Information Geometry Bridges Fisher Metric and Integrated Information in IIT — E8 Intelligence Research

FINDING: Information geometry provides a Riemannian metric (Fisher metric) on statistical manifolds, which IIT uses to define a "qualia space" where conscious experience corresponds to integrated geometric structure. MATH: Fisher information metric: \( gᵢⱼ(θ) = E_X [ ∂ log p(x|θ)/∂ θ^i ∂ log p(x|θ)/∂ θ^j ] \). IIT's integrated information \(Φ\) measures deviation from a disconnected product manifold: \(Φ = minₚₐᵣₜᵢₜᵢₒₙ [ distance(pfull, pₚₐᵣₜᵢₜᵢₒₙ) ]\), often using the Kullback-Leibler divergence or Wasserstein distance. Qualia space is a high-dimensional manifold of probability distributions over system states. CONNECTION: The Fisher metric is invariant under reparameterization, linking to the constant curvature of statistical manifolds. For Beta/Dirichlet distributions, the Fisher metric yields constant negative curvature (hyperbolic g Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com