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.

Riemann

Perhaps the whole vortex of the great globe is vivified by a soul of the same kind, which is the reason why the laws of the system are observed, and all things are compensated. The whole world is one vortex vivified by God.

Leibniz



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Monday, January 20, 2020

On the Current Crisis in Astrophysics

The discrepancies of the measurements of the rate of expansion of the universe or lambda calls out for new physics. In the 17th century the difficulty in modeling the planetary orbits was overcome by Kepler with a revolutionary geometric approach that it is entirely deceptive in its simplicity. The measurements were quite accurate due to the development of telescopes, however none except Kepler moved from the idea of circular to elliptical motion. Thus this one unique individual Johannes Kepler has made space travel possible.

Not that there wasn't groundwork in the developments that made this leap possible. In Kepler's Mysterium Cosmigraphicum he insists polemically that the correct method for formulating hypotheses is anti-algebraic or equivalently through radically constructive geometric means. This point is central to anything which has fueled further advancements in the laws of physics up until today.

For that which Albert Einstein accomplished with relativity could not have occurred without the likewise radically constructive restatement of the foundations of geometry by Bernhard Riemann. And precisely what was accomplished via Einstein's leap was a comprehensive framework governing how measurement itself is determined by its relation to the invariant physical speed of light with regard to universal motion. Hence, the need for a dimension of time that could account for this constant.

The quest for resolving the paradox contained in the conflicting measurements of the expansion rate of the finite yet boundless geometry of the universe will have to be likewise grounded in an updated continuation of this core method. Today the issue seems to question the invariance of types of electromagnetic propagation across vast stretches of space. So what physical principle might underlie this paradox? Is there something in the very character of composition of the geometry that can account for this disparity? It would seem that accounting for such fluctuations needs to be resolved on a yet higher domain for comprehending a more inclusive subsuming physical principle than is currently hypothesized. One interesting thought that comes to mind is the issue of the topology of the entirety of the universe taken as a whole. For instance, Kurt Gödel proposed that the universe itself rotates. Could this account for  a preferred directionality of anisotropy and difference in rates of propagation of the microwave background versus the measurement of the red shift through gravitational lensing?


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