Operationalizing The Urn: Part 3

This post is the third in a series on operationalizing the method of close reading in Cleanth Brooks’s The Well Wrought Urn. The first post had laid out the rationale and stakes for such a method of reading, and the second post had performed that distant reading in order to test Brooks’s literary historical claims. This final post will explore the statistical model in order to ask whether it has captured Brooks’s definition of irony.

Irony (& Paradox & Ambiguity)

For Cleanth Brooks, the word is the site where irony is produced. Individual words do not carry meanings with them a priori, but instead their meanings are constructed dynamically and contingently through their use in the text: “[T]he word as the poet uses it, has to be conceived of, not as a discrete particle of meaning, but as a potential of meaning, a nexus or cluster of meanings” (210). This means that words are deployed as flexible semantic objects that are neither predetermined nor circumscribed by a dictionary entry. In fact, he refuses to settle on a particular name for this phenomenon of semantic construction, saying that further work must be done in order to better understand it. Brooks uses the terms paradox and ambiguity at several points; however, as a shorthand, I will simply use the term irony to refer to the co-presence of multiple, unstable, or incommensurate meanings.

This commitment to the word as a discrete-yet-contextualized unit is already encoded into the distant reading of the previous post. We had found provisional evidence for Brooks’s empirical claims about literary history, based on patterns across words that traverse multiple textual scales. The bag-of-words (BOW) model used to represent texts in our model had counted the frequencies of words as individual units, while the logistic regression had looked at trends across these frequencies, including co-occurence. (Indeed, Brooks’s own interpretive commitment had quietly guided the selection of the logistic  regression model.)

Previously, I described the process of learning the difference between initial and final BOWs in terms of geometry, however I now will point us to the only-slightly grittier algebra behind the spatial intuition. When determining where to draw the line between categories of BOW, logistic regression learns how much to weight each word in the BOW while making its consideration. For example, the model may have found that some words appear systematically in a single category of BOW; these have received larger weights. Other words will occur equally in both initial and final BOWs, making them unreliable predictors of the BOW’s category. As a result, these words receive very little weight. Similarly, some words are too infrequent to give evidence one way or the other.

Word Weight
chapter -7.65
oh -5.98
yes -5.40
took -4.67
thank -4.57
tall -4.33
does -3.74
sat -3.51
let -3.12
built -3.10
Word Weight
asked 4.76
away 4.33
happy 3.62
lose 3.51
forever 3.50
rest 3.48
tomorrow 3.21
kill 3.20
cheek 3.16
help 3.12

Table 1. Top 10 weighted initial and final words in the model. Weights reported in standard units (z-score) to facilitate comparison

We can build an intuition for what our model has found by circling back to the human-language text.1 Weights have been assigned to individual words — excerpted in Table 1 — which convey whether and how much their presence indicates the likelihood of a given category. It is a little more complicated than this, since words do no appear in isolation but often in groups, and the weights for the whole grouping get distributed over the individual words. This makes it difficult to separate out the role of any particular word in the assignment of a BOW to a particular category. That said, looking at where these highly-weighted words aggregate and play off one another may gesture toward the textual structure that Brooks had theorized. When looking at the texts themselves, I will highlight any words whose weights lean strongly toward the initial (blue) or the final (red) class.2

Let us turn to a well-structured paragraph in a well-structured novel: Agatha Christie’s The A.B.C. Murders. In this early passage, Hercule Poirot takes a statement from Mrs. Fowler, the neighbor of a murder victim, Mrs. Ascher. Poirot asks first whether the deceased had received any strange letters recently. Fowler guesses such a letter may have come from Ascher’s estranged husband, Franz.

I know the kind of thing you mean—anonymous letters they call them—mostly full of words you’d blush to say out loud. Well, I don’t know, I’m sure, if Franz Ascher ever took to writing those. Mrs. Ascher never let on to me if he did. What’s that? A railway guide, an A B C? No, I never saw such a thing about—and I’m sure if Mrs. Ascher had been sent one I’d have heard about it. I declare you could have knocked me down with a feather when I heard about this whole business. It was my girl Edie what came to me. ‘Mum,’ she says, ‘there’s ever so many policemen next door.’ Gave me quite a turn, it did. ‘Well,’ I said, when I heard about it, ‘it does show that she ought never to have been alone in the house—that niece of hers ought to have been with her. A man in drink can be like a ravening wolf,’ I said, ‘and in my opinion a wild beast is neither more nor less than what that old devil of a husband of hers is. I’ve warned her,’ I said, ‘many times and now my words have come true. He’ll do for you,’ I said. And he has done for her! You can’t rightly estimate what a man will do when he’s in drink and this murder’s a proof of it.

