I understand that the Riemann curvature tensor is a rank-4 tensor, in other words a 4x4x4 cube of 64 numbers (which can be reduced because of symmetries etc.)
The tensor represents the tidal force that a rigid body is experiencing when moving a long the shortest path between two points.
It also represents how much a vector is changed after parallel transporting.
I am really curious what exactly the $R_{231}$ entry represents. I am looking it up but I only get lost in christoffel symbols and very long derivations. What exactly does that entry mean specifically? I know it is very complicated stuff, but the metric tensor is basically a list of numbers that represent the distance you make when you put a small step in a certain direction and the stress-energy tensor is just a list of numbers representing flow across an area. I very much hope there is a way to understanding the Riemann curvature tensor (and the derived Ricci tensor etc).
My guess is that $R_{231}$ represents the difference between a vector transported in the $3$? direction and then the $1$? direction that is pointed in the $2$? direction? How can you get the tidal force from this? Or how is it related to the volume of something that gets transported?