Pantography

Pantography tweets a message every hour. 1 Each one is consecutive: the first was ‘0’ and the last will consist of 140 zeds. Between these two extremes, every possible message will have been tweeted: a description of every feeling you’ve ever had, anything you’ve ever overheard or will overhear, any headline that has ever caught, or could ever catch, your eye, everything you—and everyone else—has ever thought, or could ever think. (As long as you, and everyone else, thinks in spurts of no more than 140 characters, consisting of 26 Roman letters, ten Arabic numerals and a handful of punctuation marks.)

That’s the good news. Come that final message heralding the sleep of tweeting, everything will have been said and we can get on with our lives; uncommentated, untagged, unlinked—a life lived with both hands.

The bad news is that it will take some time. 2.97 ²³⁷ years.

The idea of a Universal Library is best known from Jorge Luis Borges’ famous short story, The Library of Babel. Some years before writing this story, Borges had written an essay called The Total Library in which he traces the germ of the idea of a library that contains all possible texts as far back as the atomists Democritus and Leucippus, by way of Aristotle, and several  mediaeval writers. But it was in the early 20th Century, he says, that the idea was given full form, first by Gustav Theodor Fechner and later, in the form of a fictional dialogue between a “professor” and a magazine editor, by Kurd Laßwitz. Borges remarks that it is a wonder how long it took anyone to come up with the idea.

Outside Borges, Montaigne, in Of Vain Cunning Devices, mentions a reference of Plutarch’s to a calculation of the size of such a library and Tristram Shandy looks forward to the end of any more possible texts. Faced with the alphabet, and the daily drudge of blackening paper with its letters, few writers could have failed to notice that they were working with a finite resource, a fixed number of permutations of the same letters.

Although the alphabet itself consists of a pre-determined number of letters, the length of a text is as long as the proverbial piece of string. The idea of the Universal Library, of a finite number of permutations is thus open-ended. Each book in Borges’ library of Babel, we are told, “contains four hundred ten pages; each page, forty lines; each line, approximately eighty black letters.” That’s 1,280,000 characters in each book. Laßwitz is slightly more economical. “I should think  that one can exhaust a theme pretty well with five hundred book pages,” his editor says authoritatively. “Let’s say that there are forty lines per page and fifty characters per line, we’ll have forty times fifty times five hundred characters per volume.” The professor quickly does the math: one million characters.

Laßwitz’s world-weary editor may think that a theme should be pretty well exhausted in five hundred pages, and if not the theme, then perhaps the reader. But would he truncate Ulysses? (264,861 words.) Would he cut Burton’s Anatomy of Melancholy? Now, you may say that whatever is truncated from one volume will be found in another—but that fragment would be in a different context, and form a different book. More seriously, there are millions upon millions of shorter books that, in these libraries, would have no place since they would all be transformed by an unfamiliar coda in order to make up the required length.

Both Borges’ 1,280,000 and Laßwitz’s 1,000,000 characters are arbitrary lengths, just the number of letters that an “average”-sized book contains. Whatever we decide that size to be, we can always think of larger, and smaller volumes, briefer or more prolix in their contents.

A surprising new direction emerged around the turn of the 21st Century. We discovered that a theme can be exhausted pretty well in 140 characters. Romance flickered, revolutions erupted, lives were saved, riots organised, opinions shared, events documented, rendezvous planned, mothers reassured, voters coaxed, customers mollified—all in 140 characters or less. God knows what we used to say in the remaining 999,860. In 2010 alone, 6.1 trillion SMS messages and 25 billion tweets were sent.

The brevity enforced by these media gives the project of a Universal Library fixed parameters. The length of each text is no longer arbitrary. It is the length within which we know we can say everything we need to say.

The most famous image of an automatically-generated text is certainly that of Émile Borel’s Infinite Monkey Theorem, in which a monkey bashes randomly at a typewriter’s keys. Assuming that this monkey is left to do its work indefinitely, and that it does not develop human-like contrariness, it will eventually produce every possible book. 2

But this would be a very wasteful way of going about things. Not particularly because the monkey will produce reams of gibberish—but because it will almost certainly repeat itself many millions of times. What we need is a methodical, exhaustive, monkey: infinity, and randomness, is precisely what we are trying to avoid. Our aim is to reduce the production of all texts to a finite task, and there is one simple way to achieve this: by producing each text incrementally.

The algorithm used to generate each new pantograph 3 is straightforward. We are treating the fifty-four letters of our alphabet (including alphabetic and numerical characters, punctuation marks and a space) as if they were numerals in a number system to base 54.

Our “alphabet” consists of:

0123456789.,;:_@!?/#()%'-+= abcdefghijklmnopqrstuvwxyz

So our first message is “0”, the next one is “1”, and so on. Our fifty-fourth message is “z”. Now, our fifty-fifth message is “00”, our fifty-sixth “01” and so on until “0z”. The next one is “10”. By these increments, we will produce 54 ¹⁴⁰ messages, right up to our final one consisting of 140 zeds.

