Another way this might fail is if fluid dynamics is too complex/difficult for you to constructively argue that your semantics are useful in fluid dynamics. As an analogy, if you wanted to show that your semantics were useful for proving fermat’s last theorem, you would likely fail because you simply didn’t apply enough power to the problem, and I think you may fail that way in fluid dynamics.
I’d expect that if the natural-abstractions theory gets to the point where it’s theoretically applicable to fluid dynamics, then demonstrating said applicability would just be a matter of devoting some amount of raw compute to the task; it wouldn’t be bottlenecked on human cognitive resources. You’d be able to do things like setting up a large-scale fluid simulation, pointing the pragmascope at it, and seeing it derive natural abstractions that match the abstractions human scientists and engineers derived for modeling fluids. And in the case of fluids specifically, I expect you wouldn’t need that much compute.
(Pure mathematical domains might end up a different matter. Roughly speaking, because of the vast gulf of computational complexity between solving some problems approximately (BPP) vs. exactly. “Deriving approximately-correct abstractions for fluids” maps to the former, “deriving exact mathematical abstractions” to the latter.)
Another way this might fail is if fluid dynamics is too complex/difficult for you to constructively argue that your semantics are useful in fluid dynamics. As an analogy, if you wanted to show that your semantics were useful for proving fermat’s last theorem, you would likely fail because you simply didn’t apply enough power to the problem, and I think you may fail that way in fluid dynamics.
I’d expect that if the natural-abstractions theory gets to the point where it’s theoretically applicable to fluid dynamics, then demonstrating said applicability would just be a matter of devoting some amount of raw compute to the task; it wouldn’t be bottlenecked on human cognitive resources. You’d be able to do things like setting up a large-scale fluid simulation, pointing the pragmascope at it, and seeing it derive natural abstractions that match the abstractions human scientists and engineers derived for modeling fluids. And in the case of fluids specifically, I expect you wouldn’t need that much compute.
(Pure mathematical domains might end up a different matter. Roughly speaking, because of the vast gulf of computational complexity between solving some problems approximately (BPP) vs. exactly. “Deriving approximately-correct abstractions for fluids” maps to the former, “deriving exact mathematical abstractions” to the latter.)