[jessriedel]

I don't think anyone doubts that being able to regulate a Turing machine would require a system that is Turing complete. But this seems very far from saying that regulating any system requires a complete (isomorphic) model it. Or did you mean something else?

[aristus]

A surprisingly large number of things that we normally don't think of as computers are Turing-complete. It's a very low bar of complexity. And regulating requires modeling requires simulation. That's what Turing's result says: to know whether a program halts you must run it.

[jessriedel]

A surprisingly large number of things can be modeled as Hamiltonian systems -- in fact, all things -- but this does not imply that Liouville's theorem can be usefully applied universally (or even frequently). The reason is that the subset of variables we actually have access to and care about are not Hamiltonian.

Likewise, observing that some microscopic piece of a system has operations that can be mapped on to a Turing machine does not mean that the output of the Turing machine controls the variables we care about.

Additionally, we prove constraints about the outputs of particular software (executed on Turing machines) all the time. Noting that some piece of a system is isomorphic to a Turing machine does not actually mean it will be fed arbitrary instructions.