abstract principles one

Description Redux, Again: On the Methodological Centrality of Diagrams

Broadly considered, description is how phenomena are brought into intellectual discourse. Such discourse is thereby bounded by the scope of the descriptive powers at its disposal. What descriptive techniques are at the disposal of the literary critic?

The question is a real one, and has real answers, but I ask it rhetorically. Whatever those techniques are, diagrams do not figure prominently in them. One can read pages and pages and pages of first class literary criticism and never encounter a diagram.

The argument of this essay is that we’ve gone as far as we can go down those various paths. If we are to create a new literary criticism for this new millennium, then we must have some new conceptual tools, and some of those must be visual. The diagrams I imagine, not to mention the diagrams I have been doing for the last four decades, are tools to think with. They are not mere aids to thought, they are the substance of thought itself. Not all thought, of course, but some thought.

These diagrams are descriptive tools. Some describe texts and textual phenomena, while others describe the mental machinery underlying texts. The distinction is critical, and will occupy much of this essay.

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Diagrams of various kinds are central to objectification, which we can consider a particular mode of description. The aim of objectification is to make a sharp distinction – as sharp as possible – between the things we are talking about, aka the objects under discussion, and our means of talking about them.

As my principal concern is with naturalist literary criticism, I have to consider the difficulties of talking about language. On the one hand, we do it all the time. Recall that in Jakobson’s well-known characterization of the speech situation metalingually is one of the functions of language. But such usage is casual and does not aim at understanding of language itself.

Nor, for that matter, does literary analysis aim at understanding language itself. Yes, it aims at the understanding of language, as literature is in part constructed of language. That is the most ‘visible’ aspect of the literary work, it’s ‘skin’ so to speak. But works of literary art are also constructed of feelings, perceptions, ideas, emotions, desires, dreams, and so forth, none completely assimilable by language. We must be as clear as possible in our descriptions so that we may be in a position better to keep track of what we’re talking about.

I begin by outlining the ambiguous states the concept of the “text” has within literary criticism, though I don’t come anywhere near the idea that all the world is a text, which is slipped in under the far reaches of the ambiguity I look at. From there I offer a few words about scientific description, ending with the characterization of the shape of the DNA molecule. From there I go to literary description, the text proper, and the description of conceptual structures, mental machinery behind the text.

The Ambiguity of “Text”

What do literary critics mean when we refer to “the text”? there are times, of course, when we mean the physical thing, whether written or spoken, e.g. when analyzing the a poem’s rhyme scheme. But generally we mean to indicate something more diffuse, something anchored in that physical text, those marks on paper or waves in the air, but going beyond them. Just what that “something more” is, that’s not so clear.

Thus, as used in literary critical discourse, the concept of the text is ambiguous as between the physical signifiers and the signifieds, the concepts linked to those signifiers via linguistic convention. When we talk about the text, we generally mean to include the ordinary process of reading exclusive of any secondary exegesis or explication.

Within computational linguistics, however, there is a sharp distinction between the physical sign, whether written or oral, and the literary critic’s text, as I’ve defined it above. Optical character recognition (OCR) takes a written text as input and produces a machine-readable text as output. OCR software works very well for typed and typeset text; errors will be made, but they are relatively few. OCR software works poorly for text written in cursive script. Whatever the source text, OCR software makes no attempt to “understand” the text, but text understanding – in some sense of the word – is of enormous interest and practical value. It is also very difficult to do, and I’m talking about text understanding merely at the literal level. Feed the computer a news story about, say, the recent typhoon in the Philippines and ask it simple questions: What city was hit hardest? How many people have died so far? That’s simple basic stuff, for a human. Not so simple for a computer, though still basic.

When I get to talking about ways of describing literary texts I will be interested in techniques that are sensitive to the distinction between the physical texts, the signifiers, and the process of understanding the meaning of those signifiers at the most basic level, the level without which more sophisticated understanding – if such is called for – is not possible.

Scientific Description

Many scientific phenomena are characterized, at least in part, by numerical information: weight, linear and volumetric size, temperature, speed, count (how many?) and so forth. A lot of scientific instrumentation is devoted to getting some of these measurements. One can do simple counts, though, by the naked eye: how many sheep in the meadow? What color is the metal? And many measurements can be made by simple devices, rulers and simple scales.

But number is not all. Biology has made extensive use of drawings, and later photographs, all accompanied by verbal description and counts and measurement of various kinds.

And then we have maps. Until quite recently no one ever saw, for example, continental Africa from above. How then, did we form an image of Africa’s shape? That required a lot of work by a lot of people spread over time and space. Locations on the ground had to be tied to some coordinate system. Where did that coordinate system come from? And that coordinate system had to be projected onto a planar surface using one of the many available projections. Then you could draw a two-dimensional picture of Africa. Long before than, of course, people were drawing simpler maps of more restricted physical scope.

What’s interesting about maps is that the descriptive image is not available directly to the eye in the way that, for example, a maple leaf is directly visible to the naturalist, or even the cells of the leaf as seen through a microscope. One has to make a bunch of discrete observations which are then assembled into a descriptive image inscribed on a suitable surface. It is the inscription on this surface that we see as the shape of, for example, Africa.

And so it goes with the standard double-helix model of the DNA model (see, e.g. THIS POST).

double helix

There are no naked eye observations at all. Rather, we have a series of two-dimensional photographs showing the scattering of x-rays as they pass through crystalized DNA.

DNA smudge

The researchers then examine these images and “reverse engineer” a molecular structure that would produce them. It is that reverse engineered model that enters into scientific discourse about molecular DNA. That’s a far cry from simple naked eye observation where you count the petals on a flower and draw pictures of it.

The science, this science, cannot be done without the pictures.

Literary Description

But what of literary texts? How do we describe them?

I suppose our most precise descriptions are for verse forms: number of lines per stanza, number of feet per line, number of syllables per foot, number of stanzas per poem (if fixed), number of lines per poem (if fixed), rhyme scheme (if any), and so forth. This kind of information hardly ever figures in our interpretive work in any fundamental way. A given critic may believe that versification is central to how the poem functions as a work of art, but interpretive techniques make little use of that information.

More broadly, Aristotle’s Poetics is broadly descriptive in character, as is narratology. Genre types such as tragedy and comedy are descriptive or, rather, are defined descriptively. Certain things are required to have a comedy and certain things are required. And when Franco Moretti classified novels by genre and then creates graphs depicting the historical emergence of those novels – as he does in the first section of Graphs, Maps, Trees, those graphs are descriptive, too. Each type of novel is characterized by some description; when a novel is assigned to a type, the types can then be counted and graphed.

In my work in literary criticism I’ve used a number of descriptive devices beyond the usual verbal description and categorization. To visualize the rhythm of a Hemingway sentence I reset it so that each phrase began a line:

hemingway gallo

To visualize the so-called ring-form of Dylan Thomas’s “Author’s Prologue” I created this simple illustration, which also revealed that he mirrored line-lengths before and after the center point:

thomas chiasmus

As for the qualification of “ring-form” by “so-called”, that usage is metaphorical. The poem doesn’t take the physical form of a ring but rather, to use the language of conceptual metaphor theory, the features of the poem are “mapped” onto the image schema of a ring by some mental mapping process.

In working on Heart of Darkness I used a bar chart to visualize paragraph lengths from the beginning to the end of the text:

HD whole

This is basically the same thing I did with the Hemingway sentence. What matters in once case is the physical length of the phrase and, in the other case, the physical length of a bar that represents a segment of the text.

I also sorted the paragraphs into order by length to produce this chart:

HD whole ordered 2

In a related investigation I became curious about the appearance of “Kurtz” in the text. I divided the text into “bins” (another metaphor) of 500 works and counted the occurrence of “Kurtz” in each bin. This is the result:


Notice that “Kurtz” appears in the text at more or less regular intervals and that the number of appearances doubles roughly halfway through, at the paragraph I’ve called the nexus because it’s the structural center of the text. By this time in the story we’re well up the river to the Central Station.

All of the previous diagrams are describing only the physical text. To the extent that they are interesting – and I find them quite interesting – that is because meanings are “attached” to that text. The mental act of recovering meaning for physical signs occurs in time, a physical phenomenon after all, and displays rhythmic characteristics.

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I took tree diagrams from linguistics and used them to visualize the part-whole structure of “Kubla Khan” and “This Lime-Tree Bower My Prison”. These diagrams also describe the physical text, breaking it into continuous parts and their continuous subparts. The analyst, however, sometimes has to take meaning into account in order to determine the location of structural breaks.

The following tree depicts the first 36 lines (first movement of two) of “Kubla Khan”, with three verbal descriptors added as points of orientation indicating the location of the tree structure with respect to the text:

1 tree

I’ve drawn part of the tree in red to call attention to part of the tree structure. Those triple-branchings are important feature of this particular text.

