## Tuesday, June 28, 2022

### “Kubla-Khan” in Light of the Relational Nets Primer

This is another post in my series of post-Relational-Net-Primer reflections.

“Kubla Khan”, as I’ve explained many times, originally in this piece first published in 1975, is what sent me chasing after computational semantics, in graduate school in the mid-1970s, and connected with my ongoing interest in the brain in a long article I published in 2003, “Kubla Khan” and the Embodied Mind. The nature of my interest is easily stated: Why does that poem have the structure that it does? I could launch out into a digression into just what kind of question that is – in what way does it differ from a similar question about sonnets? – but I won’t.

The Structure of “Kubla Khan”

Instead, I’ll present you with the structure (I list the whole poem in an appendix):

That diagram doesn’t present the rhyme scheme, which is also part of the puzzle, but you will find a discussion of that in the “Embodied Mind” paper. I inserted the long arrow to remind us that we read poems from beginning to end. We don’t have the overview perspective afforded by that diagram.

The diagram is simple enough. It is what linguists call a constituent structure tree, and it is over whole poem, which is 54 lines long. (Such trees are generally used in the analysis of sentence structure, not the structure of whole texts.) The first part, numeral 1 in the diagram, is 36 lines long, from line 1 to line 36. The second part, numeral 2 in the diagram, is 18 lines long, from line 37 to line 54. That divides the whole string into two parts. Each of those strings is in turn divided into substrings, as indicated by the tree. If you want to know how I arrived at the divisions, consult the “Embodied Mind” paper. But I will note that in many cases I did it by treating punctuation marks like brackets and braces in a mathematical expression. That is, my decision procedure was mindlessly mechanical.

Let’s take a simple arithmetic expression: 3 + 5 * 9. What’s the value of that expression? Unless you adopt a convention about the order in which you apply opperators, the expression is ambiguous and so could evaluate to either 56 or 48. We can eliminate the ambiguity by adding parenthese, giving us ‘(3 + 5) * 9’ or ‘3 + (5 * 9)’.

In looking at the poem, then, I assumed that the underlying process which determines the meaning of the string is segmented according to the boundaries between substrings. That’s not an odd assumption to make, but, given that we don’t understand that process, it must be considered an assumption.

Note: I regard that tree structure as an analytic device, but not as something that is explicit in the underlying neural mechanisms. Just what those mechanisms are is not, of course, known. This should not be taken to mean that I do not think “Kubla Khan” is divided into substrings in the way indicated by that tree. It is, but that tree does not need to be a component of the mechanism that understands or that wrote the poem. For a discussion of this point see the discussion of description vs. catalysis in the opening of Sydney Lamb’s paper, Linguistic structure: A plausible theory, and Lamb’s discussion of descriptive vs. cognitive linguistics in Pathways of the Brain (1999).

Notice that I’ve presented part of the tree in red. Looking at the red edges we see that the first part of the poem (ll. 1-36) is divided into three parts, the middle of those is, in turn, divided into three parts, and the middle of those, in turn, is divided into three. All other divisions are binary. The same thing is true of the second section (ll. 37-54).

If such structures were common we could say, “Oh, it’s just another one of those.” But, alas...we don’t know whether or not such structures are common, because literary critics don’t analyze poems like that. Still, as far as we know, such structures are not common. It certainly surprised me when I first discovered it.

So, that’s one thing, the fact that each part of them poem has a nested structure, like matryoshka dolls. By the time I’d discovered that structure, however, I’d taken an introductory course in computer programming, and so I thought I might be looking at the trace of some kind of nested loop structure. That is to say, I took it to be some kind of computational structure. I still do, though I no longer think it’s nested loops.

Now, look at the diagram. The last line of the first par, line 36, is “A sunny pleasure-dome with caves of ice!” Now look at the second part, the middle of the middle or the middle, that is to say, the structural center. That’s line 47: “That sunny dome! Those caves of ice!” It’s almost an exact repedition of line 36. What’s that line doing in that place?

Now, these questions would have one valence if, upon consulting Coleridge’s notebooks, we found notes where he laid this scheme out and gave his reasons for so doing. But no such notes exist and, as you may know, Coleridge himself disavowed the poem, saying it came to him in an opium dream. He just channeled the vision but played no active role in writing it.

You can believe what you will about that, the point is that we have no evidence that this structure reflects conscious planning on Coleridge’s part. It’s sources are unconscious. That’s what I’m trying to figure out.

Now, at this point you might wonder what’s happening in the structural center of the first part (1.222). A mighty fountain is breaking ground, spewing rocks into the air, and giving rise to the sacred river, Alph. And that leads to the question: What’s that fountain have in common with that line that both of them occupy the structural center of their respective parts of the poem? That’s a very good question, but I’m going to leave it alone. If you’re curious, consult “Embodied Mind.” I want to stick with that one repeated line.

Semantic Dimensions in “Kubla Khan”

Let’s return to the first part of the poem. The first of its three parts (1.1) is characterized by an emphasis on spatial orintation and location and the visual mode. The second part (1.2) is characterized by an emphasis on sound and on time. The third part (1.3) encompasses both sight and sound, time and space. That is, it weaves the two worlds of 1.1 and 1.2 together. There is, of course, more going on. Part 1.1 has Kubla Khan as the major agentive force while 1.2 has that fountain. Neither Kubla nor the fountain are present in 1.3, but their creations, the dome and the river, both are.

