Summations Only

Barycenter or center of mass is not a scalar, a measure of mass, but a vector, a measure of coordinates. It is that unique point in a massive system where the average density of mass for a coordinate point is equal in all directions and thus sums to 0.The center of gravity is that unique point in the coordinate system where the gravity on all sides is equal and thus sums to 0.Quite the opposite of what you are saying it is not the "densest average density", whatever the hell that is supposed to mean, but is the point at which the forces or masses balance in all directions. Sum to 0.

Be careful here, Taq, it was not what he was talking about, I know, but there isn't anything else holding up the plank and bearing its entire load.