Experiment 4: The Transfer Test (The Unity of Physical Laws)

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 whether a chaos-based AI system can discover universal physical principles that transfer across different physical domains, breaking free from domain-specific "cages" that constrain human thinking. We test two versions of the transfer learning paradigm, where models are trained on one physical system and evaluated on a different system that shares the same underlying mathematical structure.

Objective

To determine if a chaotic optical reservoir can recognize and transfer universal mathematical patterns across different physical contexts, even when trained on only one domain. This tests the hypothesis that chaos-based systems can discover deep physical principles that humans took centuries to recognize (e.g., that springs, pendulums, and LC circuits all follow simple harmonic motion).

Scientific Design Principles

1. Same Physical Quantity: Both domains predict the same physical quantity (period or decay time) with the same units and similar scales
2. Shared Mathematical Structure: Both domains follow the same mathematical relationship
3. Different Physical Context: Domains differ only in physical interpretation (mechanical vs. electromagnetic)
4. No Feature Engineering Bias: Models receive raw inputs without explicit feature engineering
5. Impartial Evaluation: Same evaluation criteria applied to both baseline and universal models
6. Negative Controls: Unrelated physics domains included to verify models fail appropriately

Methodology

Version 1: Harmonic Motion Transfer

Domain A: Spring-Mass Oscillator

• Formula: $T = 2\pi\sqrt{m/k}$
• Input: $[m \text{ (kg)}, k \text{ (N/m)}]$
• Output: Period $T$ (seconds)
• Dataset: 3,000 samples
• Parameter ranges: $m \in [0.1, 10]$ kg, $k \in [1, 100]$ N/m
• Period range: 0.22 - 18.17 seconds

Domain B: LC Resonant Circuit

• Formula: $T = 2\pi\sqrt{LC}$
• Input: $[L \text{ (H)}, C \text{ (F)}]$
• Output: Period $T$ (seconds) - same as Domain A
• Dataset: 1,000 samples
• Parameter ranges: $L \in [0.01, 10]$ H, $C \in [0.0001, 0.1]$ F
• Period range: 0.10 - 6.12 seconds
• Scale ratio: LC/Spring mean = 1.138

Shared Structure: Both follow $T \propto \sqrt{\text{inertia}/\text{restoring\_force}}$

Version 2: Exponential Decay Transfer

Domain A: Damped Mechanical Oscillator

• Formula: $\tau = 2m/\gamma$
• Input: $[m \text{ (kg)}, \gamma \text{ (kg/s)}]$
• Output: Decay time $\tau$ (seconds)
• Dataset: 3,000 samples
• Parameter ranges: $m \in [0.1, 5.0]$ kg, $\gamma \in [0.1, 2.0]$ kg/s
• Decay time range: 0.01 - 86.25 seconds
• Includes 3% measurement noise

Domain B: RC Circuit

• Formula: $\tau = RC$
• Input: $[R \text{ (Ω)}, C \text{ (F)}]$
• Output: Decay time $\tau$ (seconds) - same as Domain A
• Dataset: 1,000 samples
• Parameter ranges: $R \in [100, 10000]$ Ω, $C \in [10^{-5}, 0.01]$ F
• Decay time range: 0.01 - 96.44 seconds
• Scale ratio: RC/Mechanical mean = 3.077
• Includes 3% measurement noise

Shared Concept: Both follow exponential decay with $\tau = \text{inertia}/\text{resistance}$

Negative Control: Parallel Resistors

• Formula: $R_{\text{total}} = R_1 R_2 / (R_1 + R_2)$
• Unrelated to exponential decay
• Used to verify models fail appropriately on unrelated physics

Models

Baseline Model (Domain-Specific)

• Simple reservoir with random projection
• No feature engineering
• Expected to learn domain-specific patterns and fail at transfer

Universal Chaos Model

• Chaotic optical reservoir with FFT mixing
• No explicit feature engineering
• Hypothesis: Chaos can discover universal patterns organically

Both models use Ridge regression readout with identical hyperparameters.

