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. Mon, 23 Jan 2012 12:09:52 -0800 http://wordpress.org/?v=2.9 hourly 1 By: Rollingforest http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-64039 Rollingforest Sun, 27 Feb 2011 11:46:19 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-64039 It should be noted that many scientists believe that the universe is infinite. The big bang was not, according to them, the creation of the universe, but rather the creation of the <i>observable</i> universe. The infinite universe, according to them, expanded with the big bang. http://www.astro.ucla.edu/~wright/infpoint.html So if the universe is infinite, then no, not everything would exist, but everything that is <i>physically possible</i> would exist provided that matter was distributed throughout the universe. Due to quantum fluctuations and other random events, anything that could theoretically happen on earth or in space would by necessity happen because it would come up in infinite space. So there is a world where Hitler was killed in 1932 before he could take over and there is a world where he succeeded in conquering everything. There is a world exactly like this one except that you wore a different color shirt today. In an infinite universe with infinite matter, if it is physically possible it will happen. The library sounds incredible, but I'm not really all that impressed when I think about it further. I mean, I could, given enough time, imagine everything that had ever happened in the universe just using my own brain. I'd never know if I was right or not, but I could do it. Having every possible thing written out doesn't do me any more good. It should be noted that many scientists believe that the universe is infinite. The big bang was not, according to them, the creation of the universe, but rather the creation of the observable universe. The infinite universe, according to them, expanded with the big bang.

http://www.astro.ucla.edu/~wright/infpoint.html

So if the universe is infinite, then no, not everything would exist, but everything that is physically possible would exist provided that matter was distributed throughout the universe. Due to quantum fluctuations and other random events, anything that could theoretically happen on earth or in space would by necessity happen because it would come up in infinite space. So there is a world where Hitler was killed in 1932 before he could take over and there is a world where he succeeded in conquering everything. There is a world exactly like this one except that you wore a different color shirt today. In an infinite universe with infinite matter, if it is physically possible it will happen.

The library sounds incredible, but I'm not really all that impressed when I think about it further. I mean, I could, given enough time, imagine everything that had ever happened in the universe just using my own brain. I'd never know if I was right or not, but I could do it. Having every possible thing written out doesn't do me any more good.

]]> By: ctd http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-61945 ctd Thu, 16 Dec 2010 01:28:31 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-61945 There is a difference between "countably infinite" vs. "really big finite". There is a finite number of books in the Library of Babel: 25^1312000 - 1; large indeed, but hardly infinite. (The "-1" is, of course, "Ethel the Aardvark Goes Quantity Surveying" having been deliberately destroyed, as well it should be. The Library would, however, contain both the full and expurgated versions of "Olsen's Standard Book of British Birds".) Elsewhere someone computed a sobering view of this issue: (as I recall...) should every particle in the universe be assigned a 1-byte random value, the largest string size which has a 50/50 chance of being found in that random sequence would be about ... 312 characters. This rather puts monkeys pounding out a random copy of the much larger "Hamlet" at a rather, um, large (albeit not infinite) number. There is a difference between "countably infinite" vs. "really big finite". There is a finite number of books in the Library of Babel: 25^1312000 - 1; large indeed, but hardly infinite. (The "-1" is, of course, "Ethel the Aardvark Goes Quantity Surveying" having been deliberately destroyed, as well it should be. The Library would, however, contain both the full and expurgated versions of "Olsen's Standard Book of British Birds".)

Elsewhere someone computed a sobering view of this issue: (as I recall...) should every particle in the universe be assigned a 1-byte random value, the largest string size which has a 50/50 chance of being found in that random sequence would be about ... 312 characters. This rather puts monkeys pounding out a random copy of the much larger "Hamlet" at a rather, um, large (albeit not infinite) number.

]]> By: tritium http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-60248 tritium Mon, 11 Oct 2010 06:24:26 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-60248 Comment #13 by: robnjr has the correct treatment to this case. Seems there is a lot of confusion here with the Infinite. As some here have already suggested, many of you really need to study Cantor and transfinite Set Theory, before making pronouncements on topics involving the infinite. It is NOT necessarily true (or to be more exact, sufficient) that given an infinite amount of time... "Any type of event that has nonzero probability will happen infinitely many times". The Set of Even numbers has the same size (cardinality) as the Set of Intergers (or Rational Numbers). However, every member of the Set of Integers is NOT in the Set of Even numbers, even though they both constitute a denumerably infinite set, and have an exact one to one correspondence. Discrete events in Space-Time may also be "countably" infinite and have a cardinality equal to Aleph Nought. In which case they may be infinite, but not necessarily exhaustive, just like the Even numbers are infinite, but do not contain the Odd integers. The same principle may apply with The Library of Babel. The total number of books would be countably infinite, with a cardinality of Aleph-nought. However, it does not follow that every possible book could be contained within. I especially know, for a fact, that the book "Ethel the Aardvark Goes Quantity Surveying" would NOT be found in the Library of Babel :) Comment #13 by: robnjr has the correct treatment to this case.

Seems there is a lot of confusion here with the Infinite. As some here have already suggested, many of you really need to study Cantor and transfinite Set Theory, before making pronouncements on topics involving the infinite.

It is NOT necessarily true (or to be more exact, sufficient) that given an infinite amount of time... "Any type of event that has nonzero probability will happen infinitely many times". The Set of Even numbers has the same size (cardinality) as the Set of Intergers (or Rational Numbers). However, every member of the Set of Integers is NOT in the Set of Even numbers, even though they both constitute a denumerably infinite set, and have an exact one to one correspondence.

Discrete events in Space-Time may also be "countably" infinite and have a cardinality equal to Aleph Nought. In which case they may be infinite, but not necessarily exhaustive, just like the Even numbers are infinite, but do not contain the Odd integers.

The same principle may apply with The Library of Babel. The total number of books would be countably infinite, with a cardinality of Aleph-nought. However, it does not follow that every possible book could be contained within.

I especially know, for a fact, that the book "Ethel the Aardvark Goes Quantity Surveying" would NOT be found in the Library of Babel :)

]]> By: D http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-57524 D Sat, 19 Jun 2010 07:05:43 +0000 http://www.daylightatheism.org/2006/03/how-big-is-the-library-of-babel.html#comment-57524 I'm late to the party, but tommy asked for more stories in #19 and one of my favorites is <a href="http://www.hccp.org/borges-judas.html" rel="nofollow"><i>Three Versions of Judas</i></a>. I'm still surprised that some people think that a brute force method for creating every possible book of a given length will still leave room for something that "counting with letters" somehow omitted. Simply baffling. Of course, though you'd have every possible correct medical text, you'd have unimaginably more incorrect ones, the majority of which would contain errors subtle and lethal. Oh, man... that's gonna blow my mind or keep me up all night... crap. I'm late to the party, but tommy asked for more stories in #19 and one of my favorites is Three Versions of Judas.

I'm still surprised that some people think that a brute force method for creating every possible book of a given length will still leave room for something that "counting with letters" somehow omitted. Simply baffling. Of course, though you'd have every possible correct medical text, you'd have unimaginably more incorrect ones, the majority of which would contain errors subtle and lethal. Oh, man... that's gonna blow my mind or keep me up all night... crap.

]]> 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.

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