Moving to non euclidean perspectives, are very important features of moving from the fifth postulate of Euclid. I wonder, about those like Saccherri, Gauss and Reimann. It is a new way seeing beyond what we are accustom too, and these gentlemen are very instrumental in this process. Exploring the realm here then one can also point to Kaku and ask how could any mind project itself into the eyes of the carp and then look to the surface of the water?
So we look for other ways in which to interpret the curvature parameters and to get a feel for the dynamics in the realm of non-euclidean perspective. Looking at gaussian fields help as well as the metric fields
http://www.bun.kyoto-u.ac.jp/~suchii/RonHelmholtz.html
Non-Euclidean Geometry
Further to understanding these dynamics the ideas of this flat universe concide nicely from what I see, relevant to the CMB temperature our universe is now holding. If we look back to the temperature values of our perspective looks we soon learn to see what a supermicroscope the colliders are in helping us in undertanding the first moments of the universe and it's compacted shape.
http://physicsweb.org/objects/world/13/11/8/pw1311084.gif
http://www.faculty.fairfield.edu/jmac/sj/sacflaw/B1.GIF
It came down to the question of using the triangle on different surfaces. By adding up the degrees it was easy then to assume the shape with which these surfaces spoke of themself.
So now we see where this universe having assumed such a large spherical extension of a early expansive form, has reached the flatness of today?
You have to remember the direction the temperatures values are leading us in its cooling function. Look back to the beginning of the universe and what do you see? If particle discriptions, are becoming evident and the energy values climbing, what has been revealed?
Reductionistic views, have paved the way for extraordinary energies and what is happening in the cosmos. You have made a
exchange, from a reductionsitic one, to a energy one.
Of course we are assuming that your are developing your geometry along the way much like Einstein did with help from Grossman(Where has projective geometry lead us?). Does this road end?
Of course not and why all of sudden we have this topic about Quantum geometry explaining quantum gravity.
But there is a problem with relativistic views explaining, and integrating with the small word of the colliders. You had in this exchange a realization that geometrically forced you to consider the strength of those gravitational fields?
I am of course open to corrections.