Integrated Information Theory: Phi as Irreducible Cause-Effect Power via Earth-Mover Distance — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) — the irreducible cause-effect power of a system's mechanism over its own past and future states, measured via the earth-mover distance between probability distributions. | MATH: Φ = minimum over partitions of the earth-mover's distance (Wasserstein-1) between the system's full cause-effect repertoire and the partitioned (disconnected) repertoire. IIT 4.0 refines this via intrinsic existence, using the *intrinsic difference* (ID) measure, not KL-divergence. Key quantities: φ_max (for a mechanism), Φ (for the whole system), and the "cause-effect structure" (CES) — a set of distinctions and relations, each with its own φ value. No universal constant emerges; Φ is system-specific, scale-free, and not a scalar but a structured object. | CONNECTION: The earth-mover distance is a metric on probability spaces — it induces a geometry where the "distance" between system states is measured by minimal work
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
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BibTeX
@misc{caldin2026integrated,
title = {{Integrated Information Theory: Phi as Irreducible Cause-Effect Power via Earth-Mover Distance — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635097},
url = {https://zenodo.org/records/23635097},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Integrated Information Theory: Phi as Irreducible Cause-Effect Power via Earth-Mover Distance — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635097
UR - https://zenodo.org/records/23635097
AB - FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) — the irreducible cause-effect power of a system's mechanism over its own past and future states, measured via the earth-mover distance between probability distributions. | MATH: Φ = minimum over partitions of the earth-mover's distance (Wasserstein-1) between the system's full cause-effect repertoire and the partitioned (disconnected) repertoire. IIT 4.0 refines this via intrinsic existence, using the *intrinsic difference* (ID) measure, not KL-divergence. Key quantities: φ_max (for a mechanism), Φ (for the whole system), and the "cause-effect structure" (CES) — a set of distinctions and relations, each with its own φ value. No universal constant emerges; Φ is system-specific, scale-free, and not a scalar but a structured object. | CONNECTION: The earth-mover distance is a metric on probability spaces — it induces a geometry where the "distance" between system states is measured by minimal work Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -