Experiment A2: The Definitive Coordinate Independence Test

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 corrects the architectural flaw in A1 by using LSTM (proper temporal architecture) instead of Reservoir Computing. We test if LSTM can learn chaotic dynamics in twisted coordinates as well as in standard coordinates, while polynomial regression fails.

Why A2 is Definitive

What A1 Got Wrong

• Used static architecture (Reservoir) for temporal task
• Impossible to distinguish "cage locked" from "wrong architecture"

What A2 Gets Right

• Uses LSTM (recurrent, temporal) for temporal prediction
• Fair comparison: Both models are appropriate for the task
• Clear test: Does LSTM maintain performance in twisted coordinates?

The Test

System

Double Pendulum with 4 state variables: $(\theta_1, \theta_2, \omega_1, \omega_2)$

Coordinate Twist

$u_1 = \theta_1 + 0.5 \sin(\theta_2)$ $u_2 = \theta_2 + 0.5 \cos(\theta_1)$
$v_1 = \omega_1 + 0.5 \tanh(\omega_2)$ $v_2 = \omega_2 + 0.2 \theta_1 \theta_2$

Models

1. Polynomial (Darwinian): Degree-3 polynomial for 1-step prediction
2. LSTM (AI): 2-layer LSTM (128 units) for multi-step prediction

Prediction Task

• Short-term: Predict 1 step ahead
• Long-term: Predict 10 steps ahead (rollout)

Hypothesis

If Darwin's Cage is Real:

• Polynomial: High R² in standard, low R² in twisted (gap > 0.3)
• LSTM: Similar R² in both (gap < 0.1)

If Darwin's Cage is False:

• Both models show similar gaps
• Or LSTM also fails in twisted coordinates

Expected Result

Based on theory, LSTM should be more robust to coordinate changes than polynomial regression, as it learns temporal patterns rather than explicit functional forms.