[lumost]

I suspect something similar happens with manifolds for GR. Riemanian manifolds aren't a big deal when you contrast them to what happens inside of a DNN, but physical analogs for these structures start to break down.

e.g.

Imagine a 4-dimensional hyperbolic surface defined by the lightcone of a particular point in space-time, now imagine that this surface is stretched/compressed by the distortions of gravity. Now let's talk about equations which are only loosely tied to this surface.

vs.

Consider the metric tensor defined by this 4x4 matrix g_xz. Distance is computed as a^x b^z g_xz, now consider all possible walks from point a to c to b. Now let's show the relation between these walks and a quantity we'll call the stress-energy tensor which represents the energy/momentum density at any particular point in space, and it's flux towards any other direction in space.

The latter is a very algebraic description, which does not rely on the audience having to visualize the constructs involved. Practically, even if you get a feel for what a Riemanian manifold looks like in 4-dimensions - you'll struggle to visualize the Riemann tensor, or Christophel symbols.