Babylonian Base-60 Arithmetic and Plimpton 322: Ancient Lattice-Based Precision Computing — E8 Intelligence Research

FINDING: Babylonian base-60 arithmetic and Plimpton 322 reveal a computational system optimized for high-precision rational arithmetic and geometric problem-solving, prefiguring modern lattice-based numeration. | MATH: Base-60 (sexagesimal) positional system; Plimpton 322 contains Pythagorean triples (a² + b² = c²) in sexagesimal form, likely generated via reciprocal pairs (p, q) with a = p² - q², b = 2pq, c = p² + q². Key constants: 60 as radix, 1/60 = 0.01666..., 1/3600 = 0.0002777... | CONNECTION: Base-60 factors as 2² × 3 × 5, enabling exact representation of fractions with denominators dividing 60 — directly related to crystallographic root system lattices (e.g., A₂, G₂) which also exhibit 6-fold and 3-fold symmetries. The reciprocal method mirrors Weyl group reflections in root lattices. | DEPTH: 8 FINDING: Weyl groups and root systems from Lie algebras classify all finite reflection groups, directly linking to crystallographic symmetry groups in 3D and higher. | MATH: Weyl grou Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com