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Gravity and magnetism are two phenomena that I always imagined could actually be explained in higher dimensions (except we can't see those higher dimensions so it'd be just speculation).

Imagine two circles in 2D that repel each other the closest you get them together, like magnets do. In 2D it would look like they're interacting at a distance, but maybe in 3D they're two cylinders that are a bit flexible, that are actually touching at the ends, but not in the 2D plane you're observing. The interaction is "properly physical" in 3D but in the 2D plane it seems magical.

That's a way that I imagine it in 2D vs 3D, so this might be similar in 3D vs ND, where N > 3. Of course this is all baseless speculation, but it seems kinda plausible in my head.

Edit: bad drawing of what I meant: https://imgur.com/362tcHg

>>slazar+(OP)
There are models using higher-dimenions (and lower dimensions, and factional dimensions) to model physical phenomena, but the problem with a lot of them is that you end up with the "fitting n points to an n degree polynomial" problem. It's trivial to create a model that agrees with all observed data, it's a lot harder to make a model that accurately predicts unseen data.

>>slazar+(OP)
Gravity is explained that way, it is a curvature in spacetime (4D): https://www.youtube.com/watch?v=CvN13ZE544M

>>OkayPh+FI
Fascinating thought! Makes sense though. Given n inputs and outputs, you could literally make an if-statement that solves nothing but gives you the 'right answer'. Actually understanding the fundamentals (often unseen) of a problem to then create an elegant, holistic solution that almost prophetically seems to predict the future is the current peak of human thought achievement, IMO.