Sumerian Base-60: A Superior System for Divisibility and Exact Fractions — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The Sumerians chose base-60 (sexagesimal) for its superior divisibility and computational efficiency, enabling exact handling of reciprocals, fractions, and large numbers in a positional system. | MATH: 60 = 2² × 3 × 5; divisors of 60: {1,2,3,4,5,6,10,12,15,20,30,60} — 12 total, giving exact terminating sexagesimal fractions for all reciprocals of numbers whose prime factors are ≤5 (e.g., 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, 1/12=0;5). Regular numbers (5-smooth) have finite sexagesimal expansions. | CONNECTION: Base-60 is the lowest number with 12 divisors (highly composite); its prime factors {2,3,5} generate the 5-smooth lattice — directly linked to the crystallographic root system of A₄ (tetrahedral symmetry, order 60) and the icosahedral/dodecahedral symmetry group (also order 60). The ratio 60/37.5 = 1.6 (near φ=1.618) and 60/97.5 ≈ 0.615 (near 0.618) emerge in sexagesimal divisions; 1/60 = 0.01666… and 60×0.618 = 37.08 (close to 37;30
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026sumerian,
title = {{Sumerian Base-60: A Superior System for Divisibility and Exact Fractions — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616711},
url = {https://zenodo.org/records/23616711},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sumerian Base-60: A Superior System for Divisibility and Exact Fractions — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616711
UR - https://zenodo.org/records/23616711
AB - FINDING: The Sumerians chose base-60 (sexagesimal) for its superior divisibility and computational efficiency, enabling exact handling of reciprocals, fractions, and large numbers in a positional system. | MATH: 60 = 2² × 3 × 5; divisors of 60: {1,2,3,4,5,6,10,12,15,20,30,60} — 12 total, giving exact terminating sexagesimal fractions for all reciprocals of numbers whose prime factors are ≤5 (e.g., 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, 1/12=0;5). Regular numbers (5-smooth) have finite sexagesimal expansions. | CONNECTION: Base-60 is the lowest number with 12 divisors (highly composite); its prime factors {2,3,5} generate the 5-smooth lattice — directly linked to the crystallographic root system of A₄ (tetrahedral symmetry, order 60) and the icosahedral/dodecahedral symmetry group (also order 60). The ratio 60/37.5 = 1.6 (near φ=1.618) and 60/97.5 ≈ 0.615 (near 0.618) emerge in sexagesimal divisions; 1/60 = 0.01666… and 60×0.618 = 37.08 (close to 37;30 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -