Monthly Archives: May 2020

The Fourth Dimension

The fourth; the dimension of stillness.
And the power over wild beasts.

Ezra Pound, Canto 49

In physics, the fourth dimension is time. In poetry, however, and especially poetry that is inspired by Chinese literature and philosophy (as Pound’s was), the passing of time is approached in experiential terms, not simply as a measurable dimension. Since Pound tried to situate his poetry spatially “in periplum”, as if drawing a map of the coastline as it appears from a ship, not as it looks from above, it makes sense for him to describe the fourth dimension as “stillness”. Time is what happens — the only thing that happens — when we’re sitting utterly still, when we have completely suspended our motion through space. As when we’re reading a book.

It is this stillness that literature appeals to. In fact, we can say that a writer demands such stillness from the reader; the writer demands the reader’s attention. By meeting this demand, by paying attention, the reader produces the requisite stillness. Perhaps this is what Huineng was talking about in that famous koan about the two monks who are arguing about whether it is the flag or the wind that is moving. “You’re both wrong,” Huineng tells them. “It is the mind that is moving.” Most people understand (or fail to understand) that as a profound truth about reality in itself, but I sometimes think he was being ironic: “Right now, it’s your mouths that are moving. Stop arguing. Be still, and you’ll see what’s really going on.” Sit down, young grasshoppers, in other words, and shut up.

This is what every text implicitly tells you to do. Learning to read is learning to find that calm place in your mind where real insight is possible. The discipline of reading is that of letting words that someone else has chosen pass through your mind in an order that is as little under your control as the motion of a flag in the wind. The stream of words is punctuated, forming sentences that evoke images, and these, too, are not yours to determine. You let the words and the images pass through your imagination; you give yourself over to their power.

This civilizes us. We entrust our minds to books because we know they are not a battery of sticks and stones pointed in our direction. If they abuse our trust, if they make us imagine things we don’t want to see, then we can always close them and put them down. While we are not in control of what happens when we read, we are in control of whether to continue reading. We are perfectly safe and it is this presumption of safety that makes literature so valuable. The writer should feel free to speak from what Lisa Robertson called “the motion of her own mind.” Neither the page nor the reader’s lips move. The mind moves.

To write is to occupy your reader’s time, not to encroach on their space. The two-dimensional page and the three-dimensional book are merely instruments, incidental to the main purpose of the text, which is to get the reader into the right frame of mind. It is a way for the text to interact with the four-dimensional space-time we call reality and establish the right kind of attention. Once this has been accomplished, the materiality of the text should fade into the background, noticed (like Luzhin’s matches) only unconsciously, or when something goes wrong, such as when we accidentally flip two pages at once and nothing makes sense any longer. Normally, the text is not merely superficial but altogether tenuous; oblivious to the height and width and depth of life, it proceeds, one word after another, along a single line that the writer has drawn. The reader, sitting still, follows it.

The Three-Dimensional Book

“So we are nearing the end. The right-hand, still untasted part of the novel, which, during our delectable reading, we would lightly feel, mechanically testing whether there was still plenty left (and our fingers were always gladdened by the placid, faithful thickness) has suddenly, for no reason at all, become quite meager: a few minutes of quick reading, already downhill, and…” (Vladimir Nabokov, Invitation to a Beheading)

Some books are famously “thick”. In the old days, before Kindle, this was a physical fact about them. Thickness was a palpable reality, something you felt in your hands as you read the book. It also meant that you knew when the end was coming — you could feel it approaching between the index finger and thumb of your right hand. Surely, this feeling is part of the experience of reading, part of our training in books. (I know that people still read books, and even before kindle, some books were gathered together in collections and anthologies so that the end of one novel, and the beginning of the next, could occur anywhere. But I think you understand my point.) A book is not just the text that is printed on its pages; it is also a physical, three-dimensional object. Just as we can enjoy the two-dimensional surface of the page on purely aesthetic grounds, we can derive pleasure from the texture of the binding and the way pages are cut, the weight of the book and the thickness of the paper.

