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Ex Bibliotheca

February 21st, 2012

On Tumblr, earlier, I saw this:

Here is a site that offers digital renderings of some of the books in the unimaginably vast universe of information (and un-formation) described in Jorge Luis Borges’ story the Library of Babel

Explore, but remember that the possibility of of discovering your Vindication within the Universal Library “can be computed as zero.”

An interesting idea, but given Borges’ kabbalistic leanings, his remark that there is no form of capital lettering, no digits, and his insistence on the twenty-two letters and their fixed, symmetrical forms, it is most likely that he meant for the Library’s volumes to be expressed in the block Hebrew script, which he has admired in other places, though any language might be encyphered in that alphabet in the Library’s vast holdings, such as his “Samoyed-Lithuanian dialect of Guarani, with classical Arabic inflections” (“un dialecto samoyedo-lituano del guaraní, con inflexiones de árabe clásico“) mentioned in the story.

Other possibilities do present themselves, however, for clues suggest the language of the southern hemisphere of Tlön. How so? In “The Library of Babel”, Borges gives us explicit “titles” for three volumes: “trueno peinado“, “el calambre de yeso” and “axaxaxas mlö“. The first could be the “Combed Thunder”, the second “The Plaster Cramp”, but what of the third? If one were to read “Tlön, Uqbar, Orbis Tertius“, from the same 1944 collection (Ficciones [Spanish, English]) in which “The Library of Babel” appeared, one would encounter a passage reading, “Surgió la luna sobre el río se dice hlör u fang axaxaxas mlö“, “‘The moon rose over the river’ would be said hlör u fang axaxaxas mlö.” In the additional text, he indicates all words are verbs in that language, and that “axaxaxas” would mean something resembling “flowing like a river”, while “mlö” would be “shining (or perhaps rising) like the moon”. Translate it however we will, there remains the point that at least one book in the Library is titled by one of the Tlönistas. Or by coincidence would appear to be.

This provides much of a proposed alphabet: in addition to the three titles, Borges also wrote that the combination of letters “dhcmrlchtdj” would appear in the Library and that there is one volume that consists of endlessly repeated “mcv”s. Taken together, sorted alphabetically with duplicate letters removed, this leaves us with 20 or perhaps 21 letters: a, b, c, d, e, h, i, j, l, m, n, o, p, r, s, t, u, v, x, y—and, as he does distinguish it, possibly ö. The alphabet in use on the above linked site adds f, g and q but omits the u needed for “trueno” and doesn’t distinguish the ö from o. If we accept that the line from the story of Tlön is of the same language or alphabet, as at least the title seems to be, then we also see evidence of the f and g in use. If we adapt those, but hesitantly combine the o and ö, we will have another set of twenty-two letters.

It likely doesn’t matter:

Un número n de lenguajes posibles usa el mismo vocabulario; en algunos, el símbolo biblioteca admite la correcta definición ubicuo y perdurable sistema de galerías hexagonales, pero biblioteca es pan o pirámide o cualquier otra cosa, y las siete palabras que la definen tienen otro valor. Tú, que me lees, ¿estás seguro de entender mi lenguaje? (Borges, “La biblioteca de Babel”)

An n number of possible languages use the same vocabulary: in some, the symbol “library” admits the correct definition: “an enduring, ubiquitous system of hexagonal galleries”, but “library” is “bread” or “pyramid” or anything else [in others], and the seven words that define it have other meanings. You who are reading me, are you certain you understand my language?

Many years ago (2003) my fascination with the idea of this library, from Kurd Laßwitz’s much earlier story (“Die Universalbibliothek“, 1904) on through Borges’ (whose 1941 variant of the tale I prefer by far) and similar themes (e.g., Arthur C. Clarke’s “The Nine Billion Names of God“, 1954), etc., had me working out the elaborate mathematics of the whole and being in awe at the staggering numbers. For instance, given that Borges explicitly defined the volumes of the library as containing 410 pages, each page containing 40 rows of text with 80 characters per line (including punctuation and spaces), defined there to be exactly 25 possible characters, and said that the library contained exhaustively everything it is possible to express with them and that no two books were identical, we can calculate that the library must have exactly 25^(80*40*410), or 25 to the 1,312,000th power volumes. To put that in perspective, that is 1.956 x 10^1834097 books, a number 1,834,098 digits long. If you were to write out five digits a second, it would take you more than four days of non-stop writing just to transcribe the whole number.

One of the most enchanting things about the library is, of course, that in its seemingly endless volumes you may find everything that it is possible to write down—including your own life story (your “vindication”), perhaps spanning multiple volumes in elaborate detail, as well as countless millions of erroneous copies whether differing by a single letter or missing entire events or with events that end otherwise than reality’s version, the answer to every mystery or riddle that it’s possible to answer, truly everything. The damning part is that these volumes can be scattered anywhere throughout the universal library and your chance of finding the one you seek is only 1 in 25^1312000, which is so incredibly small it is for all practical senses zero. Should you by luck find one good volume of a multivolume set, you have again those vast odds against your ever finding the next.

Yet perhaps the most damning, or tantalizing, aspect of it all is that you could calculate any or all of these volumes and discern the universal order of the whole by a task no more arduous than counting by ones.

