Experiment 1: The Chaotic Reservoir (The Stone in the Lake)

Credits and References

Darwin's Cage Theory:

• Theory Creator: Gideon Samid
• Reference: Samid, G. (2025). Negotiating Darwin's Barrier: Evolution Limits Our View of Reality, AI Breaks Through. Applied Physics Research, 17(2), 102. https://doi.org/10.5539/apr.v17n2p102
• Publication: Applied Physics Research; Vol. 17, No. 2; 2025. ISSN 1916-9639 E-ISSN 1916-9647. Published by Canadian Center of Science and Education
• Available at: https://www.researchgate.net/publication/396377476_Negotiating_Darwin's_Barrier_Evolution_Limits_Our_View_of_Reality_AI_Breaks_Through

Experiments, AI Models, Architectures, and Reports:

• Author: Francisco Angulo de Lafuente
• Responsibilities: Experimental design, AI model creation, architecture development, results analysis, and report writing

Abstract

This experiment investigates the emergence of physical predictive capabilities from an unstructured, chaotic system. Specifically, we test whether a "Chaotic Optical Reservoir" can learn to predict the landing location of a ballistic projectile without any prior knowledge of Newtonian mechanics.

Objective

To demonstrate that a fixed, random optical interference pattern contains sufficient high-dimensional information to map initial conditions (velocity $v_0$, angle $\theta$) to a physical outcome (distance $R$).

Methodology

1. The Physical Ground Truth

$R = \frac{v_0^2 \sin(2\theta)}{g}$ Dataset: 2,000 trajectories, $v_0 \in [10, 100] m/s$, $\theta \in [5, 85]^\circ$.

2. The Optical Chaos Model

1. Input: Normalized $[v_0, \theta]$.
2. Projection: Random complex matrix ($N=4096$).
3. Interference: FFT mixing.
4. Detection: $\tanh(|\text{FFT}|^2 \cdot 0.001)$.
5. Readout: Ridge Regression.

Results

Standard Performance

Benchmark & Critical Audit

We performed a rigorous audit (benchmark_experiment_1.py) to determine how the model learns.

1. Extrapolation (Generalization)

• Test: Train on $v < 70$, Predict $v > 70$.
• Result: R² = 0.751 (Partial Pass).
• Analysis: The model struggles to generalize to unseen high-energy states, unlike Experiment 2. It behaves more like a local approximator than a universal law discoverer in this context.

2. Noise Robustness

• Test: 5% Input Noise.
• Result: R² = 0.981 (Robust).
• Analysis: The system is highly stable, suggesting the learned solution relies on broad, robust features rather than fragile interference fringes.

3. Cage Analysis (The Revelation)

We analyzed the internal chaotic features to see if they correlated with human concepts.

• Max Correlation with Velocity: 0.9908
• Max Correlation with Angle: 0.9901
• Status: 🔒 CAGE LOCKED

Conclusion

Unlike Experiment 2 (Relativity), where the AI found a novel geometric path, in Experiment 1 (Newtonian), the chaos collapsed into order. The system effectively "reconstructed" the variables of Velocity and Angle internally.

This suggests a fundamental distinction:

• Simple Physics (Newton): Chaos converges to known human variables. The "Cage" is rediscovered.
• Complex Physics (Relativity): Chaos finds distributed, non-intuitive solutions. The "Cage" is broken.

Files

• Stone_in_Lake.py: Experiment code.
• benchmark_experiment_1.py: Audit script.
• experiment_1_results.png: Performance graph.
• benchmark_results.png: Audit graph.

Reproduction

python Stone_in_Lake.py
python benchmark_experiment_1.py