I don’t want to trivialize the aesthetics of reading books. But I do need to point out that, unlike the painter, who works on the canvas, or the sculptor, who works in the marble, the writer does not put a book together in the same sense as the book binder. A writer does not make a book, does not see the book emerging physically as a result of the work. A writer composes a text. The materiality of the book is not part of the writer’s experience, and not even the layout of the page is usually part of the writing process. (There are exceptions, especially in poetry.) How the book will finally look and feel is not under the control of the writer in the moment of writing. (Writers may, however, try to influence this later on.) Its contribution to the thickness of the book has little bearing on the choice of one word over another.

Today, the popularity of audio books shows how incidental the physical presence of a book is. A book can be purchased in a form that can unfold only in the single dimension of time — the time it takes someone else to read it aloud. And writers are now entitled to fetishize this performance as much as the look of bold black marks on creamy, high quality paper. I suppose they’re even entitled to imagine their favorite actor’s silky voice.

This is all obvious stuff, perhaps. But I’m leading up to something important, I hope, which I’ll get to in my next post. (Can you guess what it will be called?) I want to make it very clear what a writer of scholarly of prose is doing when writing — what the scholar makes out of words. Like a painter and a sculptor, the writer makes something that must be beheld by another human being to be meaningful. The relationship of the beholder to the beauty of the work, however, is located, not in the eye, but in the mind. The mind’s eye, if you insist, but we must, in any case, not be distracted by the visual, manual, and auditory incidentals of the presentation. Writing is not intended just to be seen. And it is meant to be read not heard, we might add. We must, to use Roland Barthes’ phrase, find pleasure in the text.

The Two-Dimensional Page

Gottlob Frege, Begriffsschrift, 1879
Image source: Frank Hartman)

When I started writing papers at university, I fetishized the visual impression of the page. This was in the 1990s, relatively early days of word processors (I was using Word Perfect), and I spent a significant amount of time worrying about font, spacing, margins, and layout. I liked pages that included a paragraph break or two and, if possible, a block quotation. I sought to have one every other page or so, simply for the look of “scholarly” prose. I also liked footnotes, and the air of erudition they immediately suggested. Even as a PhD student, I recall writing entire papers simply to earn the right to use a clever footnote I had thought of. (These papers never amounted to much more than stylistic experiments, of course.) I don’t recommend this fetish to students starting out today, but I’m sure it’s still common, and it can be a legitimate part of what George Orwell called the “aesthetic enthusiasm” of writers. If it gives you pleasure (real pleasure), by all means, enjoy the layout of the page.

In 1879, Gottlob Frege published a peculiar book called Begriffsschrift. The title is translated variously; I settled on Conceptual Notation long ago. His aim was to present the content of our thinking in a more “perspicuous” way than words normally allow. To this end, he proposed to use “the two-dimensional extension of the writing surface” to foreground the conceptual relationship between propositions, their logical interdependence. I’ve provided a sample at the top of the post so you can see what it looks like; the idea is that truth flows through this system, somewhat like a circuit. Once you have understood his notation, you can analyze your thinking in terms of the consequences of the truth or falsity of individual propositions on other propositions. “A good notation,” said Bertrand Russell in his introduction to Wittgenstein’s Tractatus, “[is] almost like a live teacher … and a perfect notation would be a substitute for thought” (p. xviii). One can decide that it is hyperbole, or that nothing is ever perfect, but Russell’s remark definitely captures the spirit of Frege’s project. If we could write our concepts down in a perfectly “surveyable” manner, he thought, the surface of the page would do the thinking for us, like a computer circuit calculates a sum for us inside our calculators.

