Monthly Archives: October 2017

Knowledge and Imagination

Simplifying somewhat … In his Critique of Pure Reason, Kant was trying to understand how imagination makes knowledge possible. The implication, of course, is that without imagination there can be no knowledge, i.e., it would be impossible to know anything if we could not imagine anything. Indeed (and I think I’m remaining faithful, in my simple-minded way, to Kant here) it is possible to know things only in so far as we imagine them as objects. Objects are just things construed in terms of the conditions of the possibility of knowing them, and those conditions are, let’s say, “imaginary”.

I’m not just trying to be profound here. I think many students and scholars today have forgotten the importance of imagination, not in the romantic sense often associated with artists, but in the more mundane sense of picturing facts. “We make ourselves pictures of the facts,” said Wittgenstein. And a fact is merely a collection of things in one of many possible arrangements. The possibility of these arrangements is determined by the objective properties of the things in question. That is, an object is a thing construed in terms of its possible combination with other things to form facts. To know a thing, then, requires us to literally imagine its possibilities.

Like I say, I think we need to remind ourselves of the importance of imagination. We need to keep it in mind when reflecting on what we know. In fact, there are a number of cognitive steps between our knowledge and our imagination that are worth keeping in mind as well.

First, remember that you can’t know anything if you don’t form a belief about it. This belief will, of course, have to be true in order to really count as knowledge, and in that sense we have to accept that we can’t ever be certain that we know anything. The best we can do is to have good reasons for holding beliefs and be prepared to abandon them when better reasons against our beliefs emerge. At the end of the day, whether or not we really know something depends on the facts and not only are they not always in plain sight, they have a habit of changing. What’s true today may be false tomorrow, and the things themselves seem in no hurry to inform of us of their new arrangements. Nonetheless, at any given moment, we must hold beliefs, and those beliefs, when true and justified, are our knowledge. If we believe nothing, we know nothing.

But this should not render us simply credulous. We should not easily believe the things we want to know about, for appearances can be deceiving. Before forming a belief about something, therefore, we must investigate the matter carefully and this will require us to, first of all, understand what we were are looking at, or what we are being told. Often we will form a belief on the basis of nothing other than someone else’s testimony, often in writing. We read an account of a historical event or the analysis of a dataset and we form a belief about the reality it represents. Here it is clearly not enough to believe; we might well misunderstand the conclusions reached by author. While the account or analysis we’ve read is perfectly correct, and while the author therefore holds a true belief, i.e., knows what they’re talking about, we might yet form a false belief simply by misreading the text. Without belief there can be no knowledge, then, but we should not believe things we cannot understand. As scholars, in particular, we should not believe things we have not made a serious effort to understand.

And this brings us back to where I started. In order to understand something we must be able to imagine it. We should be able to “picture” the situation or population that we are forming a belief about. What’s really happening here is that we are ensuring that we are not forming a belief about an impossible arrangement of things. To say that something is imaginable is simply to say that it is “possible” in the broadest possible sense. It is logically possible. We can imagine a horse with a horn (a unicorn) or a horse with wings (Pegasus) but not a horse that is both all white and all black (not like a zebra, but like one horse that would have to be two horses at the same time). But notice that fantastic creatures are only “possible” on the background of a good deal of ignorance. An evolutionary biologist might have a much harder time imagining a winged horse than you or me simply because they know that wings evolved from arms, so a four-legged creature with an extra set of wings doesn’t really fit anywhere on the tree of life. I don’t know if it’s easier to imagine a unicorn in nature, but I suspect it is since there are rhinoceroses and reindeer in nature already. You and I can imagine Pegasus because we don’t know that much about horses and wings. A biologist, however, must suspend disbelief.

These considerations, like I say, are pretty elementary, simple-minded even. But they do suggest a heuristic for thinking about what you know and how you know it: imagine, understand, believe. Don’t claim to know something you don’t believe; don’t believe something you don’t understand; and don’t try to understand something you can’t imagine. As a scholar, your job is to get things to make sense. As a student, you’re trying to make sense of things too. It takes imagination to do it well.

(See also: my post on knowledge, imagination and intuition, feat. Ezra Zuckerman and Catherine Turco.)

