If I were to take an affine connection say $\Gamma_A$ and another affine connection $\Gamma_B$, and I were to plot on the surface of the sphere two geodesics that arise from these two connections, they would in general be different.
As in say if I was starting from scratch and I only had access to what affine connection I was using. Could I determine the geometrical shape by embedding it in an $\mathbb{R}^n$ just by knowing the affine connection?
@Slereah I'm just a bit confused about how the geometry of a surface in question isn't entirely determined by the affine connection chosen. It seems weird that one has geodesics arising from an affine connection, but one doesn't even know what shape they are talking about
It's difficult to define because I assume many people think they understand it when they just have a superficial understanding of tensor index gymnastics
@Interstellar It's difficult to define because there are different levels of understanding. But say enough to give a short course of introductory lectures confidently up to deriving the EFE.
" At that time, Cunningham and Eddington were streets ahead of the majority of their Cambridge colleagues, who dismissed Einstein’s work, ignored it or denied its significance."
