Culture Magazine

Some Informal Remarks on Jockers’ 3300 Node Graph: Part 1, “a Generic Time Trend” [#DH]

By Bbenzon @bbenzon
For some time I’ve thought my intellectual mission was to examine “stuff” that has been developed through largely discursive and informal methods and bring it to a form where real mathematics, of an appropriate kind, can be employed to gain further insight. I note that I have little mathematical training beyond high school, but I have developed sophisticated intuitions through reading and through interacting with thinkers having more mathematical knowledge than I have. My interests take me toward literature, art, music and the like, while my intellectual predilections move toward the mathematical. And so I find myself enacting the role of a bridge.
That’s what I’ve been doing with the 3300 node graph from chapter 9 of Matt Jockers’ Macroanalysis (2013). Here it is [1]:
Some informal remarks on Jockers’ 3300 node graph: Part 1, “a generic time trend” [#DH]
In this post and the next I’d like to make some informal observations about how I think about Jockers’ 3300 node graph. This post is about time and evolution while the next one will be about structure and computation.
Generic time trends
In dismissing that graph, Nan Da said that Jocker had simply given us “a generic time trend” and, as supporting evidence, she informs us [2]:
If you take a similar dataset (texts over one hundred years) and regress absolute Euclidean distances (based on similarly determined features) on absolute distances in time, you will see super significant positive correlation.
But she doesn’t tell us what that “similar dataset” is. You have to go to the online material to find out. It turns out that it’s the set of journal articles that Goldstone and Underwood used for their study of academic literary criticism. So, it’s a different kind of text, expository prose vs. fiction, and a different century, 20th vs. 19th. But still, what you see is that texts that are close together in time are also highly similar according to the same kind of metric – assuming Da did her work well in this case, and I’m willing to grant her that.
I think she’s right about this being a “generic” time trend. Where I differ is that I don’t for a minute think we should take it for granted. Students of the nineteenth century novel – can’t say that I’m one, but I’ve read a bunch of them – will have read many texts. I rather suspect they believe that there is an element of necessity, if you will, in the order in which they were written and published, at least by the decade if not by the exact year. They’d be very surprised to see something like Pride and Prejudice coming out in 1893 and something like The Adventures of Huckleberry Finn coming out in 1829. That’s just not how it works. Similarly, no one was writing like Kenneth Burke in 1993 and critics would be deeply puzzled to find Jameson texts in 1910. That’s just not how it works.
In the case of critical texts, some critics might be willing to admit to, you know, intellectual “progress”, and not worry too much about being charged with promoting a Whig view of the profession’s history. But progress would be much more problematic in the case of those novels. Does Tess of the D’Urbervilles represent some kind of progress over The Heart of Midlothian? We can drop the word, “progress”, but the directionality remains to be accounted for. Before we can begin to account for it, though. we need to tease these texts away from the familiar comfortable “face” they present to us, the one we embed in Da’s notion of a generic time trend. And Jockers’ graph does that rather nicely, especially if we keep firmly in mind that each node ‘encapsulates’ a fairly rich – if of an odd an unfamiliar kind – representation of a text.
So that’s one thing.
Back when I first read Macroanalysis, and after I’d had a chance to think about that graph a bit, I thought, “the rough temporal ordering of those representations (of texts) is evidence of an underlying evolutionary process: evolution, descent with modification.” And I set about rationalizing that original intuitive judgment. That process of rationalization, of course, is ongoing.
Now, I have a long standing interest in evolution, first biological evolution, and then, a bit later, cultural evolution. I’m sure this goes back to my undergraduate years at Johns Hopkins, where I also became interested in “the arrow of time”. It seems that many/most physical laws are time symmetrical; they work the same regardless of the direction of time. Thus, while you can use Newtonian mechanisms to predict future positions of the planets, you can also use them to recover past positions. But nonetheless the universe does seem to have a temporal direction. Why? That takes us to thermodynamics and entropy, which is sometimes thought to be about increasing disorder but, my scientist friend, Tim Perper, tells me that’s not quite it. Entropy is about the irreversibility of a process [3].
