Would any continuous model of the universe have/be based on hypercomputational laws?
If you are interested in the effect of being able to compute with continuous real numbers, you might enjoy learning about the Blum-Shub-Smale theory of computation with the reals.  A good survey is Computing over the Reals: Where Turing Meets Newton by Lenore Blum.  Wikipedia states that the set of functions that are computable in this model are incomparable with the set of functions that are computable in the usual model, and gives a citation where you can read more.  It's not clear to me exactly how that result should be interpreted, though.