Kolmogorov Complexity and Integrated Information in Consciousness — E8 Intelligence Research

FINDING: Kolmogorov complexity defines randomness as incompressibility; consciousness research attempts to quantify integrated information via algorithmic information theory, but the core mathematical object is the minimal program length. | MATH: Kolmogorov complexity \(K(x) = minp: U(p)=x |p|\) for a universal Turing machine \(U\). Randomness of a string \(x\) of length \(n\) iff \(K(x) ≥ n - O(1)\). Conditional complexity \(K(x|y)\). For consciousness: \(Φ\) (integrated information) proposed as \(K(x) - ∑_i K(x_i)\) over partitions, but the 2014 critique (Griffith) shows lossy integration fails — the correct measure must be lossless, leading to \(K(x) - maxₚₐᵣₜᵢₜᵢₒₙ ∑_i K(x_i)\) with a correction term for mutual algorithmic information. No specific numeric constants emerge from these sources. | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) appears. However, the structure of algorithmic randomness is intimately tied to measure the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com