It seems that Mathematics as we know it (Russel's axioms) is both an emergent phenomenon as well as the most basic law of them all. In macroscopic physics we observe that two rocks next to three rocks is five rocks, two hydrogen atoms next to three hydrogen atoms is five hydrogen atoms, two oscilliations of a cyclic system followed by three more is five such, and so on and so forth... But the Schrodinger equation contains addition of complex numbers, which we know to be a superset of the naturals.

Man, I really need to write a top level article on the Tegmark IV Hypothesis.