Not linear algebra. Artificial neural networks create arbitrarily non-linear functions. That's the point of non-linear activation functions and it's the subject of the universal approximation theorems I mentioned above.
An LLM thinks in the same way excel thinks when you ask it to fit a curve.
So classes of functions (ANNs) that can approximate our desired function to arbitrary precision are what we should be expecting to be working with.
To model a process with perfect accuracy requires recovering the dynamics of that process. The question we must ask is what happens in the space between bad statistical model and perfect accuracy? What happens when the model begins to converge towards accurate reproduction. How far does generalization in the model take us towards capturing the dynamics involved in thought?
It seems like, we can at best, claim that we have modeled the human thought process for reasoning/analytic/quantitative through Linear Algebra, as the best case. Why should we expect the model to be anything more than a model ?
I understand that there is tons of vested interest, many industries, careers and lives literally on the line causing heavy bias to get to AGI. But what I don't understand is what about linear algebra that makes it so special that it creates a fully functioning life or aspects of a life?
Should we make an argument saying that Schroedinger's cat experiment can potentially create zombies then the underlying Applied probabilistic solutions should be treated as super-human and build guardrails against it building zombie cats?