You're welcome.
In other words, the two paradigms disagree on which is more basic, the frog perspective of the observer or the bird perspective of the physical laws. The Aristotelian paradigm prefers the frog perspective, whereas the Platonic paradigm prefers the bird perspective....
Lousy analogy.
A mathematical structure is an abstract, immutable entity existing outside of space and time.
Unproven, unprovable, therefore, irrelevant theory. There is no evidence that anything "exists" outside space/time.
If history were a movie, the structure would correspond not to a single frame of it but to the entire videotape.
It isn't a movie, therefore, irrelevant.
Consider, for example, a world made up of pointlike particles moving around in three-dimensional space. There is no such thing. In four-dimensional spacetime--the bird perspective--these particle trajectories resemble a tangle of spaghetti. If the frog sees a particle moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. If the frog sees a pair of orbiting particles, the bird sees two spaghetti strands intertwined like a double helix. To the frog, the world is described by Newton's laws of motion and gravitation. To the bird, it is described by the geometry of the pasta--a mathematical structure. The frog itself is merely a thick bundle of pasta, whose highly complex intertwining corresponds to a cluster of particles that store and process information.
This is just a pile of hypotheticals that mean absolutely nothing. No one knows what a frog sees, or a bird, or a horse or whatever. It is all fantasy projection to prove a point that cannot be proven.
Fact is Platonism has no, can have no, verifiable evidence for its existence. Therefore, it is irrelevant.
By your comments, I conclude that you must be a Nominalist. Since I am a philosophical Realist we have precious little common ground to share views.