There is a melancholy fantasy, propounded a century and more ago by the
psychologist Theodor Fechner and taken up by Kurt Lassiwitz, Theodor Wolff,
Jorge Luis Borges,
George Gamow, and Willy Ley, of a complete library. The
library is strictly complete, boasting as it does all possible books within
certain rather reasonable limits. It admits no books in alien alphabets,
nor any beyond the reasonable length say of the one you are now reading,
but within those restrictions it boasts all possible books. There are
books in all languages, transliterated where necessary. There are coherent
books and incoherent, predominantly the latter. The principle of accession
is simple, if uneconomical: every combinatorially possible sequence of
letters, punctuation, and spaces, up to the prescribed book length,
uniformly bound in half calf.
Other writers have sufficiently belabored the numbing combinatorial
statistics. At 2,000 characters to the page we get 500,000 to the 250-page
volume, so with say eighty capitals and smalls and other marks to choose
from we arrive at the 500,000th power of eighty as the number of books in
the library. I gather that there is not room in the present phase of our
expanding universe, on present estimates, for more than a negligible
fraction of the collection [Though a virtual version
fits on my desk
--Al]. Numbers are cheap.
It is interesting, still, that the collection is finite. The entire and
ultimate truth about everything is printed in full in that library, after
all, insofar as it can be put in words at all. The limited size of each
volume is no restriction, for there is always another volume that takes up
the tale -- any tale, true or false -- where any other volume leaves off.
In seeking the truth we have no way of knowing which volume to pick up nor
which to follow it with, but it is all right there.
We could narrow down the choice by weeding out the gibberish, which makes
up the bulk of the library. We could insist on English, and we could
program a computer with English syntax and lexicon to do the scanning and
discarding. The residue would be an infinitesimal fraction of the
original, but still hyperastronomic.
There is an easier and cheaper way of cutting down. Some of us first
learned from Samuel Finley Breese Morse what others of more mathematical
bent knew before this time: that a font of two characters, dot and dash,
can do all the work of our font of eighty. Morse actually used three
characters, namely dot, dash and space; but two will suffice. We could use
two dots for the space and then admit no initial or consecutive dots in
encoding any of the other old characters.
If we retain the old format and page count for our volumes, this move
reduces the size of the library's collection to the 500,000th power of two.
It is still a big number. Written out it would fill a hundred pages in
standard digits, or two volumes in dots and dashes. The volumes are
skimpier in thought content than before, taken one by one, because our new
Morse is more than six times as long-winded as our old eighty-character
font of type; but there is no loss in content over all, since for each
cliff-hanging volume there is still every conceivable sequel on some shelf
This last reflection -- that a diminution in the coverage of each single
volume does not affect the cosmic completeness of the collection -- points
the way to the ultimate economy: a cutback in the size of the volumes.
Instead of admitting 500,000 occurrences of characters to each volume, we
might settle for say seventeen. We have no longer to do with volumes, but
with two-inch strips of text, and no call for half-calf bindings. In our
two-character code the number of strips is 2^17, or 131,072. The totality
of truth is now reduced to a manageable compass. Getting a substantial
account of anything will require extensive concatenation of out two-inch
strips, and re-use of strips here and there. But we have everything to
The ultimate absurdity is now staring us in the face: a universal library
of two volumes, one containing a single dot and the other a dash.
Persistent repetition and alternation of the two is sufficient, we well
know, for spelling out any and every truth. The miracle of the finite but
universal library is a mere inflation of the miracle of binary notation:
everything worth saying, and everything else as well, can be said with two
characters. It is a letdown befitting the Wizard of Oz, but it has been a
boon to computers.
[Of course, by trimming down the books this much, it has become impossible
to discover new things -- you have to put the symbols together so that
they mean something. There is no longer, somewhere on the shelves, the
answers to your questions just waiting to be discovered and read. You
have to come up with your own answers, and the only things in this library
are the things that you bring into it. This, of course, may be the point
that Borges had in mind all along. --Al]