That is not as smart of a question as you want it to be. Unfortunately for you, not everything can be modeled mathematically, or if you wish to be extremely minute, not everything can be currently mathematically modeled efficiently and precisely because it would require knowledge or resources far eclipsing what we have available. If you just want to push up your glasses and ACKSHUALLY me, then it's also possible to do anything, hurr hurr.

To even fucking PRETEND that we can model a brain right now is hilarious to me, but to equate that to LLMs is downright moronic. Human brains are not created, trained, or used in any way similar to LLMs, no matter what anyone says, but you are insinuating that they are somehow similar??? They are a simulation of a learning algorithm, trained through brute force tactics, and used for pattern completion. That's just not how that works!

And yet, in spite of the petabytes of data they fucking jam into these pieces of shit, they still can't even draw hands correctly. They still can't figure out the seahorse emoji. They still don't know why strawberry has two Rs! They continuously repeat only the things they hear, and need to have these errors fixed manually. They don't know anything. And that's why they aren't intelligent. They are fed data points. They create estimations. But they do not understand what the connections between those points are. And no amount of pointing at humans will fix that.

Information Integration Theory would suggest that phi (Φ) can be used to measure the degree to which a system generates irreducible, integrated cause–effect structure. The irreducible nature of something is exactly as you postulate: it cannot possibly be modeled mathematically. If it could, that would make it reducible to smaller parts.

You can describe the function of the human brain mathematically, of course… For example, some low hanging fruit might be:

• Define the system’s transition probabilities.
• Define its cause–effect repertoires.
• Define Φ mathematically.

But that’s not going to model human experience. The experience isn’t reducible. That, instead, models something closer to the quality of experience. Human rationality is derived downstream of human experience. So it’s just not a fair argument to say that a tool mimicking only the downstream patterns of human experience will somehow also possess the upstream experience capacity, or even a relatable sense of rationality at all.

I don’t think we’re going to get a deterministic explanation for human behavior, ever. Most likely just statistical truths. Unless you can somehow mathematically model the entire universe as well. Good luck, because now the endeavor sounds god-like.