The real numbers are irrational almost everywhere, they are uncomputable 'almost everywhere' also. “what type of discrete systems give rise to the observed mac

The real numbers are irrational almost everywhere, they are uncomputable 'almost everywhere' also. “what type of discrete systems give rise to the observed macro behavior” is what we have been doing forever through Laplacian determinism. There are no alternative numbers systems that get around this. That is the whole point of the problem of the cardinality of the continuum. We know that Laplacian determinism fails, with quantum mechanics being the easiest counterexample but Cantor diagonalization is another. The sofar unsuccessful efforts to produce string theory is an example of this effort, changing world lines into sheets. With the discovery of strange non chaotic attractors and the discovery that our numerical systems are subject to the WadA property in time delayed and Hamilton systems it is possible that a unified model may not exist. None of this is undergrad though, due to how we have chosen to teach it. But it is very possible that existential quantifiers are what math limits is to building models of.