Vector semantics and the (in-context) construction of meaning in Coleridge’s “Kubla Khan”

Cross posted from New Savanna.

Whatever else I have been interested over a long and varied intellectual career, I have always been interested in Coleridge’s “Kubla Khan.” I have been interested in the mind and culture, and “Kubla Khan” is my touchstone – as the title of an early autobiographical essay has it – on where things stand. I first read the poem in my senior year in college, in a course taught by Earl Wasserman. I then went on to write a 1972 master’s thesis on it, THE ARTICULATED VISION: Coleridge’s “Kubla Khan.”

https://​​​​search/​​label/​​Kubla_Khan I published a somewhat revised version of that in 1985, Articulate Vision: A Structuralist Reading of ”Kubla Khan.” I jettisoned most of the philosophical setting of the MA thesis and added some diagrams derived from my work on computational semantics with David Hays. Almost 20 years later, in 2003, I published a long essay, “Kubla Khan” and the Embodied Mind, in PsyArts: A Hyperlink Journal for the Psychological Study of the Arts. That version has many more diagrams than the 1985 version, and they were in color, something that’s trivially easy for online publication, but expensive in print publication. I regard these as significant advances, 1985 over 1972, and 2003 over 1985. Those two papers are my only formal academic publications on “Kubla Khan,” but I’ve done two unpublished working papers since then, Calculating meaning in “Kubla Khan” – a rough cut (2017), and most recently, Symbols and Nets: Calculating Meaning in “Kubla Khan” (2022). In addition to those major pieces, I’ve written many blog posts either centered on “Kubla Khan” or somehow commenting on it.

The question I’m now addressing is whether or not recent work in machine learning gives me any tools I can use in investigating “Kubla Khan.” It’s a tricky question.

But first, one might ask: Why spend so much time thinking about that one poem? For one thing it’s an important poem, one of the best known and most anthologized in the English language, and arguably one of the greatest. For what it’s worth, there’s nothing else quite like it. Beyond this, it’s one of the few canonical poems that has had an impact on popular culture – see my working paper, One Candle, a Thousand Points of Light: The Xanadu Meme. It put the word “Xanadu” on the map. The poem itself inspired a song by the rock group, Rush, and Coleridge’s alleged forgetfulness inspired Ted Nelson’s hypertext Project Xanadu. Then we have the hit song, “Xanadu,” the movie, and the Broadway show. And that’s just the most obvious examples.

But all that’s after I became interested in the poem. What sparked my interest? After more work that I care to recount – which I did in that autobiographical essay linked above – I discovered that the poem was structured like a pair of Matryoshka dolls. The poem has two parts, each of which is structured like a doll within a doll within a doll. The last line of the first part is, quite remarkable, the innermost doll of the second part. That smelled like computation – think of nested loops. And that’s what I’ve been pursuing ever since. Not only computation in “Kubla Khan,” but computation in the human mind.

I’ve included a complete text of the poem in an appendix. The next part of this essay is about that line, the one that ends the first part of the poem and is at the structural center of the second part. I have come to think of it as an emblem, for it spans the whole poem and gathers it within itself.

The emblem and the construction of meaning

The first 36 lines of the poem consists of three parts. The first part, ll. 1-11, centers on Kubla, his decree, the dome, and is expressed in imagery having to do with light and space. The second part, ll. 12-30, centers on a wailing woman, and the fountain, and is laid out in time and sound. The third part, 11-36, blends these two semantic worlds together. This diagram depicts that structure as a tree:

Look at the red links. The whole is divided into three; the middle of that is divided into three; and once more, the middle is divided into three. That – the middle of the middle of the middle – is where an energetic and raucous fountain erupts into Xanadu.

