Darwin's Cage: A Critical Experimental Review

Final Professional Report

Date: November 26, 2025 Author: Francisco Angulo de Lafuente Project: Darwin's Cage Experiments

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

1. Executive Summary

The "Darwin's Cage" project investigates whether Artificial Intelligence can discover physical laws independent of human conceptual biases. The core hypothesis posits that human-derived concepts (like "velocity", "energy", or "time") form a "Cage" that limits our understanding. A "Cage Locked" status implies the AI has reconstructed these human variables, while a "Cage Broken" status suggests the discovery of novel, potentially superior representations.

This review analyzed 10 experiments comparing a "Darwinian" baseline (polynomial regression) against a "Chaos" model (optical reservoir computing).

Verdict: The experimental results do not support the hypothesis that the Chaos model consistently breaks the cage to discover superior physics. Instead, the "Cage Broken" status is frequently associated with model failure or spurious correlations, while "Cage Locked" simply indicates successful learning of the underlying function. The Chaos model demonstrated significant limitations in handling basic mathematical operations (division, multiplication of variables) and high-dimensional linear mappings, often underperforming the simple Darwinian baseline.

2. Methodology

• Darwinian Baseline: A polynomial regression model representing standard human-derived mathematical approaches.
• Chaos Model: An "Optical Interference Machine" using a fixed random reservoir (simulating optical scattering) followed by a non-linear readout. It aims to find patterns without explicit feature engineering.
• Cage Analysis: Measures the correlation between the model's internal state and known human physical variables.
  • Locked (> 0.9): High correlation.
  • Broken (< 0.3): Low correlation.

3. Experimental Findings

Phase I: The Successes (Experiments 1-3)

These experiments showed the Chaos model's strength in learning continuous, multiplicative relationships.

• Exp 1: The Chaotic Reservoir (Ballistics):

  • Result: Success (R² = 0.9999).
  • Cage: Locked. The model reconstructed velocity and angle.
  • Insight: The model effectively learned the parabolic trajectory $y \propto x \tan(\theta) - x^2/v^2$.

• Exp 2: Einstein's Train (Time Dilation):

  • Result: Success (R² = 1.0000).
  • Cage: Broken (initially thought).
  • Insight: The model learned $\gamma = 1/\sqrt{1-v^2}$. The "Broken" status was due to a lack of linear correlation with $v^2$, but the model clearly learned the function.

• Exp 3: The Absolute Frame (Hidden Variables):

  • Result: Success (R² = 0.9998).
  • Cage: Broken.
  • Insight: The model successfully extracted phase information hidden in the complex domain, which intensity-based methods missed. This was a genuine success of the complex-valued architecture.

Phase II: The Structural Failures (Experiments 4-7)

These experiments revealed fundamental mathematical limitations of the Chaos architecture.

• Exp 4: The Transfer Test:

  • Result: Failure.
  • Insight: The model failed to transfer knowledge between mechanical (springs) and electrical (LC circuits) domains, despite identical mathematical structures. This indicates overfitting to specific input scales rather than learning universal laws.

• Exp 5: Conservation Laws:

  • Result: Failure (R² = 0.28).
  • Insight: The model struggled with division and conservation constraints in 1D collisions. The Darwinian baseline (R² = 0.99) vastly outperformed it.

• Exp 6: Quantum Interference:

  • Result: Failure (R² ~ 0.0).
  • Insight: The model could not learn the interference term $\cos(d \cdot x / \lambda L)$ because it cannot easily form the product/division of input variables required for the phase argument.

• Exp 7: Phase Transitions (Ising Model):

  • Result: Failure (R² = 0.44 vs Baseline R² = 1.0).
  • Insight: The model failed to learn a simple linear target (Magnetization = mean of spins) from high-dimensional inputs (400 spins). The non-linear reservoir projection destroyed the linear information.

Phase III: Complexity & Dimensionality (Experiments 8-10)

These experiments tested the "Complexity Hypothesis" (Simple = Locked, Complex = Broken).

• Exp 8: Classical vs Quantum:

  • Result: Failure on both (R² ~ 0).
  • Insight: Both problems required learning variable-frequency oscillations ($\cos(\omega t)$). The reservoir failed to form the $\omega \cdot t$ product, leading to failure in both "Simple" and "Complex" cases.

• Exp 9: Linear vs Chaos:

  • Result: Failure on both.
  • Insight: The Lorenz attractor (Chaos) was too difficult to predict globally from initial conditions. The Linear RLC circuit failed for the same reason as Exp 8 (variable frequency).

• Exp 10: Low vs High Dimensionality:

  • Result: Mixed.
  • 2-Body (Low Dim): Success (R² = 0.98). Cage Locked.
  • N-Body (High Dim): Failure (R² < 0). Cage Broken.
  • Critique: The "Broken" cage in the N-Body case is a result of the model failing to learn anything, not a discovery of novel physics. The 2-Body success is notable but likely relies on the fixed domain of the angle $\theta$.

4. Critical Analysis

The "Cage" Metric is Flawed

The primary metric for "breaking the cage" (low correlation with human variables) is trivial.

• If the model learns successfully, it must correlate with the inputs that define the physics. Thus, a good model is almost always "Cage Locked".
• If the model fails, it outputs noise or constants, which have low correlation with inputs. This leads to a "Cage Broken" status that signifies incompetence, not insight.

Architectural Limitations

The Optical Chaos model (Reservoir Computing) has specific mathematical weaknesses:

1. Product/Division: It struggles to form products of input variables (e.g., $\omega \cdot t$, $x \cdot d / L$) unless they are explicitly engineered.
2. High-Dimensional Linearity: It degrades the performance of simple linear tasks (like averaging) when the input dimension is high (Exp 7).
3. Global Prediction: It cannot easily approximate complex global functions (like chaotic trajectories) from static parameters without iterative feedback (Exp 9).

The "Darwinian" Advantage

The polynomial baseline, while "biased" by human concepts, proved far more robust. It trivially solved problems involving multiplication and powers (Exp 1, 2, 5) and handled high-dimensional linear tasks perfectly (Exp 7).

5. Conclusion

The "Darwin's Cage" hypothesis remains unproven. The experiments demonstrate that "breaking the cage" is often indistinguishable from failing to learn the physics. The Chaos model, while capable of impressive interpolation in specific domains (Exp 1, 2), lacks the compositional reasoning (multiplication, division, transfer) required to discover universal physical laws.

Recommendation: Future research should focus on:

1. Symbolic Regression: To actually discover laws (equations) rather than just fitting data.
2. Graph Neural Networks (GNNs): For N-body and structural physics, which naturally handle interactions.
3. Iterative Solvers: For chaotic dynamics (Neural ODEs) rather than static mapping.