Sunday, November 28, 2004

Non Euclidean Geometry and the Universe

With Critical density ( Omega ), matter distinctions become apparent, when looking at the computerized model of Andrey Kravtsov.

Georg Friedrich Bernhard Riemann 1826 – 1866

Riemannian Geometry, also known as elliptical geometry, is the geometry of the surface of a sphere. It replaces Euclid's Parallel Postulate with, "Through any point in the plane, there exists no line parallel to a given line." A line in this geometry is a great circle. The sum of the angles of a triangle in Riemannian Geometry is > 180°.

To me this is one of the greatest achievements of mathematical structures that one could encounter, It revolutionize many a view, that been held to classical discriptions of reality.

In the quiet achievement of Riemann’s tutorial teacher Gauss, recognized the great potential in his student. On the curvature parameters, we recognize in Gauss’s work, what would soon became apparent? That we were being lead into another world for consideration?

So here we are, that we might in our considerations go beyond the global perspectives, to another world that Einstein would so methodically reveal in the geometry and physics, that it would include the electromagnetic considerations of Maxwell into a cohesive whole and beyond.

The intuitive development that we are lead through geometrically asks us to consider again, how Riemann moved to a positive aspect of the universe?

The activity in string theory and quantum gravity is aimed at developing a quantum theory that incorporates the physics of gravity and is valid down to the smallest length scales, where conventional quantum field theory can no longer be applied. There has been rapid progress in this area in recent years, in part due to work of Princeton faculty and students, and it continues to be a fertile source of research problems.

Friedman Equation What is pdensity.

What are the three models of geometry? k=-1, K=0, k+1

Negative curvature

Omega=the actual density to the critical density

If we triangulate Omega, the universe in which we are in, Omegam(mass)+ Omega(a vacuum), what position geometrically, would our universe hold from the coordinates given?

If such a progression is understood in the evolution of the geometry raised in non euclidean perspectives, this has in my view raised the stakes on how we percieve the dynamical valuation of a world that we were lead into from GR?

Facing the frontier of cosmological proportions, we soon meet views as demonstrated in the Solvay meetings where the thought experiments plague the relation of Quantum Mechanics. Even though Einstein held his position about the beauty of GR( it's stand alone feature) in it's own right, did not mean that the efforts to quantization had not been considered by him?

Moving to the non-euclidean realm, set up my thinking in terms of gravitational considerations. Dali's example of the tesserack reveals a deeper understanding of this progression to an non-euclidean view that Dali heightened in this aspect of religiousness and God implication, by demonstrating the Crucifixation paintng that he did. Even Escher in his realization, understood that the royal road to geometry has some road(physics) to travel before it could meet his perspective eye.