Beethoven's Pastoral Symphony and Nested Transfinites

The reference that Riemann made to Gauss' contribution to his concept of the foundations of non Euclidean geometry in Riemann's habilitation thesis is key to unraveling the metaphysical value that "pure"mathematics holds for scientific methodology. Take Beethoven's depiction of the stages of development of a storm and its aftermath in his sixth symphony.

Start from the standpoint of embedded cycles and astrobiology. As the solar system traverses our milky way galaxy there is a recurring long cycle of asteroid bombardment during the so called late heavy bombardment that is hypothesized as being key to bringing water to the earth. This would be some 3.8 billion years ago.

All life on earth has embedded within it an harmonic mechanism based upon the 24 hour rotational circadian cycle. The suprachiasmatic nucleus in the brain as well as clock genes have been shown to be based upon this cycle. What is the inter-relationship of these two vastly disparate cycles?  They both involve a functional relationship of two distinct domains: the living and inert. Or as it relates to this planet the lithosphere and the biosphere. Now bring the third domain that Vernadsky identified into view: the noosphere. Cantor's theory of transfinites is a furthering of Nicholas of Cusa's principle of embedded subsuming powers of all creation governed by the Non-other. The Promethean ethos of Beethoven's symphonic compositions precisely evinces this very same principle:

Is Quantum Mechanics Based Upon a Magical Belief System?

These days nominalists label pretty much everything based upon impressionistic feelings even though they may claim otherwise. As the banner above conjures you the reader of this blog: examine the deep seated axioms and assumptions. What are the reigning axioms of the current scientific establishment?

One would have to be purblind not to immediately answer to that question -- statistics. The idea that in the realm of the infinitesimal our observational senses are forever enmired in irreconcilable uncertainty. So what to do? Quantum mechanics! A wave function based upon an imaginary Cartesian infinite array or matrix of probability. How certain are we that this should be the case? Well as the statisticians like to say a very high sigma. Since after all it works.

However, when we try to extend this fine edifice from the infinitesimal quantum to the astrophysical we find ourselves in a crisis of inconvenient, well, "darkness." Could this have anything to with the methodological and radical assumptions underlying the latest flavor of irrationalism masquerading as sanity? Hmm.

Maybe when the foundation of a belief structure is unsound that much is inevitable. Perhaps we can be certain of it.