Babylonian Base-60 and Liouville Sign Patterns: Computable Normality — E8 Intelligence Research

FINDING: Babylonian base-60 numeration and modern equidistribution results on Liouville-function sign patterns converge on the theme of *computable normal numbers* and *base-dependent equidistribution*, linking ancient computational pragmatics to modern limits of knowledge. | MATH: Base-60 (sexagesimal) positional system; Liouville function λ(n) ∈ {−1,+1}; the computable real α = Σ_{n≥1} (1+λ(n))/2^n is simply normal in base 4 (proved unconditionally). Equidistribution of double sign patterns of λ is unconditional — i.e., for any fixed pattern (ε₁,ε₂) ∈ {−1,+1}², the frequency of consecutive pairs (λ(n),λ(n+1)) = (ε₁,ε₂) tends to 1/4. | CONNECTION: Base-60 is *not* a geometric ratio, but it is highly composite (60 = 2²·3·5), yielding exact fractions for 1/2, 1/3, 1/4, 1/5, 1/6, 1/10, 1/12, 1/15, 1/20, 1/30 — a *lattice of divisors* that mirrors crystallographic root-system divisibility (e.g., A₄, H₃ symmetries). The base-4 normality of α relates to dyadic structure (2²), echoing binary Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com