Comments on: How Big is the Library of Babel? http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html NIGHTTIME IS FOR DREAMING. DAYLIGHT IS FOR ACTION. Thu, 18 Mar 2010 22:39:26 -0700 http://wordpress.org/?v=2.9 hourly 1 By: knotty http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-51563 knotty Mon, 09 Nov 2009 23:35:58 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-51563 regarding quath's comment: we're really dealing with big-ass numbers, not infinities. regarding quath's comment: we're really dealing with big-ass numbers, not infinities.

]]> By: ashmeriel http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-51516 ashmeriel Sun, 08 Nov 2009 22:22:11 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-51516 The point entirely of Borges was to obfuscate the nature of God and to elevate himself, in a blasphemous irony, to a god-like status in a universe that might itself be the conundrum of some clever, but, nonetheless very human writer. As these comments attest, Borges has set individuals speculating and arguing over the imaginary architecture of the world, just as physicists, philosophers, and theologians debate the intrinsic fabric of our own. "This is not a pipe." And ulitmately the conundrum will give birth to a host of ideas and philosophies that will in time assume the skin and bone of religious fervor and, consequently, of oppression and liberation. God may be nothing more than an imaginative being, who, speculating on the nature of his far more complex universe, has "imagined" ours as a way of gaining insight into His. There are individuals in the Library who have created similar analogies to the library that may involve bird cages or caskets, and have become gods in their own finite, yet infinitely probable universes. What then is the point of speculation? What then is the point of investigation? If the universe is both a riddle and a joke, the dream of a charlatan, or the work of an artist, or a thing in its own right? The act of drawing two points to determine a line is both expressive and repressive, creating possibility while excluding others. Human existence is itself the ire of human existence. Borges has illustrated the most convincing portrait of hell. The point entirely of Borges was to obfuscate the nature of God and to elevate himself, in a blasphemous irony, to a god-like status in a universe that might itself be the conundrum of some clever, but, nonetheless very human writer. As these comments attest, Borges has set individuals speculating and arguing over the imaginary architecture of the world, just as physicists, philosophers, and theologians debate the intrinsic fabric of our own. "This is not a pipe." And ulitmately the conundrum will give birth to a host of ideas and philosophies that will in time assume the skin and bone of religious fervor and, consequently, of oppression and liberation. God may be nothing more than an imaginative being, who, speculating on the nature of his far more complex universe, has "imagined" ours as a way of gaining insight into His. There are individuals in the Library who have created similar analogies to the library that may involve bird cages or caskets, and have become gods in their own finite, yet infinitely probable universes. What then is the point of speculation? What then is the point of investigation? If the universe is both a riddle and a joke, the dream of a charlatan, or the work of an artist, or a thing in its own right? The act of drawing two points to determine a line is both expressive and repressive, creating possibility while excluding others. Human existence is itself the ire of human existence. Borges has illustrated the most convincing portrait of hell.

]]> By: Binguslootruss http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-50697 Binguslootruss Tue, 06 Oct 2009 18:28:37 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-50697 My favorite book in the library starts out identically to the script to the imagined Broadway musical "Osprey With Pure Intentions", but somewhere in act II it suddenly turns out that the hero & heroine are, in fact, two severed rabbit feet in a fountain which grows feathers backwards, and then rapidly degenerates into a story of lobsters and all the things they have stolen from me over the years, finally culminating in a stupendous climax of sex, gore, and betrayal around page 409, and then the last few pages contain beautiful ASCII-art renderings of hookah-smoking robots... My favorite book in the library starts out identically to the script to the imagined Broadway musical "Osprey With Pure Intentions", but somewhere in act II it suddenly turns out that the hero & heroine are, in fact, two severed rabbit feet in a fountain which grows feathers backwards, and then rapidly degenerates into a story of lobsters and all the things they have stolen from me over the years, finally culminating in a stupendous climax of sex, gore, and betrayal around page 409, and then the last few pages contain beautiful ASCII-art renderings of hookah-smoking robots...

]]> By: Boogiemanx http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-49499 Boogiemanx Tue, 18 Aug 2009 15:43:50 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-49499 Derek- All the ideas for books that you have presented are already in the collection as you are creating them with the symbols being utilized by the library. Don't confuse ideas with presentation. As long as the ideas you have are formulated and presented by the stringing together of a selection of the 25 symbols used by the library, (e.g. "Speaking Russian to Widowed Pink Tasmanian Yaks on Tuesday Mornings") your thoughts will never be truly infinite in nature, as you, like the library, are limiting your total conceptual output via the set of symbols you are using. It might seem like you could "outsmart" the library by coming up with yet another random series of words, but as long as you continue to use it's limited set of symbols, the library will have already thought of it first. If you want to outsmart the library, you will need to think of an idea that cannot be presented or translated using the symbols provided. The number of ideas and concepts you can think of using the 25 symbols is large, but the use of a structured language to communicate those ideas to others inherently prevents that number from being infinite. Derek- All the ideas for books that you have presented are already in the collection as you are creating them with the symbols being utilized by the library. Don't confuse ideas with presentation. As long as the ideas you have are formulated and presented by the stringing together of a selection of the 25 symbols used by the library, (e.g. "Speaking Russian to Widowed Pink Tasmanian Yaks on Tuesday Mornings") your thoughts will never be truly infinite in nature, as you, like the library, are limiting your total conceptual output via the set of symbols you are using. It might seem like you could "outsmart" the library by coming up with yet another random series of words, but as long as you continue to use it's limited set of symbols, the library will have already thought of it first. If you want to outsmart the library, you will need to think of an idea that cannot be presented or translated using the symbols provided. The number of ideas and concepts you can think of using the 25 symbols is large, but the use of a structured language to communicate those ideas to others inherently prevents that number from being infinite.

]]> By: Cris Comeau http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-49095 Cris Comeau Fri, 07 Aug 2009 02:40:19 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-49095 The numbers for the Library are not random and is easier to calculate to the nth digit than Pi. 0.12345678910111213... For example, The googolth and googol+1'th digits are 5 and 6. This number also includes it's own card catalog in every base, although it has different values, such as 0.1 10 11 100 101 110 111 ... in binary is approximately 0.86 in base 10, and therefore the spigot algorithm is adjusted for different bases. Base 27 would seem more appropriate for English literature. The monkeys finished their job an eternity ago. The library doesn't need any space in the universe anymore than does Pi or e. " 0.123...ALL 4 FREE ". The numbers for the Library are not random and is easier to calculate to the nth digit than Pi. 0.12345678910111213... For example, The googolth and googol+1'th digits are 5 and 6. This number also includes it's own card catalog in every base, although it has different values, such as 0.1 10 11 100 101 110 111 ... in binary is approximately 0.86 in base 10, and therefore the spigot algorithm is adjusted for different bases. Base 27 would seem more appropriate for English literature. The monkeys finished their job an eternity ago. The library doesn't need any space in the universe anymore than does Pi or e. " 0.123...ALL 4 FREE ".

]]> By: mark http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-47862 mark Tue, 16 Jun 2009 20:45:22 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-47862 A single irrational number could in principle I think have the same information content as the entire Library. It might have to be a transcendental number as well though. But a number with an infinite decimal expansion that is utterly random could be used to encode the information in each book. If so then the entire Library exists on the number line between 0 and 1 (or a space a lot smaller, of course)! A single irrational number could in principle I think have the same information content as the entire Library. It might have to be a transcendental number as well though. But a number with an infinite decimal expansion that is utterly random could be used to encode the information in each book. If so then the entire Library exists on the number line between 0 and 1 (or a space a lot smaller, of course)!

]]> By: jd eveland http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-42040 jd eveland Fri, 05 Dec 2008 06:29:46 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-42040 I would suggest that the information content of the Universe is, if not infinitely, then at least substantially smaller than the information content of the Library. And in turn, the information content and information-processing capabilities of a human being are smaller in turn by thousands if not billions of orders of magnitude. Despite the enormous complexity of the human brain and the synaptic network enacted within it, very little of the universe is actually accessible to us. If we partition the universe of information into four quadrants based on two axes -- things we know vs. things we don't know, and things we know about vs. things we don't know about, then all we can actually deal with is "things we know about things that we know about". Thus while I could cheerfully spend the remainder of my corporeality spinning off verbal combinations of the "Tasmanian yak" variety, I would be utterly unable to even formulate meaningful combinations about anything in the other three quadrants. So the value of my combinatorial efforts is enhanced by my concentrating on the limited range of phenomena that I personally can affect in one way or another. And even there efficacy varies -- witness my recent lack of effectiveness in preventing my retirement funds from losing half their value in a month or so. I think perhaps simply pulling the covers over one's head and reading Borges with the aid of a flashlight and a topped-off snifter makes as much sense as any other intervention into the world at this point... I would suggest that the information content of the Universe is, if not infinitely, then at least substantially smaller than the information content of the Library. And in turn, the information content and information-processing capabilities of a human being are smaller in turn by thousands if not billions of orders of magnitude. Despite the enormous complexity of the human brain and the synaptic network enacted within it, very little of the universe is actually accessible to us. If we partition the universe of information into four quadrants based on two axes -- things we know vs. things we don't know, and things we know about vs. things we don't know about, then all we can actually deal with is "things we know about things that we know about". Thus while I could cheerfully spend the remainder of my corporeality spinning off verbal combinations of the "Tasmanian yak" variety, I would be utterly unable to even formulate meaningful combinations about anything in the other three quadrants. So the value of my combinatorial efforts is enhanced by my concentrating on the limited range of phenomena that I personally can affect in one way or another. And even there efficacy varies -- witness my recent lack of effectiveness in preventing my retirement funds from losing half their value in a month or so.

I think perhaps simply pulling the covers over one's head and reading Borges with the aid of a flashlight and a topped-off snifter makes as much sense as any other intervention into the world at this point...

