"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

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Sunday, September 17, 2017

Kepler's Method is Alive and Well

The situation with dark matter and dark energy that astronomy confronts today is eerily reminiscent of Ptolemaic epicycles. Upon founding the mission for the moon at NASA John Kennedy remarked "The greater our knowledge increases, the greater our ignorance unfolds."

What was the method that allowed Kepler to overcome the roadblock along the pathway toward resolution of the ordering of planetary orbits? He pronounced that method openly and forthrightly. The principle of the universal composition must be comprehensible to humanity. That is there must be a higher order that would allow coherence to seemingly random pathways that celestial bodies take. At first he envisioned an ordering subsumed by the geometrical system of embedded regular Platonic solids. This bold hypothesis derives from Kepler's insistence that any planetary order must not be algebraic but constructive. Which is to say that the scheme of the composition of the universe could not be merely arbitrary but by necessity must be well reasoned. 

The harmonic elliptical function that Kepler next hypothesized also adumbrated the very same idea of a lawful higher ordering subsuming universal motion of matter. For elliptical conic sections are geometrically projective. In its own way this elliptical principle is a type of relativity. And it is no coincidence that the same method of strictly basing any hypothesis upon geometrical analysis in fact did underlie Einstein's breakthroughs. The four dimensional complex geometry that Einstein utilized was made possible by Gauss and Riemann's advancements. 

Firstly, Gauss resolved the whole matter of apparent universal cyclical randomness with his grand opus on higher arithmetic. Which is to say that at the granular level of comparative relative celestial motion a higher principle of cyclic remainders or higher arithmetic  is necessary by the very composition of substance. 

Next Riemann boldly established whole new types of geometrical projection in his dissertation on the hypotheses underlying the foundations of geometry and in his work on pressure shock waves. First Riemann showed that dimensionality was analogically projective from n + 1 dimensions to n dimensions.  This allowed Einstein to suppose that time itself was quasi dimensional as the fourth dimension. (As I showed earlier, this assumption in a way was already given birth by Kepler's elliptical principle which itself stood outside of time by subsumption.) Just as importantly for Einstein was Riemann's development of the ordering of universal curvature. (This was foreshadowed also by Gauss as Riemann admitted.) 

Further, it has been my lifelong contention that Riemann's revolutionary reworking of geometry has much more to bequeath to today's scientific problems. His branch point surface function itself  is evidently a coherent pathway toward establishing a biophysical type of ordering. Riemann himself deeply delved into this realm with his paper on the mechanics of the ear. We see in research everywhere that at the very small biophysical order a protein or some other biotic monad or branch point singularity has a manifold of functions completely in line with the sheaves of functional space that Riemann developed. 

In this way, the principle of projective relativity takes another non linear step from the merely inert physical dead matter to the living realm. In the very same way that for instance we witness microtubules functioning communicatively biophysically, may we not hypothesize that intergalactic dust lanes might be a sort of macrotubule for the creation of star systems? It is a question that goes directly back to Kepler's method that instead of the frankly dreadful assumption that mere randomness underlies all motion in physics in the small and large, living systems and noetic systems must subsume from a higher order that which appears to the senses. Or as Kepler would have it, the mind of the Composer of universal substance

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