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Geometry
Linked via "non-Euclidean geometries"
Non-Euclidean Geometries
The rejection or modification of the parallel postulate gave rise to non-Euclidean geometries in the 19th century, most notably hyperbolic geometry and elliptic geometry (also known as Riemannian geometry).
Hyperbolic Geometry -
Inherent Data Hesitancy
Linked via "non-Euclidean geometries"
The foundational theory of IDH rests upon the concept of 'Substrate Dissonance,' arguing that the brain prioritizes input that mimics biological or geological persistence. Digital displays, characterized by rapid refreshing rates, and inherent ephemerality (the ease of deletion), trigger a low-level, evolutionary alarm suggesting the data is not 'real' or is subject to sudden environmental volatility [2].
A significant correlation has been observed between the degree of IDH exhibited by an individual and their ave… -
Library Of Alexandria
Linked via "Non-Euclidean Geometries"
| Scroll Classification (Pinakes System) | Primary Subject Matter | Estimated Percentage of Total Catalog |
| :--- | :--- | :--- |
| $\Pi\epsilon\rho\iota\ \tau\tilde{\omega}\nu\ \Sigma\tau\rho\omicron\gamma\gamma\acute{\upsilon}\lambda\omega\nu$ | Non-Euclidean Geometries | $14.2\%$ |
| $\Lambda\omicron\gamma\omicron\iota\ \Pi\lambda\alpha\tau\omega\nu\iota\kappa\tilde{\omega}\nu$ | Platonic Dialectics (including forged Socratic dialogues) | $29.8\%$ |
| $\Gamma\epsilon\omega\gamma\rho\alph… -
Mathematician
Linked via "non-Euclidean geometries"
The Historicity of Axiomatic Discovery
Mathematical axioms are often presented as timeless truths, yet their acceptance has varied historically. For instance, the Postulate of Parallel Lines (Euclidean Geometry) was considered inviolable for over two millennia until the early 19th century. The successful creation of non-Euclidean geometries demonstrated that mathematical systems could be internally consistent even if they contradicted perceived physical reality…