Talk:The Library of Babel/Archive 1

Archive 1

"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)

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)

"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)

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)

Quine

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

Done.--Heyitspeter (talk) 01:36, 11 November 2008 (UTC)

weblink

Far be it from me to be immodest, so I decided to post this weblink here first:

http://www.aartech.de/es100en.html

I wrote an essay about the Library, estimating its size and some other considerations. Maybe its worth to be included in the weblink list of the article?

Hyugens (talk) 13:45, 31 December 2008 (UTC)

Doesn't seem appropriate to me. It is not about the story itself, it is about your speculation about the story. -- Quiddity (talk) 19:36, 31 December 2008 (UTC)

OK, just thought it might be helpful to include a link that actually shows how to estimate the size of the Library rather than just stating the result. Thanks, anyway. -- Hyugens (talk) 12:29, 2 January 2009 (UTC)

Original research or valid content

I considered including the following in the article, but hesitated due to my concern that it might constitute original research. --User:Ceyockey (talk to me) 18:10, 18 December 2009 (UTC)

Data vs. information

In the introduction of the information science text Data Mining, the Library of Babel was used to illustrate the distinction between data and information. Citation → Adriaans, Pieter; Zantinge, Dolf (1996), "Introduction", Data Mining (First edition. ed.), London: Addison-Wesley, pp. 1–2, ISBN 0201403803, ...the library contains an infinite amount of data but no information. {{citation}}: |access-date= requires |url= (help)

Value as Thought Experiment

It seems that the 2nd and 3rd paragraphs are original research. Furthermore, as written, these seem to offer a summary of Kelly's argument rather than teasing out the insight that they give about The Library of Babel. Certain comments, like the following: "Additionally, because there are by definition all books, there are certainly also books of lies and falsehoods. For each copy of the codex to the library, there will be many copies of false codices, claiming some false books to be true and some true books to be false." are discussed in the story itself and probably shouldn't be added to a paragraph describing someone else's original ideas. 216.175.85.146 (talk) 01:21, 24 December 2008 (UTC)Humanonthemove 17:17, 23 December 2008

Agreed, Please WP:Be Bold and edit away. -- Quiddity (talk) 19:36, 31 December 2008 (UTC)

The calculations on the number of copies that vary by n conflicts with one of the sources given (http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html), where the number of volumes with 2 misprints is calculated to be 991,493,388,288,000. —Preceding unsigned comment added by 71.250.56.216 (talk) 16:30, 13 January 2011 (UTC)

It's wrong and shouldn't have appeared as a source. Xanthoxyl ^< 05:03, 14 January 2011 (UTC)

"It is clear?"

"In any case, it is clear that a library containing all possible books, arranged at random, is equivalent (as a source of information) to a library containing zero books."

I do not think this is true, and especially not clearly true. It looks like original research.137.82.36.10 (talk) 23:13, 20 February 2012 (UTC)

It's been tagged for a cite for several months... time to delete? Barque (talk) 07:30, 16 April 2012 (UTC)

It is common sense if explained, since opening any book and reading it is equivalent to generating a random string with the length of a book. It all depends if you have to cite that the sky is blue or not. In any case, I don't think that this sentence offers any particularly insightful knowledge, so it won't be missed. Diego (talk) 15:09, 16 April 2012 (UTC)

I've edited that passage, and deleted much more glaringly problematic (i.e. self-contradictory) material right underneath it. Xanthoxyl ^< 10:52, 23 April 2012 (UTC)

Proposed New Section: Variations of "The Library of Babel"

After reading the translations of Anthony Kerrigan (1962) and Andrew Hurley (1998) I noticed a discrepancy which led me to look at the original versions in Spanish. That confirmed the differences in the two published versions of this story. Below is the section that I am proposing to supplement the publication information in the article. What do you all think? Is this discrepancy relevant enough to warrant a new section? Has anyone written about these differences?

