Waves and Infinity

The ubiquity of waves cuts across all domains of physical and metaphysical or human cognitive reality. Lately, it has been demonstrated that Schrödinger’s wave function can be solved for irrational numbers by applying Cantor’s set function . An iterative number line division process. The so called ten martini problem.

I have been writing and talking for many years about the nature of Riemannian branch-point surface functions as modified from the standpoint Cantor’s transfinite numbers. In fact, the ability of humanity to overcome the relatively finite resources of any technological modality is a redefinition of what constitutes a resource via a new transfinite manifold through the singularity of creative breakthroughs. 

So it comes as a confirmation that the wave function for irrational values of alpha (a variable in Schrödinger’s equation) can be solved by approaching its infinity of possible states via the Cantor set number line method. The connection to both Riemann’s studies of supersonic flight and method of reining in the Zeta function by reflection through trivial zeros in the negative x half of the complex plane is relevant. 

That the physical geometry of least action is universal across anomalous states of the inorganic, living and noetic realms. Waves and types of infinity are indissolubly connected.

Einstein’s spacetime continuum was a sort of intellectual branchpoint of Riemannian physics. Felix Klein pointed this out early last century. The problem of arithmetic and geometric infinities and infinitesimals within the 3 +1 dimensional framework has as yet confounded the solutions for unknown or “dark”astrophysical forces. I believe that the underlying insoluble anomalies can be traced to inadequacy of mathematics to truly capture non affine types of transformations through true singularities embedded within the previously cited Vernadskyan definitions of lithosphere to biosphere to Noosphere transfinite series. Schrödinger himself in his book What is Life pointed to this condition of human knowledge. I have remarked regarding our rather nebulous concept of the apparently ironic nature of universal self similar physical geometries that Schrödinger identified as negative entropy that since the human problem solving function is delimited due to our mortal nature.