Quantifying Consciousness: Phi as Irreducible Cause-Effect Power — E8 Intelligence Research
Zenodo (CERN European Organization for Nuclear Research) September 7, 2026 DOI: 10.5281/zenodo.22631876 (opens in new tab)
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AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Key points | Argues that Integrated Information Theory quantifies consciousness as Φ, the irreducible cause-effect power of a system, computed via the PyPhi algorithm using the Earth Mover's Distance. Proposes that the cause-effect structure is a directed acyclic graph with topological symmetries, and that the EMD metric is a Wasserstein distance reducible in 1D to an L1 integral. |
Abstract
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