There are several turns in the paragraph, and we find that Mrs. Fowler’s train of thought (quietly guided by Poirot’s questioning) is paralleled by the color of the highlighted words. The largest turn occurs about midway through the paragraph when the topic changes from clues to the murder itself. Where initially Mrs. Fowler had been sure to have no knowledge of the clues, she confidently furnishes the murder’s suspect, opportunity, and motive. Structurally, we find that the balance of initial and final words flips at this point as well. The first several sentences rest on hearsay — what she has heard, what has been let on or uttered out loud — while the latter rests on Fowler’s self-authorization — what she herself has previously said. By moving into the position of the author of her own story, she overwrites her previously admitted absence of knowledge and validates her claims about the murder.

The irony of Fowler’s claiming to know (the circumstances of murder) despite not knowing (the clues), in fact does not invalidate her knowledge. Her very misunderstandings reveal a great deal about the milieu in which the murder took place. For example, it is a world where anonymous letters are steamy romances rather than death threats. (Poirot himself had recently received an anonymous letter regarding the murder.) More importantly, Fowler had earlier revealed that it is a world of door-to-door salesman, when she had mistaken Poirot for one. This becomes an important clue toward solving the case, but only much later once Poirot learns to recognize it.

Zooming our attention to the scale of the sentence, however, leads us to a different kind of tension than the one that animates Poirot. At the scale of the paragraph, the acquisition and transmission of knowledge are the central problems: what is known and what is not yet known. At the scale of the sentence, the question becomes knowability.

In the final sentence of her statement, Mrs. Fowler makes a fine epistemological point. Characterizing the estranged husband, Franz:

You can’t rightly estimate what a man will do when he’s in drink and this murder’s a proof of it.

Not simply a recoiling from gendered violence here, Fowler expresses the unpredictability of violence in a man under the influence. The potential for violence is recognizable, yet its particular, material manifestation is not. Paradoxically, the evidence before Fowler confirms that very unknowability.

Again, we find that the structure of the sentence mirrors this progression of potential-for-action and eventual materialization. A man is a multivalent locus of potential; drink intervenes by narrowing his potential for action, while disrupting its predictability; and the proof adds another layer by making the unknowable known. Among highlighted words earlier in the paragraph, we observe this pattern to an extent as well. Looking to a different character, the moment when Mrs. Fowler’s girl, Edie, came into the house (both initial words) sets up the delivery of unexpected news. And what had Fowler heard (initial)? This whole business (final). The final words seem to  materialize or delimit the possibilities made available by the initial words. Yet the paths not taken constitute the significance of the ones that are finally selected.

To be totally clear, I am in no way arguing that the close readings I have offered are fully articulated by the distant reading. The patterns to which the initial and final words belong were found at the scale of more than one thousand texts. As a result, no individual instance of a word is strictly interpretable by way of the model: we would entirely expect by chance to find, say, a final word in the beginning of a sentence, at the start of a paragraph, in the first half of a book. (This is the case for letters in the paragraph above.) This touches on an outstanding problem in distant reading: how far to interpret our model?

I have attempted to sidestep this question by oscillating between close and distant readings. My method here has been to offer a close reading of the passage, highlighting its constitutive irony, and to show how the model’s features follow the contour of that reading. The paragraph turns from not-knowing to claiming knowledge; several sentences turn from unknowability to the horror of knowing. Although it is true that the sequential distribution of the model’s features parallel these interpretive shifts, they do not tell us what the irony actually consists of in either case. That is, heard-heard-heard-said-said-said or man-drinkproof do not produce semantic meaning, even while they trace its arc. If, as in Brooks’s framework, the structure of a text constitutes the solution to problems raised by its subject matter, then the distant reading seems to offer a solution to a problem it does not know. The model is merely a shadow on the wall cast by the richness of the text.