Results

Version 1: Spring-Mass → LC Circuit

Within-Domain Performance (Springs)

• Baseline R²: 0.6454
• Universal R²: 0.5105

Cross-Domain Transfer (Springs → LC Circuits)

• Baseline Transfer R²: -1.5519
• Universal Transfer R²: -0.5119
• Transfer Advantage: +1.0401

Analysis: Both models fail at transfer (negative R²), indicating poor generalization. The universal model shows a marginal advantage, but neither model successfully transfers knowledge across domains.

Version 2: Damped Oscillator → RC Circuit

Within-Domain Performance (Mechanical Oscillators)

• Baseline R²: 0.6126
• Universal R²: 0.2697

Cross-Domain Transfer (Mechanical → RC Circuit)

• Baseline Transfer R²: -0.8726
• Universal Transfer R²: -247.0237
• Transfer Advantage: -246.15

Negative Control (Mechanical → Parallel Resistors)

• Baseline R²: -34.54
• Universal R²: -1.75

Analysis:

• Both models fail at transfer, with the universal model performing significantly worse
• Negative control correctly shows both models fail on unrelated physics
• The universal model's poor performance suggests the chaotic transformation may be too sensitive to input distribution differences

Discussion

Key Findings

1. Transfer Learning is Challenging: Even when domains share identical mathematical structures (Version 1) or similar physical concepts (Version 2), both models fail to transfer knowledge effectively.

2. Scale Sensitivity: Despite matching output scales, the models are sensitive to differences in input parameter distributions and ranges between domains.

3. Chaos Model Limitations: The universal chaos model does not show clear advantages over the baseline. In Version 2, it performs significantly worse, suggesting that the chaotic transformation may amplify domain-specific features rather than extracting universal patterns.

4. Negative Control Validation: Both models correctly fail on unrelated physics, confirming they are not simply memorizing arbitrary patterns.

Limitations

1. Limited Training Data: Models are trained on only 3,000 samples, which may be insufficient for learning transferable representations.

2. No Explicit Structure Learning: Neither model explicitly learns the mathematical structure (e.g., square root of ratio). They rely on pattern matching in high-dimensional spaces.

3. Scale Mismatch Sensitivity: Even with matched output scales, input parameter distributions differ significantly between domains, which may hinder transfer.

4. Single Transfer Direction: Only one transfer direction is tested (A → B). Bidirectional transfer or multi-domain training might yield different results.

Implications

The results suggest that discovering universal physical principles through transfer learning is a genuinely difficult problem, even when domains share mathematical structures. This aligns with the historical observation that humans took centuries to recognize these unities. The failure of both models indicates that:

1. Surface Features Dominate: Models may be learning domain-specific surface features rather than deep structural patterns.

2. Representation Gap: The high-dimensional chaotic representations may not naturally encode the low-dimensional mathematical structure shared between domains.

3. Need for Explicit Structure: Future work might require explicit architectural biases or feature engineering to guide models toward universal patterns.

Conclusion

This experiment provides a rigorous, impartial test of transfer learning across physical domains. The results demonstrate that:

• Transfer is difficult: Even with shared mathematical structures, models fail to transfer knowledge
• No clear advantage for chaos: The universal chaos model does not show consistent advantages over the baseline
• Negative controls work: Models appropriately fail on unrelated physics, validating the experimental design

These findings suggest that discovering universal physical principles through pure pattern recognition in high-dimensional spaces is a challenging problem that may require additional inductive biases or architectural constraints.

Files

• experiment_4_transfer.py: Version 1 (Harmonic Motion Transfer)
• experiment_4_improved.py: Version 2 (Exponential Decay Transfer)
• experiment_4_transfer.png: Visualization for Version 1
• experiment_4_rigorous.png: Visualization for Version 2

Reproduction

python experiment_4_transfer.py
python experiment_4_improved.py

References

This experiment is part of the "Darwin's Cage" series investigating whether AI systems can discover physical laws without human conceptual biases. The design principles emphasize scientific rigor, impartial evaluation, and honest reporting of results.