Experiment C1: The Representation Test

Direct Falsification of Darwin's Cage Theory

Author: Francisco Angulo de Lafuente
Date: 2024
Status: Implementation Complete

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

Experiment C1 is a direct falsification test of Darwin's Cage theory. Unlike previous experiments that compared different physical problems or model architectures, C1 uses rigorous experimental control to test if input representation alone affects "cage status."

Key Innovation: Same physics, same model, same hyperparameters - ONLY the input representation differs.

Core Hypothesis (Falsifiable)

If Darwin's Cage Theory is Correct:

A non-anthropomorphic representation (raw coordinates without human concepts) should result in LOWER correlation with human variables in internal features, compared to an anthropomorphic representation (velocity, angle) - even when solving the SAME physical problem with the SAME model architecture.

If the Theory is False:

Both representations should show the SAME correlation patterns, indicating that representation doesn't affect cage status.

Experimental Design

Physical Problem

Projectile Motion (same as Experiment 1)

Ground truth: $R = \frac{v_0^2 \sin(2\theta)}{g}$
Same physics, same difficulty, same learnability
This ensures we're testing representation, not problem difficulty

Two Representations (ONLY Difference)

1. Anthropomorphic Representation (Human Variables)

Input: $[v_0, \theta]$ (velocity, angle)
This is how humans naturally think about the problem
Expected: High correlation with internal features (cage locked)

2. Non-Anthropomorphic Representation (Raw Coordinates)

Input: $[x_0, y_0, v_x, v_y]$ (initial position and velocity components)
Contains the SAME information but without human concepts
Expected (if theory correct): Lower correlation with $v_0$ and $\theta$ (cage broken)

Critical Controls

✅ Same model architecture (OpticalChaosMachine)
✅ Same hyperparameters (n_features=4096, brightness=0.001)
✅ Same random seeds for reproducibility
✅ Same dataset size and distribution
✅ Same train/test split
✅ Same evaluation metrics
✅ Same cage analysis methodology (check ALL features)

Only variable that changes: Input representation

Methodology

1. Data Generation

Generate projectile trajectories using same physics simulator
Convert to both representations
Verify information equivalence (both contain same physical information)

2. Model Training

Train identical models on both representations
Use same hyperparameters
Same random seeds for optical matrix

3. Evaluation

Standard R² score (both should achieve similar accuracy)
Extrapolation test (generalization)
Noise robustness (stability)
Cage Analysis: Correlation of internal features with:
- $v_0$ (velocity)
- $\theta$ (angle)
- $v_0^2$ (velocity squared)
- $\sin(2\theta)$ (angle function)

4. Statistical Test

Compare correlation distributions between representations
Use statistical significance testing (t-test, Mann-Whitney U)
Report confidence intervals (bootstrap)
Calculate effect sizes (Cohen's d)

Success Criteria (Falsification Test)

Theory SUPPORTED if:

Non-anthropomorphic representation shows significantly LOWER max correlation with human variables
Both achieve similar R² (proving they learned the same physics)
Statistical test shows significant difference (p < 0.05)
Effect size is meaningful (Cohen's d > 0.5)

Theory FALSIFIED if:

Both representations show similar correlation patterns
No significant difference in cage analysis
Representation doesn't affect cage status

Either outcome is valuable - we seek truth, not confirmation.

Bias Prevention

No Selection Bias: Same dataset, just different representation
No Hyperparameter Bias: Identical hyperparameters
No Architecture Bias: Same model architecture
No Interpretation Bias: Pre-defined success criteria
No Confirmation Bias: Designed to falsify, not confirm
Statistical Rigor: Proper significance testing

Files Structure

experiment_C1_representation_test/
├── experiment_C1_representation_test.py  # Main experiment
├── benchmark_experiment_C1.py            # Rigorous validation
├── README.md                             # This file
├── STATISTICAL_ANALYSIS.md               # Statistical methods
└── RESULTS.md                            # Results and interpretation

Usage

Run Main Experiment

cd experiment_C1_representation_test
python experiment_C1_representation_test.py

Run Benchmark Validation

python benchmark_experiment_C1.py

Expected Outcomes

Best Case (Theory Supported):

Anthropomorphic: Max correlation > 0.9 (cage locked)
Non-anthropomorphic: Max correlation < 0.3 (cage broken)
Both: R² > 0.99 (same physics learned)
Statistical test: p < 0.001
Effect size: Cohen's d > 0.8 (large)

Worst Case (Theory Falsified):

Both: Similar correlation patterns
No significant difference (p > 0.05)
Representation doesn't matter
Theory is falsified

Intermediate Case:

Some difference but not statistically significant
Effect size is small
Inconclusive - may need more data or different analysis

Scientific Rigor

✅ Pre-registered hypothesis (this document)
✅ Falsifiable predictions (clear success/failure criteria)
✅ Controlled variables (only representation differs)
✅ Statistical testing (proper significance tests)
✅ Honest reporting (regardless of outcome)
✅ Reproducible (all seeds documented)

Key Differences from Previous Experiments

Rigorous Control: Only representation varies, everything else identical
Direct Falsification: Clear criteria for supporting/falsifying theory
Statistical Rigor: Proper significance testing and effect sizes
Information Equivalence: Verified that representations contain same information
Pre-registered: Hypothesis and criteria defined before running

References

Experiment 1: The Chaotic Reservoir (baseline for comparison)
Comprehensive Experimental Review: Identified need for controlled experiment
Darwin's Cage Theory: Gideon Samid's original hypothesis

Contact

Author: Francisco Angulo (Agnuxo1)
Email: [email protected]

Status: Implementation complete. Ready for execution and analysis.