6 ms·
Study enough information theory, and it will start seeming obvious on a gut level that a library containing all possible books has less information in it than a
by Eliezer 16y ago
Study enough information theory, and it will start seeming obvious on a gut level that a library containing all possible books has less information in it than a library containing one book.
- achompas 16y agoCan you expand on this please, so I don't clutter my own personal bookshelf (so to speak)?
- seltzered 16y agoI think he's relating to the "book of five rings" / "art of war" way of writing books. Theres many big long books that are merely churned out, or are written before an author has reached a point of completeness about the subject he's writing on. Worse, they could be written as "wines of fear" where they are written not to directly offend anyone. On the other hand, there are a few beautiful books that are short, yet establish mental frameworks that cover all the other books. The book of five rings is touted as one. Personal example: There's volumes of business books that all harken back to people being some mixture of evangelist, maven, or relater. Books like "the human fabric" or religious books like the "bhagavad gita" establish the same framework.
- dandelany 16y agoI'm not well-versed in information theory, so this may be a misinterpretation. But this strikes me as a beautiful truth that rewards careful pondering. A library containing all possible books may contain all the gems of knowledge in the world, but it also contains far more nonsense: Books full of random letters that mean nothing, as well as real books with changes made to them, both unnoticeable and noticeable. Such a library, though containing all information, would not contain any information about which books contain real information and which do not. A single real book, though, while it may contain factual errors, can at least be guaranteed to contain the beliefs and assumptions of its author, which is more than you can say about the infinite library. Look at it this way: an infinite list of strings containing all possible strings (or even a finite list of strings containing all possible strings shorter than a given length) contains less information than a program or essay that I wrote, because the infinite list gives no indication about which strings are "important", "informational" or "useful", while my one essay or program contains concise, easily-extractable information intended for a particular purpose. One more example, just for fun: Imagine I'm a stupid bank robber who keeps all the plans for my heists and the names of my partners in one Word document on my hard drive. If the police arrest me, they have enough information to send me and my partners to jail. However, imagine that I've written a program that makes a million copies of my secret plan and changes the names and locations inside all of the copies to random values. Now, if I get caught, without knowing which document is real and which are fake, the authorities don't have any useful information.
- Psyonic 16y ago"Such a library, though containing all information, would not contain any information about which books contain real information and which do not." Actually, by definition, it would contain that information. But you have the same problem finding it.
- mitcheme 16y agoAnd it would also contain an infinite number of books which claim to list which books contain real information, but actually contain some titles that contain nonsense & lies and/or are missing some titles that contain real information. So the chance of you finding a fake information-listings book is far greater than you finding the real one.
- Psyonic 16y agoSo in other words, you have the same problem finding it?
- mitcheme 16y agoHmm, sorry. I thought you were referring to the book being difficult to find because it would be mixed in with an infinite number of other books, not specifically that there would be an infinite number of fake versions of that book.
- Eliezer 16y agoIt requires only a very short program to print out all possible books, and a much longer program to print out one particular book. To look at it another way, by the trivial isomorphism between any class and its complement, the library containing all possible books has just as much information as the library containing no books.
- th 16y agoSo a library containing one book has just as much information as a library containing all books except for that one book? That doesn't seem right.
- pessimizer 16y agoWould it seem right that the mold for casting a tin soldier would have the same detail as the tin soldier cast?
- copper 16y agoA better way of stating this would be to look at how much information you can extract from the library with one book in a given time, as compared to the library that contains "all" books: nearly all such books would have gibberish in them. Eliezer's statement would be a lot less surprising with a proper definition of "all" :)
- Eliezer 16y agoWell, it is right. Takes around the same size of computer program to print out the library either way.
- deleted 16y ago[deleted]
- defen 16y agoThink about how you would specify a book in the "all possible books" library - you would need a number at least as large as the book itself, in the general case! This might be easier to see if you imagine the "library" as the set of all possible numbers (in binary) up to a certain reasonable maximum. So you specify the book...by giving the binary representation of the book, which is simply its index if you order them by their numerical value. So you can see how having all books in your library is the same as having no books.
- edanm 16y agoThis reminded me of an awesome short story by Jorge Luis Borges, about a library that contains every possible 410-page book. Read more about it here: http://en.wikipedia.org/wiki/The_Library_of_Babel http://en.wikipedia.org/wiki/The_Library_of_Babel