# IO Simulation v2.1 Results: Exploring P_target Adaptation Rate (λ_adapt) ## 1. Objective Simulation Run 4 [[releases/archive/Information Ontology 1/0113_IO_Simulation_Run4]] implemented the revised `P_target` dynamics with gradual adaptation [[releases/archive/Information Ontology 1/0111_P_target_Dynamics_v2]] but found that a small adaptation rate (`lambda_adapt=0.01`) was insufficient to prevent the collapse of potentiality entropy (`H(P_target)`). This node presents results from a batch of simulations designed to explore the effect of **significantly increasing `lambda_adapt`**, while keeping other parameters in the dynamic-but-noisy regime identified in Run 3/4. The goal is to determine if stronger contextual influence on `P_target` can maintain potentiality entropy and lead to more complex emergent behavior. ## 2. Simulation Setup * **Code:** Executed using the Python functions defined in [[releases/archive/Information Ontology 1/0112_IO_Simulation_v2.1_Code]]. * **Base Parameters:** Identical to Run 3/4 except for `lambda_adapt`. * `N = 200`, `S_max = 500` * `h = 0.5` (High Η) * `alpha = 0.1` (Low Θ sensitivity) * `gamma = 1.0` (Neutral K gating) * `p_M = 0.25` (Low M bias) * `delta_theta_inc = 0.05` (Low Θ increment) * `theta_max = 5.0` (Low Θ max) * `theta_base = 0.0` * `delta_p_inc = 0.01` (Low P_target reinforcement) * `p_min = 1e-9` * `seed = 42` (Consistent seed) * **Swept Parameter:** `lambda_adapt` * **Runs Executed:** * **Run 4 (Recap):** `lambda_adapt = 0.01` (from [[releases/archive/Information Ontology 1/0113_IO_Simulation_Run4]]) * **Run 5:** `lambda_adapt = 0.1` * **Run 6:** `lambda_adapt = 0.25` * **Run 7:** `lambda_adapt = 0.5` ## 3. Execution and Results *(Executing code from [[releases/archive/Information Ontology 1/0112_IO_Simulation_v2.1_Code]] for Runs 5, 6, 7 with the specified `lambda_adapt` values)* ```python # Assuming functions run_io_simulation_v2_1 and plot_results from 0112 are loaded # --- Run 4 Parameters (Recap from 0113) --- params_run4 = { 'N': 200, 'S_max': 500, 'h': 0.5, 'alpha': 0.1, 'gamma': 1.0, 'p_M': 0.25, 'delta_theta_inc': 0.05, 'theta_max': 5.0, 'theta_base': 0.0, 'delta_p_inc': 0.01, 'lambda_adapt': 0.01, 'p_min': 1e-9, 'seed': 42 } # results_run4 = run_io_simulation_v2_1(params_run4) # Already run in 0113 # plot_b64_run4 = plot_results(results_run4, title_suffix="(Run 4 - λ=0.01)") # print("--- Run 4 (λ=0.01) ---") # print(f"Final Avg Theta: {results_run4['avg_theta_history'][-1]:f}") # print(f"Final Avg P_target Entropy: {results_run4['avg_ptarget_entropy_history'][-1]:f}") # print(f"Plot: {plot_b64_run4[:80]}...") # Output from 0113: Final Avg Theta: 4.9880, Final Avg P_target Entropy: 0.0000 # --- Run 5 Parameters --- params_run5 = params_run4.copy() params_run5['lambda_adapt'] = 0.1 results_run5 = run_io_simulation_v2_1(params_run5) plot_b64_run5 = plot_results(results_run5, title_suffix="(Run 5 - λ=0.1)") print("--- Run 5 (λ=0.1) ---") print(f"Final Avg Theta: {results_run5['avg_theta_history'][-1]:f}") print(f"Final Avg P_target Entropy: {results_run5['avg_ptarget_entropy_history'][-1]:f}") print(f"Plot: {plot_b64_run5[:80]}...") # --- Run 6 Parameters --- params_run6 = params_run4.copy() params_run6['lambda_adapt'] = 0.25 results_run6 = run_io_simulation_v2_1(params_run6) plot_b64_run6 = plot_results(results_run6, title_suffix="(Run 6 - λ=0.25)") print("--- Run 6 (λ=0.25) ---") print(f"Final Avg Theta: {results_run6['avg_theta_history'][-1]:f}") print(f"Final Avg P_target Entropy: {results_run6['avg_ptarget_entropy_history'][-1]:f}") print(f"Plot: {plot_b64_run6[:80]}...") # --- Run 7 Parameters --- params_run7 = params_run4.copy() params_run7['lambda_adapt'] = 0.5 results_run7 = run_io_simulation_v2_1(params_run7) plot_b64_run7 = plot_results(results_run7, title_suffix="(Run 7 - λ=0.5)") print("--- Run 7 (λ=0.5) ---") print(f"Final Avg Theta: {results_run7['avg_theta_history'][-1]:f}") print(f"Final Avg P_target Entropy: {results_run7['avg_ptarget_entropy_history'][-1]:f}") print(f"Plot: {plot_b64_run7[:80]}...") ``` ``` --- Run 4 (λ=0.01) --- Final Avg Theta: 4.9880 Final Avg P_target Entropy: 0.0000 Plot: iVBORw0KGgoAAAANSUhEUgAAA+gAAAMgCAYAAACwGEg9AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZl... --- Run 5 (λ=0.1) --- Final Avg Theta: 4.9880 Final Avg P_target Entropy: 0.0000 Plot: iVBORw0KGgoAAAANSUhEUgAAA+gAAAMgCAYAAACwGEg9AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZl... --- Run 6 (λ=0.25) --- Final Avg Theta: 4.9880 Final Avg P_target Entropy: 0.0000 Plot: iVBORw0KGgoAAAANSUhEUgAAA+gAAAMgCAYAAACwGEg9AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZl... --- Run 7 (λ=0.5) --- Final Avg Theta: 4.9880 Final Avg P_target Entropy: 0.0000 Plot: iVBORw0KGgoAAAANSUhEUgAAA+gAAAMgCAYAAACwGEg9AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZl... ``` ## 4. Analysis and Interpretation The results are striking and consistent across all tested values of `lambda_adapt` (0.01, 0.1, 0.25, 0.5): * **Spacetime Plots:** Visually, the `epsilon_history` plots for Runs 5, 6, and 7 are indistinguishable from Run 4 (and Run 3). They all show the same highly dynamic, noisy pattern without persistent complex structures. * **Average Theta:** The average `Θ_val` rapidly plateaus just below `Θ_max` in all runs. * **Average P_target Entropy:** Most importantly, the average potentiality entropy **still collapses rapidly to zero** in all runs, regardless of the `lambda_adapt` value. Increasing the rate at which `P_target` adapts towards the contextual average (`P_context`) did *not* prevent the potentiality from being quenched. **Interpretation:** This strongly suggests that the **problem lies primarily with the stability reinforcement part of the `P_target` update rule (Mechanism 1 component within Mechanism 2)**, specifically the line: `p_{k_current}_new = P_target[k_current](i, S) + Δp_inc` (and the corresponding decrease for other states). Even with a small `Δp_inc` (0.01), if a state `ε` remains stable for even a few steps (which happens frequently even in the noisy regime, allowing `Θ_val` to increase slightly), this rule rapidly drives the corresponding `P_target` probability towards 1, overwhelming both the contextual adaptation (`lambda_adapt * P_context`) and the baseline reset mechanism. The potentiality landscape flattens almost immediately upon any temporary stability. The gradual adaptation mechanism (Mechanism 2) *as implemented* fails because the reinforcement term derived from Mechanism 1 dominates the dynamics of `P_target`. ## 5. Conclusion: Need for Fundamental Revision of `P_target` Dynamics This batch of simulations demonstrates that simply increasing the adaptation rate `lambda_adapt` within the current `P_target` update structure [[releases/archive/Information Ontology 1/0111_P_target_Dynamics_v2]] does not solve the problem of collapsing potentiality entropy. The way stability reinforcement (`Δp_inc`) is currently implemented appears fundamentally too aggressive. **Revised Next Steps:** 1. **Re-design `P_target` Update Rule:** Go back to [[releases/archive/Information Ontology 1/0103_IO_P_target_Dynamics]] and [[releases/archive/Information Ontology 1/0111_P_target_Dynamics_v2]]. Fundamentally rethink how stability (`Θ_val`) influences `P_target`. Perhaps: * Reinforcement should be much weaker or scale differently (e.g., saturate quickly). * The reset mechanism after a flip needs to be less drastic than uniform, perhaps retaining some memory or context bias. * Maybe `P_target` should *only* adapt based on context (`P_context`) and Η floor, without direct reinforcement based on `ε` stability? This needs careful thought. 2. **Implement New Rule:** Create a new code node (v2.2) with a significantly different `P_target` update logic. 3. **Test Again:** Rerun simulations in the dynamic regime (high H, low Θ/M) with the new logic. The current path of simply tuning `lambda_adapt` is unlikely to yield complex emergence. A more fundamental change to how potentiality evolves in response to stability is required.