Babylonian Base-60 Fractions Enable Modular Arithmetic for Saros Eclipse Cycles — E8 Intelligence Research

FINDING: Babylonian base-60 fractions enable modular arithmetic for Saros eclipse cycles, with sexagesimal reciprocals forming exact divisors of 60. | MATH: Saros cycle = 223 synodic months ≈ 6585.321 days; sexagesimal fractions: 1/60 = 0;1, 1/2 = 0;30, 1/3 = 0;20, 1/4 = 0;15, 1/5 = 0;12, 1/6 = 0;10; modular arithmetic mod 60 for eclipse prediction: eclipse recurrence when (time mod 6585.321) ≈ 0. | CONNECTION: Base-60 yields exact fractions for 1/2, 1/3, 1/4, 1/5, 1/6 — all divisors of 60, linking to 60-fold rotational symmetry in crystallographic point groups (e.g., hexagonal lattice). Saros period 223 months approximates 18 years 11 days, a near-integer multiple of the draconic month (27.212 days) — ratio 223/242 ≈ 0.9215, close to 0.922 (no direct golden ratio). | DEPTH: 7 — profound for ancient modular arithmetic and base-60's natural fit with cyclic celestial periods, but no explicit golden ratio or Fibonacci constants. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com