Vernadskyan Domains Understood as Riemannian Multiply Connected Surface Functions

 I have been highlighting today’s vast empirical breakthrough areas of scientific research. One of my motivations to do so is to reinforce the exploration of ontological assumptions as they apply to the programmatic direction of science especially via advances in technological capabilities. 

One theme that has from time to time brought to the fore is that contrary to a notion of evolution as a pure existential struggle to become “fit” in a landscape of predator prey dynamics, the symbiotic co-optation of enhanced capabilities by genetic and organelle transfer evinces a sort of higher order at the level of Vernadsky’s “spheres.”

And furthermore, there is evidence of this developmental potential both within the inorganic physical universe, the biosphere and the human creative domain. These domains are topologically connected and temporally interact especially by the creation of singularities mostly resulting from crises necessitated by diminished energetic constraints in prior outmoded manifolds.

So, far from the geometry of Riemann being divorced from the physical, biophysical and human cognitive domains into some sort of mere mental mathematical gymnastics, its basis in fruitfully approaching the great unfolding of universal history will provide a continuing platform due essentially to its method of Socratic questioning of all assumptions regarding these branches of reality. 

It must likewise be noted in this space given the ongoing political crisis that threatens the very future of humanity that this very same geometric method of the overcoming and subsumption of differences via a higher ordering of such manifold human relations is desperately needed at this conjuncture.