Writing and Drawing

“Is a bit of white paper with black lines on it like a human body?”
Ludwig Wittgenstein

I know a painter whose instinctive response to people who claim they don’t know how to draw is: “How do you see?” I sometimes feel the same way about people who claim they can’t write: How can you think? How can you be sure you know anything at all? Here’s a post I wrote on my old blog on this theme:

One sense that the OED gives to the verb “to draw” is “to make (a picture or representation of an object) by drawing lines.” There’s something unsatisfactory about the circularity of this definition (it uses the word “drawing” to define the verb “to draw”) but I suppose we all know what it means. To draw is to make a picture of an object out of lines, and a picture is a two-dimensional representation of an object (or scene). The lines are important. A photograph, though two-dimensional, is not a drawing, nor is a painting (which makes the picture out of broad and fine strokes rather than lines.)

The status of the “object” in this definition also needs some clarification. After all, it is possible to “draw” a unicorn, so the object in question need not actually exist. You can draw a line or square, too, so it doesn’t have to be three-dimensional, though the representation will always be two-dimensional.

For some time, now, I have been trying to get writers to understand their work in similarly straight-forward terms. They have some object in mind, and they want to render it on the surface of the page. Their object is often four-dimensional—a story that unfolds in space and time, for example, or a data set from a time series—but their “picture” (the writing not the drawing) is always one-dimensional. Writing is linear: one word follows another in a sentence. One sentence follows another in a paragraph. Calligrams and other stunts not withstanding, the sense of a piece of writing is whatever emerges from reading the words in an order determined by convention.

Just as the meaning of one line in a drawing depends entirely on the meaning of the lines around it, so, too, do the words in a piece of writing depend on the words around them. Writing and drawing are both arts of arrangement. If you want to master either art, it is worth approaching it in the simplest form first. Consider the problem in terms of “marking up” a piece of white paper, either with two or three pencils of different grades (perhaps also an eraser), or with the letters of the alphabet and basic punctuation marks. (I would include italics among your basic resources for writing, but not boldface.) Imagine the drawing occupying about two thirds of the space of the page (leave a lot of white space) and imagine a paragraph of at least six sentences and at most two-hundred words, in a nice easy-to-read serif font, double-spaced, with no right justification.

The challenge is to render an object or fact accurately in that form and to do so within a manageable amount of time—twenty-seven minutes, for example. If you don’t choose something to draw—a hand, a face, an apple, a cup—you won’t expect to succeed. The same is true of writing. Choose some fact you know to be true or some event you know has occurred. Then describe it; write it down. It will help you immensely if you choose the fact to write down (or even the object you want to draw) the day before. This will give your subconscious time to prepare.

Once you have made your attempt, step back from it and look at it, or read it out loud. Do you like the way it looks or sounds? Consider again the object or fact or event you were trying to represent. Did you do it justice? Be honest with yourself, but not mean. Don’t dwell on it too long. Tomorrow, do it again.

Power Poses and Learning Postures

There’s a long and interesting article in the New York Times Magazine that all researchers in the social (and perhaps all) sciences do well to read. It’s about the “revolution” in statistical methods that has been going on for some time now and that we ignore at our peril. (The key text is already mentioned in my readings section.) But it’s also about more inframethodological concerns, specifically the way we deal with our mistakes.

The article’s author, Susan Dominus, clearly has a great deal of sympathy for the predicament that her subject, Amy Cuddy, has found herself in. As result, we get a great deal of information about Cuddy’s emotional response to having her work on “power posing” criticized in a very public way. I strongly recommend reading Andrew Gelman’s reflections on the article and the issue at his blog as well (also on my blogroll, of course). There’s some lively discussion in the comments, which is both a discussion of critical posture and a series of examples. Indeed, I think this whole thing is a master class by Andrew Gelman in giving and taking criticism!

