Babylonian Reciprocal Tables Built via Recursive Base-60 Factorization, Not Enumeration — E8 Intelligence Research

FINDING: Babylonian reciprocal-table construction method is clarified via a recursive, base-60 factorization algorithm, not brute-force enumeration. | MATH: For reciprocal \(n \mapsto 1/n\) in sexagesimal, tables were built using \(n = a \cdot 60^k + b\), with reciprocals derived from \(1/(a \cdot 60^k) \cdot (1 + b/(a \cdot 60^k))^{-1}\) — exploiting the geometric series \(1/(1+x) = 1 - x + x^2 - \dots\) truncated to finite sexagesimal precision. The paper (arXiv:1401.0065) shows the construction reduces to factoring regular numbers (those with only 2, 3, 5 as prime factors) into pairs \((p, q)\) such that \(p \cdot q = 60^k\), using the identity \(1/p = q / 60^k\). | CONNECTION: **Base-60 is the direct ancestor of our 360° circle and 60-minute hour** — the sexagesimal system encodes the harmonic ratios 1/2, 1/3, 1/4, 1/5, 1/6 as terminating fractions, which are precisely the divisors of 60. The reciprocal pairs \((p, q)\) form a **lattice structure** in the 3-dimensional space of pri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com