We make two exceptions to our treatment of our letters as if they were numbers in a numerical system. Although the space is treated as one such numeral, it is not allowed to lead or trail a message, nor do we allow two or more spaces to appear consecutively since multiple spaces have no symbolic value over single ones.

There is also no concept of a “true” zero in our numerical system. Although the character “0” does appear, as the first character, in our alphabet, it has no special mathematical properties.

Determining which letters are to be included in Pantography’s “alphabet” is crucial. We need an alphabet that can express every possible - effable - thought. Each orthographic symbol adds millennia to our task. Each letter we add increases the number of texts that need to be generated by a factor of x.

It is important, therefore, to use only the characters that are strictly necessary for all our messages to be rendered completely.

But the above statement would suggest that there is a body of pre-existing utterances out there, existing objectively, waiting for us to express them. But this is whimsical. It is far more plausible to extrapolate forwards and say, The alphabet will produce every utterance that is contained within it.

4

A certain amount of arbitrariness has to be embraced here. Every mark is a distinction. Whether it is acceptable to assume that capital letters offer no indispensable nuance is, really, up to us. Laßwitz’s “professor,” despite playing the role of the hard man of science, decides that such a loss of colour would be unacceptable: "[...] let’s just stick to the upper- and lower-case letters of the Latin alphabet,” he says, “the customary punctuation marks and the space that keeps the words apart.” That inflates his library by a cool 26 ^1,000,000.

Despite the far more mystical tone of Borges’ story, and the tomes he reports in his library, his alphabet is far more economical. “The original manuscript has neither numbers nor capital letters; punctuation is limited to the comma and the period. Those two marks, the space, and the twenty-two letters of the alphabet are the twenty-five sufficient symbols.” Here Borges has dispensed with the x, the q and the w, as he predicts in The Total Library.

Since we are dealing with a particular medium, Twitter, we can more manageably predict which symbols our alphabet requires. Upper-case letters, though frequently used, are hardly indispensable in this medium, and we sometimes tend to enter into that mode of utterance, somewhere between speech and writing, as in the medium’s grandfather, the SMS message. Conversely, punctuation marks are even more prominent than in other media, and we will here use every mark required to form a sentence, assemble a url, refer to another user and indicate a tag.

Faced with the enormity of the task of assembling the Universal Library, it is tempting to look for ways to economise on the alphabet employed. Dispensing with capital letters, punctuation marks, low-prestige letters such as the J or the W—all these stratagems can make the task lighter. Borges says, “the alphabet could relinquish the q (which is superfluous), the x (which is an abbreviation), and all the capital letters”. By using similar economies, George Gamow in One, Two, Three... Infinity, manages to reduce his alphabet to twenty-five letters.

Theodore Pavlopoulos goes further. He suggests using an alphabet of 100 language-independent characters so that each character can be substituted for any letter in a given language. “&@#$*$ could be thought of as representing the words ABUSES, IMPEDE, SCORER etc. for an English language reader, the words ΣΟΒΑΡΑ, ΘΡΑΣΟΣ, ΕΙΡΗΝΗ etc. for a Greek language reader, and the words СОБАКА, ЯБЛОКО, ГИТАРА etc. for a Russian language reader.” Unlike the stratagem of dropping an x here and a q there, the benefit is far from negligible, “The size ratio between the thus resulting library and the Universal Library is much smaller than the one between an atom and the whole universe.”

WV Quine goes further still. 5 He first suggests using Morse Code while retaining the length of 500,000 characters. Then he cuts down the number of characters, arbitrarily, to seventeen, while retaining Morse Code. Then he delivers his final economy: “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.”  6

Quine is led to his “ultimate absurdity” by the observation that “a diminution in the coverage of each single volume does not affect the cosmic completeness of the collection”. When he substitutes letters for Morse he says the thought content is reduced—since Morse is more long-winded—but the library is still complete 7. After all, every conceivable string is still being written out using his chosen alphabet. Then, when he decides to cut down on the length of each string—after all, every string is continued in many, if not all, others—he realises that “a diminution in the coverage of each single volume does not affect the cosmic completeness of the collection”. Next thing you know, he is using binary notation, and trusting that the reader will combine the two symbols to write out any conceivable message.

Something has obviously gone wrong here; though it is not immediately obvious quite what. At first, Quine’s humorous essay may seem to be satirising the idea behind The Total Library (if, indeed, such a preposterous idea can be satirised) but it equally makes a mockery of any attempt to make the task manageable. His proposal is the equivalent of moving all the elements of an equation to the left side, putting a zero on the right—from a + b = c to (a+b)—c = 0—and then claiming to have solved the equation. 8

Morse itself, like electronic text, is an abstraction of an abstraction. We use dots and dashes, or zeroes and ones, to stand in for letters which, in turn, when grouped together, stand for things in the world. Now there is no reason why Morse code itself could not constitute an orthography for a  natural language. It is not impossible to imagine someone who has so internalised the musical stream of dots and dashes that they would not need to transliterate messages into the alphabet of their language before understanding them and responding. One suspects that this must have happened in the case of very experienced Morse operators.

