You act as though the only datatype usable by computers is bool. That's ridiculous. Yes, computers are binary, but they can compute analog things just fine via floating or fixed point arithmetic to arbitrarily high precision, among many other things. To claim that the brain has a fundamental advantage over a Turing machine is to claim that there's some magical quantum (or otherwise) advantage in the brain's physical system that is un-simulate-able by a Turing machine.

You can't even argue that analog provides superior precision to digital representation of continuous values, because the analog part of the brain is represented with discrete units (accumulation of neurotransmitter molecules in various parts of the neuron)! In other words, our brain actually uses fixed point math (granted, incredibly complicated fixed point math :))