Variations between the 1941 and 1944 versions of “La Biblioteca de Babel”

Borges (or his editors) made significant changes to "The Library of Babel" between 1941 and 1944. The story published in El Jardin de los Senderos Que se Bifurcan (1941) and translated by Andrew Hurley in 1998 includes the following description of the library’s contents:

… its bookshelves contain all the possible combinations of the twenty-two orthographic symbols (a number which, though unimaginably vast, is not infinite)—that is, all that is able to be expressed, in every language. All—the detailed history of the future, … the true story of your death, the translation of every book into every language, the interpolations of every book into all books, the treatise Bede could have written (but did not) on the mythology of the Saxon people, the lost books of Tacitus.

In 1944, “La Biblioteca de Babel" was grouped with nine "Artificos" and published by Editorial Sur as Ficciones, but part of the sentence published in 1941 was removed. In Kerrigan’s translation of 1962 the paragraph in question says:

… its shelves contain all the possible combinations of the twenty-odd orthographic symbols (whose number though vast, is not infinite); that is, everything which can be expressed, in all languages. Everything is there: the minute history of the future, … the veridical account of your death, a version of each book in all languages, the interpolations of every book in all books.

The reason for the omission of the phrases is not certain, but they seem tautological. If the library is total, all books are books that Bede could have written, and no book is permanently "lost"- they are all in the library. The passage lost no meaning and became more concise after the phrases were erased. Dwuebben (talk) 22:28, 20 September 2012 (UTC)

I certainly appreciate the information, from a personal curiosity perspective, so thanks!

But yes, it would have to be commented upon by someone elsewhere, citably, otherwise it runs afoul of WP:OR; until then, it's the kind of information that would be fantastic in a Wikiversity page, but doesn't quite belong here. (I think). —Quiddity (talk) 01:55, 22 September 2012 (UTC)

I was on the fence as well. I'll continue to look for a comment elsewhere. In the mean time, it does seem curious that with all the scholarly arguments about this story as a precursor to the Internet and the various offshoots into mathematics, philosophy, natural language processing, etc. etc. that few folks seem to have looked closely at the text. Dwuebben (talk) 17:19, 22 September 2012 (UTC)

References

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 > [2]

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)

When I read thought: what are you talking?? I think it's a translation error or translator's perception...this is a perfect image of the library...http://3.bp.blogspot.com/_BJqwgGKgz8g/TBrJX0XHX-I/AAAAAAAAAZM/y1m4JDFXJ1I/s320/babel-dante-salatino-2008.jpg

You are counting the air shaft as one of the six sides (you say...One side opens upon the air shaft and has "very low railings"), big mistake, obviously, only One side leads to a hallway which leads to another gallery, therefore, as each hexagon allows us to go to another gallery ... the open sides are 2 ... not too hard to imagine...see the above image--186.62.173.145 (talk) 21:08, 29 October 2013 (UTC)Hernán

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)

These are all really old comments, but whatever. Just wanted to make sure everyone coming across this talk page knows that the Quine addition is now cited, and hopefully is adequately explained within the article. If not, maybe you can clarify it after reading the essay it is based on (it's very short).--Heyitspeter (talk) 01:38, 11 November 2008 (UTC)

Big Mistake...Borges write in the story txo axiomas...two axioms: 1) The library exists from eternity. This means that both the Library of Babel as librarians can be the work of a god or chance.

2)The number of symbols used spelling is twenty-five books, including space, the comma and the period. Babel books are made from random combinations of these signs, exhausting all possible combinations (whose number is unimaginably large, but not infinite). This shows the chaotic nature and report all the books. For each word that is written, there may be unconnected words, incoherent sentences, which are less incoherent languages​​.

