strikes me as original research, and sloppy at that. I cut the sentence that said that the similarity of the name "El Aleph" to "Aleph Null" is noteworthy: it's not noteworthy, it's merely coincidental as far as I know, unless Cantor's use, like Borges, was an allusion to the Kaballah, in which case it deserves mention, but in an article on "El Aleph", not here. But that aside: who are the "mathematicians" who "have noticed..."? If this has actually been said by some notable mathematician, cite it. Otherwise... Borges makes it quite clear that the Library is not infinite, just horribly large. Yes, I guess the idea of one big finite number being lost in a far bigger finite number is sort-of-kind-of like a smaller infinity being lost in a larger infinity, but so what? It doesn't seem very deep. Unless someone can give a citation, I'm very inclined to remove this paragraph. -- Jmabel | Talk 05:56, May 12, 2005 (UTC)

Sure cut it all. Or give me a chance to work on it, I'm new here. I agree it's currently clumsy. The story's analogy with real numbers is very striking and deserves comment. If you feel you own the article I'll write one called Mathematics in the Writings of Borges or something. There is enough material. I've cut infinity from the original article, because, as you point out, the library isn't infinite. Can't log in for some reason to add my sig.

I've removed my piece. In researching my argument I've found much more; for instance J.E.I translates "The impious maintain that nonsense is normal in the Library and that the reasonable (and even humble and pure coherence) is an almost miraculous exception." while Hurley uses "rational" for "reasonable" (with many other differences). So now I'm looking at the Spanish and how rational numbers are termed. I'm not completely concerned about authorial intention, but if this is an artifact of translation, rather than an unintended coincidence of Borges', I'd be less interested. I'll probably work up a seperate article.--Mongreilf 11:20, 13 May 2005 (UTC)

Borges uses "razonable". Rational numbers are racional. I hate Hurley.--Mongreilf 11:46, 13 May 2005 (UTC)

[edit] Is "The Total Library" a story or an essay?

Perhaps it's been too long since I read it, but I definitely recall finding it in the Selected Non-Fictions collection. Moreover, I recall it being speculative but factual—instead of claiming the Library did exist, it pondered what it would be like if it did (and Pascal's "frightful sphere" was probably in there too). By way of comparison, everybody calls Vannevar Bush's "As We May Think" an essay, even though the machine he describes was never built and probably never will be built. It's still an essay, not a science-fiction story about the memex! Anville 11:15, 24 January 2006 (UTC)

You may be right; I'd check but, sadly, most of my Borges books are in storage at the moment and it's not in the three volumes I have handy. - Jmabel | Talk 02:59, 29 January 2006 (UTC)

I did a little webcrawling (see [1]), and I found that the bookseller named after fierce warrior women from Greek mythology (say what?) has the Selected Non-Fictions table of contents available online. "The Total Library" is on page 214. I think this warrants changing "story" back to "essay". Most of the web pages which mention "The Total Library" specifically are mirrors of this article, it seems, so we should probably take an effort to do it right. Anville 08:37, 29 January 2006 (UTC)

Thanks. - Jmabel | Talk 06:09, 2 February 2006 (UTC)

You're welcome! (smiles) Anville 09:02, 2 February 2006 (UTC)

[edit] "Borel's dactylographic monkey theorem"...yeah, right

Granted, it's a redirect to Infinite Monkey Theorem, but the phrase only shows up on that page and this page. Unless there's a good reason, that should probably become Infinite Monkey Theorem. —The preceding unsigned comment was added by 129.44.237.7 (talk • contribs) 26 May 2006.

The phrase wasn't mine, and though I'll admit that in the context I like the baroqueness, but I wouldn't fight to keep it. I guess I'll just have to concede another victory to the relentless war on prose. - Jmabel | Talk 16:18, 8 June 2006 (UTC)

[edit] Quine

The Quine material is a good addition, but can someone cite for it? - Jmabel | Talk 01:03, 4 July 2006 (UTC)

[edit] RE: Comments by Quine -- What? There ARE no symbols 1 and 0 in the library.

>Note also that the subset of books that only employs the symbols 1 and 0 contain...

What's with this section? The narrator only ever mentions that there are "twenty-five orthographical symbols". In the footnote it is revealed that the narrator's manuscript limits itself to "the comma and the period" plus "the space and the twenty-two letters of the alphabet" and that "these twenty-five symbols are considered sufficient by this unknown author."

This would suggest there are no numerals in the library.

