[E]ach book is made up of four hundred and ten pages; each page, of forty lines; each line, of some eighty black letters—this last is plainly impossible, since the symbol set of the Library consists of twenty-two letters, the period, the comma, and the space. (We will ignore incompleteness deriving solely from symbol set incompatibility as too trivial to take notice of.) Suffice it then to say that each line consists of eighty characters, and those lines that seem to terminate with fewer are in fact padded with spaces. Thus each book consists of 1,312,000 symbols (call this number s), in some order or another, and there are 25**s=a big honkin' number (1,834,098 digits!) different books. (There are also titles on the spines, but no further information is given than that they exist.)
Now it is not exactly said that all works are to be found in the library, though it is said that
the Library is total and that its shelves contain all the possible combinations of the twenty-odd orthographic symbols … that is, everything which can be expressed, in all languages. Everything is there: the minute history of the future, the autobiographies of trhe archangels, the faithful catalogue of the Library, thousands and thousands of false catalogues, a demonstration of the fallacy of these catalogues, the Gnostic gospel of Basilides, the commentary on this gospel, the commentary on the commentary of this gospel, the veridical account of your death, a version of each book in all languages, the interpolations of every book in all books.
There couldn't be all works because there would be no way to distinguish between the Don Quixote of Cervantes and that of Menard (I have always thought that Menard's story is an allegory of reading or reception, and not a delineation of a certain kind of conceptual work, but no matter) (except, perhaps, but title, actually, now that I think of it, though the narrator of the story doesn't seem to consider the titles as possible differentiators of books in his discussion later) and we will suppose that these are different works. (Just as a gallery containing all possible arrangements of paint on canvas couldn't distinguish between the visually identical illustrations of Newton's three laws in The Transfiguration of the Commonplace, except, of course, by caption.) We can accomodate texts whose length isn't s quite simply: if they are shorter than s, there will be a book in the library consisting of the text in question, followed by some number of spaces; texts of length t > s are divided into ⌈t/s⌉ volumes, the last of which will be padded with s-(t%s) spaces. With respect to very long works, then, the books of the library form something like an alphabet with extremely cumbersome letters.
But this means two things: first, some books will be part of multiple texts (which, perhaps, cannot therefore be in the library simultaneously), and second, some texts can't be in the library at all. I mean "be in the library" in the following sense: if there is a multivolume set in a library, one ought in some sense to be able to have all the volumes together. Otherwise the set isn't really in the library. Obviously in the Library of Babel it is practically impossible, for most sets, to assemble all the volumes together, because of its unwieldy hugeness (and, of course, because although a catalogue exists—which is presumably itself many many volumes long—it's impossible to tell if you've found the right one). But in most cases of long texts with which we are acquainted (say Gibbon) there will be some set of volumes which make it up to be found somewhere in the library.
Suppose, though, that there is some text that has at least s consecutive characters in common with a different text, starting in the one book at symbol number sn and in the other at symbol sm (these books are zero-indexed, of course). Then it will be impossible to have both sets simultaneously, since, each book occuring only once in the library, there will be only one book corresponding to the intersection. (This becomes much clearer when the number of symbols making up the units of the alphabet is smaller. With a one-symbol alphabet, in which there would only be 25
books, you couldn't simultaneously have
And it gets worse! Just as one couldn't have
baa in the one-symbol case, so too one could not have, in the Library of Babel, a text which had two identical sequences of s (or more) consecutive symbols starting at character positions sn and sm, n ≠ m. Such a text is not inconceivable. One could take as one's model "Franz Kafka in Riga", a story the reading of which is a postrequisite for all those who have read or intend to read "Pierre Menard, Author of Don Quixote" (and indeed, should I be fortunate enough to be the TA for this course, and should this most recently mentioned Borges story remain on the syllabus, I intend to force the Mathews on my students all unwary, and that even though it quite plainly isn't on the syllabus, and even though I myself don't have anything to say about it, but rather merely find it interesting, or perhaps even merely "neat"—anyway, it's short). If the text between "I decided to climb these steps" and "threatened to blow away my" were in each case much, much longer, and the text before the first appearance of the string, and the text between the two, were of precisely the right length, each bit could fall at precisely the right position to occupy the entirety of a Library of Babel volume.