This diagram is one of many I drew for “Kubla Khan” and it represents a different aspect of the text:


The color-coding represents different semantic domains (which may or may not correspond to mental spaces in the terminology of cognitive linguistics) and so encodes the critic’s judgment about semantics; this involves the mind’s interpretive machinery at a fairly elementary level. The rectangle at the upper left represents the first eleven lines of the poem (at node 1.1 in the previous diagram); it is a physical string. They are inscribed within a semantic domain that is visual and spatial in kind. The rectangle at the upper right represents the next 19 lines of the text (at node 1.2), which are inscribed in a domain that is auditory and temporal in kind.

The gray rectangle at the bottom represents the semantic domain of the final six lines of that movement of the poem. It contains percepts, the image (shadow) of the pleasure-dome, the sounds from the fountain and the caves. The yellow-orange rectangle represents the domain of line 31 (node 1.311): “The shadow of the dome of pleasure…” while the blue rectangle represents to domain of line 32 (node 1.312): “Floated midway on the waves;…”

While I’ve had to draw nine such diagrams in my description of “Kubla Khan” I didn’t do any for my description of “This Lime-Tree Bower My Prison.” As the diagrams are systematically and transparently related to the structure of the text, that difference reflects differences between these two poems.

Depicting Conceptual Structure

Now I want to look at a different kind of diagram. This kind of diagram is fairly technical in nature, so I won’t try to explain it in any detail. That’s not necessary. All that’s necessary is that you recognize that it’s different from the above diagrams and that it represents, not the physical text, but the mental machinery for “extracting” meaning from the text.

These kinds of diagrams were developed in the 1960s and 1970s by researchers in computational linguistics (CL), artificial intelligence (AI), and cognitive psychology. In CL and AI they are high-level representations of structures to be implemented in computer code. In cognitive psychology they are taken to represent mental structures, structures somehow implemented in neural tissue. Just how they would be represented in neural tissue is under intense investigation.

Here we have the basic idea:


This is a mathematical object called a directed graph and the conceptual object it represents is generally called a semantic or cognitive network. The nodes are taken to represent concepts while the arcs (also called links) between the nodes represent relations between concepts. For example:


Here the red link indicates a specific path through the network:


Such a path represents the semantic “deep” structure of a chunk of language, written or spoken. In the next image the path is divided into three segments, which might be different phrases within a sentence, different sentences within a discourse, different paragraphs, or even larger units, as the case may be:


But all that is mental machinery. We don’t yet have a physical text, written or spoken. Here’s some more mental machinery. This diagram is based on my work on Shakespeare’s Sonnet 129:


Many physical characteristics of that diagram are technically significant, but we need not worry about that now. At the center and the right we have a three part sequence in which a person is 1) consumed by lust and so pursues a suitable object, 2) has sex with that object and 3) feels guilty and shameful afterward. Each of those text balloons is a proxy for a network of some complexity (some details can be found in my two papers, dated 1976 and 1981). That’s all we need to know for my present purposes.

Now consider this diagram, in which I have taken lines from the poem and superimposed them on the lust sequence with pointers from words in the text to nodes in the network:


Those words ARE (from) the text of Shakespeare’s sonnet. In the diagram they are physically distinct from the mental machinery postulated to be supporting their meaningfulness. Notice that many words are without pointers. The diagram is incomplete, which is obvious at a glance. That’s a virtue, not the incompleteness, but that fact that it is readily apparent. Note also the question mark at the upper right, where we have two nodes from the word “hell” into the network. Which node is the one activated by that word? Or are both activated? Does it matter? Those are technical questions; they require answers. But not here and now.

What’s important here and now is one thing: the mental model and the physical text are clearly distinguishable. They are distinctly different conceptual objects. Given such a mental model, one can then begin to “account” for the poem by following the path it traces through the network as one moves through the poem word-by-word and phrase-by-phrase.

So, we’ve got one kind of descriptive object for bringing the text into intellectual discourse. We’ve got another kind of descriptive object for bringing underlying mental mechanisms into intellectual discourse. The two kinds of descriptive object are different.

On the Value of Diagrams for Objectification

Let’s turn to Franco Moretti, who is perhaps best known these days as a proponent of “distant” reading, which is obviously somewhat different from the mechanistic “close” reading I’ve outlined in the previous section. This is from page four of a recent pamphlet, Network Theory, Plot Analysis:

Third consequence of this approach: once you make a network of a play, you stop working on the play proper, and work on a model instead: you reduce the text to characters and interactions, abstract them from everything else, and this process of reduction and abstraction makes the model obviously much less than the original object – just think of this: I am discussing Hamlet, and saying nothing about Shakespeare’s words – but also, in another sense, much more than it, because a model allows you to see the underlying structures of a complex object.

This is an important methodological point, very important. By drawing a network of character relationships one has created a model that is clearly distinguishable from the (physical) text itself. One has objectified an (aspect of an) underlying mechanism.

Moretti’s observation bears comparison with a similar observation by Sydney Lamb, a linguist of Chomsky’s generation but of a very different intellectual temperament. Lamb cut his intellectual teeth on computer models of language processes and was concerned about the neural plausibility of such models. He is one of the first thinkers to use networks as representations of language structures and processes. In his major systematic statement, Pathways of the Brain: The Neurocognitive Basis of Language (John Benjamins 1999) remarked on importance of visual notation (p. 274): “. . . it is precisely because we are talking about ordinary language that we need to adopt a notation as different from ordinary language as possible, to keep us from getting lost in confusion between the object of description and the means of description.” That is, we need the visual notation in order to objectify language mechanisms.

What’s important is to have two distinctly different modes of thought available, each used for a distinct intellectual purpose.

Lévi-Strauss – if I may switch gears a bit – understood that, at least on an intuitive level if not at the level of explicitly formulated methodological rules of thumb. Consider his early essay, “The Structural Study of Myth” (in Structural Anthropology, Basic Books, 1963, pp. 202-228). It only has one diagram as such (p. 214), and I don’t see it as being terribly important as a tool to think with. But it has at least seven tables, some larger and more complex than others, that contain the substance of his thinking – eight including the initial ‘pro forma’ table to illustrate the concept. Those are essential to his argument.

The material in them really cannot be effectively presented in prose, as there’s no way to indicate the relationships between the items in the table. One must be able to visualize them in two dimensions and scan one’s eyes over the table, exploring those relationships.

Lévi-Strauss’s use of visualized conceptualization did not, of course, end with that paper. It was a feature of his thinking throughout his career. I was particularly influenced by a diagram from The Savage Mind (Chicago, 1966). It’s from the chapter entitled “Categories, Elements, Species, Numbers” and depicts what he calls the totemic operator (p. 152). It’s a complicated diagram, too complicated to redraw (at 6AM) much less to discuss. But let’s give it a little try.

The diagram takes the form of a very specialized directed graph:

totemic operator

This depicts the top and bottom of Lévi-Strauss’s diagram; the complex bulk of it is in between. For each of the three species, seal, bear, and eagle, Lévi-Strauss depicts three individuals. Each of those individuals is then decomposed into three components, head, neck, and feet. Then Lévi-Strauss links seal head, bear head, and eagle head to the generic head (at lower left) and so with the necks and feet. Then, at the very bottom, we see the generic head, neck, and feet combined into the generic individual. This, so goes Lévi-Strauss’s argument, is a highly abstracted depiction of the inner logic of (at least certain) totemic classification systems.

Now, consider this rather different diagram that I used to depict the relationship between text units and semantic categories in Coleridge’s “This Lime-Tree Bower My Prison” (LTB) and in “Kubla Khan” (KK). The two movements of LTB are on the left while the two movements of KK are on the right.


Follow the color-coded arrows, where color indicates semantic category. “Red” elements from both movements of LTB are mapped to the same movement in KK, which is different from movement to which the “green” elements are mapped, and so with the “blue” and the “black” elements. At a first glance it seems to me that the principle of segmentation and redistribution that obtains between the top and the bottom of Lévi-Strauss’s totemic operator is similar to the one that (I argue) obtains between LTB and KK.

Whether that similarity will hold up on further examination is a matter to be explored. But the question has been posed visually, that is, geometrically. It really cannot be posed in prose at all. Prose simply isn’t adequate to the task.

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There is, of course, much more to be said. My listing of diagramming conventions for textual phenomena is only indicative, and my two examples of conceptual structure – cognitive networks and Lévi-Strauss’s totemic operator – are chosen from hundreds, if not 1000s, of such conventions. If we want to develop a literary criticism in which we can create a rich body of objective knowledge of literary phenomenon we are going to have to develop the appropriate visual tools.