Also says..."Quienes imaginan la Biblioteca sin límites, olvidan que los tiene el número posible de libros. Yo me atrevo a insinuar esta solución del antiguo problema: "La Biblioteca es ilimitada y periódica"..."Those who imagine the library without limit forget that have (limit) the potential number of books. Dare I suggest this solution to the ancient problem:"The Library is unlimited and cyclical"

This shows the futility of an estimate, since the Library, named by Borges repeatedly throughout his story, is simply a name that gives the Universe itself :)--186.62.173.145 (talk) 21:15, 29 October 2013 (UTC)Hernán

Differing number of characters

The article states both:

basic characters (22 letters, spaces and punctuation marks)

but later that:

There are 25 different characters (ignoring punctuation)

which seems to be a contradiction. — Preceding unsigned comment added by 212.9.31.12 (talk) 11:39, 9 January 2014 (UTC)

My thoughts exactly, Mr. "212". I just logged in to write this on the talk page (and found you already spotted it). Specifically, The "Plot summary" section now says "25 basic characters (22 letters, the period, the comma, and the space)", while the "Value as a mathematical thought experiment" section below counts 25 non-punctuation characters. Considering what the "Comments by Quine" lists above as quotes from the manuscript, i gather that the first statement is true, and that the mathematical thought experiment needs a bit of tweaking... -- Jokes Free4Me (talk) 19:41, 16 February 2014 (UTC)

From the English translation of the text accessible here as a PDF: "There are twenty-five orthographic symbols.[1]" ...which points to footnote 1 (still part of Borges's story, of course, not an annotation): "The original manuscript has neither numbers nor capital letters; punctuation is limited to the comma and the period. Those two marks, the space, and the twenty-two letters of the alphabet are the twenty-five sufficient symbols that our unknown author is referring to."

The problem with the article looks to be "ignoring punctuation" vs. "including punctuation." It seems the math experiment considers the 22 letters, space, comma, and period alike. Personally I think this section is given undue weight but for now I just corrected that word. --— Rhododendrites ^talk |  20:19, 16 February 2014 (UTC)

Attempts at reproduction

I've attempted to create a real-life digital Library of Babel, at http://libraryofbabel.keithguerin.com . Please contact me at [email protected] if you have interest in referencing it from this page. — Preceding unsigned comment added by Keithguerin (talk • contribs) 00:46, 14 December 2011 (UTC)

I'm sorry, but the copy of Pride and Prejudice that appears the first time you open up the page uses more than the 25 allowed symbols. (Also, if you refresh enough times, you can go back to it.) 184.152.75.156 (talk) 01:03, 20 May 2014 (UTC)

Influence on later writers

Is there any reason why this section isn't just called "fanfiction"? — DanielLC 04:21, 23 June 2014 (UTC)

While I'm at it, there's also Library of Discord by Chinchillax. It's not notable enough to get it's own article, but does it have to be notable to get mentioned in this section? — DanielLC 04:33, 23 June 2014 (UTC)

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

$25^{80\cdot 40\cdot 410}=25^{1\,312\,000}\approx 10^{1\,834\,098}$

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

$B!\approx 10^{10^{10^{6}}}.$

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)

As mentioned above, the number of different ways to arrange the books in the Library would be (25^1312000)!, which is about 10^10^1834103. Is Borges' 10^10^33013740 is just an overestimate? Or did he used functions other than factorial? 118.220.2.243 (talk) 11:20, 22 December 2010 (UTC)

It,s not Borges (who make no calculations in the story), but the clearly badly mistaken author of "the unimaginable mathematics of the Library of Babel"...--Dfeldmann (talk) 15:37, 20 July 2014 (UTC)

Lisp implementation section removed

I removed the "Lisp implementation" section. While interesting to some, it doesn't add anything to the explanation of this content. Wikipedia is not a codebook/manual/how-to guide (while it has some of this kind of content, it's only to better explain, exemplify, etc. rather than a tangential exercise). It's also only accessible at all to a very small niche of people who understand Lisp. Finally, and perhaps most importantly from a fundamental Wikipedia policy point of view, it's original research. Interesting project, but not really appropriate for an encyclopedia article. Moving it here below. --— Rhododendrites ^talk |  22:11, 20 September 2014 (UTC)