Please correct me if I'm wrong, but doesn't this mean Quine (whoever he is) didn't read the story very carefully, or has otherwise been misquoted. Quine's point could still be made if this above sentence were rephrased with "IF" -- which is, I suspect, how it was originally given.

I don't know anything about Quine's thought's on the story, but would somebody please either correct this section, qualify it, or remove it. It misleads the reader about Borges' story, which is, after all, what the article is meant to be about. —The preceding unsigned comment was added by Ulrich kinbote (talk • contribs) .

I agree. That section is very odd, and sounds like dubious original research. Also babel isnt mentioned anywhere on the linked Quine article. Removing section. -Quiddity 06:41, 20 July 2006 (UTC)

Hiya - I was able to find the reference. It's from Quine's philosophical dictionary - "Quiddities". Here's the entry for the Babel Library example: http://jubal.westnet.com/hyperdiscordia/universal_library.html. It's very late at night, but on a glance reading, the original addition to the Babel article wasn't very clear - hopefully Quine made himself reasonably clear here (see link). FranksValli 09:10, 20 July 2006 (UTC)

I'd say there is some merit in the Quine material, although its not been sourced. Quine was one of the most important philosophers of the late 20th century, who has worked on philosophical problems relating to this field. It would not surprise me if Quine has written about the library at some point.

Logically the number of symbols used is unimportant (provided there is at least two), so its not important logically if the set of symbols is 0,1 or a,b,c,d... Further, its a standard logical procedure to reduce the cases to their simplest form which would be two symbols which are typically called 0 and 1. You could also consider a computer representation of each book, ultimately these would consist of the two binary digits 0 and 1.

The rest of the logic also seems sound to be, the number of pages in each book is unimportant. The final conclusion: that there is no useful information in the set of all books is sound. You need a librarian to tell you which are the interesting books.

A possible reference is Searching for meaning in the Library of Babel: some thoughts of a field semanticist which cites: Quine, Willard V. 1960. Word and Object. Cambridge, Mass.: MIT Press.

--Salix alba (talk) 09:19, 20 July 2006 (UTC)

I agree that the original addition to the Babel article wasn't at all clear, as well as switching a morse-code explanation for a binary-code one (assuming Franks' source is the original/intended source). Worse though, were the conclusions stating that it "exploded the conceit of the library", and "The library contains no information at all", neither of which are even hinted at in the potential source. The source is merely suggesting that the 'conceptual infinite library' can be adequately represented by the pure-abstraction of 2 symbols: dot and dash. But all that proves is that the idea can be minimally abstracted, not that the idea itself is hollow.

If the section is to be re-added, it should also be vastly expanded with all the other philosophers and thinkers who have commented upon the Babel work/concept, of which (I believe) there are many, many more than just Quine. -Quiddity 20:38, 20 July 2006 (UTC)

[edit] The middle page?

Has anyone cracked the enigma of the middle page?

[R]igorously speaking, a single volume would be sufficient, a volume of ordinary format, printed in nine or ten point type, containing an infinite number if infinitely thin leaves. (In the early seventeenth century, Cavalieri said that all solid bodies are the superimposition of an infinite number of planes.) The handling of this silky vade mecum would not be convenient: each apparent page would unfold into other analogous ones; the inconceivable middle page would have no reverse.

Why is the middle page inconceivable and, moreover, why does it have no reverse?

I believe there is a solution and it involves the mobius strip.

--Ulrich kinbote 18:00, 31 July 2006 (UTC)

"No reverse" never made much sense to me. And I always wondered why you couldn't just slip a bookmark into a page you wanted to find again. "Inconceivable" because it would be (it seems to me) merely a limit (if each apparent page unfolds into more, it must do so also, no?). - Jmabel | Talk 17:46, 3 August 2006 (UTC)

I think I understand this now. The middle page cannot be turned to, since from the front of the book you face the binary relation x<∞, where x (the pages turned) is any finite number, however large. The probability of finding the middle page by letting the book fall open at random is expressible as 1:∞. I am not a mathematician, but this is surely computable at zero. However, if one does in fact find the middle page, the binary relation ∞=∞ would be numerically unaltered by the addition or subtraction of pages. Therefore, when you turn the middle page, it "reappears" on the recto as soon as it has been laid down on the verso; and therefore the "middle page" becomes the page preceding the middle page when the page succeeding the "middle page" becomes the middle page. I have made a diagram to explain what I mean: > [2] The middle page is a continuous surface produced by the exposure of the obverse surfaces of turning pages. Like the Möbius strip, is has no reverse. --Ulrich kinbote 00:05, 10 August 2006 (UTC)

