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.
"Universal Library" by Willard van Orman Quine
ReplyDeleteThere 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.
ReplyDeleteOther 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.
ReplyDeleteIf 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.