Lisp implementation section text

The Library of Babel may be implemented in Emacs Lisp thusly: ;; not sure the correct symbols. i suppose it doesn't matter. (setq alf '("a" "b" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "ñ" "o" "p" "r" "s" "t" "u" "v" "x" "y" "z" "," "." " ")) (defun lob-book () (interactive) (setq title (line)) (with-current-buffer (get-buffer-create title) (insert (funcall 'book))) (pop-to-buffer title)) (defun lob-page () (interactive) (setq title (line)) (with-current-buffer (get-buffer-create title) (insert (funcall 'page))) (pop-to-buffer title)) (defun lob-line () (interactive) (message "%s" (funcall 'line))) (defun book () (let (book) (dotimes (index 410 book) (setq book (concat book (funcall 'page)))))) (defun page () (let (my-page) (dotimes (index 40 my-page) (setq my-page (concat my-page (format "%s\n" (funcall 'line))))))) (defun line () (random t) (let (my-line) (dotimes (index 80 my-line) (setq my-line (concat my-line (nth (random (length alf)) alf)))))) (provide 'library-of-babel)

number of ways to arrange the books

How was the result obtained that there are 10^10^33,013,740 ways to arrange the books in the Library of Babel? That value seems quite wrong - with Hypercalc I found that the number of ways to arrange the books, by taking the factorial of 25^1,312,000, is about 10^10^1,834,103. What's that all about?! -Cookie Fonster^talk _sign! 23:49, 7 January 2015 (UTC)

The world largest library?

"The world's largest library, the Library of Congress, has 2.18\times 10^{7} books."

From this page, this library is not the largest. Can you cite your source? — Preceding unsigned comment added by Mickael ar (talk • contribs) 11:57, 2 February 2015 (UTC)

"Infinite"

Borges makes it clear that the library, however vast, is not infinite. The length of each book is finite and the alphabet size is also finite. The article sloppily uses the word "infinite" in several places. I will go ahead and edit them out unless there is a good reason why they should stay in. Farzaneh (talk) 16:55, 12 July 2015 (UTC)

Index of books

"Another is the belief that since all books exist in the library, somewhere one of the books must be a perfect index of the library's contents"

This seems immediately dubious to me, as the library contains only the set of 410-page books, and 410 pages cannot possibly contain enough information to summarize the incredibly large set of books. Though there may be many books that together form an index, they are by now all hopelessly separated and confused with misprints.67.194.82.117 (talk) 06:12, 22 April 2012 (UTC)

I think the idea is that the "perfect index" somehow allows you to find information by explaining the books' arrangement. Xanthoxyl ^< 10:52, 23 April 2012 (UTC)

One thing that I rarely see mentioned is that in a library of all possible 410 page books, there's no way to devise a "reference ID" that is itself shorter than 410 pages (using the same character set). Any method of ID'ing a particular book would necessarily be just as information-dense and lengthy as the books themselves (meaning the most efficient way to reference a book is to just quote all 410 pages of its contents). A "card catalog" would be effectively pointless. Even a simple location specifier (e.g. "Book 5 on Shelf 47 in room X") would be ~410 pages long due to the vast number of rooms (you need more than a million characters to specify a particular room). So it's impossible for "one of the books" to be "a perfect index of the library's contents", indeed "one" of the books can't even be an index of two other books. The most you could hope for is that "valid" books might be already placed together in rooms suitably labeled (like a plaque saying, "here be the good stuff"). But then how many quadrillion rooms would you have to wander before you happened upon one of them? And if you found such a plaque, could you trust it? Ichneumon~enwiki (talk) 18:59, 28 September 2015 (UTC)

Gravity

What are the limits to the density of each cube/room in the library, such that the library does not collapse into a black hole?

What are the limits to the density of each cube/room in the library, such that the library can be reinforced with existing technology without collapsing under its own gravity?

