Differential Geometry is Overrated

Ever since Einstein introduced the fabric of spacetime in his General Relativity, differential geometry has dominated Physics.

• This is made up of arbitrary 3-dimensional shapes and “manifolds”, such as that of Gauss and Riemann .

But this arbitrariness goes against the simplicity of Nature. Even Euclid’s Elements is about 2-dimensional shapes instead of 3D ones. And so you have weird maths to describe infinite imaginative variations of spacetime.

It would be better to use 2D slices to describe Riemann Manifolds. Instead of theorizing the entire spacetime (which is impractical anyway), the better process would be:

1. Find out what you are trying to achieve with the real phenomena in the first place
2. Get data from the real phenomena
3. Plot the relations of the data in slices in the order of the sequence that they are preceived
4. Get the overall picture from those slices in aggregate

This would greatly simplify or minify the maths needed to plot the phenomenon in spacetime.

There is only Euclidean geometry. Riemann geometry is merely a mix of the properties of Euclidean geometry focusing on effects instead of causes.