Quantum-Inspired Decision-Making Using Lagrangian Mechanics and Wayfinding Principles

Overview

This project simulates Stentor roeseli's behavior using a novel decision-making framework based on Lagrangian mechanics, Wayfinding Theory and energy dynamics, integrating agentic and systemic energy. The model incorporates environmental feedback, quantum decision-making principles, and adaptive learning to mimic intelligent behaviors in unicellular organisms.

Lagrangian Mechanics: Agentic and Systemic Energy

Inspired by Lagrangian mechanics, the system balances:

• Agentic Energy: Cognitive resources for decision-making.
• Systemic Energy: Metabolic energy for actions.
  Stentor roeseli optimizes actions by minimizing energy expenditure, ensuring efficient adaptation to environmental changes.

Energy Dynamics

• Agentic Energy: Governs decision-making, depleted with complex actions. A higher agentic energy leads to more exploratory actions.
• Systemic Energy: Regulates metabolic functions and determines the viability of physically demanding actions like detachment.

Wayfinding and Decision-Making

The Stentor's decision-making mimics biological wayfinding principles, evaluating the environment, energy costs, and future risks to navigate a grid-based environment effectively.

Key Steps:

1. Environmental Assessment: Stentor evaluates current environmental states (e.g., nutrient density, predator presence) using an environmental score.

2. Dynamic Prospective Oscillations: Introduces quantum-like oscillations to adjust decision probabilities based on past actions, energy levels, and environmental factors.

3. Long-Term Prospection: Predicts future risks and rewards using environmental trends. The Stentor anticipates future conditions, adjusting its behavior accordingly.

4. Action Costs: Every action has a metabolic cost, and complex decisions reduce agentic energy. For example:

   • Detachment: High cost but leads to new opportunities if the current environment is unfavorable.
   • Bend: Low cost, used to navigate less threatening environments.

5. Modify Possibility Space: Stentor dynamically adjusts the set of possible actions based on its history, current environment, and oscillations in energy levels.

6. Quantum Decision-Making: Actions are placed in quantum superposition and resolved based on probabilities influenced by energy dynamics, uncertainty, and environmental factors.

Decision-Making Example

• Scenario: Stentor is in a nutrient-poor grid with high predator presence.
• Energy Levels:
  • Agentic Energy: Moderate, allowing complex decision-making.
  • Systemic Energy: Low, pushing Stentor to avoid high-cost actions.
• Decision: Based on quantum oscillations, Stentor weighs between detach (explore new grid) and bend (conserve energy). If future environmental trends show low nutrient improvement, Stentor may detach despite high cost.

Visualization and Environment

The environment is visualized as a 2D grid where each cell represents environmental factors like nutrient density, predator presence, and toxin levels. The Stentor moves across the grid, evaluating each cell’s environmental score.

Visualization:

• Color-coded Grids: Cells are shaded based on environmental score (e.g., red for high risk, green for favorable conditions).
• Action Representation: Actions (e.g., bend, detach) are visually distinct, with bead sizes representing stimulus intensity.

Key Quantum Functions:

1. Dynamic Prospective Oscillation: Introduces variability in decision-making by simulating quantum-like oscillations in agentic energy. These oscillations ensure the Stentor doesn't take a deterministic path but explores various actions depending on its energy and environmental feedback.

2. Quantum Feedback Loop: Refines the action selection based on real-time environmental feedback, adding adaptability to the decision-making process.

3. Quantum Path Dependency: The Stentor’s past actions influence its future possibilities, simulating how habits or decision biases develop over time.

Conclusion

This model integrates cutting-edge quantum-inspired decision-making principles with energy management dynamics, creating a robust system that mimics real-life adaptive behaviors. The simulation explores how a unicellular organism can intelligently navigate its environment, balancing energy costs, environmental risks, and future rewards.