The universe (which others call the Library) …

Jorge luis Borges

Borges’s famous “Library of Babel” contains every possible 410-page book, 40 lines to the page, 80 characters to the line, 25 characters to choose from. William Goldbloom Bloch has written a fascinating study of its “unimaginable mathematics” in which we are told, among many other things, that it contains 25^1,312,000 books. To put this in perspective (if we can call it that), Goldbloom also informs us that stuffing the known universe with nothing but books would require only 10⁸⁴ books. Perhaps we can put that into further perspective by considering that Queneau’s hundred thousand billion (10¹⁴) poems would fill the pages of 2.4 x 10¹¹ 410-page books. That, at least, is a possible arrangement of some of the 3.28 x 10⁸⁰ particles that our real universe consists of.

Borges’s library, by contrast, is impossibly large. I agree with Goldbloom that it is in some sense “unimaginable” and that the wonder is that it is nonetheless quantifiable. We can put numbers on it but we simply cannot make sense of it. We can’t get our minds around it. While the library contains all the great works of literature that ever have been and ever will be written, it also contains a version of each with every imaginable combination of misprints. There are books with pages and pages of mostly As and others with mostly Bs. Borges tells us that there is no discernable order to the way the books have been arranged, which means that the odds of picking a random book off the shelf that contains the text of, say, Hamlet, are astronomically low. The vast majority of the books in this library will contain nonsense. In that sense, the library, which Borges calls “the universe” is absurd.

In his “intermittently philosophical dictionary,” Quine has proposed a simple way to understand this absurdity, a way to get our minds around its unthinkability, a way to see that Borges’s universe is not, properly speaking, a library at all and that what it contains are not, properly speaking, books. (To anticipate a later post, let’s say that they could not, properly speaking, be written.) He begins by reminding us what we’re dealing with:

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.

Quine (1989), p. 224

The fact that the size of each volume is both arbitrary and unimportant suggests a way of reducing the amount of books. Instead of using every combination of 25 characters we could write all the books in Morse code, i.e., in sequences of dots and dashes. We now have 2^1,312,000 rather than 25^1,312,000 books. This will give us less information per page and therefore less information in each book. But, as Quine reminds us, “since for each cliff-hanging volume there is still every conceivable sequel on some shelf or other,” the library would still contain everything ever written by human hands (along with much, much more nonsense never seen by human eyes). We can go further.

There will be a great many books whose first or last halves are identical. So, if we split all the books in half, and discard all but one of the now identical ones, and then allow ourselves to serialize them when necessary to produce 410-page (and longer) works, no information is lost. And it is just as easy (i.e., it is impossible) to find what you’re looking for in this much smaller library (2^656,000 books.)

Let us press on: the library could of course simply contain all possible pages of 3200 characters of Morse code (there are just 2³²⁰⁰ such possible pages). But we can do better. Remembering Queneau’s sonnets, where each line is printed on a separate slip of paper, we can also imagine a library of all possible lines of 80 characters (only 2⁸⁰ lines), or even, as Quine now suggests, strips of seventeen characters. That gives us a mere 2¹⁷ or 131,072 strips. By combining them any which way we can produce everything that Borges’s library contained. And, still, it will be as easy to produce Hamlet by these random combinations as it would be to find a reasonably legible copy of it in the chaos of the universal library.

Quine now puts a button on the thought experiment:

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 (1989), p. 225

Perhaps you can see where this is going? Perhaps you briefly saw a Library of Tokens flash before your eyes? We’ll get there. For now, I merely want to point out how truly artificial the Library is. It cannot occur in nature. It is what happens when you put no natural constraints on a model and the let the possibilities multiply, if not endlessly, then at least perfectly, imagining the instantiation of every arbitrary combination of already arbitrary signs. It is not a natural language model and its books are not displays of intelligence.

See also: “Robot Writes” and “A Hundred Thousand Billion Bots”

A poem is a machine made of words.

