People have been doing thigs millenia before they understood them. Did primitive people understood the mechanism behind which certain medicinal plants worked in the body, or just saw that when they e.g. boil them and consume them they have a certain effect?
We've only had the tech to be able to research this in some technical depth for a few decades (both scale of computation and genetics / imaging techniques).
Even skin cells exchange information in neuron-like manner, including using light, albeit thousands times slower.
This switches complexity of human brain to "86 billions quantum computers operating thousands of small neural networks, exchanging information by lasers-based optical channels."
But sure, instantiating these capabilities in hardware and software are beyond our current abilities. It seems likely that it is possible though, even if we don’t know how to do it yet.
I will argue that the following capacities: 1. creating rules and 2. deciding to follow rules (or not) are themselves controlled by rules.
For example how much rain is going to be in the rain gauge after a storm is uncomputable. You can hook up a sensor to perform some action when the rain gets so high. This rain algorithm is outside of anything church turing has to say.
There are many other natural processes that are outside the realm of was is computable. People are bathed in them.
Church turing suggests only what people can do when constrained to a bunch of symbols and squares.
This is in the same sense that while it is technically correct to describe all physically instantiated computer programs, and by extension all AI, as being in the set of "things which are just Markov chains", it comes with a massive cost that may or may not be physically realisable within this universe.
Rainfall to the exact number of molecules is computable. Just hard. A quantum simulation of every protein folding and every electron energy level of every atom inside every cell of your brain on a classical computer is computable, in the Church-Turing sense, just with an exponential slowdown.
The busy beaver function, however, is actually un-computable.
