Dear Noson,
A nice thought provoking essay. You are the expert, but if a non-expert may point out a few things, here are some;
"Galilean relativity demands that the laws of motion remain unchanged if a phenomenon is observed while stationary or moving at a uniform, constant velocity. Special relativity states that the laws of motion must remain the same even if the observers are moving close to the speed of light"
In founding special relativity following the historic 1887 MM experiment, none of the observers, receptors or instruments was moving at the speed of light. This statement may therefore need some tweaking.
Then, talking about the farmer and his apples and oranges, who eventually arrives at the mathematical expression 9 4 = 13. When you say, this pithy little statement encapsulates all the instances of this type of combination, would it apply at all scales? Would it apply to a farmer of quantum particles as well? An unstated caveat in that statement 9 4 = 13 is that things that are being added are eternally existing things. But supposing existing things do perish, will 9 4 always equal 13? Suppose, things not existing come to exist, will 9 4 still equal 13? Although, not the main theme of my essay I find this statement 9 4 = 13 as being under the Parmenidean spell that, 'what exists cannot perish'. But if the universe itself can perish, how much more an apple? If the universe that was non-existent comes to exist, how much more a quantum object coming to exist and distort the equation 9 4 = 13? I therefore agree with your suggestion that going forward, the only way to capture all of the bundled perceptions of physical phenomena of a particular law is to write it in mathematical language which has all its instances bundled with it.
Finally, instead of mathematics belonging to one universe and physical reality belonging to another, why cant both be in the same universe? That is, why can't a mathematical object be equivalent in all respects to a physical object? Why can't the objects of geometry, like points, lines, surfaces and bodies not be same with physically real objects? Are we humans not the cause of this dichotomy of universes? I suggest we are, and as a result Nature presents us with paradoxes to guide us. If you eventually get to read my essay, I mention a few. In particular, I will like to know your opinion on how a line can be physically or mathematically cut if it is constituted of an infinite number of points, which are indivisible?
I cannot but agree with your statement that, "The point we are making is that mathematics works so well at describing laws of physics because they were both formed in the same way". But I venture to say further, not only formed in the same way, but living in the same place.
Best regards,
Akinbo