Frankly, as a mathematician, this strikes me as nonsense. It's like saying that because there is a continuum of real numbers between 0 and 1, 0.5 isn't really there in the precise middle. Of course it is. Now, it's true that there would be an infinite regress approaching it, and that any apparent middle page of finite thickness could be split into two, but that is no different than any other page in the hypothetical book. - Jmabel | Talk 20:09, 13 August 2006 (UTC)

I don't know why you are speaking of pages of finite thinness being split in half. The pages of this book are infinitely thin. Also, the definition of the middle page (of any book) is numerically relative to the other pages (the middle page is that page with an equal number of pages on either side). "Middleness" is a relation to the other pages in the mind of an observer. And because this relation in the case of a book with infinite pages is unchanged by the turning of pages (again, because ∞= ∞ is unchanged by the turning of pages) means the middle page is any page you happen to be turning, until it has been turned. For my diagram to express this properly would require an infinite number of steps. But what I am trying to illustrate is that the middle page (the page being turned) ceases to exist before the reverse can be seen.

No book with an even number of pages actually has a single middle page. In a book with 211 pages, for example, page 106 is the middle page: it has 105 pages on either side. But a book with 200 pages does not have a middle leaf (page 100 has 99 pages on one side, and 100 pages on the other). Most books consist of folded and bound leaves, which results in an equal number of pages, and no middle page. A book with an infinite number of pages, however, is not bound by this restriction. When a book with an infinite number of pages is open, (and all its pages are horizontal) it is as though it has an even number of pages (∞/∞) and no middle page. When you turn a page of the book, the page you are turning becomes the middle page since it is flanked by an infinite and equal number of pages and the book functions as though it has an odd number of pages (∞/middle page/∞). When the middle page laid horizontally on the verso, it ceases to exist, and the initial state is restored (∞/∞).

If you are going to pooh-pooh this second explanation, I hope you will also be generous enough to enlighten me as to your own explanation of what Borges meant by "the inconceivable middle page has no reverse." My scratch hypothesis is based on three assumptions: 1. Borges must have meant something. 2. To find out what he meant, implausible ideas are acceptable if they could plausibly be Borges's implausible ideas. 3. A bad hypothesis (either as a place to start, or as something that can later be eliminated from the pool of candidate hypotheses) is better than no hypothesis at all. --Ulrich kinbote 16:26, 15 August 2006 (UTC)

• I said "apparent" pages. - Jmabel | Talk 03:59, 17 August 2006 (UTC)

You have nothing interesting to say. That only thing interesting about you is that your intellectual hauteur sustains itself without an intelligent underwriting argument. Ulrich kinbote 14:58, 17 August 2006 (UTC)

Be nice. --Quiddity·(talk) 17:33, 17 August 2006 (UTC)

Despite your incivility: Borges was capable of being wrong. He relished paradox, but was not necessarily a great mathematician. As for the "no reverse": I don't see how any page in the book can really be said to have a reverse. And I do believe the word "apparent" is operative. Anything that appears to be a page and its reverse will prove not to be, because it can always be further divided. And any apparent page has, in this respect, the same property as the whole book. - Jmabel | Talk 19:04, 19 August 2006 (UTC)

According to your interpretation, Borges wrote "middle page" when he meant "any page", and "reverse" when he meant "either side". If this is obvious to me, it was certainly obvious to Borges. (Ulrich Kinbote)--124.59.25.144 03:07, 24 August 2006 (UTC)

I still think you are trying to turn poetry into mathematics. And this is probably the last I will say on it. You are welcome to the last word. - Jmabel | Talk 06:05, 25 August 2006 (UTC)

[edit] A major problem with the design of the library.

The library is made up of six-sided galleries. One side leads to a hallway which leads to another gallery and in which are two closets and a stairwell. One side opens upon the air shaft and has "very low railings". The remaining four sides house floor to ceiling bookshelves.

However, these hexagonal galleries cannot tessellate in a way that allows one to move horizontally through the library further than one gallery.

