There's a remarkable consistency between what our models (theories) predict, and our descriptions of our perceptions (also models). This is all easily explained by the simple observation that we all share in a common mind, of type: 'human', (which is yet, another model of type: 'testable').In physics, we occasionally predict never before seen things in nature.
Accurately.
With breath taking accuracy.
That's how we realize the theories are not arbitrary.
Instead, the theories are finding pieces of reality itself, amazingly.
We find, as @sjastro pointed out, Nature really is accurately mathematical.
It's not a fooling ourselves with a 'model'. It's the opposite. Finding what is actually real.
That's how physics (and all applied sub sciences) isn't like other ideas we have like about people or ourselves or any of a million models we also come up with.
Physics is a separate category from mere modeling, and unlike modeling.
Across the population of human types, there are some variations. No two minds perceive in exactly the same ways, eg: a 'rock' perceived by one person, might be described by another as 'a big stone', or 'granite', or 'sandstone', some people might perceive 'a deity' there (who's worthy of immediate worshipping), or a child/sentimentalist might perceive 'a pet' etc. Regardless of the variations there, when they describe their perceptions using in-common language however, they all become models of two distinct types: either testable or untestable.
The things is though, everything I say there, is all objectively testable and produces abundant evidence for obvious mind dependency ... and exactly *zip* for something existing independently from those minds. If you think there is evidence of mind independence, then cite the mind independent objective test for us, that would leave us with no other logical alternative. (Good luck with that .. and invoking philosophical Realism, (Popper's or otherwise), won't work either, because philosophy is clearly focused on the many different ways our minds think with no mind independence there, in the slightest).
Mathematics is a type of language based on logical tautologies which leaves an audit trail for retracing back back to base axioms. In physics which uses models described with math, the axioms have already been objectively tested and the math processes serve to track the consistency with that set of base axioms. Often the relationships with those base, (already tested), axioms are unclear to us. What is then 'discovered', (or revealed to us), is those previously obscured relationships. There's nothing magical about math .. but its ability to reveal these relationships, is a constant 'mystery' for most of us, yet serves as no evidence for something existing independently from the mind of a mathematical thinker (despite what 'the 'Maxs': (Tegmark/Headroom) might have to say about that).
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