Babylonian Reciprocal Tables Built via Recursive Base-60 Factorization, Not Enumeration — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Babylonian reciprocal-table construction method is clarified via a recursive, base-60 factorization algorithm, not brute-force enumeration. | MATH: For reciprocal n ↦ 1/n in sexagesimal, tables were built using n = a · 60k + b, with reciprocals derived from 1/(a · 60k) · (1 + b/(a · 60k))−1 — exploiting the geometric series 1/(1+x) = 1 − x + x2 − … 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 · q = 60k, using the identity 1/p = q / 60k. | 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
Related
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BibTeX
@misc{caldin2026babylonian,
title = {{Babylonian Reciprocal Tables Built via Recursive Base-60 Factorization, Not Enumeration — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658232},
url = {https://zenodo.org/records/23658232},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Babylonian Reciprocal Tables Built via Recursive Base-60 Factorization, Not Enumeration — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658232
UR - https://zenodo.org/records/23658232
AB - FINDING: Babylonian reciprocal-table construction method is clarified via a recursive, base-60 factorization algorithm, not brute-force enumeration. | MATH: For reciprocal n ↦ 1/n in sexagesimal, tables were built using n = a · 60^k + b, with reciprocals derived from 1/(a · 60^k) · (1 + b/(a · 60^k))^−1 — exploiting the geometric series 1/(1+x) = 1 − x + x^2 − … 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 · 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
ER -