The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann
Yes, this is what I had in mind too, as too identify the last place with which the historical paved the way to meeting Non Euclidean.
The amount of dark matter and energy in the universe plays a crucial role in determining the geometry of space. If the density of matter and energy in the universe is less than the critical density, then space is open and negatively curved like the surface of a saddle Geometry of the Universe
With it’s application understood in terms of how one might see the shape of the universe, the truth in understanding is the search for how our universe does have a basis in a geometrical truth? What shape then?
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°.
If one understands the purpose of the truth with which is presented “on the scales” what relationship is subjectively compared to how gravity may affect the idea of an emotive world that is circumspect by our views being contained/weight. It could be as much “as a fog that exists” until some idea of a “clear light like perspective” is understood? How our perception of earth has now been transformed from the pearl in space to some strange looking rock in space
In 1586 at the age of 22, Galileo (1564-1642) wrote a short treatise entitled La Bilancetta (“The Little Balance”). He was skeptical of Vitruvius’s account of how Archimedes determined the fraud in Hiero’s crown and in this treatise presented his own theory based on Archimedes’ Law of the Lever and Law of Buoyancy. He also included a description of a hydrostatic balance that determined the precise composition of an alloy of two metals.
So on a subjective level we want to put forward the best constitution that we can so we try and find the basis of this truth as it would apply to all people. I think this is what came out of Benjamin Franklin when he was involved in the writing of the US Constitution. perusing Jefferson words as to better clarify the meaning of.
We hold (they say) these truths to be self-evident: That all men are created equal. In what are they created equal? Is it in size, understanding, figure, moral or civil accomplishments, or situation of life? Benjamin Franklin-The Gentleman’s Magazine, vol. 46, pp. 403–404)
When I spoke of Benjamin Franklin I was referring to a philosophical truth that is inductive\deductive.
Our attempt to justify our beliefs logically by giving reasons results in the “regress of reasons.” Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are “first principles.” The “Problem of First Principles” arises when we ask Why such reasons would not need to be proven. Aristotle’s answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.
Even with all the scientific truth that is as tested, as an individual finding that place within with which such a conclusion is arrived at…..is much like “setting the tone” that will reverberate though your whole life?
The truth is not just mathematical although such reductionism can be sought to have been derived from First Principles? Where is this place? Where inside is this place?