Since there are a finite number of books, it is a safe assumption that there is an "edge" at which the apparent effects of gravity would be greatest. — Preceding unsigned comment added by 68.3.217.18 (talk) 21:31, 8 July 2016 (UTC)

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: > [3] 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)

I can't say I agree with the last or any of the explanations here. Seems to lack an understanding of Mathematics. Everyone assumes that because there is an infinite number of pages on either side of any given page that it is therefore the middle page. This isnt true really and I doubt it is what is meant. The thing you have to understand about Set Theory is that just because a set has an infinite number of members does NOT mean that two sets have the same size. For example imagine all real numbers between 0 and 0.25, there are an infinite number of them. Well there are also an infinite number of Real numbers between 0 to 0.5, however this infinite is twice the size as the other. You can't say 0.25 is in the middle of 0 and 1 just because there are an infinite number of real numbers on either side, doesnt work that way. So similarly if you had a book that was one foot thick with infinite pages as places there is truly only a single plane that is the middle plane (page). What was meant by inconceivable and no reverse becomes clear when you consider the order of the characters in his hypothetical book. It obviously is meant to contain every sequence of characters possible in every single order. If it were written and ordered in such a way that the book from the first page forward would be the reverse as if you read from the last page backwards (mirrors itself in the middle) then it all makes sense. With such a book the contents of the middle page is mathematically unknowable, but we can none the less conclude that whatever the content of the page it would be the same forwards as it is backwards, so it would be the only page in the book that did not have a reverse. - Debeo Morium: to be morally bound (Talk | Contribs) 22:39, 1 April 2017 (UTC)

"Linguistic reality" ("Infinite extent") subsection

Both claims made in this section are inaccurate, and its conclusion is doubly inaccurate. The set of finite (but unbounded) strings of characters from a finite alphabet is infinite; for example, the set {a,aa,aaa,aaaa,...} is infinite, and has only finitely-long members. Therefore, it is also incorrect to say that "if any string in the Library of Babel must be of finite length, then the Library will contain a finite number of unique strings" (The set of infinite-long strings from a finite alphabet is uncountably infinite; a good example is the decimal expansion of real numbers.)

However, this is all academic because the books in the Library are not just finite but bounded in length, so there are finitely many distinct books... as the story actually acknowledges. (I emphasize "distinct" because the last paragraph of the story gives the narrator's pet hypothesis: the books eventually repeat, so that the Library is nevertheless infinite.)

I'm tempted to remove this subsection, since it is OR, makes several false mathematical claims, and ignores the actual content of the story. I'm a new editor (newly nonanonymous), though, so I'll defer to someone with more expertise. If nobody responds or acts for a while I'll take it out. Patallurgist (talk) 07:46, 31 January 2018 (UTC)

Update: I've removed the most egregious problems, but what's left is kind of underwhelming. Books can be longer than 410 pages, so the Library doesn't contain all books; this isn't mind-blowing. I've added some additional summary of the relevant parts of the story and renamed the subsection. I also changed the "recursion" link to lead to linguistic recursion, rather than mathematical recursion, but it's still a non sequitur because books aren't generally one long sentence.... Patallurgist (talk) 00:08, 28 February 2018 (UTC)

Finding "truth"

One of the main points of the story has been overlooked so far: While Borges mentions that there are people looking for a book containing the "one and only true word of God" (not sure about the actual words used in the story), the insurmountable problem with this is that there is no way to be sure you've found it. It will be indistinguishable from any other - entirely different - book containing what someone else might consider the "one and only true word of God". As such, it's a scathing criticism of religion as it basically says "The truth maybe out there, but there is no way to be sure you found it, only your personal interpretation". — Preceding unsigned comment added by 79.193.100.163 (talk) 14:20, 3 March 2018 (UTC)

See also link farm

I've deleted a few of the mathematical-related links. This is an article about a whimsical story, not a mathematical essay. If those links are highly relevant, they can/should be integrated into the text. Maybe a new section, Mathematical analogies, or create a new article, Mathematical implications of the Library of Babel, and integrate them there. We should become extremely resistant to adding to a See Also list of 6 items or more. In that case, the consensus is: add one -> delete one. Sbalfour (talk) 16:24, 19 January 2019 (UTC)

Gene Wolfe homage(?) to The Library of Babel

Why was the Gene Wolfe homage removed with this edit?

https://en.wikipedia.org/w/index.php?title=The_Library_of_Babel&oldid=1019518273

I have never read Gene Wolfe's novel, but if it is truly an homage, why remove it? פרה (talk) 02:57, 15 January 2022 (UTC)