I think that the scientific rather than platonic explanations are more truthful and less “magical” (and less ridiculous honestly).
So try this: We can act in four dimensions of the physical universe, measure in four dimensions of the physical universe, and model four dimensions of the physical universe with mathematics. However, we can use the same techniques to model purely logical relationships, as we do to model physical relationships. It requires quite a bit of skill to keep track of what you’re doing, but when we are modeling very complex things, like waves, magnetism, forces, economic phenomenon, we can perform very complex calculations – not because these spaces exist, but because we can use the techniques we developed in the more simple physical spaces consisting of a small number of dimensions of change, to solve problems with many many, dimensions of change. It’s not that complicated really. It just sounds complicated because of the old fashioned (archaic) language we use to describe what we’re doing.