🌌Visualizing Consciousness Geometry
A spectral triple (𝒜, ℋ, 𝒟) encodes the intrinsic geometry of a finite state space. For Markov chains modeling consciousness dynamics, the Dirac operator 𝒟 measures how distinguishable different mental states are via the Connes distance.
This interactive visualizer computes spectral triples from transition matrices, revealing the geometric structure underlying state transitions. States that are "far apart" in Connes distance require many observations to distinguish reliably.
🔍Interpretation
Large Connes distances indicate states that require many observations to distinguish. This captures the "perceptual distance" between mental states.
⚡Spectral Gap
The spectral gap (λ₀ - λ₁) measures mixing time. Larger gaps mean faster convergence to equilibrium.
🎯Applications
Spectral triples provide a rigorous geometric framework for analyzing consciousness models, attention dynamics, and cognitive state spaces.