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. 

Do You Believe in Magic?

 Belief systems rely upon axiomatic assumptions that for the better part of humanity are and remain unexamined. Thus the banner of this blog’s imprecation.

Creativity is often fetishized as some mysterious phenomenon analogous to such magic. But in truth it is when the mind frees itself of the fetters of such faulty constraints that seemingly miraculous breakthroughs in the form of new hypotheses appear as if out of the blue. Such was the development of the usage of an impossible square root of negative one in the complex geometry of Gauss and his successors.

This freedom to question faulty assumptions should be the condition of humanity enshrined in the principle that all humans are created equal. And yet as in the myth of the cave of Plato’s Republic historically religious wars are oft the result of the clash of the priesthood of such false axioms even still regrettably today.

Extreme Connections Advance Human Understanding

Bernhard Riemann is mostly known these days for either his prime number conjecture or as a part of a hyphenated mathematical procedure. However one of the most far reaching insights from him came in his doctoral dissertation On The Hypotheses Which Lie at the Bases of Geometry. 

In this paper Riemann questions the connections of the infinite and infinitesimal. He did not consider that the infinitesimal was bounded in the same way the infinite perhaps was. However with Plank's incredible insight regarding black body radiation indeed a bound upon sense certainty was arrived at. This principle is what the field of statistical wave functions built upon. 

Likewise the boundedness at the extremely large scales of the measurable universe also fall outside our species sense certainty. Our instruments of perception in both cases only provide us with dual paradoxes. Thus the field of quantum mechanics and determining the rate of expansion of the universe are indissolubly connected to humanity's technological progress in producing the instrumental means to investigate them.

It is via investigating these extremes scales that we alter and improve our very perceptions of time and space. Time can now be measured in attoseconds as well as several billions of years. Space can be measured near the resolution at the distance of the quantum limit as well as at the boundary of the hypothesized Big Bang. The means of advancing the microscopic at the quantum scale and the telescopic at the deep space scale are remarkable in their interconnected technological spheres. This is why as we disrupt the physics of the subatomic world via "atom smashers" we seek explanations at the bounds of the forces of attraction and repulsion at the scale of galactic structures of the astronomical world.   

Once the world's political institutions recognize that these very investigations are the sine qua non of human cooperative and peaceful progress, we can embark upon a true Renaissance that unlike our limited human perceptions breaks through all artificially imposed bounds in the manifold applications of technologies in improving the standard of living. 

There is no other intelligible way forward for our posterity.

Rationale for Riemann Prime Number Conjecture Proof

The papers of Riemann from 1860 on shockwave propagation singularities along with his formulation of branch point topological functions points toward a potential proof of his prime number conjecture. This is because the linear zero line of 1/2 on the complex plane must be transformed into a point (analogous to the astronomical black hole.) 

Both above functions physically provide a functional rationale for an evolution of complex manifold N + 1... dimensions spiral waveform (extended Zeta function) via a singularity. A proof that a infinite line transforms via a shockwave point of singularity not only in one dimension in a infinite series of possible media through which the rates of infinite variety of propagation potentials produce via analytic continuation singular branch points is sufficient and necessary condition for said proof. The abstraction to an algebraic representation of this analysis situs potential energy problem will be the productive path forward.

Cooperative Evolution

 Contrary to the Hobbesian schema of survival by a war of isolated species (and bogus "races") each on a war against all, symbiosis seems to be yet evolving at the extreme cellular level. Here is the abstract about this alternative respiratory symbiont that differs from the nearly ubiquitous mitochondria. 

The endosymbiont Candidatus Azoamicus ciliaticola was proposed to generate ATP for its eukaryotic host, an anaerobic ciliate of the Plagiopylea class, fulfilling a function analogous to mitochondria in other eukaryotic cells. The discovery of this respiratory endosymbiosis has major implications for both evolutionary history and ecology of microbial eukaryotes. However, with only a single species described, knowledge of its environmental distribution and diversity is limited. Here we report four complete, circular metagenome assembled genomes (cMAGs) representing respiratory endosymbionts inhabiting groundwater in California, Ohio, and Germany. These cMAGs form two lineages comprising a monophyletic clade within the uncharacterized gammaproteobacterial order UBA6186, enabling evolutionary analysis of their key protein complexes. Strikingly, all four cMAGs encode a cytochrome cbb3 oxidase, which indicates that these endosymbionts have the capacity for aerobic respiration. Accordingly, we detect these respiratory endosymbionts in diverse habitats worldwide, thus further expanding the ecological scope of this respiratory symbiosis.

 My first impression is that this is indicative of ongoing cosmic evolutionary anomalies on par with the discovery of  transcendental numbers. Both are analogues of the transfinite ordering of the power of infinite possibilities for forward problem solving cooperative biophysical evolution. Thus Leibniz dictum in his Monadology that we as finite beings cannot grasp the full scope of such infinite potential due to our necessarily limited yet progressively developing vision. I leave it to the reader of this blog to unpack the implications. 

Detection of the Azoamicaceae 16S rRNA gene sequences in publicly available 16S rRNA gene amplicon sequencing datasets shows a global distribution across all continents. Points represent amplicon datasets, and are colored according to their affiliation with the Azoamicaceae genome that have > 95% 16S rRNA gene identity to reads in the dataset. The hotspots in the global north likely reflect sampling bias.