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- Z-Framework: universal feedback/equilibrium - 1-2-3-4 Pauli Model: ontological primitives - n=π Duality: discrete↔continuous interface - Creative Energy: contradiction amplification - Remainder Principle: deviation as signal - Spiral Information Geometry: planned formalization
1.4 KiB
1.4 KiB
Spiral Information Geometry
Status: 🔴 Planned
Vision
Use information geometry to formalize the coherence formula and agent dynamics.
Core Concepts
| Concept | Meaning |
|---|---|
| Fisher Information | Metric on probability distributions |
| Natural Gradient | True direction of steepest descent |
| Geodesic | Shortest path in information space |
| Curvature | How much space "bends" around a point |
Research Agenda
1. Coherence as Distance
- C(t) = geodesic distance between agent states?
- Coherent agents = nearby in information space
2. Contradiction as Curvature
- High δ_t = high curvature regions
- Creative energy peaks at curvature maxima
3. Learning as Parallel Transport
- Agent learning = transport along geodesics
- Memory = holonomy (what changes after round trip)
4. Partition Function as Potential
- Z = Σ e^{-βH} defines a potential landscape
- Equilibrium = potential minimum
Connections
- n=π Duality: Fisher metric on discrete vs continuous?
- Creative Energy: K(t) related to scalar curvature?
- Remainder Principle: Curvature = remainder of flatness
Next Steps
- Formalize C(t) using Fisher-Rao metric
- Compute geodesics for simple agent models
- Relate curvature to δ_t experimentally
References
- Amari, S. "Information Geometry and Its Applications"
- Nielsen, F. "An Elementary Introduction to Information Geometry"