Axioms

I think you are very confused about the dimensions thing in physics.

Physics tries to model measurements.

So for example you measure a planet that is orbiting, make an equation, and see if tomorrow the equation and the position are the same (within a certain range of precision).

Before Galileo saw that Jupiter had satellites, they had perfectly fine equations that predicted where everything would be in the sky. The problem arose because new data could not fit the model.

You can absolutely model an orbit of a planet using 3 dimensions, or you can model it in an higher space with an equation of a lower degree. Both work. We can't really know which is "exact" if both work.

You can keep adding dimensions and make equations that work, but we don't really know what the "truth" is.