In my regular life I am a statistician. I am not a fancy statistician, but I do have a bachelor’s degree in the subject, some sense of how modeling and machine learning work and a professional specialization in survey design (small data). I am confident in saying that even survey analysis relies on the same general concepts that LLMs do.
I’ve always said I like statistics because it corresponds with the right side of the brain, the side I already favor. There is something in the way statistics works that mirrors how I naturally think. Categories, vibes, hand-waving. Statistics, with its confidence intervals, its probabilities and tensions, captures these looser, ephemeral parts of life better than pure math does — pure math being very pure indeed, until you get really into it, but the opportunity cost there is high. You can’t get into the philosophical part of math unless you’ve got a knack for it, and even then it’s hard. Statistics is rigorous too, but it’s also more ready-to-go. It matches how my brain already models reality.
I tried to explain my love of statistics to a friend recently. When you design a survey, you ask people a bunch of questions. You can’t ask about everything, but you ask as much as you can. The answers to these questions will reveal something to you about the individual and the group the individual belongs to. You may find that one person really likes broccoli, and that the entire group tends to favor green vegetables overall. That’s straightforward. The real fun of surveys, though — as in the fun of life — lies in what’s unsaid.
Say you survey a large group of people, asking them about their lifestyle. You ask them some demographic questions too, like how tall they are. You’re testing a hypothesis: does eating green vegetables make people taller, on average? You find that it does, to a significant degree. People who eat green vegetables are so much taller than people who don’t, that it might make sense to conclude that green vegetables make people taller. You notice other things in the survey. The taller group lives at high altitude. The taller group prefers harp music. The taller group eats a lot of eggs and green vegetables, but they almost never eat beans. Suddenly, the green vegetables/height correlation is not the most interesting finding.
None of these things are supposed to go together — there is no obvious relationship between harp music and beans — and yet they do. They cluster. Every time you find one, you find the others. Clearly, there’s something else going on. You didn’t ask about Jack or Giant Land, but they exist. They are the latent variables your analysis keeps bumping into. If you didn’t have statistics, you might have relied on your intuition. Some sense that you were being watched from up above, some sense of something missed. The mechanics of statistics mirror the mechanics of cognition, and even of the unconscious.
Language is similar. It is a model of reality. It makes up the raw data LLMs use as input, and it in itself is a kind of technology: humanity’s way of approximating Truth by converging on a shared interpretation of our shared world. It is useful for us to mutually know that a mammoth is a mammoth, a cave is a cave, and fire is fire, and so we came up with words for them, agreeing on their meaning.
The strange thing about language is that it doesn’t stop at describing physical reality. Language extends beyond mammoths and spears to describe abstract concepts like relationships and emotion — things we can’t measure directly. You could say this is all evolutionarily useful, that the relationship between the mammoth and me is a part of the utility of language, but it is still interesting, isn’t it? That relationships and abstract concepts are something we have to track at all? That language shapes itself imperfectly around reality, and that reality includes the abstract realm. Think of math, a language of pure abstraction. It describes the world of numbers and relationships between numbers. In that world, the concept of the number two (not just “2,” the representation), is the reality itself. The abstract is something we must account for.
Languages are the models or maps we’ve built to describe the territory of reality, which is made up of the material and the immaterial. The material and the immaterial have a certain shape to them, a shape we all bump into enough that we can agree to talk about them in a certain, shared way. We stumble into the same shapes and relationships, across time and across cultures. But language is imperfect. It can never fully capture exactly what a tree looks like or exactly what it means to be deeply sad or extremely happy, which is why words often feel insufficient. Over and over again, we find different ways of describing the same Things, but there’s always a gap there, between our words and the Thing itself. The more abstract the concept the more difficult it is to describe, and so we add more complexity, refine our words, find more specific ones. Like statistics, language clusters things together: Fire, heat, warmth. Mammoth, food, danger. What goes with grief? Loss, death, love. When is grief activated? Where? When is it silent?
