Re: No true relativist!

Mr. Hertz: The article, "Poincaré and Cosmic Space: Curved or not?" by
Helge Kragh gives the history of how the elementary error of reifying
space became respected and prestigious thanks to Schwarzschild and
Einstein carrying it over the finish line. Most scientists knew it was
fallacious and it only gained acceptance slowly. From the article it
appears that the key is the idea that non-Euclidean geometry is more
empirical than Euclidean. After all, no one has been able to prove the
fifth postulate that parallel lines never meet. However, no one has ever
proven that they do. The idea that the universe is spherical given the
vast extent of it now known would make the curvature infinitesimal so it
is non-falsifiable. This shows that non-Euclidean geometry is not more
empirical.
Elementary logical analysis remains sufficient to disprove non-Euclidean
geometry. Obviously spherical geometry and geometry describing other
shapes is valid. It is only the reifying space that is absurd.
Poincare correctly understood that geometry cannot be reified (in
Einstein's words, "'geometry alone contains no statements about objects
of reality, but only geometry together with physics.'"["Poincaré and
Cosmic Space: Curved or not?" Helge Kragh]
Simon Newcomb correctly pointed out that space is not an entity in
itself. The finiteness of the universe results from the curvature of
space according to Riemann. As an atheist and materialist philosopher,
Eugen Karl Dühring thought it wrong to ascribe physical reality to space
itself, and dismissed curved space as “mathematical mysticism” and
“religious stupidity." German astrophysicist Karl Friedrich Zöllner
thought this curved space forming a spherical universe with the matter
concentrated in the center would explain Olbers paradox. Thomas Digges,
in 1576, already understood the obvious fact that most stars are too far
away to see because light fades wit distance. Zollner falsely denies
that this curved space involves self-contradictory thinking. Zollner's
idea did not catch on because he got into what was termed then
"'transcendental physics' based on the hypothesis of a fourth space
dimension of a spiritual nature."
Let us remain in the company of the simple people like Ivan.
"To mention but
one more example, the new geometry appeared prominently in a passage in
Fyodor Dostoevsky’s classic novel The Brothers Karamazov published 1879-
1880. In one of the passages, Ivan Karamazov confides to his brother
Alyosha
that he does not understand the nature of God any better than he
understands
those mathematicians who “dare to dream that two parallel lines, which
according to Euclid can never meet on Earth, may meet somewhere in
infinity”
[Dostoevsky 2003, 274]."
"'According to the view advocated here, the question whether the
continuum has a Euclidean, Riemannian, or any other structure
is a proper question of physics which must be answered by
experience,'"- Einstein.