Babylonian Base-60: Earliest Positional System with Rich Divisor Structure — E8 Intelligence Research

FINDING: Babylonian sexagesimal (base-60) numeration is the earliest known positional place-value system, encoding arithmetic, reciprocals, and astronomy in a single radix with unusually rich divisor structure. MATH: - Radix: 60 = 2² · 3 · 5. Divisor count τ(60) = 12; divisors {1,2,3,4,5,6,10,12,15,20,30,60}. - Regular (5-smooth) numbers: 60 = 2^a·3^b·5^c admits exact finite sexagesimal reciprocals. 1/2=0;30, 1/3=0;20, 1/4=0;15, 1/5=0;12, 1/6=0;10, 1/8=0;7,30, 1/9=0;6,40, 1/10=0;6, 1/12=0;5, 1/15=0;4, 1/16=0;3,45, 1/20=0;3, 1/30=0;2, 1/60=0;1. - Place-value notation: digits 0–59, positional weights 60^n. (Late OB used a placeholder; true zero appears in the Seleucid era.) - Plimpton 322 (OB, ~1800 BCE): 15 rows of Pythagorean triples (a, b, c) with a² + b² = c², tabulated via the ratio (c/a)² or equivalently sec²θ. Column headers reference "square of the diagonal" and "width." Consistent with a reciprocal-pair / trigonometric-table interpretation (Mansfield & Wildberger 2017). - Time/ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com