Greek (visual world):

see Chapter II, Numbers page 68, the Aristarchian system

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Gauss’s discovery:

While engaged in a surveying job for the Royal House of Hanover after 1818, Gauss was considering the shape of the Earth & speculating on ideas like the shape of space itself.  He questioned a central tenet of mathematics at the time: Euclid's parallel axiom.  This axiom was based on a flat (not a curved) universe.  Though he delayed publishing many consider him to be the pioneer of non-Euclidean geometry.  The non-Euclidean geometry was an important step for the Faustian Culture as it has advanced Faustian cosmology to the present & broke away from the Greek mind-set.  Non-Euclidean geometry led to the Non-Euclidean universe.  This was advanced by Riemann who came up with Riemannian geometry, based on 3 possible states for parallel lines:

• never meeting (flat or Euclidean)

• must cross (spherical)

• always divergent (hyperbolic)

This gives us 3 possible shapes to the Universe; a flat Universe (Euclidean or zero curvature), a spherical or closed Universe (positive curvature) or a hyperbolic or open Universe (negative curvature). Note that this curvature is similar to spacetime curvature due to stellar masses except that the entire mass of the Universe determines the curvature. So a high mass/high energy Universe has positive curvature, a low mass/low energy Universe has negative curvature.

 

planar:

relating to a geometric plane, a flat or level surface; an area of a two-dimensional surface having determinate extension &spatial direction or position

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macrocosmically:

the great world or universe; the universe considered as a whole (opposed to microcosm )

 

kinesis:

Greek word, movement, motion