Explain yourself. There is not a understood natural phenomenon which we could not capture in math. If you argue behavior of the brain cannot be modeled using a complex math program you are claiming the brain is qualitative different then any mechanism known to man since the dawn of time.
The physics that gives rise to the brain is pretty much known. We can model all the protons, electrons and photons incredibly accurately. It's an extraordinary claim you say the brain doesn't function according to these known mechanisms.
You are confusing the nondiscrete math of physics with the discrete math of computation. Even with unlimited computational resources, we can’t simulate arbitrary physical systems exactly, or even with limited error bounds (see chaos theory). What a program (mathematical or not) in the turing-machine sense can do is only a tiny, tiny subset of what physics can do.
Personally I believe it’s likely that the brain can essentially be reduced to a computation, but we have no proof of that.
> We can model all the protons, electrons and photons incredibly accurately.
We can't even accurately model a receptor protein on a cell or the binding of its ligands, nor can we accurately simulate a single neuron.
This is one of those hard problems in computing and medicine. It is very much an open question about how or if we can model complex biology accurately like that.
> There is not a understood natural phenomenon which we could not capture in math.
This is a belief about our ability to construct models, not a fact. Models are leaky abstractions, by nature. Models using models are exponentially leaky.
> I didn't say we can simulate it.
Mathematics (at large) is descriptive. We describe matter mathematically, as it's convenient to make predictions with a shared modeling of the world, but the quantum of matter is not an equation. f() at any scale of complexity, does not transmute.
I'm using simulate as a synonym for model. For any biological model at the atomic, molecular and protein levels, accuracy is key for useful models. What I'm saying is that accuracy at that level is a hard problem in computing and biology, and even simple protein interactions are hard problems.
> There is not a understood natural phenomenon which we could not capture in math.
You are saying "If we know how something works, we can explain how it works using math."
But we know almost nothing about how the brain works.
> The physics that gives rise to the brain is pretty much known.
...no it is not! No physicist would describe any physical phenomenon as being "pretty much known". Let alone cognition. We don't even have a complete atomic model.
I think you are mostly correct but most people don't like this explanation and choose to believe in magic or spirits or whatever instead of physical reality. For some reason the brain is "magic" and non-physical unlike other organs (and everything else that exists) to most people. It's almost impossible to convince anyone of this though and it's not even worth trying.
> most people don't like this explanation and choose to believe in magic or spirits or whatever instead of physical reality.
You have it reversed. Math is a language tool to describe things, in a limited fashion (our current modeling). One is physical matter (even if it's antimatter). If you believe that there will be a language that can describe anything, it still doesn't manifest matter by speaking that language or describing it...unless you're into magic or spirits or whatever.
This disconnect has nothing to do with how well we do or do not understand physical phenomena. I think what the OP meant to say (and probably you support) is how the "mind" or how we think, can be described with mathematical models. Maybe one day we will have a full understanding, but we're not there yet and not currently in a way that is legally compelling.
This is not a fact.