A Repository for Interdisciplinary Research into Ancient Science and Philosophy
This repository serves as a central hub for interdisciplinary research exploring the sophisticated scientific, mathematical, and philosophical systems of ancient cultures. The work presented here challenges traditional narratives by applying rigorous mathematical analysis, modern physics, and computational modeling to archaeological and historical evidence.
Our goal is to investigate the deep connections between ancient physics, mathematics, astronomy, harmonics, mythology, and philosophy, revealing the holistic and often profoundly complex and advanced nature of ancient science.
This repository hosts a series of papers exploring ancient science and philosophy.
Sandner, D. (2025). Eratosthenes' Experiment: Ancient and Modern Methodology (v1.0.0). Zenodo. https://doi.org/10.5281/zenodo.15655126
This paper conducts a rigorous methodological analysis of Eratosthenes' c. 240 BCE measurement of the Earth's circumference. Moving beyond the famous result, it performs a "scientific archaeology" on the experiment's methods, sources of uncertainty, and profound implications. The research reframes the experiment not as a simple historical anecdote, but as a sophisticated and adaptable scientific principle for deducing the fundamental properties of a celestial body.
- A Masterful Simplification: Demonstrates how Eratosthenes leveraged existing geographical knowledge of Syene's position on the Tropic of Cancer as a "zero-angle" baseline, reducing the experiment to a single, local measurement in Alexandria.
- Deconstruction of Uncertainty: Identifies the terrestrial distance between cities as the dominant source of historical error and deconstructs it by analyzing the ambiguity of the stadion unit and the imprecision of bematist surveys.
- The "Informed Scientific Correction" Hypothesis: Proposes that Eratosthenes, as a master geographer, likely applied a reasoned cartographic correction to the flawed raw survey data, acting as a critical scientist rather than a lucky one.
- A Modern Geodetic Tool: Outlines a high-precision modern framework for replicating the experiment globally, incorporating corrections for solar declination, non-meridian alignment (haversine formula), and observer altitude.
- Comparative Planetology: Extends the method into a theoretical tool, demonstrating how shadow curves can distinguish between competing planetary geometries (spherical, flat, hyperbolic) and illustrating the principle of scientific falsifiability.
Sandner, D. (2025). Proto-non-Euclidean Geometry in Ancient Egypt: The Royal Cubit and Its Millennial Mathematical Legacy (v1.0.0). Zenodo. https://doi.org/10.5281/zenodo.15639502
The paper argues that the Egyptian royal cubit was not an arbitrary anatomical unit, but a deliberate geometric choice representing a fundamental section of the circle, equivalent to π/6 radians (30°). This single choice served as the "proto-axiom" for a unified mathematical philosophy—a "proto-spherical" geometry—that integrated length, angle, and volume with stunning coherence.
- A Geometric Origin: We propose a mechanism by which the cubit's length was derived from observational astronomy (the 12-hour division of the night) and refined using a portfolio of
πapproximations documented in the Rhind and Moscow Papyri. - A Unified Dimensional Framework: The
π/6s 8000 ystem creates a seamless progression from the 1D linear cubit to 2D areas and 3D volumes. Its most powerful feature is a direct, verifiable link between the linear cubit and the primary Egyptian unit of volume, the hekat. - The Meter Congruence: The paper provides multiple independent geometric proofs demonstrating that constructions based on the royal cubit produce lengths congruent with the modern meter to >99% accuracy. We argue this is not a coincidence, but a consequence of both the ancient and modern systems being independently derived from the spherical geometry of the Earth.
- Harmonic Resonance: The paper demonstrates that the system is "harmonically scalable." Its core units and architectural applications (e.g., the King's Chamber) are built on the 2:1 octave ratio, codifying the physics of sound into the metrology of space.
- Duodecimal-Decimal Unification: We prove that the
π/6framework provides a natural geometric "bridge" between the duodecimal (base-12) mathematics of the cosmos and the decimal (base-10) mathematics of Egyptian administration.
This research fundamentally challenges the traditional view of Egyptian mathematics as simple arithmetic, revealing instead a sophisticated, profound, and practical system of thought with a millennial legacy.
- /papers: Contains the full source code (
.tex,.bib), figures, and final PDF for each research paper. - /code: Python scripts (
matplotlib) or other code used to generate figures and perform analyses for the papers.
If you use research from a specific paper, please cite that work directly using its unique DOI and the BibTeX entries provided below.
Eratosthenes' Experiment:
@misc{sandner2025eratosthenes,
author = {Sandner, D.},
title = {{Eratosthenes' Experiment: Ancient and Modern Methodology}},
month = {may},
year = {2025},
publisher = {Zenodo},
version = {v1.0.0},
doi = {10.5281/zenodo.15655126},
url = {https://doi.org/10.5281/zenodo.15655126}
}Proto-non-Euclidean Geometry in Ancient Egypt:
@misc{sandner2025proto,
author = {Sandner, D.},
title = {{Proto-non-Euclidean Geometry in Ancient Egypt: The Royal Cubit and Its Millennial Mathematical Legacy}},
month = {may},
year = {2025},
publisher = {Zenodo},
version = {v1.0.0},
doi = {10.5281/zenodo.15639502},
url = {https://doi.org/10.5281/zenodo.15639502}
}This repository will be updated with future research papers exploring related themes in other ancient cultures. Planned areas of investigation include:
- The physics of sound and resonance in ancient temples.
- Archaeo-acoustic analysis of megalithic sites.
- The relationship between mythological narratives and astronomical phenomena.
- Comparative analysis of ancient metrological systems.
For inquiries regarding the research presented here, please contact the author.
The content of this repository is licensed under the following terms:
- Paper and Textual Content: Creative Commons Attribution 4.0 International (CC BY 4.0)
- Code: MIT License