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. Tue, 6 Jan 2009 14:20:46 +0000 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.

]]> By: tommy http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-17676 tommy Wed, 28 Feb 2007 10:26:22 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-17676 Thank you so much for posting the link to the Babel short story. That was easily one of the best stories I have ever read. Any tips on links to his other stories, such as "Blue Tigers"? Thank you so much for posting the link to the Babel short story. That was easily one of the best stories I have ever read. Any tips on links to his other stories, such as "Blue Tigers"?

]]> By: meghan http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-16144 meghan Tue, 20 Feb 2007 09:36:43 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-16144 "The sucky thing is that, say you wanted to reach the edge, you might start of only 10 rooms away, but you don't know what direction to walk, and you walk in the wrong direction! And you will never even know! Ah, life." Your comment, and the story, remind me of the film <a HREF="http://www.imdb.com/title/tt0123755/" rel="nofollow">Cube</A>. A group of people find themselves stuck in a cube which has six doors, one on every side, that bring them into identical cube rooms. They eventually realize that there are coordinates for each cube, and that they are actually within a big machine that is moving and shifting the numerous cubes regularly, only briefly giving a chance for one door to lead outside of the maze. It's difficult to ever know how many cubes make up the entire maze, and actually figure out where one is within its structure as it moves. "The sucky thing is that, say you wanted to reach the edge, you might start of only 10 rooms away, but you don't know what direction to walk, and you walk in the wrong direction! And you will never even know! Ah, life."

Your comment, and the story, remind me of the film Cube. A group of people find themselves stuck in a cube which has six doors, one on every side, that bring them into identical cube rooms. They eventually realize that there are coordinates for each cube, and that they are actually within a big machine that is moving and shifting the numerous cubes regularly, only briefly giving a chance for one door to lead outside of the maze. It's difficult to ever know how many cubes make up the entire maze, and actually figure out where one is within its structure as it moves.

]]> By: Andrew http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-11556 Andrew Sun, 31 Dec 2006 07:03:20 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-11556 Well, yes the narrator said that he suspected that the library repeated after a while, but I don't think we can really know for sure. He was just one librarian, and we all develop a certain mythology/philosophy about the world we live in... sometimes wrong, no doubt. Well, yes the narrator said that he suspected that the library repeated after a while, but I don't think we can really know for sure. He was just one librarian, and we all develop a certain mythology/philosophy about the world we live in... sometimes wrong, no doubt.

]]> By: lpetrich http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-11107 lpetrich Sun, 24 Dec 2006 06:06:48 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-11107 Or else is a rectangle with periodic boundary conditions, giving it the topology of a torus (doughnut shape). Or else is a rectangle with periodic boundary conditions, giving it the topology of a torus (doughnut shape).

]]>