William carlos williams

In 1961, Raymond Queneau, a co-founder of OuLiPo, the “Workshop of Potential Literature”, published a curious book with the perfectly literal title Cent mille milliards de poèms. It consisted of ten fourteen-line sonnets with an important twist. Each page was cut, spine to outer margin under each line. That is, the book was really a booklet of 140 slips that each contained one line of the poem. True to form, Queneau had even ensured that the rhyme sounds at the end of lines were the same, line for line, in each of all ten poems. As the title suggests, the implications were rather astounding. By turning not the pages but the slips different formally correct poems could be produced from each possible combination of lines. Even keeping the lines in the same order, as the spine compels (so that line 5 in one poem could only be replaced with line 5 from another), this implied 10¹⁴ (a hundred million million, or a hundred thousand billion) unique poems. That’s more poems than anyone could ever read, write, or imagine in a lifetime.*

In 1997, a French court ruled that it was illegal to publish the poem online. You can of course find it there anyway, but it’s interesting to read Wikipedia’s account (based on a 2001 article in the French magazine Multitudes.)

In 1997, a court decision outlawed the publication on the Internet of Raymond Queneau‘s Hundred Thousand Billion Poems, an interactive poem or sort of machine to produce poems.^[8] The court decided that the son of Queneau and the Gallimard editions possessed an exclusive and moral right on this poem, thus outlawing any publication of it on the Internet and possibility for the reader to play Queneau’s interactive game of poem construction.^[8]

“Copyright law in France”, Wikipedia

Espen Aarseth (1997, p. 10) has described it as a “sonnet machine”, a key example of what he called “ergodic literature,” from ergon-hodos (work-path), i.e., a text that requires “nontrivial effort” on the part of the reader to follow, a piece of writing that it takes work to read (p. see also Hayot and Wesp, 2004). The reader is faced, not with ten poems that can be read in or out of sequence by flipping the pages of a book in the ordinary way (a “trivial effort”, let’s say), but must actively choose between 10 slips of paper for each line, assembling a poem, and then making sense of the result.

One might argue — as Queneau’s son apparently did (see Vaver and Sirinelli, 2002, pp. 267-8) — that by removing this work of active reading — by having a machine effortlessly assemble a “random” poem from the available lines and presenting it seamlessly — violates the spirit of Queneau’s original work and therefore the moral rights of its original author (in particular, “the right to the integrity of the work”).

Queneau wrote ten poems and came up with a clever gimmick that turned them into a hundred thousand billion potential poems. He is the author of the original poems and the inventor of the gimmick. “A poem is a small (or large) machine made of words,” said William Carlos Williams; this one has ten small machines (in a sense Williams would recognize) that together make one that is larger (than he or any of us can imagine). One big robot to make a hundred thousand billion little bots! Is Queneau the writer of any but the ten original poems that the reader “works” upon, labors for? If not Queneau, who is? Are those poems written at all?

Let’s say we’ve got our work cut out for us!

____________
*In the spirit of OuLiPo we should probably do the math, right? (Queneau’s co-founder was the mathematician François Le Lionnais. See Toscano and Vaccaro 2020 for more.) Let’s say it takes at least five minutes to read and appreciate a sonnet with a even a modicum of seriousness. That means it would take five hundred thousand billion minutes to read “the whole book”. Divide by 60 and we get over eight thousand billion hours. Divide by 24 and we get a little over three hundred and thirty-three billion days. Divide by 365 and we could get it done in almost a billion years.

We live in an age of science and abundance. The care and reverence for books as such, proper to an age when no book was duplicated until someone took the pains to copy it out by hand, is obviously no longer suited to ‘the needs of society’, or to the conservation of learning. The weeder is supremely needed if the Garden of the Muses is to persist as a garden.

EZRA POUND, ABC of Reading

For a couple of years now on Twitter, David Gunkel has been challenging me to “think otherwise” about robot rights. I’m still not exactly sure what (or how) he thinks about robot rights, but, to his credit, my own thinking about the issue has become clearer during the time that I’ve engaged with his work. (Most recently, see his chapter, “The Rights of Robots”.) While the subject of robot rights interests me at a gut level as an amateur philosopher, I’ve come to realize that an important part of it is actually in my professional wheelhouse. This summer, I’ve given myself the project of getting some of my thoughts written down.

