There must be an opposing critique by now about physics having all the mathematizing one could hope for and yet no clear ontology of QM. Petabytes/day at CERN, several dozen QM interpretations with math and statistics, and yet the most popular take on QM is operational, and the others are so beyond experimental capability it won’t be settled in our lifetime.<p>At least other domains have ontology as primary (physics used to too!)
Engineering, at least the ME and EE kind, is kind of a middle ground. Some physics/math envy in the sense that we usually have to use fudge factors to make our designs work in real life.<p>Of course we're too busy making stuff to spend a lot of time on envy...
I think this phenomenon detracts from important debates about what <i>kind</i> of mathematics is most appropriate in certain fields. I think there's certain predictable regularities to be found in different fields, but the way they might best be modeled isn't always the same, and holding up more "reduced", lower level fields as examples becomes sort of a red herring in a lot of ways. It's one thing to point out that certain types of math are inappropriately reductionistic, or cannot be applied due to inappropriate axiomatic assumptions; it's another to outline an alternative.
I hate this framing so much. "Ah you wish to quantify things you observe to establish relationships, how very envious-of-physics you must be".<p>If one wants to say that a given model is bad for the data, fair cop, but just say that. Ffs.
One of the use cases of studying math is the ability to quickly identify and fend off mathematical complications. In one example I could help a student of medicine tear down a wall of inappropriate statistical nonsense.