Let’s look at the concluding couplet:

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

Miracles are one thing; devices are quite something else. Humans make devices, even rare ones, through acts of will. Miracles just happen, like that erupting fountain. Similarly, the pleasure-dome and the caves of ice are opposites. “Rare device” and “sunny pleasure-done” are derived from the world evoked in section 1.1 (the first 11 lines) – I explain this is great detail in Embodied Mind paper linked above – while “miracle” and “caves of ice” are derived from the world evoked in section 1.2 (the second 19 lines). Section 1.3 (ll. 31-36) gathers these meaning up an concentrates them on the last line.

This diagram depicts those relationships, where orange is the semantic space of the first 11 lines and blue is the semantic space of the next 19:

That ‘it’ that begins line 35, just what is it? Is it the pleasure-dome decreed in line 2? Is it also those measureless caverns in lines 4 and 27? How can that be? Aren’t those different things in different places?

Yes, no, all of the above. It’s a “miracle of rare device.” It has been brought into being through the agency of this poem. Physically impossible and contradictory, it is nonetheless real.

Why not think of it as a point in a high-dimensional vector space where word meanings are embedded, but also meanings of sentences and other strings of texts? That, after all, is what it really is. It is a creature of the poetic imagination, not of physical geography and construction.

This particular point in semantic space, it was created by and through the poem. It did not pre-exit this poem. “Xanadu,” “Kubla Khan,” “stately,” “pleasure,” “decree,” “sacred,” “caverns,” and a whole host of other words, the vast majority of them in the poem, they have meanings, positions in semantic space, that pre-exist the poem. The poem coaxes them into new relationships and thereby establishes new meanings, new points in the vector space. It is thus a bit like the in-context learning that the Anthropic people are writing about.

From the time of that first MA thesis in 1972 I’ve known that the semantics deployed in 1.1 and 1.2 get gathered together in 1.3. But I’ve never had a “mechanistic” (if you will) way of thinking about how that gets done. That’s what I get from contemporary work on machine learning. In a way that’s a little thing, since the analysis and description of the poem is where the heavy-lifting is done. But what good is a careful description of a poem if you haven’t the foggiest idea about the operation of mechanism that can exhibit such behavior? We’ve now got the beginnings of that.

Now look at the tree for the second part of the poem:

Looking at the red links, you can see that it has the same overall structure as the first part. The whole is divided into three; the middle of that is divided into three; and once more, the middle is divided into three. That – the middle of the middle of the middle – is where the line that ended the first part is introduced into the second part. But it is introduced in a different mode, excited exclamation rather than the simple assertion of the first part.

Think of the poem as describing a trajectory in a high-dimensional space. In the first part of the poem that trajectory builds to a point that is, in effect, at the geometric/​topological center of the territory traversed in the previous lines. From that point the trajectory takes a “leap” and lands in different territory “A damsel with a dulcimer… But, wouldn’t you know, its trajectory takes it back to that emblematic point and through it to the end of the poem.

Problems, problems: But what? And that? That too?

Now, yes, I know. I know. There’s lots of questions. We need to do more than show how to construct that one emblematic point. We need to account for the whole trajectory of the poem. We also need to deal with the fact that the poem is a sonic object, with rhythm and an elaborate pattern of rhyme and alliteration.

We also need to get from an elaborate large language model to the human brain. Fortunately people are working on that. Moreover it seems to me a high-dimensional vector space is a good way to think about the activities of billions of neurons. Students of the complex dynamics of the nervous system are used to thinking about trajectories in spaces of very high dimensionality.

Moreover, Coleridge didn’t write just one poem. He wrote many poems. How does this one extraordinary poem relate to the others? I’ve got a few remarks about that in STC, Poetic Form, and a Glimpse of the Mind (2013), which is based on a short theoretical note I published in 1981, Metaphoric and Metonymic Invariance: Two Examples from Coleridge.

That’s a lot of work to do. But that’s the point. We now have and are developing new intellectual tools that will allow us to do that work.

More later.

“Kubla Khan” – The Text

In Xanadu did 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,
And close your eyes with holy dread,
For he on honey-dew hath fed,
And drunk the milk of Paradise. (54)

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