Would any continuous model of the universe have/be based on hypercomputational laws? I've read that when Turing-Church thesis is applied to the universe and physics, one of the three interpretations that we can use and is defended by some important physicists is that:


  "The universe is a hypercomputer and then it is possible to build more powerful machines than Turing machines. For this it would be enough for the universe to be continuous and make use of that continuity (another question is how dense its continuity is), using the results of said supercomputer as input"


Would that mean that every continious (or "continously-enough") model of spacetime and the universe could have fundamentally hypercomputational physics (physics described and based in hypercomputation and hypercomputational processes and laws/rules, describing a hypercomputer-like universe)? Or on the contrary only certain models could do it? In that case, can you think of any in particular?
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.