The reality and dimension of space and the complexity of quantum mechanics

The dimension (and signature) of space is a result of distances being real numbers and quantum mechanical state functions being complex ones; it is an inescapable consequence of quantum mechanics and group theory. So nonrelativistic quantum mechanics cannot be complete (it requiresad hoc additional assumptions) and consistent (nor can classical physics), leading to relativity, quantum mechanics, and field theory. Implications of the constraints of consistency and physical reasonableness and of group theory for the structure of these theories are considered. It appears that there are simple, perhaps unavoidable reasons for the laws of physics, the nature of the world they describe, and the space in which they act.