3 ms·

Not sure if we're on the same page here, but this does not conform to what we know about information theory. First, as someone else mentioned we'd have to hav

by bo1024 14y ago

Not sure if we're on the same page here, but this does not conform to what we know about information theory. First, as someone else mentioned we'd have to have a maximum book length or else your library contains an infinite number of books, which is simply absurd because there would, for instance, be a book that contained all of the finite books inside it, in alphabetical order. Second, using your compression technique, we'd still need to have some numbering on the volumes, and to describe a book, we'd have to do so by a list of numbers describing which volumes comprise it and in what order. Third, this makes clear what is happening in your reductio ad absurdum argument -- we can reduce the volumes down to one dash, one dot; but then each book needs to contain a listing in order of which "volume" is in which order. So we're just writing the boks in binary again.

carstimon 14y ago
or else your library contains an infinite number of books, which is simply absurd because there would, for instance, be a book that contained all of the finite books inside it, in alphabetical order. Careful, that doesn't follow. The library could contain all finite books, but no infinite book.
- bo1024 14y ago
  Absolutely correct. That was really sloppy of me.
tripzilch 14y ago
> Second, using your compression technique, we'd still need to have some numbering on the volumes, and to describe a book, we'd have to do so by a list of numbers describing which volumes comprise it and in what order. Yes, for a normal library this would be the case. But this library contains every possible book. So the index list you're asking for, describing which volumes comprise what book in what order, is the complete list of all possible orderings of volumes up to the maximum book length. You don't really need that list, because you know exactly what it looks like. But then, you don't really need the volumes either, because you know what they look like too (being all combinations of N bits). So yeah, you'd just need a 0 and a 1. I already got a copy of that library, and the cool thing is that it doubles as a light switch.
- bo1024 14y ago
  There seems to be some assumption here that books are named by their ordering of volumes. But I might know the name of a book and not its contents, so I'd need to look up the contents. (Of course, this is silly if you have every possible book, because any other naming scheme means most names will be longer than the books themselves....)

by bo1024 14y ago

carstimon 14y ago

or else your library contains an infinite number of books, which is simply absurd because there would, for instance, be a book that contained all of the finite books inside it, in alphabetical order. Careful, that doesn't follow. The library could contain all finite books, but no infinite book.

bo1024 14y ago
Absolutely correct. That was really sloppy of me.

tripzilch 14y ago

> Second, using your compression technique, we'd still need to have some numbering on the volumes, and to describe a book, we'd have to do so by a list of numbers describing which volumes comprise it and in what order. Yes, for a normal library this would be the case. But this library contains every possible book. So the index list you're asking for, describing which volumes comprise what book in what order, is the complete list of all possible orderings of volumes up to the maximum book length. You don't really need that list, because you know exactly what it looks like. But then, you don't really need the volumes either, because you know what they look like too (being all combinations of N bits). So yeah, you'd just need a 0 and a 1. I already got a copy of that library, and the cool thing is that it doubles as a light switch.

bo1024 14y ago
There seems to be some assumption here that books are named by their ordering of volumes. But I might know the name of a book and not its contents, so I'd need to look up the contents. (Of course, this is silly if you have every possible book, because any other naming scheme means most names will be longer than the books themselves....)