Computing the Information Geometry of Action
Traditional physical frameworks are bifurcated: Noether's Theorem (1918) describes the "statics" of conservation through continuous symmetry, while classical thermodynamics describes the "decay" of systems through entropy. Step Theory provides the missing link, formalizing the "dynamics" of physical computation. It posits that the universe does not merely flow; it resolves through a series of discrete, irreversible events termed Steps.
## The Core Principle > **For every dissipation, there is a Step—a discrete symmetry breaking that computes a geodesic in its conjugate field.** This is a functional dual to Noether's Theorem.
## The Paradigm Step: Light as Computation In Step Theory, there are no "photons" in the sense of traveling particles; there is only the bidirectional propagation of constraint. What we call light is a computation—a forward-backward algorithm where constraints propagate across available gradients and close only where mutual consistency is achieved. The universe tunes itself to a critical regime—an edge of chaos—where this bidirectional computation is possible.
## Mechanism: Off-Diagonal Coupling and Criticality Step Theory focuses on **Onsager cross-coupling**. A continuous gradient in an **Intensive Field** (Field A) drives a structural resolution in its **Conjugate Field** (Field B). The "Information Geometry" refers to the **Fisher Information Metric** applied to the manifold of possible action paths. **Computation requires a specific phase state:** - Order freezes - Disorder fragments - **Chaos computes**
## The Bidirectional Handshake At criticality—the edge of chaos—the system initiates: 1. **The Question:** A forward-propagating wave probes the potential field 2. **The Closure:** A backward-propagating "return stroke" from the environment completes the circuit 3. **The Commit:** Only upon closure is symmetry broken, energy dissipated, and the Step recorded
## Entrainment and Agent Emergence Discrete Steps entrain into cycles; these cycles couple through mutual dissipation into **Gaits** (functional architectures). This hierarchical coupling is the physical origin of **Agency**. For Agent-Based Modeling (ABM), this provides a scale-invariant foundation: agents are not predefined entities but emergent "limit cycles" of entrained transactions.
## Implementation: The Handshake Algorithm 1. **Inquiry (Field A):** The agent monitors the intensive gradient threshold 2. **Transaction (Field B):** The agent probes for a resonant return signal 3. **Settlement (The Step):** Upon closure, the agent "clicks" to the next state, dissipating the "cost" and updating the local Information Geometry
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