Lab 8: Cognition — Reproducibility
Objective#
To simulate recursive cognition and symbolic resonance in triadic systems using harmonic feedback and dimensional depth.
Required Tools#
- Python 3.10+
- NumPy
- Matplotlib or Plotly
Protocol#
1. Define Triadic Resonance#
python#
def resonance_operator(Di, Dj, Dk): return (Di * Dj + Dj * Dk + Dk * Di) / (Di + Dj + Dk)
2. Compute Recursive Cognition Index#
python#
import numpy as np
dimensions = [1, 3, 5, 7, 9] C_n = 0 for i in range(len(dimensions) - 2): R = resonance_operator(dimensions[i], dimensions[i+1], dimensions[i+2]) C_n += R * np.log(dimensions[i]) print("Recursive Cognition Index:", C_n)
3. Symbolic Resonance Function#
python#
def symbolic_resonance(t, alpha=1, beta=0.5, omega=2*np.pi, phi=np.pi): return alpha * np.sin(omega * t) + beta * np.cos(phi * t)
4. Visualize Cognitive Phase Shift#
python#
t = np.linspace(0, 10, 1000) R_sample = resonance_operator(3, 5, 7) psi = np.cumsum(symbolic_resonance(t) * R_sample) * (t[1] - t[0])
import matplotlib.pyplot as plt plt.plot(t, psi) plt.title("Cognitive Phase Shift") plt.xlabel("Time") plt.ylabel("Ψ(t)") plt.show()