Try it. Imagine you have a puzzle made up of hexagons with one open side. Fit them together in such a way that the open sides of any two hexagons always meet. Now imagine your finished puzzle is a maze. Take your pencil and try and move through the maze. You will only be able to move back and forth between two hexagons. Now imagine that the puzzle is repeated in innumerable vertical layers (where the stairwell between layers must pass through the contiguous open-sides of galleries because the stairwell is in the hallway that joins them). The same situation applies, except now you can move up and down columns of double hexagons. You still cannot progress horizontally any further than one hexagon.

I made this diagram to explain what I mean > [3]

The narrator speaks of travelling through the library. Does he mean up and down in his column? Is this a hidden element of confinement? Or is this a design flaw? Or am I missing something (like, perhaps, the reader is not meant to bother with these insignificant details)? --Ulrich kinbote 19:14, 5 August 2006 (UTC)

I suspect that your last parenthetical statement is the key. - Jmabel | Talk 06:38, 8 August 2006 (UTC)

Samuel Taylor Coleridge said that "Until you understand a writer's ignorance, presume yourself ignorant of his understanding" (Biographia Literaria, 1817, ch. 12). I find it hard to believe both that Borges -- a writer known for his "tight, almost mathematical style" -- intended his description of the library to be impressionistic, and that it contains this design flaw. I prefer to believe that we have overlooked something or that librarians are bound to columns which are two galleries wide and infinitely vertical. Perhaps the library itself is just a single infinite column of double galleries. --Ulrich kinbote 23:52, 9 August 2006 (UTC)

I think maybe your first paragraph is incorrect. The ventilation shaft is in the center of each room (a circle in the middle of each hexagon). The sixth side of the hexagon is never explained, but is presummably another vestibule, meaning the rooms can be anything from an infinite zigzag, to a closed loop of 3 rooms. Hence can extend infinitely sideways, as well as vertically. --Quiddity·(talk) 05:58, 17 August 2006 (UTC)

Plus, you could just rotate the middle layer of your diagram, by one room, to be able to access all 6 rooms at each level (up, right, down, right, up, right, down, right....). And swivel it out of the vertical stack, in order to have the additional (white) stacks connect. --Quiddity·(talk) 06:02, 17 August 2006 (UTC)

That's a good point, and one I considered. It had occurred to me that "vast air shafts between" meant "in the middle of each hexagon"; but then I decided that for each hexagon to have an air shaft in the middle (wide enough for a librarian's body to be thrown down and sink endlessly without careering into the wall) would require a large hexagon; and given the number of books per shelf, it didn't seem to make sense. I assumed instead that "the vast air shafts between" cut through the mass of galleries; the unexplained sixth side looks out on an air shaft; and the galleries form a wall around each of these air shafts like the wall of a well. The shafts are "surrounded by very low railings" because the galleries fit together around the air shafts so that the side with railings of one gallery is contiguous with the next (and, inevitably, the diameter of an air shaft is equal to the diameter of any one of the galleries). Why would the unexplained side, if it opened onto another gallery, not be mentioned (I mean, if one side is open, then the hexagon strictly speaking only has five sides, or a gallery is a double hexagon with ten walls); or, if the unexplained side leads to a hallway, why would the narrator say: "ONE of these sides opens leads to a small hallway which opens onto another gallery"? But I suspect now you're right. The "classic dictum" that "the library is a sphere whose centre is anyone of the hexagons" seems to require a uniform library, in which the air shafts are in the middle of the galleries. Then again: "From any one of the hexagons one can see, interminably, the upper and lower floors." --Ulrich kinbote 04:33, 18 August 2006 (UTC)

[edit] Influence on philosophy...

FYI... Borges's story has had quite an impact on philosophy - several philosophers have used the ideas to explore philosophical issues. Two of the most important are Willard Van Orman Quine and Daniel Dennett. The latter goes into much detail about the Library in his book "Darwin's Dangerous Idea". I might add a section on this later. Mikker ^(...) 03:08, 18 September 2006 (UTC)

Good scheme, if you look back in the edit history, there was a paragraph on Quine, I've been meaning to expand this but I lack in time. --Salix alba (talk) 06:44, 18 September 2006 (UTC)

For whats its worth the correct Quice cite is

W. V. Quine, Quiddites, An Intermittently Philosophical Dictionary, Belkhap Press/Harvard Press, Cambridge, Massachusetts, 1987, pp 223-225.--Salix alba (talk) 07:17, 18 September 2006 (UTC)

Cool, thanks. Will see what I can do in the next week or so. (Loved the mp3 of the story btw! That Wikipedia has such links is one of the reasons I love it so much...) Mikker ^(...) 20:55, 18 September 2006 (UTC)