Metastructuralism

What if "meaning" is a dynamically derived evaluation of intrinsic structure filtered through a given cultural context?

Bear with me. If you want theory, start here. If you want examples, skip to the end. I started this project a few years ago when LLMs first became available. Here at the end of 2024 it’s become apparent that LLMs are probably a lot more problematic than we first understood, specifically around energy consumption and externalities that are effectively being subsidized by the world population in terms of depleted resources. So I’m honestly not sure how I feel about this now, but still find the ideas compelling.

At its root, none of this requires an LLM per se - you can just “do the math” - but pragmatically “the math” is almost impossible to do by hand. So consider this to be an exploration of a theory, but I’m not planning to release this as a product or anything like that. It’s just really interesting, you know?

Note: This project is not abandoned, but was so successful that it has evolved from a math/narrative isomorphism to an entire metaphysics I’m working on summarizing now.

The Structuralist Project

The structuralists argued that just as language seemed to have internal structural rules that governed how it functioned it stands to reason that narrative, too, had an analogous set of rules. They believed that if the meaning of a sentence was encoded in some way that the human brain was optimized to extract then surely the meaning of a story was similarly derived, right? They believed that stories “worked” because they followed these rules, that these rules were universal, and that a story’s “meaning” was the product of the way these rules intersected in its text. Their goal was to reverse-engineer these rules so that they could perform formal operations on narrative and meaning.

The post-structuralists came along 20 years later and said well, look, have none of you read Borges? The same text by the same author can mean two entirely different things to two different people. Meaning can’t be derived from some invisible narrative grammar — story is a social construct, and so we have to be careful not to project things on a given text that aren’t there.

And so the structuralist project kind of died. The only way to salvage it would be to find a way to reconcile these two perspectives, and doing that has simply proven too difficult. But with the rise of LLMs the tools at our disposal for abstract reasoning have suddenly gotten a lot more powerful — and it turns out, the old structuralist project may be worth a second look.

New Eyes on Old Problems

If you think about it, structuralism is sort of saying: a story is a set of details that are all related in specific ways. If those details were different, those relationships would be different, and so the meaning of the story would be different. And we think that “meaning” happens in stories the same way it happens in sentences — there’s some sort of human cognitive mechanism that simply understands narrative when it’s framed in a certain way. Post-structuralism says well, ok, sort of — except that the “meaning” never lived in those details or the relationships between them. “Meaning” is and has always been constructed by the reader as they apply a subjective set of filters and transforms over the structures encoded in the text. But crucially they’re not denying that those structures are there — they’re simply pointing out that those structures can’t be the origin of meaning.

And so where does that leave us? Well, it means that a story becomes a sort of latent space, doesn’t it? A story is in some way isomorphic to the set of all possible interpretations that it supports. “Meaning”, then, is the result of querying that latent space with parameters that select for a specific interpretation.

Key Point

If that’s true then maybe the structuralist project was more important than anyone realized. Because this is exactly how most modern artificial intelligence systems work. They build a giant relation of everything to everything, and then they allow users to query into it with the specific context required to provide a meaningful answer. LLMs and similar systems are literally applied structuralism, and the big debate around their usage today is in many ways a recapitulation of the post-structural critique. Specifically: it’s dangerous to assume that there’s only one set of meaningful relations in a text.

This is unequivocally and critically true, and so if we can’t find a way to integrate the structuralist project with the poststructuralist critique then we are kind of in trouble, because it suggests that maybe these systems shouldn’t exist.

An Experiment

All of this is fascinating to me, because I’ve been obsessed with structuralism since learning about it in college. And if what I’ve outlined above is true — if we can think of a story as a high-dimensional latent space that can be queried for meaning — then that means that stories can be treated as mathematical functions.

And if that’s the case then maybe — just maybe — we can find a way to salvage the structuralist project.

And this brings us to my project. Metastructuralism is both a theoretical approach and a specific implementation for performing mathematical operations over narratives. I’m not sure yet if I’m going to share the secret sauce, I’ve gone back and forth, but I would like to share a glimpse into what I’m able to do. I have a few examples on this site.

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Example: Star Wars Math⁠

uses an early prototype to perform some math on Star Wars, Good Will Hunting and Muppet Treasure Island.

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Example: Analyzing Casablanca⁠

uses my most recent state-of-the art implementation to perform a series of analyses over the film Casablanca.

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Towards a Metastructuralist Glossary⁠

is my attempt to maintain an up-to-date set of definitions.

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Accessible Intro to Calculus Concepts⁠

is something I put together because it’s helpful to understand some of the things I’m doing here.

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