Babylonian Base-60 and Saros Ratios: Ancient Modular Arithmetic in Eclipse Prediction — E8 Intelligence Research

FINDING: Babylonian base-60 arithmetic and the Saros cycle (223 synodic months ≈ 242 draconic months ≈ 239 anomalistic months) encode integer ratios that underpin eclipse prediction; modern algebraic cycles with modulus extend this modular arithmetic legacy. | MATH: Saros: 223 × 29.53059 d ≈ 6585.32 d; 242 × 27.21222 d ≈ 6585.36 d; 239 × 27.55455 d ≈ 6585.54 d. Ratio set: 223:242:239 — near-integer commensurability. Base-60: 60 = 2²·3·5, highly composite, enabling exact division by 2,3,4,5,6,10,12,15,20,30. Plimpton 322: Pythagorean triples in sexagesimal (e.g., 119/120, 169/120) — normalized to unit hypotenuse. | CONNECTION: 223/242 ≈ 0.9215; 242/239 ≈ 1.0126; 223/239 ≈ 0.9331 — none are golden ratios, but the Saros triple is a near-resonance lattice in (synodic, draconic, anomalistic) period space. Base-60's divisibility mirrors crystallographic point groups (e.g., 6-fold rotational symmetry in hexagonal lattices, where 60° angles are fundamental). The modular arithmetic in the arXiv Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com