bc063c0b74
- 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
52 lines
1.4 KiB
Markdown
52 lines
1.4 KiB
Markdown
# Spiral Information Geometry
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> Status: 🔴 Planned
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## Vision
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Use **information geometry** to formalize the coherence formula and agent dynamics.
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## Core Concepts
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| Concept | Meaning |
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|---------|---------|
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| Fisher Information | Metric on probability distributions |
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| Natural Gradient | True direction of steepest descent |
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| Geodesic | Shortest path in information space |
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| Curvature | How much space "bends" around a point |
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## Research Agenda
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### 1. Coherence as Distance
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- C(t) = geodesic distance between agent states?
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- Coherent agents = nearby in information space
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### 2. Contradiction as Curvature
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- High δ_t = high curvature regions
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- Creative energy peaks at curvature maxima
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### 3. Learning as Parallel Transport
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- Agent learning = transport along geodesics
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- Memory = holonomy (what changes after round trip)
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### 4. Partition Function as Potential
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- Z = Σ e^{-βH} defines a potential landscape
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- Equilibrium = potential minimum
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## Connections
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- **n=π Duality**: Fisher metric on discrete vs continuous?
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- **Creative Energy**: K(t) related to scalar curvature?
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- **Remainder Principle**: Curvature = remainder of flatness
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## Next Steps
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1. Formalize C(t) using Fisher-Rao metric
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2. Compute geodesics for simple agent models
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3. Relate curvature to δ_t experimentally
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## References
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- Amari, S. "Information Geometry and Its Applications"
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- Nielsen, F. "An Elementary Introduction to Information Geometry"
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