Advanced Riemann spaces for dummies

Let us take our tree, the standard abstract model I use, a two color, roots and branch.

My algebra says that my pit boss fingers can wrap the trunk around the roundest spot and hold on to that as the most linear thing in our tree. At that ring point, the pit pit boss is free to stretch the tree trunk and bend it slowly to precision so the hologram effect of the branches and roots is not disturbed.
The ring point on the trunk, if you slice it with chain saw, then an axis up the middle is a perpendicular, your trunk axis. You ring point is round, the slice is a tangent space, we call it, I think.  Even on stretching the trunk at the ring, a cut still make the perpendicular.

In our case, there is a perpendicular axis separating deposits and loans.  It actually is a line at the bank. You can measure your distance from the entry point to yourself, and measure the traffic flow accurately, because the line is not bunching and unbunching wildly.  Any observer can lok in the lobby and decide, quickly, to do banking in the morn or afternoon, he can warp his Riemann space.

There, an online  Phd, send me a check.