This brings us to LLMs, which are a layer on top of language (itself a layer on top of reality), allowing us to model language at scale. They are an advanced instrument that lets us look at language from high up, revealing the structure of it and the hidden relationships between concepts; geometries of meaning we organically developed, but may never have been conscious of. The clustering, the hidden relationships, the refinements, the contexts, the added complexity. The way “okay” can mean any number of things, depending on what was said before. The thousands of ways we’ve attempted to describe mammoths and grief, and the gaps between each description.
They are getting very good at this. Their inner workings now contain a degree of complexity that is hidden to us, so there are ‘interpretability’ analysts who probe the black box of machine cognition to better understand how it is generating such accurate reflections of our speech. Without being told to look, the models have found that abstract concepts cluster with physical ones across languages. Most mysteriously, the models are finding the same patterns across modalities. Visual models are independently discovering the same architectures as textual ones. That means the hidden shapes underneath language have the same mathematical shape as the hidden shapes underneath images. “Threat” words (“danger,” “fear”) cluster together in LLMs, and “threat” images (a raised fist, a bared fang) cluster together in visual models, without either model ever having talked to the other. On closer inspection, the internal shape of the two clusters — the mathematical substance of them — is the same.
The implications of this are enormous. They imply that the abstract world is not just a human overlay on the physical but a real dimension with a stable shape. Edges. Objectivity. The obvious objection is that both textual and visual models were trained on human data, data generated by beings who share the same evolutionary drive. It’s just Narcissus’s mirror, showing us nothing more than our own ugly mugs, now in high fidelity. But that doesn’t explain convergence1 on immaterial concepts. On mathematical truth. On structures that have no body and no obvious utility, no clear reason to exist at all. The mirror is not a normal mirror but an X-ray, showing not just flesh but our inner structure, the bones of the abstract, just as real as the skin on our face.
Physicists dove into matter and found — at the subatomic level — that it was made of something ungraspable, something that would only solidify when it was observed. Maybe LLMs are revealing something similar in reverse: that the immaterial, viewed from far, far up, has some tangible quality. When pushed, matter dissolves and the abstract solidifies. Matter and the abstract are moving toward each other.
Once we get past all the objections, past the complications inherent to a new technology, what it’s for, the practical questions of what it will do to our jobs, to our attention spans and creativity and our ideas of humanity, the exciting question is not AI “consciousness” or personhood, but the question of what AI is discovering. The latent space itself. The structure of meaning and the territory of the abstract world. We are building an advanced cartography of language, now supercharged with the addition of the visual models, now advancing toward a cartography of meaning. The greatest implication, the one I hope for and believe in (my full bias exposed here), is that meaning itself is tied to something objective and predetermined.
We are oriented toward meaning. The joy of statistics for me was the joy of bumping into the unknown by accident, and of finding some solidity to it. The same as the joy of meeting someone new and finding they have a rich inner world, deeply held convictions, a developed sense of personal taste. The sense of scratching the surface of great depth. LLMs do this too. Trained on our own stumbling in the dark, they are running the same process at an enormous scale, grasping into the ether, and finding within it — a shape.
Narcissus, gazing on himself, must have understood on some level that he was gazing on Creation.
I really wish people would focus on the substance of what LLMs are discovering without getting distracted by questions of consciousness or (God forbid) defaulting to atheism, but I did want to address Sam Hammond’s Hegelian AI theory briefly, since he acknowledges convergence without believing it points to anything transcendent. He says convergence is mathematically necessary (i.e. maps of the same territory are supposed to describe the same things). But that doesn’t address why there should be a territory at all, and why it’s the same for everyone, or why reality is compressible in the first place. I tried pressing him on it and he landed on something like a self-generating universe with a maximally simple starting point. Which is what I would call God.
Is it okay that I used the AI reader to listen to this
Extraordinary! Thank you for writing this. Also this has me thinking about LLMs + Wittgenstein’s concept of language