The Infinite Library
"The Library of Babel" depicts an infinite library with a finite amount of books repeated an infinite amount of times. My biggest question is where you would find such a library. Where on earth could you possibly host an infinitely large library? The story mentions people from the outside world coming to search the library, so the library can't entail the whole earth. Also, why would you need an infinitely large library if the number of books is finite, just to have a repeating cycle of books?
The one thing that I thought was cool to think about was how destroying one book wouldn't really be destroying anything, since there are 24 books where only one character in the whole thing is changed, and 576 books where only two characters are changed, and 24^n books where n characters are changed. It really is mind boggling to just consider the intensity of the number of possible combinations of letters you could find in these books; but at the same time, we do have to remember that it is a finite number.
The one thing that I thought was cool to think about was how destroying one book wouldn't really be destroying anything, since there are 24 books where only one character in the whole thing is changed, and 576 books where only two characters are changed, and 24^n books where n characters are changed. It really is mind boggling to just consider the intensity of the number of possible combinations of letters you could find in these books; but at the same time, we do have to remember that it is a finite number.
I would say that you are correct in that such a library could not exist physically on Earth. If the volume of a book is roughly 21.6 cm x 28 cm x 4 cm = roughly 2400 cubic centimeters, and the volume of the observable universe is roughly 3.58e86 cubic centimeters, we need 1.5e83 books. Your math is slightly wrong because you only take into account one specific character that can be changed, but there are 1,312,000 characters in each book. Thus the number of single character variants is 24*1,312,000. The number of two character variants is even larger. It turns out that this gets large very very quickly, fast enough to fill the observable universe with books after just a dozen character changes ((1,312,000*24)^12 = 9.5e89 books). So the library of Babel cannot physically exist. Period.
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