]]> By: lpetrich http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-37734 lpetrich Tue, 12 Aug 2008 18:55:15 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-37734 If all books with at most some length are present, then the total number is finite. But in the absence of that restriction, then the total number is infinite. In fact, it is countably infinite or countable. That will be the case even if one restricts the books' contents to syntactically and semantically correct language. That can be seen by constructing a subset of such books. The first contains "This is a sentence." The second contains "This is a sentence. This is a sentence." The third one contains three repetitions. Etc. It can be shown that the number of such books is countable. And since the set of linguistically-correct books is a superset of that set of books and a subset of books with all possible character combinations, it also has countable size. If all books with at most some length are present, then the total number is finite. But in the absence of that restriction, then the total number is infinite. In fact, it is countably infinite or countable.

That will be the case even if one restricts the books' contents to syntactically and semantically correct language. That can be seen by constructing a subset of such books. The first contains "This is a sentence." The second contains "This is a sentence. This is a sentence." The third one contains three repetitions. Etc. It can be shown that the number of such books is countable. And since the set of linguistically-correct books is a superset of that set of books and a subset of books with all possible character combinations, it also has countable size.

]]> By: derek hudson http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-37731 derek hudson Tue, 12 Aug 2008 09:29:46 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-37731 Thanks for answering.....BUT....given that all the books in the library ARE of a FINITE length the number of possible subjects even in books of a finite length still SEEMS to be infinite. BUT, if the library contains ALL POSSIBLE books of a finite length then, by definition, EVERY imaginable book of a finite length must be there, mustn't it? For example, my example of "Speaking russian to widowed pink Tasmanian yaks on Tuesday mornings" MUST be there!! Am I missing something or is my logic faulty? The conflict in my mind is between the FACT that all possible books of a finite length MUST be present, but I think I can invent (write) books which are NOT there, as the number of possible subjects (even of a finite length) seems to be in finite. Am I crazy or just wrong? Thanks for answering.....BUT....given that all the books in the library ARE of a FINITE length the number of possible subjects even in books of a finite length still SEEMS to be infinite. BUT, if the library contains ALL POSSIBLE books of a finite length then, by definition, EVERY imaginable book of a finite length must be there, mustn't it? For example, my example of "Speaking russian to widowed pink Tasmanian yaks on Tuesday mornings" MUST be there!! Am I missing something or is my logic faulty? The conflict in my mind is between the FACT that all possible books of a finite length MUST be present, but I think I can invent (write) books which are NOT there, as the number of possible subjects (even of a finite length) seems to be in finite. Am I crazy or just wrong?

]]> By: Ebonmuse http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-37723 Ebonmuse Mon, 11 Aug 2008 22:56:05 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-37723 Derek, The answer to your dilemma is that the Library of Babel contains all possible books of a given, <i>finite</i> length. The total number of possible books is unlimited, but only because the potential length of a book is unlimited. That said, you can make any potential book, no matter how long, by binding together an appropriate number of volumes from the Library of Babel and treating the result as a single book. Derek,

The answer to your dilemma is that the Library of Babel contains all possible books of a given, finite length. The total number of possible books is unlimited, but only because the potential length of a book is unlimited. That said, you can make any potential book, no matter how long, by binding together an appropriate number of volumes from the Library of Babel and treating the result as a single book.

]]> By: derek hudson http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-37717 derek hudson Mon, 11 Aug 2008 17:02:24 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-37717 The number of books in the library of Babel is finite, and has been calculated. But the number of possible (impossible?) subjects SEEMS to be infinite....a book on painting the hairs on Tunisian bees....a copy of the Bible with every other word being a swear word in Spanish....a book about drinking rabbit's blood while wearing pink boots.etc How long is the etc??? Surely I will never exhaust the list of titles I can concoct. I will I? Please help!! The number of books in the library of Babel is finite, and has been calculated. But the number of possible (impossible?) subjects SEEMS to be infinite....a book on painting the hairs on Tunisian bees....a copy of the Bible with every other word being a swear word in Spanish....a book about drinking rabbit's blood while wearing pink boots.etc How long is the etc??? Surely I will never exhaust the list of titles I can concoct. I will I? Please help!!

]]> By: David http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-28875 David Thu, 29 Nov 2007 04:06:09 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-28875 Number of rooms in the library of Babel: You can do this with logarithms: There are 25^(1312000) books, if there are 640 in a room then the log of the number of rooms is: 1312000*log(25) - log(640) = 2624000*(0.699) - 2.806 which means there are about 1.563*10^1834173 rooms. By the way, if each room is 1000 cubic meters, which seems reasonable, this gives us a volume of 1.563*10^1834170 cubic meters, which is something like a cube 10^611374 light-years on a side. This is 10^611356 times the radius of the observable universe. If you think its a long way to the drugstore . . . It's big, folks. Number of rooms in the library of Babel:

You can do this with logarithms:
There are 25^(1312000) books, if there are 640 in a room then the log of the number of rooms is:
1312000*log(25) - log(640) = 2624000*(0.699) - 2.806

which means there are about 1.563*10^1834173 rooms.

By the way, if each room is 1000 cubic meters, which seems reasonable, this gives us a volume of 1.563*10^1834170 cubic meters, which is something like a cube
10^611374 light-years on a side. This is 10^611356 times the radius of the observable universe. If you think its a long way to the drugstore . . .

It's big, folks.

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