Languages as designed latent spaces

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Languages as designed latent spaces

Some thoughts about what problem-solving even is

2026-07-22

This post is an edited version of a<br>Mastodon thread I wrote recently.

I have been thinking recently about how language is a high entropy latent space and what<br>that means.

Latent spaces are sort of magic: they don’t just reduce the dimensionality of a higher<br>dimensional space, they also constrain it such that arbitrary movement in the latent<br>space maps to some meaningful position in the higher dimensional space. Think about<br>how almost any textual prompt you give to an image generator results in a picture with<br>recognisable shape and form, yet the vast majority of the possible images are basically<br>just random noise.

Language is, obviously, like this. Once you’ve learned to conquer the basic structural<br>rules like syntax, grammar, and basic pattern matching of words with similar semantic<br>clustering, movement within it almost always produces ‘meaningful’ (read: intelligible,<br>not philosophically meaningful) results. Consider how an articulate human being can<br>fairly easily produce passable bullshit in a field with which they have no experience<br>simply by reading a little of the field’s jargon and improvising, but would utterly fail<br>to demonstrate practical ability in the field.

Language as technology

One way to think about this is that language is a tool that makes conceptual reasoning<br>easy: once you have the basic rules laid down, it’s almost more difficult to produce an<br>output that doesn’t carry some meaning than it is to produce an output that does.

Consider a strongly-typed programming language like Rust, Haskell, Lean, whatever: like<br>human language, almost every well-typed transformation of the code corresponds to some<br>meaningful change. In the same way that programmers can ‘bounce off’ the barriers of a<br>type system to avoid bugs, a user of human languages can ‘bounce off’ conceptual<br>barriers that would otherwise lead to them producing unintelligible nonsense, simply by<br>following the grammatical rules of the language.

However: the map is not the territory. For every well-typed transformation, there are<br>innumerable invalid transformations that would correspond to meaningless rubbish in less<br>expressive languages. Effectively, the language is turning the problem of domain<br>reasoning into one of pattern-matching and symbol manipulation by constraining the<br>set of possible programs to a small latent space within that covers a particularly high<br>concentration of meaningful programs.

Much of the confusion stems from the fact that, for all of human history before about<br>2016, symbol manipulation has been seen as very difficult because it’s something that<br>is less immediately intuitive to our brains. So, whenever we see someone - or<br>something - perform manipulation of a latent space like language, our tendency is to<br>presume that they first did their reasoning in the low-entropy, noisy, complicated space<br>of reality and then transformed it into the latent space as a final step. But there is<br>no reason for a machine to take this course of action: why should it, when simply<br>modelling language at the level of grammar and pattern-matching more readily satisfies<br>a fitness function?

Many problems can’t be solved in language-space because the language doesn’t exist to solve them yet

The point I’m very slowly getting to is that human language is a latent space that we<br>have fashioned over millennia of careful analysis, categorisation, taxonomic research,<br>and study of the real world. That is a specific kind of work that we usually forget<br>about in our text-and-language-filled lives where we live in the map and forget that the<br>territory even exists. It’s also work that an LLM cannot do: they are symbol<br>manipulators, not creators of symbols.

Their reasoning is bounded by the linguistic latent space that we have laid down before<br>them (as are we all, to some degree). But our unique ability is that we can operate<br>outside that latent space too, and grow its scope by making use of the world model in<br>our heads that has the ability to inquire and test hypotheses without relying on<br>training data to provide an answer.

It’s often seen as curious and a little bemusing that machines can generate mathematical<br>proofs or find counterexamples to long-held conjectures while simultaneously being<br>incapable of performing basic tasks like frying an egg or folding clothes, but perhaps<br>it should not be: the former requires only rapid manipulation of the semantically rich<br>latent space that has already been mapped by human minds, while the latter requires more<br>robust reasoning about a noisy reality with lots of dead-ends, the sort of thing that<br>only a world model can excel at.

If you find this a difficult notion to entertain, consider how capable a human being is<br>with almost no training data to learn from. Do we just have the benefit of an...