[benlivengood]

I don't mean expressing human culture in purely mathematical terms, which sounds intractable.

I mean expressing the relationships and abstractions between the different levels at which we model the world. If you need to explain horses to whales, you probably need to drop down to a biological level to at least explain keratin for hooves to e.g. the baleen whales. Other than that, common experiences of mammals probably suffices to explain social and mating differences (assuming sufficient abstractions in this hypothetical whale languages)

If you need to explain horses to aliens, you'd drop all the way down to mathematics and logic and go back up through particle physics to make sure both parties were grounded in the way we talk about objects and systems before explaining Earth biology and evolutionary history. Behavioral biology would have to be the base for introducing cultural topics and expressing any differences in where we lump behaviors in biology vs. culture, etc.

My basic claim is that if we had a pretrained model over human languages and one hypothetical alien language then either a human or an alien could learn to speak the other's language and understand the internal world model used by the other, because the amount of information contained in large LLMs covers enough of our human world model that it can translate between human languages and also answer questions about how our world-models at various levels of abstraction are related to and built upon each other via definitions.

I am less certain if that same hypothetical LLM could accurately translate between an alien language and human language; I think that the depth required to translate across potentially several layers of abstractions might not fit in the context windows and attention-span of LLMs. I think ~current LLMs will be able to accurately translate inter-species on earth if we can get enough animal language+behavior data into them.