JF Ptak Science Books Post 2538

“Cataloguing is an ancient profession; there are examples of such “ordainers of the universe” (as they were called by the Sumerians) among the oldest vestiges of libraries.” ― Alberto Manguel, *A History of Reading *(and also translator of Borges and co-editor of *A Dictionary of Imaginary Places*, a book worthy of high consideration as the The Book that you could have with you on a desert island.)

- [On the other end of the infinite library, see an earlier post here on "The Library of One Book", here: http://longstreet.typepad.com/thesciencebookstore/2009/10/the-library-of-one-book.html]

In Jorge Borges' "The Library of Babel" (published in 1944 and translated into English in 1962) we find that an infinity, or a universe, or a heaven, is declared to be a sort of endless library, stocked with hexagonally-shaped rooms books filled with books, all the same size, with the same number of characters. The rooms are endless, as are the books, which are written in every conceivable language and containing 29 necessary elements (including the alphabet, and the period, comma, and very interestingly concluding with the space). There are endless varieties of possibilities, and the place is staffed by librarians who have interests and obsessions from, well, A to Z, or A^{z^Z^Z^Z }to Z^{A^A^A} and so on, until we run out of time. (Others have done some smart thinking on Borges' great thought experiment/short story, and have estimated the size of the library in terms of stacked orders of magnitude beyond the atoms of the universe--but you can find all of that stuff elsewhere with a quick google search.)

And then there's this sample fro Borges on what sorts of books make up the library:

*"...*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 true story of your death, the translation of every book into every language . . ."

Here's how you arrange an infinite library: you don't.

The books are not sorted to any sort of classification, only collected to the point that they are together.

The many seem to be written in indefinable languages. Some of the librarians spent their time pursuing the holy grail--since all books that could ever be published would be present here, which theoretically include an index to library, or some sort of organizing principle.

But since there was no verifiable organizing principle at play here, the library was useless as a "library", though for the individual bits, it was perfectly fine. The structure though just turned into a long, endless, shelf. This might explain why the caretaker/librarians of the place are so desperate.

I cannot recall a mention of a card catalog, which I guess could be as all-powerfully impossible as the library, given that the library is not-classifiable. This is particularly true when you consider that there must also be a catalog of the arrangement of all possible false catalogs of all possible false books in the library, in addition to the true catalog. Perhaps the cards from this catalog would take up all of the space in the universe that would bump up against our own.

On the other hand, the logician W.V.O. Quine has written in a short piece that the Borges library is finite, because at some point there will come a time that all that can be written or will be written has been written:

"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."

He reduces this argument elegantly but completely without the humor of Borges, and says that all that is known can be represented in two symbols from which everything else can be derived--a dot, and a dash. He writes:

"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."^{}

"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." [Quine's "Universal Library" is found at Hyperdiscordia, here: http://hyperdiscordia.crywalt.com/universal_library.html]

Quine's approximation cuts way down on the size of the library, which evidently would not fit in the known universe, which opens the gates for Heaven, which I think doesn't depend on such restrictions--unless of course it was too big for that, which means believers would be in trouble, and none too happy with being kicked out of paradise to make space for a book.