There can be many different parametrizations of the same surface, but they will each have the same topological and geometric properties.
So we could have several correct models—i.e. parametrizations which have the correct characteristics—and a single theory—i.e. set of characteristics with which to choose parametrizations. But each model will predict different yet-undiscovered characteristics. Using these new characteristics to make predictions would constitute different theories which are consistent-as-of-yet. Given the current state of quantum physics, different theories seem to be able to remain consistent for a while.
My use of model and theory have been prescriptive based on my interpretations of the thread below. I didn’t intend this but all of the confusion and disagreement seems to have been in our minds.
There can be many different parametrizations of the same surface, but they will each have the same topological and geometric properties.
So we could have several correct models—i.e. parametrizations which have the correct characteristics—and a single theory—i.e. set of characteristics with which to choose parametrizations. But each model will predict different yet-undiscovered characteristics. Using these new characteristics to make predictions would constitute different theories which are consistent-as-of-yet. Given the current state of quantum physics, different theories seem to be able to remain consistent for a while.
My use of model and theory have been prescriptive based on my interpretations of the thread below. I didn’t intend this but all of the confusion and disagreement seems to have been in our minds.
We certainly seem to be arguing about words—you’re probably right that the confusion is just in our minds.