It sounds like log-probability is the manifold surface area. Distribution of potential over negative potential. Negative potential is the "surface area", and a

It sounds like log-probability is the manifold surface area. Distribution of potential over negative potential. Negative potential is the "surface area", and available potential distributes itself "geometrically". All this is iterative obviously, some periodicity set by universal speed limit. It really doesn't sound like you disagree with me.