We all know that technology has had a profound effect on writing practices. Just in the last thousand years of human history, the transitions from manuscripts to moveable type, from typing to word-processing, from dictionaries to spell checkers, from style guides to grammar checkers, and from spell and grammar checking to autocompletion, have gradually, albeit with increasing intensity, transformed what it means to say that someone has “written” something. The day is already upon us when a properly trained language model like GPT-3 can produce a plausible blog post with very little human guidance. The day when it can be trained to produce a coherent, scholarly prose paragraph that meets my formal definition (if not my personal standards) is probably not far off. Indeed, I’d be surprised if at least one hasn’t already been produced.

This raises the question, “Can a robot be an author?” (I have said it can produce text, and this is undeniable, but can it write?) The question is analogous to questions about the “moral standing” of robots or their “status as persons” and can be made explicitly a “rights” issue by asking, under what circumstances might a machine be given the “moral right to be identified as the author” of a text?

If you or I write a poem, we can assert the moral right to be identified as the author of that poem. Now, a canso, for example, is a relatively simple structure with relatively simple purpose. Over a hundred years ago, writing about the troubadour’s predicament as it stood already eight centuries ago, Ezra Pound put it as follows:

After the compositions of Vidal, Rudel, Ventadour, of Bornelh and Bertrans de Born and Arnaut Daniel, there seemed little chance of doing distinctive work in the ‘canzon de l’amour courtois’. There was no way, or at least there was no man in Provence capable of finding a new way of saying in six closely rhymed strophes that a certain girl, matron or widow was like a certain set of things, and that the troubadour’s virtues were like another set, and that all this was very sorrowful or otherwise, and that there was but one obvious remedy.

Ezra Pound, “Troubadours—Their Sorts and Conditions”

I immediately imagine prompting GPT-3 with “Write six closely rhymed strophes that say that a certain girl, matron or widow is like a certain set of things, and that the troubadour’s virtues are like another set, and that all this is very sorrowful or otherwise, and there is but one obvious remedy.” With a little training (the canso provides a rich tradition of exemplars to be devoured by a “learning machine”), I’m sure GPT-3 could produce a poem equal to one I could produce on an average day (without the intercession of the Muses, let’s say). But who is the author of that poem? Was this poem actually “written”? Can a sufficiently trained language model claim authorship of the poem?

A language model can also be trained to summarize a journal article, or even a whole set of journal articles, and a few years ago Springer published a book about lithium batteries that was written by such a machine. Who (if anyone) is the author of that book? And under what circumstances would we grant an algorithm either (legal) copyright or (moral) standing as an author? Why would we do so? Why might we have to? What would it mean if we did?

These are the questions that I would like to explore over the summer. I’m expecting to learn something as I look into this (I’m already learning about autogressive language models and deep learning from people like Jay Alammar, for example), but I won’t keep you guessing about my views going in. Under no circumstances can a machine be an author. Robots can’t write. Writing is not merely text prediction, and scholarly discourse is not merely a language model. As Borges put it long ago, “a book is more than a verbal structure or series of verbal structures; it is the dialogue it establishes with its reader and the intonation it imposes upon his voice and the changing and durable images it leaves in his memory” (“A Note on (toward) Bernard Shaw”, Labyrinths, p. 213). Properly speaking, there can be no artificial writing because there is no artificial imagination. Imagination precedes artifice.

A paper presents the results of study. Indeed, it often presents the results of a study, i.e., a particular attempt to answer a particular question. This goes for whether you’re a first-year university student who is taking a class and been given a prompt for a midterm paper or a full professor who has completed a five-year research project. Even if the only “study” you are presenting is your attempt to keep up with the required reading for the course, your paper will present what you have learned and, even if you have been struggling with the question for decades, the purpose of your study was to learn something. A paper presents what you have learned through study.

