An emergent property is precisely one that obtains unexpectedly from simple components. For instance, it is supposed by some that the universe truly consists of nothing more than electrons and quarks and what have you which interact in relatively simple ways, and that subjective human experience emerges from that. We then have a situation that is easier for us to reason about using higher level concepts, but there isn't a chapter in the laws of physics called "subjective human experience". That's in the book called "diverse applications of the basic laws of physics".

In any case, I dispute your facts too. I don't think we have the ability to cross apply our heuristics. I can calculate fairly accurately a lot of mathematical problems when I'm riding my bike, but put me in a maths class and I'm stuffed. I don't have independent access to those hacks.