Chaitin's Omega: Algorithmic Randomness Linking Halting Probability to Base-60 Uniform Distribution — E8 Intelligence Research

FINDING: Chaitin's Omega (Ω) is a real number whose base-60 digits are algorithmically random and encode the halting probability of a universal Turing machine, linking computation limits to number theory and uniform distribution. MATH: - Ω = Σ_{p halts} 2^{-|p|}, where |p| is program length in bits. - Ω is uncomputable and normal in base 2 (Borel normality proven by Calude et al.), but normality in base 60 is conjectured, not proven. - Base-60 digits of Ω are uniformly distributed if Ω is normal in base 60; this would imply each sexagesimal digit 0–59 appears with equal asymptotic frequency 1/60. - No closed-form equation exists; Ω is defined via algorithmic information theory (Kolmogorov complexity). CONNECTION: - Base-60 (sexagesimal) is the ancient Babylonian system, which is highly composite (divisible by 2,3,4,5,6,10,12,15,20,30) and naturally relates to 360° circles and 60-minute hours. - Uniform distribution of base-60 digits in Ω would mirror the equidistribution Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com