Riemann Sphere

My last post on constitutive exceptions made me think (again) of the Riemann Sphere (it's been at my elbow for a couple of weeks now).  The Riemann Sphere maps the Complex Plane (x,y) onto a sphere of unit diameter with its center on the z axis.  Every point in every direction maps via a straight line to the 'north pole' of the sphere to a single point on its surface. 0,0 on the plane is touching 0,0,0 on the sphere. As the points go to Infinity, their mapping on the surface forms an ever-decreasing horizon around the north pole.

The Riemann Sphere is (maybe) an interesting illustration of the power of a king, or of God.  Or maybe I am about to succumb to theosophism and pieces of my brain are falling away like a wet cake (to quote Bernard Black).  The Riemann Sphere is definitely like something about my previous post, but what?

The complex plain, stretching to infinity in every direction, is where we naturally are, stuck all on the same level, with no meaningful orientation possible, and the infinite always infinitely far away in every direction.  On the sphere though, by recognizing a third dimension, the infinite becomes a specific locus. It becomes knowable.  The infinite plain is now visible and transformed into a finitude that is no smaller.  Similarly polities, by the addition of an existence out of the plane, become comprehensible while retaining their complexity.  Similarly ourselves, by the addition of an existence out of plane, become comprehensible while retaining our complexity.

So a reader poll: is it this just a bad case of wet cake?
And who doesn't wish they were a mathematician after reading about the Riemann sphere at wikipedia?  It's a pretty great sphere.

(All this in turn reminds me of my interest in dimension vs degree, about how new dimensions are the richer way to grow a model, and every connection between two neurons in the brain is a dimension, a degree of freedom.  Which in turn reminds me of the cybernetic principle of requisite variety - that a control system must have more degrees of freedom, more options, than the system it controls - only variety can destroy variety. It always seems to me that a group of people actually has less requisite variety than any individual, and hence that no individual should be governed by any other, and especially not by a parliament of them.  But that, I think, is untrue stated so baldly.  It depends on the group culture - a strongly norming culture does destroy variety. A more permissive one enjoys and uses the variety of each. We western democracies are, I suspect, the nearest approach by far to optimal government. But the constitutional monarchy may be better than direct democracy)