But it does not present this learning in order to teach it to the reader. This is easy for students to understand since they are not expecting their examiners to learn anything from what they have written. They are expecting to be judged according to whether they’ve learned something that their teachers already knew. Even if they have the somewhat healthier attitude that I recommend, namely, that they address their reader as a peer and are imagining the reader as a student in their cohort, they are going to be imagining a reader who has already learned the same things. Scholars, likewise, don’t present their results assuming that their readers (also peers) will simply believe (and ultimately know) what they learned. In all cases, there is something much more important going on between the writer and the reader, something more critical.

A paper exposes the writer’s ideas to the criticism of their peers. The paper tells the reader what motivated the study, how it was framed, what methods were used, what was found, and what the writer thinks the implications of these findings are for theory or practice. At each point, the peer is qualified to tell the writer that they are wrong. The research question may not be interesting. The theory may not be compelling. The methods may not be credible. The results may not be valid (even given the method). And the implications that the writer draws may be unreasonable. By writing the paper, a scholar or student exposes their work to criticism on all these fronts. That’s why it’s so important to choose (to imagine) a reader that deserves some respect.

A peer is someone who studies things that are similar to the things you study and studies them in similar ways. They are motivated by similar questions, focused by similar theories, guided by similar methods, analyze similar objects, and are led to similar implications. Being a peer means that you are like them in these ways; it may even mean that you like them. But you definitely respect their competence to critique your work, their ability to notice things that could have been done better or even shouldn’t have been done in the first place. Your aim in writing the paper is, first and foremost, to let them check your work in this way. If they come away with some new insight into matters that interest them — if they learn something from you that they did not already know — all the better. But it’s their critical eye you’re looking for.

This means that each paragraph must be written to make its central idea as vulnerable as possible to criticism. You are telling your reader something you think is true (ideally, something you actually know) and presenting your best reasons to think so in the clearest possible terms. You do this with a sensitivity for the difficulty the reader will have with your idea. Will a competent peer need help believing, understanding, or agreeing with your claim? They will be critical of the support, elaboration, or defense you provide accordingly. And in each case, you’re simply and honestly explaining how you learned the truth you are putting before them. You are describing the study that came before the paper.

I originally proposed my forty-paragraph outline as a guide for writing what I call “the standard social science paper”. This is the kind of paper that presents the result of an empirical study, framed by a familiar theory, guided by an accepted methodology, with identifiable implications. Many such papers make a “theoretical contribution” too, of course, but some papers, often called “theoretical” or “conceptual” papers, make this contribution by purely theoretical means. I want to write a few posts about variations on the standard research paper this summer, starting with this one, which is perhaps the most common.

Theories, Bourdieu tells us, are “programs of perception”. They condition what researchers see when they look at the world. They are also systems of expectation; they condition what people expect of your object. But in a theoretical paper, there is no specific empirical object. Instead, there is a general class of objects—the kinds of things you are able to see, but have not looked at. Your reader has certain expectations of these objects, is programmed to perceive them in certain ways. You are trying to change those expectations, reprogram them, and you are trying to do so without showing them anything about any particular object. What you are bringing to bear on their expectations is more theory—that is, other expectations, other parts of their program.

Normally, those who hold a particular theory have a kind of knee-jerk version of it in mind. When you mention a social practice, they’ll immediately theorize it in a certain way, and this will reduce the complexity of their image of the object. In an empirical paper, you use your data to push against this simplified image. That’s how you “artfully disappoint your reader’s expectations of the object” as I usually say. But in a purely theoretical paper, you are trying to reconfigure your reader’s expectations by activating other expectations. This may be accomplished by drawing in other theorists that the reader is, if perhaps only vaguely, aware of but does not use in the initial conceptualization of a practice. You here argue that these other theorists should affect our expectations of the object in question, that they should have a stronger influence on us. If your argument holds, the reader’s expectations will change without being confronted with any new empirical data.

Alternatively, you can offer a closer reading of the theory in question. You can show that our expectations of our object have been formed by superficial or careless readings of the major theorist in the field. Since your readers presumably respect the work of this theorist, this may go some way towards changing their expectations.

