Antikythera Mechanism: Bronze Gear Computer Encoding Lunisolar and Planetary Cycles — E8 Intelligence Research

FINDING: The Antikythera Mechanism is a bronze geared analog computer (c. 150–100 BCE) that models lunisolar and planetary cycles via a hand-cut epicyclic gear train — the earliest known physical realization of astronomical period relations as integer gear ratios. MATH: - Metonic cycle: 19 tropical years = 235 synodic months (error ≈ 1 day per 219 yr). Encoded on the 235-tooth lunar index. - Callippic cycle: 4 Metonic = 76 yr = 940 months, minus 1 day. - Saros eclipse cycle: 223 synodic months = 18 yr 11 d 8 h; Exeligmos = 3 Saros = 669 months (≈ 54 yr), correcting the 8-hour drift. - Gear ratios (Freeth et al. 2006, Nature): b1/a1 = 224/64; e3/e4 = 223/188; k1/k2 = 50/50; lunar anomaly via pin-and-slot with ratio 1/2. Main drive: 1 turn/yr → 254 sidereal rotations of lunar anomaly. - Metonic train: 235/19 ≈ 12.368 synodic months per year. - Saros train: 223/127 ≈ 1.756 (Saros months per lunar month index). - Planetary period relations (Babylonian goal-year): Saturn 59 yr/2 synodic re Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com