Universal Library
Willard van Orman Quine
from Quiddities: An Intermittently Philosophical Dictionary (1987)
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. 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
or other.
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 work with.
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.