Humans have a neuro-chemical system that performs operations with electrical signals.

That's the level to look at, unless you have a dualist view of the brain (we are channeling a super-natural forces).

Yep, just like like looking at a birds feather through a microscope explains the principles of flight…

Complexity theory doesn’t have a mathematics (yet), but that doesn’t mean we can’t see that it exists. Studying the brain at the lowest levels haven’t lead to any major insights in how cognition functions.