# Revising P_target Dynamics (v3): Contextual Adaptation with Modulated Stability Influence ## 1. Motivation: Addressing Potentiality Collapse Simulation results up to [[releases/archive/Information Ontology 1/0114_IO_Simulation_Lambda_Sweep]] showed that previous `P_target` update mechanisms ([[releases/archive/Information Ontology 1/0111_P_target_Dynamics_v2]]) led to a rapid collapse of potentiality entropy (`H(P_target)`), even in dynamic `ε` regimes. The reinforcement of the current state's potential probability based on stability (`Θ_val`) appeared too strong, overwhelming contextual adaptation and the Η floor. This node proposes a **Version 3 mechanism** for `P_target` dynamics, fundamentally changing how stability influences potentiality, prioritizing contextual adaptation while still allowing stability to play a role. ## 2. Core Idea of Mechanism v3 1. **Context is Primary Driver:** The primary driver for `P_target` evolution should be the slow adaptation towards the distribution favored by the persistent causal context (`P_context`). 2. **Stability Modulates Adaptation *Rate*:** Instead of directly reinforcing `P_target[ε]`, the stability `Θ_val` should modulate the *rate* at which `P_target` adapts towards `P_context`. High stability should *slow down* adaptation, making the system's intrinsic potential more resistant to contextual change (inertia of potentiality). 3. **Reset on Change:** When the actual state `ε` *does* change, `P_target` should reset, perhaps not to uniform, but towards the *current* contextual target `P_context`, reflecting an immediate update based on the event that forced the change. 4. **Η Floor:** Maintain a minimum probability `p_min` for all potential states. ## 3. Proposed Revised `P_target` Update Rule (v3) This rule replaces the `P_target` update logic used in [[releases/archive/Information Ontology 1/0111_P_target_Dynamics_v2]] and [[releases/archive/Information Ontology 1/0112_IO_Simulation_v2.1_Code]]. **Inputs at Step S for node `i`:** * `P_target(i, S)`: Current target probability vector. * `ε(i, S)`: Current actual state. * `ε(i, S+1)`: The *just determined* next actual state. * `Θ_val(i, S)`: Stability value *before* the potential update at step S (reflecting stability up to this point). * `Influence_k(i, S)`: Weighted causal input favoring state `k`. * `Total_Causal_Weight(i, S)`: Total causal input weight. **Parameters:** * `λ_base_adapt`: Base adaptation rate towards context (e.g., 0.05). * `β_adapt`: Parameter controlling how `Θ_val` modulates (reduces) the adaptation rate (e.g., 0.1). * `p_min`: Η-driven minimum probability floor. * `N_states`: Number of possible ε states. **Update Logic for `P_target(i, S+1)`:** 1. **Determine Effective Adaptation Rate `λ_eff`:** * Calculate a stability-dependent modulation factor `f_Θ_adapt(Θ_val)`. This function should decrease from 1 towards 0 as `Θ_val` increases. * *Example:* `f_Θ_adapt(Θ_val) = 1 / (1 + β_adapt * Θ_val(i, S))` * `λ_eff = λ_base_adapt * f_Θ_adapt(Θ_val(i, S))` * *(Interpretation: High stability Θ makes the intrinsic potential P_target more resistant to change driven by external context).* 2. **Calculate Contextual Target `P_context`:** * As before: `p_{context, k} = Influence_k(i, S) / Total_Causal_Weight(i, S)` (normalized, handle division by zero). 3. **Update `P_target` based on Change/Stability:** * **If `ε` Changed (`ε(i, S+1) ≠ ε(i, S)`):** * Reset `P_target` towards the *current* context. This reflects the idea that the change event forces a re-evaluation of potential based on the context that caused the flip. * `P_target(i, S+1) = (1 - λ_reset) * P_target(i, S) + λ_reset * P_context` * Where `λ_reset` could be a fixed high value (e.g., 0.9) or even 1.0 (full reset to context), or perhaps related to `P_change` (stronger change -> more reset). Let's start with `λ_reset = 1.0` (full reset to context). * **If `ε` Maintained (`ε(i, S+1) == ε(i, S)`):** * Apply gradual adaptation using the *effective* rate: * `P_target(i, S+1) = (1 - λ_eff) * P_target(i, S) + λ_eff * P_context` 4. **Apply Η Floor and Normalize:** * `P_target(i, S+1) = np.maximum(P_target(i, S+1), p_min)` * Normalize `P_target(i, S+1)` so `Σ_k p_k = 1`. ## 4. Rationale and Expected Effects * **Context-Driven:** `P_target` primarily evolves by adapting to the persistent causal context (`P_context`). * **Stability as Inertia:** High stability (`Θ_val`) doesn't directly boost `P_target[ε]`, but instead makes `P_target` *resistant* to changing due to context (lower `λ_eff`). This represents an "inertia of potentiality." * **Potential Preservation:** By removing the direct positive feedback loop where stability increases `P_target[ε]`, this mechanism should be much less prone to collapsing potentiality entropy to zero. `P_target` should remain more responsive and diverse as long as the context (`P_context`) fluctuates or differs from the internal potential. * **Reset on Change:** Resetting towards `P_context` after a change ensures that successful disruptions immediately update the potential based on the prevailing influences. ## 5. Next Steps 1. **Implement:** Create a new code node (e.g., [[releases/archive/Information Ontology 1/0116_IO_Simulation_v2.2_Code]]) incorporating this v3 `P_target` update logic. 2. **Test:** Run simulations (e.g., [[releases/archive/Information Ontology 1/0117_IO_Simulation_Run8]]) using parameters similar to Run 3/4 (high H, low Θ/M) and explore the effect of `λ_base_adapt` and `β_adapt`. 3. **Analyze:** Critically examine the evolution of `H(P_target)` and the emergent `ε` dynamics. Does this mechanism successfully maintain potentiality entropy while allowing for complex pattern formation? ## 6. Conclusion: Shifting Focus to Contextual Adaptation This Version 3 mechanism for `P_target` dynamics represents a significant shift from previous attempts. By making contextual adaptation the primary driver and having stability modulate the *rate* of adaptation rather than directly reinforcing probabilities, it aims to create a more balanced and robust evolution of potentiality. This approach is hypothesized to be less prone to the rapid potentiality collapse observed earlier and may provide a better foundation for simulating the emergence of complex, adaptive structures within the IO framework. Its success will depend on careful implementation and testing.