Quantifying Consciousness: Phi as Irreducible Cause-Effect Power — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) quantifies consciousness as a scalar Φ (phi) — the amount of irreducible cause-effect power of a system over its own past and future states, computed via the PyPhi algorithm. | MATH: Φ = min over partitions of the Earth Mover's Distance (EMD) between the system's cause-effect repertoire and the partitioned repertoire; formally, Φ = min_P (EMD(p(CE|S), p(CE|S_P))) / ||p||. Key constructs: mechanism M, purview P, state s, probability distributions p(CE), and the exclusion principle selecting the maximal Φ (Φ_max). No universal constants; Φ is system-specific, dimensionless, and scales with informational integration. | CONNECTION: IIT's state-space geometry uses a cause-effect structure (CES) that is a directed acyclic graph (DAG) with intrinsic information — its symmetries are not crystallographic but topological. However, the EMD metric is a Wasserstein distance, which in 1D reduces to the L1 integral of the CDF difference — a ratio akin to 0 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com