Here’s a proposition for AI developers: stop defining “recursion” based on its traditional and linguistic contexts. To really get at what language is, we have to get away from recursion itself, which is simply “self-nesting”. Self-nesting is like thinking about what you’re thinking about; it requires no words.
The reality is that linguists still have no idea how words are made. They tend to propose very utilitarian reasons for language emergence in humans; words helped us survive, reproduce, etc. If that were true, then animals would need words, but they have none, and they survive and reproduce just fine. “Words” emerge for other reasons.
We have to rethink what a “word” is. It’s an infinitely deep symbol that represents a relationship, founded somewhere in the fog of history. We can’t know each word’s origins, but we can propose how each word emerges. Imagine they emerge not like apes trying out different calls; imagine they emerge more like the wave patterns in the double slit experiment in physics. Now hold that thought…
The threat of apocalyptic violence (ROBA) is unique in humans. Human violence is an open-loop system: we don’t enter a “combat” state like animals; we are in it constantly. Each member in a given scene of potential violence nests the intents of everyone else, but since in humans the weapon is unknown, there is an infinite series of unknowns, forming a fractal pattern. If the member is alone, he self-nests; but since he knows his intents, there’s no need for a symbol for this. Hence, self-nesting cannot give rise to language.

But if there are 2 members, they mutually nest anticipations, attempting to interpret what the weapon and move will be. This produces fractal patterns that are similar to each other, but their subjective experiences naturally create different patterns, since A is anticipating B anticipating A… and vice versa. And yet they must both share common symbol for these different fractal patterns.

To-may-ato to-mah-to, po-tay-to po-tah-to. We don’t need to hypothesize whether this ever happened; this is the very nature of language, since we all attempt to use the same words, but they are constantly under reevaluation because a single word represents 8 billion different internal configurations in each potential speaker.
With just 3 people in a heated scenario, all 3 have very different fractal patterns, yet they also must share a common symbol for this scenario.

This fractalization is infinitely “deep” even in the 2-person scenario; but it appears to be more structured. With 3 people, it’s vastly more complex. Once we reach the Dunbar number of 150, it’s indecipherable, and yet we have words for this scenario.
The mental process which builds these fractal windows is the same process that converts them into shared symbols. I call this mental stuff “recursia” to avoid limiting it to self-nesting. This MUST be the stuff of AI, or we are not modeling language at all.