When I say that I see Jockers’ graph as a trace of the activity of a complex dynamical system, all I’ve got is a metaphor, but it’s a carefully considered metaphor. And it’s that metaphor that tells me that Da’s “generic time trend” is something that we should not take for granted.
And one thing that makes biological evolution so interesting is that it seems to be working against entropy, which it can do because the earth gets free energy from the sun which organizes capture and use in various ways. So the direction of time is a topic of direct relevance to biological evolution. Biologists have been very reluctant to countenance the idea that later life forms are somehow more complex than earlier ones mostly, I suspect, because they fear such ideas are just too close to the good old chain of being in a version the heads up beyond humans to the angles and finally, at the very top, the supreme deity. But it need not go there, not if you’re careful. So some years ago David Hays and I published a short article, A Note on Why Natural Selection Leads to Complexity [4]. We argue that evolution is able to produce ever more complex organisms because increased capacity for information processing is energetically cheap in relation to the increased energy capture it enables.
That seems rather remote from a unilinear direction in the trajectory of the 19th century novel. And it is. But this is informal, I'm just thinking out loud.
Is culture a complex dynamical system?
Still, I’ve got reasons. When I was working on my book on music, Beethoven’s Anvil (2001) and was in touch with and strongly influenced by the late Walter Freeman. He’d pioneered the use of complexity theory in modeling the dynamics of neural nets, real neural nets in animal brains, not the artificial neural nets of contemporary AI and machine learning. That’s pretty much the same mathematics the physicists use in statistical thermodynamics. Where they’re creating high-dimensional models with individual molecules (air, water, whatever) as the elements (a dimension [actually 6] for each individual molecule], Freeman created high-dimensional models where individual neurons are the elements (a dimension for each neuron). In the second and third chapters of that music book I extended this thinking to groups of people engaged in making music together. I didn’t actually do any math – which is beyond my technical capabilities – but I made a careful step-by-step argument. Though construction is a better word. I constructed a way of thinking about coupled brains as a single dynamical system [5].
It’s still some distance from a small band singing and dancing together to millions of people reading English language novels in the 19th century. But at least we’re now in the world of humans and human culture. So, when I say that I see Jockers’ graph as a trace of the activity of a complex dynamical system, all I’ve got is a metaphor, but it’s a carefully considered metaphor. And it’s that metaphor that tells me that Da’s “generic time trend” is something that we should not take for granted. It is something that must be explained.
Just what form that explanation will take, that’s not all obvious to me. I think a lot of construction is going to have to take place to do the job. On the one hand, we need to “open up” that graph and get a handle on what features seem to be driving the temporal trend. That’s one kind of intellectual work. Figuring out just WHY that happens, that’s something else. But surely we can make progress on figuring out just what has happened without having to work out the mechanisms driving it, no?
Some informal remarks on Jockers’ 3300 node graph: Part 1, “a generic time trend” [#DH]
[1] For an explanation of the graph you can of course read Jockers’ book. In fact you should read the book, because understanding the earlier chapters will give you a richer understanding of the graph. For a refresher that doesn’t depend directly on the book see, for example, my post, Notes toward a theory of the corpus, Part 1: History [#DH], New Savanna, May 9, 2019,
[2] Nan Z. Da, The Computational Case against Computational Literary Studies, Critical Inquiry 45, Spring 2019, 601-639.
[3] I’ve written an informal little paper on this, complete with photos, A Primer on Self-Organization: With some tabletop physics you can do at home, 2014,
[4] William Benzon and David G. Hays, A Note on Why Natural Selection Leads to Complexity, Journal of Social and Biological Structures 1990,
[5] William Benzon, Beethoven’s Anvil: Music in Mind and Culture, Basic Books 2001. You can download the final drafts of the second and third chapters here, That’s where I do most, but not all, of the constructing.

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