For my part, I think Cuddy should just have acknowledged that the effect of power posing has not been scientifically demonstrated after all and stayed on the tenure track. I don’t want to get too much into it here, but I do want to make a confession of sorts. In my writing seminars I actually recommend a form of “power posing” that I learned from Benjamin Zander:

My version of this advice isn’t about making mistakes but discovering you don’t know what you are are talking about as you begin your writing moment. Don’t put your head in your hands and moan about how stupid you are. Throw up your arms and say, “Interesting! Ignorance!” and then spend 18 or 27 minutes exploring the depth and breadth of your own own unknowning. Ignorance is an important experience to face in research; indeed, it should be a familiar one. People who are afraid of their ignorance will have a hard time learning anything. Let’s call this the Learning Posture.

Now, I’m careful not to claim that I have science to back me up on this. It just strikes me as a good attitude to have, a good pose to strike, when you’re trying to write down what you know. And, as Zander points out, it’s an excellent attitude to adopt when you make mistakes. Be fascinated by them! When you make them, get into them, be curious about them, try to figure them out. This is where you’re going to learn something.

Ironically (and as Dominus begins by suggesting), perhaps Cuddy should have taken her own advice and struck a power pose when she began to receive criticism. “I’m wrong? How fascinating! Let’s get into it.” This is certainly what I recommend doing. Hopefully that is also the lesson that you, dear reader, will take away from all this.

A Paragraph about Paragraphs

Paragraphs are the units of scholarly prose composition. They normally consists of at least six sentences and at most 200 words that support, elaborate or defend a single well-defined claim. The claim is stated in the “key sentence”, and the rhetorical posture of the paragraph depends on the difficulty that this sentence presumably poses for the reader. If the reader should find the claim hard to believe, the paragraph will support it with evidence. If the reader should find the claim hard to understand, the paragraph will elaborate on it with description or definition. (This paragraph, for example, elaborates on the composition of paragraphs.) If the reader, having already formed a contrary opinion, finds it difficult to agree with the claim, the paragraph will defend the claim against the reader’s objections. Whatever its posture, the sentences in the paragraph are trying to leave the claim in the key sentence with the reader. It is what readers should take with them into the next paragraph. A simple list of the key sentences in a scholarly text, therefore, should provide an accurate sketch of the whole composition.

Addition and Composition

Imagine an accounting teacher who discovers that a significant number of her students can’t add up a column of, say, ten eight-digit numbers manually. They can put them into a spreadsheet and SUM a column, but they are not able to add numbers together themselves without the aid of the computer. Next, imagine an English teacher who discovers that a significant number of his students can’t compose a paragraph of complete, grammatical sentences. They throw a bunch of words together (some copied from the Internet) in their word processor and let the grammar checker tell them what to do with them. The accounting teacher, of course, ultimately wants to teach her students, among many other things, how to depreciate assets and write off liabilities. The English teacher ultimately wants to teach his students how to do everything from scanning a poem to deconstructing a narrative. But is there any hope if the students have not mastered these basic skills of adding and writing?

I think the obvious answer is no and, fortunately, the situations I describe are not very common. I do wonder, however, if we test these abilities often enough. I fear that we let students get away with an inability to add and compose far too long. I could blame primary and secondary education for this, but I think universities must themselves insist on a certain standard and not admit students that did not acquire basic competences in school. Those that manage to get in should immediately feel their incompetence if it’s there. For those that recognize their limitations, there is, fortunately, a lot of hope.

I’m sometimes told by teachers in the quantitative disciplines that their students understand perfectly well how to make up for any deficiencies they might have. If they’re not used to solving math problems, they know they must simply dedicate a number of hours every week to training the relevant skills. Indeed, I’ve always found it amusing that “the suffering of learning” was called “pathei-mathos” in Aeschylus’s original Greek. The passion of math is to suffer and learn. This, like I say, is well understood by students and scholars in the mathematical disciplines.

I try to normalize the struggle to write well in the same way. Writing isn’t just something you’re good at or not; is is something you undertake to become at better at through suffering. That’s sort of a melodramatic word, but any good writer will tell you I use it advisedly.  I’ve recently been trying to argue that writing instruction should not always try to be “helpful” to students. We should not show them ways around the difficulty; we should encourage them to face it. It is only by going through the suffering of the trying to write down what they know, with sincere aim of discussing it with other knowledgeable people, that they will learn how to write strong scholarly prose. Words can, perhaps, be “processed” by a machine. But sentences and paragraphs must be composed by living brains. Life includes moments of struggle. Writing moments.