Something one should consider is that while math is surprisingly applicable, and as you correctly picked up I was making a reference to the "Unreasonable Effectiveness" quote, it is never exact.
Newton's laws are enough for us to fling rockets and robots to Mars, but they are not good enough for us to create our GPS system. And Relativity is amazingly good, but still not good enough to model black holes, dark matter, and dark energy. The breadth of equations in Quantum Mechanics are also supremely successful, and yet they don't work well in the realm of Relativity. The Standard Model doesn't know what dark matter or dark energy is.
So yes, all of this math we have is Unreasonably Effective. But it's still a model, and a model that is not 100% correct. We have gaps in our models and as we figure out better and better approximations for them we move to them.
In my first post I made a small comment about those who are Platonist "mistaking the map for the territory". This is a logical fallacy where one is confusing/conflating the semantics (in this case mathematics) with what it represents, reality.
Math, and by extension logic and any other model, or heuristic, that we use to make our way through this world is the map, it is amazingly effective. Just because a map is not the territory does not mean it's not useful.
Newton's laws are enough for us to fling rockets and robots to Mars, but they are not good enough for us to create our GPS system. And Relativity is amazingly good, but still not good enough to model black holes, dark matter, and dark energy. The breadth of equations in Quantum Mechanics are also supremely successful, and yet they don't work well in the realm of Relativity. The Standard Model doesn't know what dark matter or dark energy is.
So yes, all of this math we have is Unreasonably Effective. But it's still a model, and a model that is not 100% correct. We have gaps in our models and as we figure out better and better approximations for them we move to them.
In my first post I made a small comment about those who are Platonist "mistaking the map for the territory". This is a logical fallacy where one is confusing/conflating the semantics (in this case mathematics) with what it represents, reality.
Math, and by extension logic and any other model, or heuristic, that we use to make our way through this world is the map, it is amazingly effective. Just because a map is not the territory does not mean it's not useful.