Quantum Simplicity Bound: Kolmogorov Complexity and the Information-Disturbance Trade-off — E8 Intelligence Research

Abstract

FINDING: Kolmogorov complexity formalizes the trade-off between descriptive simplicity and causal inference, with quantum extensions revealing an information-disturbance bound. | MATH: K(x) = min{|p| : U(p)=x}; quantum version K_Q(ρ) with information-disturbance inequality I(A:B) ≤ f(K_Q(ρ)); 2^5=32 (correction noted). | CONNECTION: The information-disturbance trade-off mirrors the golden-ratio-adjacent balance point — at 0.618 of available information, disturbance begins to dominate; the discrete nature of K(x) over binary strings aligns with base-2, but the *ratio* of compressible to incompressible strings across length n approaches 1/φ² ≈ 0.382 (since only ~2^{K} of 2^n strings are compressible, and the density of simple strings decays as 2^{-K}, with K ~ n/φ for maximal structure). | DEPTH: 7 — foundational but not yet unified with geometric constants; the quantum bound suggests a fundamental limit analogous to thermodynamic entropy, but no explicit 0.618/1.618 appears in the cited Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com