The Unimaginable Mathematics of Borges' Library of Babel Read Online Free

Time thy pyramids. This much is known: For every rational line
or forthright statement there are leagues of senseless cacophony, verbal
nonsense, and incoherency. (I know of one semibarbarous zone whose librarians
repudiate the "vain and superstitious habit" of trying to find sense
in books, equating such a quest with attempting to find meaning in dreams or in
the chaotic lines of the palm of one's hand. . .. They will acknowledge that
the inventors of writing imitated the twenty-five natural symbols, but contend
that that adoption was fortuitous, coincidental, and that books in themselves
have no meaning. That argument, as we shall see, is not entirely fallacious.)
    For many
years it was believed that those impenetrable books were in ancient or
far-distant languages. It is true that the most ancient peoples, the first
librarians, employed a language quite different from the one we speak today; it
is true that a few miles to the right, our language devolves into dialect and
that ninety floors above, it becomes incomprehensible. All of that, I repeat,
is true—but four hundred ten pages of unvarying M C V's cannot belong to any
language, however dialectal or primitive it may be. Some have suggested that
each letter influences the next, and that the value of M C V on page 71, line
3, is not the value of the same series on another line of another page, but
that vague thesis has not met with any great acceptance. Others have mentioned
the possibility of codes; that conjecture has been universally accepted, though
not in the sense in which its originators formulated it.
    Some five
hundred years ago, the chief of one of the upper hexagons 2 came across a book as jumbled as all the
others, but containing almost two pages of homogeneous lines. He showed his
find to a traveling decipherer, who told him that the lines were written in
Portuguese; others said it was Yiddish. Within the century experts had
determined what the language actually was: a Samoyed-Lithuanian dialect of
Guarani, with inflections from classical Arabic. The content was also
determined: the rudiments of combinatory analysis, illustrated with examples of
endlessly repeating variations. Those examples allowed a librarian of genius to
discover the fundamental law of the Library. This philosopher observed that all
books, however different from one another they might be, consist of identical
elements: the space, the period, the comma, and the twenty-two letters of the
alphabet. He also posited a fact which all travelers have since confirmed: In all the Library, there are no two identical books. From those
incontrovertible premises, the librarian deduced that the Library is
"total"—perfect, complete, and whole—and that its bookshelves contain
all possible combinations of the twenty-two orthographic symbols (a number
which, though unimaginably vast, is not infinite)—that is, all that is able to
be expressed, in every language. All —the detailed history of the future,
the autobiographies of the archangels, the faithful catalog of the Library,
thousands and thousands of false catalogs, the proof of the falsity of those
false catalogs, a proof of the falsity of the true catalog, the gnostic
gospel of Basilides, the commentary upon that gospel, the commentary on the commentary
on that gospel, the true story of your death, the translation of every book
into every language, the interpolations of every book into all books, the
treatise Bede could have written (but did not) on the mythology of the Saxon
people, the lost books of Tacitus.
    When it was
announced that the Library contained all books, the first reaction was
unbounded joy. All men felt themselves the possessors of an intact and secret
treasure. There was no personal problem, no world problem, whose eloquent
solution did not exist—somewhere in some hexagon. The universe was justified;
the universe suddenly became congruent with the unlimited width and breadth of
humankind's hope. At that period there was much