Orwell was right to identify the page itself as an object of desire for writers. “[They] may feel strongly about typography, width of margins, etc.,” he said. And he was right to describe this feeling as “aesthetic,” meaning roughly what art critics mean by that term. I’ve always felt that that beauty is an experience that improves experience. I tell myself that that this is a “pragmatic” approach to art; the purpose of visual art is to make us see better, of music, to make us hear better, of poetry, to make us feel better. A beautiful page is not only easier to read, reading it makes us read better, makes us better able to discern the texture and cadence of the words we use. A messy, ugly page (like, in my opinion, those of many textbooks) is destructive to our sense of text, just as bad architecture and industrial noise disorients the senses and wears us down. If good notation is like a live teacher, a beautiful page is like a good friend. We enjoy the company independent of what is being said. It’s like someone speaking in a pleasant, familiar tone of voice.

As far as I’m aware, Frege didn’t speak directly about the “beauty” of his notation. But he must have felt some analogue of Orwell’s “enthusiasm” for his lines and functions. Many logicians and mathematicians find their formulas and equations beautiful, which partly explains their choice of vocation, of course. Just as a good poem might help you feel better — not happier, mind you, but more precisely happy or sad — a good conceptual note will help you think more clearly about something — clarity feels good to a logician. And if it doesn’t actually manage to replace your thinking, learning a system of notation will help you organize your thinking in general. It will improve the rigor of your “scientific experience”, allowing you to pass more easily from observations to implications, from premises to conclusions. If that doesn’t give you pleasure, research may not be the right career for you.

But as I hinted in my last post, this aesthetic project, whether philosophical or poetic, may be taking a bit of license with space and time. In prose, we have only one dimension — the order of words passing forward in time. Using this highly restricted medium (and Frege, remember, said that his notation was intended to do something that was not possible with words) we can conjure up the entire four-dimensional universe of ordinary experience, not to mention the higher dimensions of the quantum multiverse. Prose is capable of representing (in its way) virtually anything. When poets space out the words on the page, or use enjambment, or even resort to calligrams, they are, like Frege, exploiting “the two-dimensional extension of the writing surface.” They are using language more freely than is allowed in prose, which moves forward only along a single line. In a sense that I will return to in another post, they are cheating. They are using tricks and devices that go beyond the resources of scholarly prose. The results are often beautiful, and even at times useful, but they are not prosaic. I will leave for later the question of whether these aesthetic concerns are ancillary to our research, or merely incidental, but they are not, I want to insist, the substance of academic writing.

One-Dimensional Prose

“I don’t transgress against this order of things; I merely disperse its elements” (Stéphane Mallarmé, quoted by Jan Mieszkowski, Crises of the Sentence, p. 167.)

We experience ordinary life in four dimensions. Things are either near us or far away, to the right or to the left of us, above us or below us, before or after the present moment, which is simply where, when, and who we are right now. Henri Bergson said that “time is that which keeps everything from happening all at once”; space, we might say, keeps everything from piling up in the same place. We use these categories to keep things orderly. Some things we leave for later and others we leave in the past. Some things we keep close, while we hold others at a distance, and some things, finally, are neither here nor there.

Sometimes we make pictures of things. In Danish, a sculptor is a “picture carver” (billedhugger), someone who carves images out of stone. We can think of this as the removal of a dimension. The sculptor “captures” a living, four-dimensional human being in a moment in time, reducing them to a three-dimensional object. Of course, it’s not really three dimensional. It is still subject to the passing of time, but it is time as “experienced” by a block of marble — geological time, we might say — barely perceptible to the human eye. We can now take our time when we gaze upon its surfaces, which don’t change. We can walk all the way around the sculpture and return to the place we started. We can stare at it at as long as we like. It won’t move.

The painter, removes another dimension, fixing our perspective. Except in special cases, we can walk back and forth in front of a painting, step forward and step backwards, and we’ll see nothing more. The painting itself will usually indicate an ideal point from which to view it. (In some tricky cases, it will indicate two or more.) All other positions only let us us see it more or less badly. We may stand too close or too far away. We may look at it from too far above its horizon or too far below, too far to the right of its vanishing point or too far to the left. But everything is there on the surface.

