Kolmogorov Complexity and Integrated Information: Geometric Constraints on Computation and Consciousness — E8 Intelligence Research

FINDING: Kolmogorov complexity measures algorithmic randomness; integrated information theory (IIT) quantifies consciousness via causal structure; both link to geometric constraints on computation and knowledge. | MATH: Kolmogorov complexity \( K(x) = \min\{ |p| : U(p) = x \} \) (shortest program length for string \( x \) on universal Turing machine \( U \)); IIT 4.0 uses \(\Phi\) (integrated information) derived from cause-effect repertoire, often computed via PyPhi. No explicit constants or ratios given in these sources. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60 or crystallographic symmetries appear in the provided findings. However, IIT's causal structure can be mapped to lattice or graph symmetries (e.g., maximum \(\Phi\) occurs in symmetric, integrated networks), and Kolmogorov complexity relates to algorithmic probability, which has deep links to fractal geometry and self-similarity (e.g., Chaitin's constant \(\Omega\) is algorithmically ran Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com