To add to the fallacy that to think that simply because computations by common computers are done with a bits-and-bytes approach hardware-wise and processes in the brain are not that computers wouldn't be able to express computation that comes very close to processes in the brain:

This is exactly a mapping from one computational calculus (e.g. "brain calculus") to another (e.g. binary logic) with a compiler. While it still might be that the physical processes governing brain functioning somehow elude computational description with digital logic (i.e. such a compiler can not exist. Not sure how this could be the case given the notions of universality by way of Turing machines attached to that), surely this would mean we'd have a new class of computational power on our hands.

And to say that brains are capable of more than Turing-complete (ignoring memory constraints) computation seems hard to believe (see also https://en.wikipedia.org/wiki/Digital_physics). Now how to factor true randomness (if it exists in our universe) into this I don't know, and maybe it doesn't even play a role...