It’s a question of granularity, of resolution. The alphabet allows us to make a given number of statements, at a particular level of detail, in a given amount of length, or time. When we take a digital photograph, we are aware that we are using a certain number of pixels. We can always choose to use a smaller file size, using fewer pixels, but it would have less detail. If it has too few, then it is useless, it fails to reproduce what we see to an acceptable level. We can also choose to use more pixels, and render more detail. If we choose too many pixels then we are gathering redundant information. The upper limit is, of course, the resolution of our own eyes. Sub specie aeternitatis, the upper limit would probably be far closer to atomic density, or even something like Leibniz’s monad 9, but in order to reproduce our visual experience, to represent what, to all intents and purposes, the world is to us, we need go no further. 10

The resolution of our retinas seems to be a far harder barrier than the granularity offered to us by the alphabets of our natural languages. It is a physical barrier. But our alphabets, trimmed and augmented over centuries, offer us a hint of a human scale of the granularity of our experiences. There is great variety, of course, between the number of letters in the various alphabets, but with a certain number of shims and hoists, it represents the variety of sounds we make when we speak. 11 It is a closed system that expresses human experience at a particular level of granularity, at a particular scale.

Many attempts at making the project of the Total library more manageable seek to make the texts themselves shorter. Gamow does it, and so does Quine. After all, the argument goes, a text can always be continued in another one. There would also be many texts that explicitly say this, of course, providing convenient markers at the beginning and end of the texts. A text (in reality, millions upon millions of texts) would end with “continued on text 11172”. And sure enough, there would be many texts that would announce themselves to be Text 11172.

Perhaps because the image of a library served as the prime metaphor, Borges and Laßwitz’s texts were book-length. A book is a text of a length we have culturally settled upon, a length in which we can explore a subject at substantial but not overwhelming detail. The book itself is made of smaller components: chapters, sections, paragraphs, sentences, words and, ultimately, letters. We are well aware that the larger parts are made of the smaller but what constitutes a book is that it is made up of those particular parts, and of a given number of them. If we decide to cut up a book into chapters, or a paragraph into sentences then it is no longer a book, no longer a single, coherent exposition on a given subject.

The Total Library is a closed system that plays out every given permutation of a text of a given length, using a given set of characters. It is not the playing out of all human thought. The fact that we take our books to contain human thought, to be human thought itself, is another matter.

Pantography exploits the fortuitous circumstance of the 140-character message. We know the things we can say, we know the kind of human experience these messages express. In the fullness of time, of course, these messages could be joined up to form larger works. Indeed, the messages will themselves suggest ways in which they can be joined into larger texts. But that is no different than joining sentences to form paragraphs. It is the joining up that constitutes the text, and that is the work we expect Pantography to do for us. Pantography, and all other similar projects, and in reality, any single text, are not about the potential locked inside language, not about mental projection, but about the literalness, the writing out. 12

The Fallacy of Noise

The realisation that such a project would contain all possible texts quickly floods the imagination with the sheer exhaustiveness of all the texts that woud be revealed. Of his Total Library, for instance, Borges says:

{insert: /citations/88}

Pantography, producing shorter texts, will produce all possible one-liners and bon-mots, maxims, epigrams, apothegms, all possible newspaper headlines, curt obscenities, elaborate blasphemies, as well as many millions of libelous pronouncements.

It would also contain millions upon millions of such fantastic lists; and each one of them would be realised elsewhere in the collection.

Now, of course, all these literary nuggets would be hidden in amongst millions of other texts. As Borges puts it,

[...] but for every sensible line or accurate fact there would be millions of meaningless cacophonies, verbal farragoes, and babblings. Everything: but all the generations of mankind could pass before the dizzying shelves—shelves that obliterate the day and on which chaos lies—ever reward them with a tolerable page.  13

But to say that these texts would be meaningless is to completely ignore what Pantography is doing in its inexorable generation of one text after the other.

Firstly, on a somewhat banal level, Pantography’s internally exhaustive nature means that any phrase is defined elsewhere in the corpus so that there is always a chain of definition, or correspondence between any given text and contemporary understanding.

But more important, Pantography obliterates the distinction between meaning and meaninglessness. Claude E. Shannon defined information as a message with a lower probability than surrounding messages. Each phrase has an equal probability of appearing—i.e. 1. 14 When no phrase has a higher probability of being generated than any other, the distinction between signal and noise collapses.  15 The entire body of texts has a completely flat frequency graph 16 This is what the heat death of language looks like.

{insert: /citations/86}

When Pantography has produced all its texts, would we be able to say that each text exists? What do we mean when we say that a text exists? Obviously all the material, and the letters existed before. How much work 17 would we we need to put in to gain access to the particular sequence of letters that make up the text? The closer to zero this measure is, the more the text can be said to exist. Is it just a case of opening a book, or a pdf file, or do we need to pluck it from among the entropic miasma of letters. Do we need to infer it from the writer’s notes? Pantography will generate every tweet but once we have the entire body of tweets, we would still have to go back and discover the ones that mean anything to us. This process would require as much work from us as if we were writing them from scratch. In fact, it would be indistinguishable from writing them from scratch. Having all of them is exactly the same as having none of them.