Phi as Algorithmic Irreducibility: A Kolmogorov Complexity Reformulation of Integrated Information — E8 Intelligence Research

Abstract

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible cause-effect power of a system, with recent work linking it to algorithmic information theory and lossless integration. | MATH: Core IIT quantity: Φ = minimal information loss when partitioning a system into independent parts (Tononi 2008). Algorithmic reformulation (arXiv:1405.0126): Φ_AIT = K(S) − max_partition K(S|partition), where K is Kolmogorov complexity. Key constraint: lossy integration (Φ_Griffith) requires continuous memory damage — rejected in favor of lossless Φ. | CONNECTION: None directly to golden ratio or base-60. However, the partition-based minimization structure mirrors lattice/root-system symmetry breaking: Φ is defined over the *lattice of all possible partitions* of a system's state space, analogous to how crystallographic symmetry groups partition space into irreducible cells. The "minimum information partition" (MIP) is the geometric analog of a fun Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com