In Tlön, etc., Borges mentioned in passing various numerical bases, touching on the base 12 system (duodecimal) of one of the Tlönistas and the base 60 system (sexagesimal) of ancient Sumeria and Babylon (and in its way even today in our system of minutes and seconds). This is the essential clue. While base 10 (decimal) seems to have conquered all others today, other bases have been in use elsewhere: the now infamous Mayan calendar system, for instance, uses base 20; and in computing, we sometimes use base 16 (hexadecimal), base 8 (octal) or at the lowest possible level base 2 (binary). We can conceive of the Library as being expressed in base 25 (quinquevigesimal) notation, but instead of mixed case, such as with base 16 (where the “digits” are 0 through 9, then A through F, such that the decimal number 190 is expressed as BE in hexadecimal), we can define our 25 digits to be the twenty-five symbols set out by Borges, the twenty-two letters of the alphabet, the comma, the period and the space. Each volume in the library then is merely a number, and the order of their seemingly entropic arrangement is numerical. Which is also suggested in the story when he writes how some have asserted that while the books are written in the “natural symbols” of written language, any appearance of meaning is coincidental, a side effect of using those symbols. To demonstrate, we can see the same thing in hexadecimal, such as above when I pointed out that the number 190 is “BE” which could be interpreted as an English verb; or the number 57,005 is DEAD in hexadecimal, again a “word” in appearance though a number in intent, like the dreadful notion of DECAF, which represents the number 912,559. Treating the volumes as natural numbers also explains the Library’s first axiom, that it exists “ab æterno“, just as the numbers.

An example, to demonstrate. If we take the numerical order of the characters to be that in which Borges gave them in his text—to wit, “the space, the period, the comma, the twenty-two letters of the alphabet”—and set them, in the natural arrangement, as being equal to our base 10 values of 0 through 24, then our first book, corresponding to 0 would be an entirely blank volume. The second, corresponding to 1, would be entirely blank but for a single final period. The next would be the same, but with a comma. Then an “a”, a “b” and so on for the first twenty-five books, one for each symbol. The twenty-sixth would be blank but for the last two symbols which would be a period followed by another space. The sequence would continue, almost forever. In the 9,752nd volume we’d find it blank but for the last letters “mm.”; the next would be “mm,”; the next, “mma” then “mmb” and so on again. At the end of the 19,370,996,558th volume, we would find “abula‘fia”, the name of the 13th century kabbalist renowned for his combinatorial ability. The numbers have grown enormous by the time we even get beyond single sentences. And it continues, letter combining with letter, line with line, page with page, growing and growing, as the early kabbalist text, the Sefer Yetzirah, has it (IV:16, dealing with permutations):

מכאן ואילך צא וחשוב מה שאין הפה יכול לדבר ואין האוזן יכולה לשמוע׃


“From here on go out and calculate that which the mouth cannot speak and the ear cannot hear.”

Unfortunately, even with the fastest computing systems in operation today, our sun would burn out before we could generate a fraction of the library, which is moot anyway since with even the best possible compression available today, the library would require more storage space than currently exists or will exist for likely ages to come, if ever. The most recent figures I’ve seen suggest that as of 2011, the global data storage demands for all digital media of any kind covers “only” about 940 exabytes (for those of you playing along at home, that’s roughly 985,661,440 terabytes), with that number essentially doubling every two years—and with it generally pushing the limits of the amount of storage capacity we actually have available globally. Another way to look at data amounts, if every one of the 6,995,685,817 people of the current estimated world population had a full terabyte of data, the total would be roughly 6.5 zettabytes, a vast number far, far beyond current global capacity (there are 1024 exabytes in a zettabyte). At the expected rate of growth, it should take us almost six years to reach that capacity. Yet a complete digital copy of the Library of Babel, at ideal, maximum compression, would require something to the effect of 4.24562416107 x 10^1,834,075 yottabytes—where a single yottabyte is 1024 zettabytes or 1,125,899,906,842,624 gigabytes! At that projected growth rate, it should take a measly 12 million years for us to reach that capacity.

For a countering thought, Seth Lloyd, in an article (“Computational Capacity of the Universe”) in the science journal Physical Review Letters, in 2002, asserted that the total information capacity of the observable universe is only 10^92: the capacity necessary for the complete Library is over 10^1,834,099. Borges equated the Library with the Universe, yet it seems the Library is greater in scope. By far.

So it seems very possible that while the mind can conceive of the Library, can understand it, can know how to create it, its actual creation is beyond the scope not just of human ability but also beyond the scope of universal capacity, beyond the time scale of our solar system. We have to be satisfied with only knowing that these things “exist” in some abstract sense, our vindication, the answer to every pressing problem, to every question that’s ever passed our mind or anyone’s, every great novel (and every awful one!), even this post I’m writing now, exist, waiting for someone to discover them, yet outside the possibility of truly being able to search or find them in any clear or orderly fashion.

Perhaps we should, after the fashion of the site at the beginning, pick up our own “forbidden dice cup”…

“A blasphemous sect suggested that” [rather than searching for meaningful volumes] “all men should juggle letters and symbols until they constructed, by an improbable gift of chance, these canonical books.” […] “The sect disappeared, but in my childhood I have seen old men who, for long periods of time, would hide in the latrines with some metal discs in a forbidden dice cup and feebly mimic the divine disorder.”

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Daniel Dockery's Portfolio

animî nostrî dêbent interdum âlûcinâri