Let us think of each section of the poem as being organized along the kinds of dimensions that Peter Gärdenfors uses in his account of semantics (Conceptual Spaces, 2001; The Geometry of Meaning, 2014). The various words in the poem each is located in some conceptual space characterized by certain dimensions. The thing to do, then, would be to examine the dimensions evoked by each part of the poem. While I have done quite a detailed analysis of the poem (again, see “Embodied Mind”), I have yet to undertake that.

But I do want to look at the last two line of the first part from that point of view. We have:

It was a miracle of rare device,
A sunny pleasure-dome with caves of ice!

I suggest that “miracle” marks one end of a dimension while “rare device” marks the other end. Similarly, “sunny pleasure-dome” marks one end of a dimension while “caves of ice” marks the other end of that dimension. Think of these as derived or virtual dimensions; they aren’t basic to the semantic system, but arise in the context of this poem.

While I didn’t conduct my analysis in terms of dimensions, the terms I did use make it plausible to think of those two last lines as encapsulating or being emblematic of the entire semantic space evoked in the previous lines. I now suggest that those two line are a two-dimensional projection of the semantic space evoked in the first part of “Kubla Khan.”

Now we are in a position to think about what’s going on in line 47, which repeats 36. First, remember that we are dealing with the human brain not a digital computer. “Kubla Khan” can be read aloud in two to two-and-a-half minutes (I’ve timed myself). While individual neurons fire quickly and so are either on or off in a time measured in milliseconds, millions and millions of neurons would be involved in reading a poem. Thus as one reads through the poem activation is going to spread through 100s of millions of neurons, generating increased activity throughout that population. So that last line, the one that’s repeated in the second part of the poem, it is going to ‘resonate’ with the entire first part of the poem – something I suggested in Symbols and Nets: Calculating Meaning in “Kubla Khan”. So, when that line is repeated in the second part, it brings that resonance with it, almost as though the ‘meaning’ of the first part is ‘injected’ into the second part in line 47, something I describe in “Embodied Mind”.

That seems plausible enough, but could we get actual evidence of such a thing operating in the brain? I strongly suspect that one day we will. Here’s a brief email exchange I had with the late Walter J. Freeman early in this century:

Walter,

I've had another crazy idea. I've been thinking about Haken's remark that the trick to dealing with dynamical systems is to find phenomena of low dimensionality in them. What I think is that that is what poetic form does for language. The meaning of any reasonable hunk of language is a trajectory in a space of very high dimensionality. Poetic form “carves out” a few dimensions of that space and makes them “sharable” so that “I” and “Thou” can meet in aesthetic contemplation.

So, what does this mean? One standard analytic technique is to discover binary oppositions in the text and see how they are treated. In KK [“Kubla Khan”] Coleridge has a pile of them, human vs. natural, male vs. female, auditory vs. visual, expressive vs. volitional, etc. So, I'm thinking of making a table with one column for each line of the poem and then other columns for each of these “induced” dimensions. I then score the content of each line on each dimension, say +, - and 0. That set of scores, taken in order from first to last line, is the poem’s trajectory through a low dimensional projection or compression of the brain's state space.

The trick, of course, is to pull those dimensions out of the EEG data. Having a sound recording of the reading might be useful. What happens if you use the amplitude envelope of the sound recording to “filter” the EEG data?

Later,

Bill B

Not crazy, Bill, but technologically challenging! Will keep on file and get back to you.

Walter

I can live with technologically challenging. Instrumental technique has advanced since we had that exchange. Is it yet up to the job? I don’t know. But surely one day it will be.

More later.

Appendix: "Kubla Khan"

A stately pleasure-dome decree:
Where Alph, the sacred river, ran
Through caverns meaureless to man
Down to a sunless sea. (5)
So twice five miles of fertile ground
With walls and towers were girdled round:
And there were gardens bright with sinuous rills,
Where blossomed many an incense-bearing tree;
And here were forests ancient as the hills, (10)
Enfolding sunny spots of greenery.

But oh! that deep romantic chasm which slanted
Down the green hill athwart a cedarn cover!
A savage place! as holy and enchanted
As e'er beneath a waning moon was haunted (15)
By woman wailing for her demon lover!
And from this chasm, with ceaseless turmoil seething
As if this earth in fast thick pants were breathing,
A mighty fountain momently was forced:
Amid whose swift half-intermitted burst (20)
Huge fragements vaulted like rebounding hail,
Of chaffy grain beneath the thresher's flail:
And 'mid these dancing rocks at once and ever
It flung up momently the sacred river.
Five miles meandering with a mazy motion (25)
Through wood and dale the sacred river ran,
Then reached the caverns endless to man,
And sank in tumult to a lifeless ocean:
And 'mid this tumult Kubla heard from far
Ancestral voices prophesying war! (30)

The shadow of the dome of pleasure
Floated midway on the waves;
Where was heard the mingled measure
From the fountain and the caves.
It was a miracle of rare device, (35)
A sunny pleasure-dome with caves of ice!

A damsel with a dulcimer
In a vision once I saw:
It was an Abyssinian maid,
And on her dulcimer she played, (40)
Singing of Mount Abora.
Could I revive within me
Her symphony and song,
To such a deep delight ‘twould win me
That with music loud and long, (45)
I would build that dome in air,
That sunny dome! those caves of ice!
And all who heard should see them there,
And all should cry, Beware! Beware!
His flashing eyes, his floating hair! (50)
Weave a circle round him thrice,