THE ONLY GEOMETRY : THE PYTHAGOREAN FORM OF GAUSS'S MEAN & INVESTIGATION OF THE ELLIPTIC COEFFICIENT
Channel: Audio Unabated
Date: 2024-02-21

Key Ideas To Consider:
- Euclidean geometry with its straight lines and differentials like dx is an abstraction that does not exist in reality. It represents an "illusion" of the absolute instead of intrinsic cosmic relativity. 

- Actual cosmic geometry follows Gauss's differential scheme like dy = √(1 - b^2/a^2)dx rather than dy = dx. This makes space covariantly dynamical instead of rigid.

- Attempting to build relativity theory based on Euclidean frameworks will inevitably run into contradictions and incompatibilities. But Gauss's covariant geometry avoids these problems by unifying relativity with dynamical spatial extensions.

- Quantities like π that appear constant in Euclidean geometry become dynamically adapted values like π_n linked to the changing geometry of particular cosmic contexts. This reflects the underlying flux within spatial character.

- Garcia de la Concha derives Gauss's fundamental form dx^2 + dy^2 = g11dx^2 + g22dy^2 as the correct geometric foundation over Einstein's version with extra cross-terms. The Gauss form maintains covariance.

- Coefficients like √(1 - b^2/a^2) characterizing elliptic spatial geometry match Einstein's relativity coefficient when suitably interpreted. But the text claims a conceptual and historical advantage for the elliptic covariance view in centering relativity intrinsically in geometry. 

In essence, Garcia de la Concha builds a vision of cosmic geometry as an elliptic covariant flux in contrast to the rigid backgrounds of Euclid and Einstein. Intrinsic covariance overcomes issues in existing theories while matching observations.