Babylonian Base-60 and Weyl Groups: Linking Discrete Computation to Continuous Symmetry — E8 Intelligence Research

FINDING: Babylonian base-60 (sexagesimal) system provided superior computational efficiency for fractions and astronomical calculations, while Weyl groups from crystallographic root systems encode the symmetry of Lie algebras and lattices, linking discrete computation to continuous symmetry. MATH: - Sexagesimal: 60 = 2² × 3 × 5; prime factors {2,3,5} allow many finite decimal expansions (e.g., 1/2=0.30, 1/3=0.20, 1/4=0.15, 1/5=0.12, 1/6=0.10). - Weyl group: finite group generated by reflections in hyperplanes orthogonal to roots of a root system Φ; order = |W| = product of Coxeter numbers for irreducible components. - Root system axioms: (1) Φ spans Euclidean space, (2) α ∈ Φ ⇒ -α ∈ Φ, (3) reflection s_α(β) = β - 2(α·β)/(α·α) α ∈ Φ, (4) 2(α·β)/(α·α) ∈ ℤ (Cartan integers). - Coxeter graph: nodes = simple roots, edges labeled by m_ij = order of product s_i s_j (3,4,6, or ∞). - Super Weyl groups: quotients of Weyl groups of basic classical Lie superalgebras, with modified root Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com