Let us take one last glance at The ABC Murders‘s full shadow at the scale of the novel. In the paragraph and sentences above, I had emphasized the relative proportions of initial and final words in short segments of text. While this same approach could be taken with the full text, we will add a small twist. Rather than simply scanning for locations where one or the other type of word appears with high density, we will observe the sequential accumulation of such words. That is, we will pass through the text word-by-word, while keeping a running tally of the difference between feature categories: when we see an initial word, we will add one to the tally and when we see a final word, we will subtract one.3

Figure 3. Line graph representing cumulative sum of initial and final words over the book The ABC Murders. Tally rises early in the book and remains high until near the middle. In the last part of the book, the tally moves downward rapidly and ends low.

Figure 3. Cumulative sum of initial (+1) and final (-1) words over The ABC Murders. X-axis indicates position in text by word count.

In Figure 3, we find something tantalizingly close to plot arc. If initial words had opened up spaces of possibility and final words had manifested or intervened on these, then perhaps we can see the rise and fall of tension (even, suspense?) in this mystery novel. To orient ourselves, the paragraph we had attended to closely appears around the 9000th word in the text. This puts the first murder (out of four) and speculations like those of Mrs. Fowler’s at the initial rise in the tally that dominates the first half of the book. At the other end, the book closes per convention with Poirot’s unmasking of the murderer and extended explanation, during which ambiguity is systematically eliminated. This is paralleled by the final precipitous drop in the tally.

I’ll close by asking not what questions our model has answered about the text (these are few), but what the text raises about the model (these are many more). What exactly has our distant reading found? Analysis began with BOWs, yet can we say that the logistic regression has found patterns that exceed mere word frequencies?

Brooks had indicated what he believed we might find through these reading practices: irony, paradox, ambiguity. Since Brooks himself expressed ambivalence as to their distinctions and called for clarification of terms, I have primarily used the word irony as a catch-all. However, irony alone did not fully seem to capture the interpretive phenomenon articulated by the model. While observing the actual distribution of the model features in the text, I found it expedient to use those terms paradox and ambiguity at certain points, as well. Perhaps, this is a sign that our distant reading has picked up precisely the phenomenon Brooks was attending. If that is the case, then distant reading is well positioned to extend Brooks’s own close reading project.


1. This method has been used, for example, by Underwood & Sellers in “The Longue Durée of Literary Prestige.” Goldstone’s insightful response to a preprint of that paper, “Of Literary Standards and Logistic Regression: A Reproduction,” describes some of the interpretive limits to “word lists,” which are used in this study as well. For a broader discussion of the relationship between machine classification and close reading, see Long & So, “Literary Pattern Recognition: Modernism between Close Reading and Machine Learning.”

2. Not all words from the model have been highlighted. In order to increase our confidence of their validity, only those whose weight is at least one standard deviation from the mean of all weights. As a result, we have a highlighted vocabulary of about 800 words, accounting for about 10% of all words in the corpus. In the passage we examine, just over one-in-ten words is highlighted.

The full 812-word vocabulary is available in plaintext files as initial and final lists.

3. Note that it is a short jump from this accumulative method to identifying the relative densities of these words at any point in the text. We would simply look at the slope of the line, rather than its height.


Brooks, Cleanth. The Well Wrought Urn: Studies in the Structure of Poetry. New York : Harcourt, Brace, Jovanovich. 1975.

Christie, Agatha. The ABC Murders. New York: Harper Collins. 2011 (1936).

Goldstone, Andrew. “Of Literary Standards and Logistic Regression: A Reproduction.” Personal blog. 2016. Accessed March 2, 2017. https://andrewgoldstone.com/blog/2016/01/04/standards/

Long, Hoyt & Richard So. “Literary Pattern Recognition: Modernism between Close Reading and Machine Learning.” Critical Inquiry. 42:2 (2016). 235-267.

Underwood, Ted & Jordan Sellers. “The Longue Durée of Literary Prestige.” Modern Language Quarterly. 77:3 (2016). 321-344.

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