We don't know the violations of the physical Church-Turing thesis that are conductive for machine learning. We don't have evidence for their existence in the brain (although, the brain would be the prime candidate for finding them as evolution works directly with the true physical laws).
BTW, large ANNs don't try to model how the brain does things. They are trying to mimic what the brain does. So, using "how many transistors/artificial neurons it takes to model a biological neuron" is not a good approach.
We have no evidence. We even have no solid theories how this can work (Penrose's OrchOR is "OrchOR somehow taps into mathematical knowledge somehow encoded into the structure of spacetime"). But people, for some reason, insist that there should be something there. I can't attribute it to anything else but to deeply entrenched feeling of human exceptionalism.
We also don't yet know how to be as efficient with training examples as any living creatures' brain, and we only partially make up for this by training on so many examples it would take you a million or so years to do the same, so we'd still stuggle with something proportionally smaller-brained such as a cat.
That said, remote controlled androids are going to be economically disruptive, as they make every (unlicensed) job open to outsourcing from an office in a low wage country.
