It was for this reason that Harsdörfer (in his Matematische und philosophische Erquickstunden, 1651) planned to display on five wheels 264 elements (prefixes, suffixes, letters, and syllables), generating through their various combinations 97,209,600 German words, including nonexistent ones. Clavius (In Spheram Ioannis de Sacro Bosco, 1607) calculated how many terms could be produced with the twenty-three letters of the alphabet, combining them in twos, then threes and so on, right down to considering words with twenty-three letters. Pierre Guldin (Problema Arithmeticum de Rerum Combinationibus, 1622), by calculating all the terms of variable length that an alphabet could generate, from two to twenty-three letters, reached the figure of seventy thousand billion billion words—to record these on registers of a thousand pages, with one hundred lines per page and sixty characters per line, would have required 8,052,122,350 libraries, each one measuring 432 feet per side. Mersenne (Harmonie universelle, 1636), taking into account not only words but also “chants” (that is to say, musical sequences), noted that the chants that can be generated by twenty-two notes number around twelve billion billion (so that if one wanted to write down all of them, at a thousand a day it would take almost twenty-three million years).
It is to mock these very combinatorial dreams that Swift put forward his antilibrary, or, rather, a perfect, scientific, universal language in which there would no longer be any need for books, words, or alphabetical symbols:
We next went to the School of Languages, where three Professors sat in Consultation upon improving that of their own country.
The first project was to shorten Discourse by cutting Polysyllables into one, and leaving out Verbs and Participles; because in Reality all things imaginable are but Nouns.
The other, was a Scheme for entirely abolishing all Words whatsoever: And this was urged as a great Advantage in Point of Health as well as Brevity. For, it is plain, that every word we speak is in some Degree a Diminution of our Lungs by Corrosion; and consequently contributes to the shortning of our Lives. An Expedient was therefore offered, that since Words are only Names for Things, it would be more convenient for all Men to carry about them, such Things as were necessary to express the particular Business they are to discourse on. And this Invention would certainly have taken place, to the great Ease as well as Health of the Subject, if the Women in Conjunction with the Vulgar and Illiterate had not threatened to raise a Rebellion, unless they might be allowed the Liberty to speak with their Tongues, after the Manner of their Forefathers: Such constant irreconcilable Enemies to Science are the common People. However, many of the most Learned and Wise adhere to the new Scheme of expressing themselves by Things; which hath only this Inconvenience attending it; that if a Man’s Business be very great, and of various Kinds, he must be obliged in Proportion to carry a greater Bundle of Things upon his Back, unless he can afford one or two strong Servants to attend him. I have often beheld two of these Sages almost sinking under the weight of their Packs, like Pedlars among us, who when they met in the Streets, would lay down their Loads, open their Sacks, and hold Conversation for an Hour together; then put up their Implements, help each other to resume their Burthens, and take their Leave. (Gulliver’s Travels, III.5)
Notice, however, how even Swift could not avoid producing something very close to the Library of Babel. For in order to name everything in the universe men would need a dictionary made up entirely of things, and the size of this dictionary would match the extent of the entire cosmos. Once more there would be no difference between Library and universe. In Swifts project we would be in the library, or rather, part of the library itself, and we would not be able to come out of it, nor could we even speak of it since, just as in the Library of Babel one can only be in one hexagon at a time, in the world we live in we could speak only of what is around us depending on the place we are in, pointing with our finger at what surrounds us.
But let us imagine for the sake of argument that Swift’s vision had triumphed and men did not speak anymore. Even in this case, as Borges warned us, the library would contain the autobiographies of angels and a detailed history of the future. And it was this particular Borgesian allusion that inspired Thomas Pavel, in his book Fictional Worlds,* to invite us to take part in a fascinating mental experiment. Let us imagine that an omniscient being is capable of writing or reading a Magnum Opus containing all the true statements regarding both the real world and all possible worlds. Naturally, since one can speak of the universe in different languages, and each language defines it in a different way, there must exist a set of all Magna Opera. Now let us suppose that God entrusts some angels to write Daily Books for each man, where they record all the statements (regarding the possible worlds of his desires and hopes and the real world of his actions) that correspond to a true statement in one of the books that make up the set of all Magna Opera. The Daily Book of each individual must be displayed on the Day of Judgment, along with the collection of those Books that evaluate the lives of families, tribes, and nations.
But the angel writing a Daily Book not only writes down true statements: he links them together, evaluates them, constructs them into a system. And since individuals and groups alike will have defending angels on the Day of Judgment, these defenders will rewrite for each of them another, endless series of Daily Books, where the same statements will be connected in a different way, and compared differently with the statements in one of the Magna Opera.
Since infinite alternative worlds are part of every one of the infinite Magna Opera, the angels will write countless Daily Books, in which there will be a jumble of statements that are true in one world but false in another. If we then imagine that some angels are not very skillful, and they mix up statements that a single Magnum Opus records as mutually contradictory, we will end up with a series of Compendia, Miscellanies, and compendia of fragments of miscellanies, which will amalgamate different layers of books of different origin, and at that point it will be very difficult to say which books are true and which are fictitious, and in relation to which original book. We will have an astronomical infinity of books, each of which hovers between different worlds, and the result will be that we regard as fictitious stories that others have considered true.
Pavel writes these things to make us understand that we are already living in such a universe, except that instead of being written by archangels, these books are written by us, from
Homer to Borges; and he implies that the bastard ontology of fiction is not an exception compared with the “pure” ontology of those books that speak about the real world. He suggests that the legend he retells depicts quite well our situation as regards the universe of statements we regularly regard as “true.” The result is that the vertigo we feel when we notice the ambiguous borders between fiction and reality is not only the same as that which seizes us when faced with the books written by angels but also the same as that which ought to seize us when faced with the series of books that, with authority, represent the real world.
The idea of the Library of Babel has now linked up with the equally vertiginous idea of the plurality of Possible Worlds, and Borges’s imagination has inspired in particular the formal calculus of modal logicians. Not only that, but the Library described by Pavel, which naturally is also made up of works by Borges, including his story about the Library, seems curiously to resemble Don Quixote’s library, which was a library of impossible stories that took place in possible worlds, where the reader lost his sense of the borders between fiction and reality.
There is another story invented by an artist that has also influenced the imagination of scientists—maybe not logicians, but certainly physicists and cosmologists—and that is
Finnegans Wake by Joyce. Joyce did not dream up a possible library: he simply put into practice what Borges would later suggest. He used the twenty-six alphabetical symbols of English to produce a forest of nonexistent words with multiple meanings, he certainly put forward his book as a model of the universe, and he definitely intended that the reading of it should be endless and recurrent, so much so that he wished for “an ideal reader affected by an ideal insomnia.”
Why do I mention Joyce? Perhaps and above all because, along with Borges, he is one of the two contemporary writers I have most loved and who have most influenced me. But also because we have now come to the point where we should ask ourselves about the parallels and differences between these two