What I will be offering here is not a normative guideline for what a theory paper should accomplish, of course, nor how exactly to accomplish it. I’ll leave that to the major theorists, especially those who serve as the editors of the journals that publish such papers. Instead, I will propose a way of organizing twenty hours work such that, at the end of it, you have produced the first draft of a 40-paragraph theory paper. This draft can then be edited into shape for publication. In outline, it will look as follows:

1. Introduction (3 paragraphs)
2. Historical Background (5)
3. State of the Art (5)
4. Critical Occasion (5)
5. Conceptual Analysis (3 x 5)
6. Discussion (5)
7. Conclusion (2)

Remember that each paragraph should make a single, easily identifiable claim and either support, elaborate, or defend it. It should consist of at least six sentences and at most 200 words. It should be written in exactly 27 minutes.

The introduction will consist of three paragraphs. The first paragraph will be devoted to a history of your field up to the present. The scope of this history will depend on your judgment. Whether your history starts in ancient Athens, in eighteenth-century England, or in Paris of 1968 depends on the contribution you want to make. The second paragraph will be devoted to the present state of the theory. What is the reigning consensus or standing controversy that defines your field of research? Obviously, this should be the state you want transform in some interesting way, either by settling a dispute or unsettling an agreement.

The third paragraph should announce your contribution. “In this paper, I will argue that…” Notice that “supporting or elaborating” this claim, which is about your paper not your theory, does not yet require you to argue your position. You only have to describe a paper that would make such a contribution. And that means you will essentially be outlining your paper. Now, you have already introduced the historical background in paragraph 1, which will have space to talk about in part two of the paper, so you don’t have say anything more here. Also, in the second paragraph you have introduced the current state of the theory, which you will elaborate in greater detail the third part of the paper. What is left is to say something about how the theoretical problem you are interested in arose and why you are the right person to deal with it, to outline your analysis a little more, and to tell us why it is important, i.e., to summarize your discussion. That is, the introduction ends with an outline of parts 4, 5 and 6 of the paper.

Part 4 takes the place of the methods section of a standard empirical paper. In a sense, you are still saying what you did, but it is perhaps more accurate to say that you are explaining what happened to you to force you into a theoretical reflection. It may simply be a development within your field (someone else’s or your own empirical results, published elsewhere) or it may be an “event” like the publication of a correspondence or a translation of a previously untranslated work by a major theorist. World events, too, may be relevant here. After 1989 and 2001 and 2008 there were all kinds of reasons to “rethink” the theories that framed work in a whole range social sciences. Since you’re saying how the problem arose, you will also need to say what materials came into view: what texts have you read and how have you read them?

Part 5 will present your argument in detail. It’s a good idea to divide the argument into sub-theses each of which can be demonstrated separately. Two to four sections of three to six paragraphs gives you some manageable space to work with here.

Finally, part 6 will cash out your analysis in consequences, usually for theory, though sometimes for practice. You might want to emphasize the important political consequences of your line of thinking, but a very common and important class of “theoretical” implications center of questions of method. If you’re right that we have to see the world in a new way (a theory is always a way of seeing the world) then perhaps we will have to do things differently too? You may have shown that capitalism is broken and we a revolution, or at least that our theories of capitalism are in crisis and a paradigm shift is coming, or you may simply have shown that if we really want to know how capitalism works we have to look in unfamiliar places.

The conclusion should consist of two paragraphs, one of which states your conceptual argument in the strongest, simplest terms you can imagine. You may want to use the sentence that completes the key sentence of paragraph three (i.e., everything after “I will argue that”) as a key sentence here. The last paragraph could suitably extend the history of the field that you presented in paragraph 1 and elaborated in part 2 by imagining a possible future.

Like I say, I don’t pretend to have given you a recipe for a publishable theory paper in your favorite journal. I have only described the task in a way that makes it amenable to “writing process reengineering”. It is a way of spending 20 hours, one moment at a time, dealing with the reader’s problems one at a time.