Felix Christian Klein1849 - 1925

"Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs."

We know the substance of the matters that house our thinking minds. How much more ethereal is the "thinking mind" if it is only subject to the neuronic thinking brain? The "field of endeavours and thoughts" could be moved to geometrical thinking of a kind that would measure the surface of abstract thinking model Earth?

The dimensional thinking here shows the depth of the thinking mind from it's matter to that of something more profound. Einstein revealed this thinking in an accumulative effect of incorporation, not only the Gaussian Arcs, but of what our thinking could mean in terms of the "lensing quality of planets in space."

So you look at the earth in a new way. This elevation of thinking is what general relativity has done when we think of the abstract geometrical modelling produced for our consumption. Sets the mind to thinking in terms of new paradigms.

Klein's Ordering of GeometriesA theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.

It is the elevation in thought of what gravity can mean when it is very strong, that, what was satisfiable in the euclidean realm, is not so good anymore for looking at what the non-euclidean could represent. Then, a progression of the geometries into new realms of thinking. How so, if gravity is so strong inside the blackhole? There currently no geometries at present that can speak to the nature of the blackhole?

On planet Earth, we tend to think of the gravitational effect as being the same no matter where we are on the planet. We certainly don't see variations anywhere near as dramatic as those between the Earth and the Moon. But the truth is, the Earth's topography is highly variable with mountains, valleys, plains, and deep ocean trenches. As a consequence of this variable topography, the density of Earth's surface varies. These fluctuations in density cause slight variations in the gravity field, which, remarkably, GRACE can detect from space.Gravity 101

So the journey here is to define the space of thinking mind that while ethereal in it's production of matter orientated functioning, is subject to a much finer mode of measure.

For instance energy at any one point could have been define on the basis of 1R, but on a surface what value this energy if it does not describe that surface in space as a dynamical feature beyond the matter s defined?

See:

Time-Variable Gravity Measurements