What about the writer? I want to suggest that the writer works along a single dimension — a line — but not in space. Just as the viewer of a statue is free to move in space, but is frozen in time, and the viewer of the painting is free to stare as long as they like but is glued to the floor, the reader has been completely liberated from space, but is compelled to move forward in time, reading one word after another as determined by the writer. Time, as we all know, only goes one way. You can’t, meaningfully, read a text backwards because the rules of grammar are like the rules of perspective. You can break them but then the “work” is no longer available to you as the artist intended. You will no longer be reading a text if you let your eye wander freely, as you would when viewing a painting. Frankly, you’re not appreciating what the writer has tried to do.

I’m not entirely sure this is true, but I sometimes think that sculpture is easier than painting, and painting easier than writing, because the sculptor has more dimensions to work with, the painter less, and the writer only one. The sculptor represents four-dimensional experience in three dimensions, the painter reduces four to to two, and the writer must capture all of time and the space in the most fleeting dimension of them all. The reader can’t just keep staring at a sentence to get more out of it. The reader can’t go backwards to see if that will help. All the reader can do is read it again, experience the sequence of words exactly as before, hoping, perhaps, there was something they missed. They can then stop or go on to the next sentence, hoping that will clear things up. Good luck, dear reader.

I’m going to develop this idea further in the posts to come. I suspect it only holds, if at all, for prose — and probably only for a rather conventional kind of prose. (Just as our “modern” painters have been subverting our perspective, our poets have been liberating our “feet”.) But conventional prose, after all, is all that this blog is trying to get to the bottom of: the craft beneath the method — not the method in the madness — of scholarly writing.


“We make ourselves pictures of the facts.”
(Ludwig Wittgenstein)

I want to end this series of posts where we started, with the peculiar human faculty of imagination. I have lamented its marginalization in scholarly writing before, and I often daydream about its return to the center of our attention. Without imagination, there can be no understanding; without understanding, there can be no believing; and without belief, there can be no knowledge. In this sense, it would be correct to say that the faculty of imagination sets a “transcendental” limit to our knowledge of things. We can’t know something we can’t imagine. So you do well to find out whether you can.

Remember what Ezra Pound said about artists: “The serious artist is scientific in that he presents the image of his desire, of his hate, of his indifference as precisely that, as precisely the image of his own desire, hate or indifference. The more precise his record the more lasting and unassailable his work of art” (Literary Essays, p. 46). These images are what he called “the data of ethics,” and it is my assertion that they also constitute the data of epistemology. They are produced by the artful exercise of imagination and are then given to the intellect for analysis. In fact, we can say that serious scientists are artistic, presenting us with images of their (justified, true) beliefs. (Vladimir Nabokov once recommended his own “rain-sparkling crystograms” to “serious psychologists” for study.) In their writing, scientists “build us their worlds” in our imaginations.

“Beauty is difficult,” said Aubrey Beardsley to Pound. But in a certain sense the image is easy — you just peel it off the appearances. It is, in any case, easier to believe something than it is to know it; it is easier to understand something than it is to believe it; and it is easier to imagine a thing than it is to understand it. The beauty of imagination lies in the way it lets us bring elements together that we don’t yet understand, so that they can shed light on each other. That is how we learn things. Of course, they also cast shadows, and it is probably more accurate to say that we arrange things in our imaginations in order to adjust the light. When we get it right, we understand them. It is a thing of beauty to behold.

I hope I’m not coming off as too much of a “romantic” about this. But I am indeed trying to emphasize that research has an “aesthetic” dimension. The beauty of your research should come across in your writing; there should be a feeling associated with what you know. And you should share that feeling with your reader.

We are conditioned to think that, beyond getting your theories and methods right, academic writing is all about referencing conventions and rules of grammar. There are dark moments, when we suspect that the only relevant feeling is boredom. But we should never forget, as Borges warned us long ago, that “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). As you struggle with the “formality” and “correctness” of your research paper, don’t forget that you are engaging with the reader’s imagination. They should see a picture. They should hear a voice.