[bnjmn]

Scientific understanding (defined by the ability to make accurate predictions) can be (must be?) anchored in both the math and physical intuitions/observations, and it's very difficult to bridge the two without resorting to natural language (even if it's just you talking to yourself in your head while you look at the equations).

The whole problem with the Navier-Stokes equations is that the math seems to work extremely well, but we have no way to be sure it actually captures every aspect of reality (given suitably accurate initial inputs). You can use the equations to generate pretty convincing simulations, but they certainly do not always predict the fine-grained behavior of real-world turbulent systems.

Feynman's lectures repeatedly stress that physical laws (and the math that formalizes them) are, at best, idealized approximations of reality. Here's one, but you can google "feynman approximation laws" for more: https://www.feynmanlectures.caltech.edu/I_01.html

[JumpCrisscross]

> Scientific understanding (defined by the ability to make accurate predictions) can be (must be?) anchored in both the math and physical intuitions/observations

I wouldn't conflate intuitions and observations like that. Observations in many physical realms are best described by math, which is used to build up a natural-language approximation for communicating of unintuitive findings.

[bnjmn]

you're right, I should have replaced "intuitions" with "observations" instead of waffling