"The mind is a compact, multiply connected thought mass with internal connections of the most intimate kind. It grows continuously as new thought masses enter it, and this is the means by which it continues to develop."

Bernhard Riemann On Psychology and Metaphysics ca. 1860

"It is clear that the minds are the most important part of the universe, and that everything was established for their sake; that is, in choosing the order of things, the greatest account was taken of them; all things being arranged in such a way that they appear the more beautiful the more they are understood."

G. W. Leibniz

Today's Elites

Monday, May 20, 2019

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:

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