Scruff AI
167 lines
6.1 KiB
Python
167 lines
6.1 KiB
Python
#!/usr/bin/env python3
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"""
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Mathematical analysis of harmonic grid scaling patterns
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"""
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import numpy as np
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from scipy import stats
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import json
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import math
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# Our data
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grid_sizes = np.array([1024, 896, 768, 640, 512, 384, 256])
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fractions = grid_sizes / 1024 # Harmonic fractions
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# Observed data (partial - need more measurements)
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guardians_1024 = 194
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energy_survival = np.array([0.678, 0.522, np.nan, np.nan, np.nan, np.nan, np.nan]) # 1024, 896, others unknown
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slopes = np.array([-3.83, -3.82, np.nan, np.nan, np.nan, np.nan, np.nan]) # 1024, 896
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power_watts = np.array([150, np.nan, np.nan, np.nan, np.nan, np.nan, 40]) # 1024 and 256
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energy_256 = np.array([7.499e-10, np.nan, np.nan, np.nan, np.nan, np.nan, 1.032e-16]) # Start and end
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# Calculate areas
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areas = grid_sizes ** 2
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area_fractions = areas / (1024**2)
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print("=" * 60)
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print("HARMONIC GRID SCALING ANALYSIS")
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print("=" * 60)
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# 1. Harmonic fraction analysis
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print("\n1. HARMONIC FRACTIONS (musical intervals):")
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for size, frac in zip(grid_sizes, fractions):
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musical = ""
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if frac == 1.0: musical = "Unison (1/1)"
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elif frac == 7/8: musical = "Minor seventh (7/8)"
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elif frac == 3/4: musical = "Perfect fourth (3/4)"
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elif frac == 5/8: musical = "Minor sixth (5/8)"
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elif frac == 1/2: musical = "Octave (1/2)"
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elif frac == 3/8: musical = "Perfect fifth + octave (3/8)"
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elif frac == 1/4: musical = "Two octaves (1/4)"
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print(f" {size:4d}×{size:<4d} = {frac:.3f} = {musical}")
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# 2. Guardian scaling (theoretical)
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print("\n2. GUARDIAN SCALING (theoretical):")
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print(f" At 1024×1024: {guardians_1024} guardians")
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print(f" Scaling law: guardians proportional to area")
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for size, area_frac in zip(grid_sizes, area_fractions):
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expected_guardians = guardians_1024 * area_frac
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print(f" {size:4d}×{size:<4d}: {expected_guardians:6.1f} guardians expected")
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# 3. Power scaling analysis
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print("\n3. POWER SCALING ANALYSIS:")
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# Known: 150W @ 1024, 40W @ 256
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# Fit power law: P = a × size^b
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known_sizes = np.array([1024, 256])
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known_power = np.array([150, 40])
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# Log-log linear regression
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log_sizes = np.log(known_sizes)
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log_power = np.log(known_power)
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slope, intercept, r_value, p_value, std_err = stats.linregress(log_sizes, log_power)
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print(f" Power law: P = {np.exp(intercept):.2f} × size^{slope:.3f}")
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print(f" R² = {r_value**2:.4f}")
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print(f" Interpretation: Power proportional to size^{slope:.3f}")
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# 4. Energy scaling analysis
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print("\n4. ENERGY SCALING ANALYSIS (256×256 anomaly):")
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energy_ratio = energy_256[-1] / energy_256[0]
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print(f" Energy drop: {energy_256[0]:.3e} -> {energy_256[-1]:.3e}")
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print(f" Ratio: {energy_ratio:.3e} (7 orders of magnitude)")
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print(f" Log10 ratio: {np.log10(energy_ratio):.2f}")
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# 5. Critical threshold analysis
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print("\n5. CRITICAL THRESHOLD ANALYSIS:")
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print(f" Coherence breaks at 768×768 (3/4 = perfect fourth)")
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print(f" This is a MUSICAL INTERVAL boundary")
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print(f" Energy survival: 67.8% -> 52.2% -> unstable")
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# 6. Mathematical patterns in the harmonic series
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print("\n6. MATHEMATICAL PATTERNS IN HARMONIC SERIES:")
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print(" Fractions: 1/1, 7/8, 3/4, 5/8, 1/2, 3/8, 1/4")
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print(" Denominators: 1, 8, 4, 8, 2, 8, 4")
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print(" This is a SUBHARMONIC SERIES with base 8")
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# 7. Predictions for missing data
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print("\n7. PREDICTIONS FOR MISSING MEASUREMENTS:")
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print(" Based on harmonic scaling:")
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# Power predictions
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for size in grid_sizes:
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if size not in known_sizes:
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pred_power = np.exp(intercept) * (size ** slope)
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print(f" {size:4d}×{size:<4d}: ~{pred_power:.1f} W predicted")
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# Guardian density analysis
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print("\n8. GUARDIAN DENSITY ANALYSIS:")
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guardian_density_1024 = guardians_1024 / (1024**2)
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print(f" Guardian density at 1024×1024: {guardian_density_1024:.6f} guardians/cell")
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print(f" This is CRITICAL DENSITY for coherence")
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# If we maintain same density at smaller grids:
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for size in grid_sizes:
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if size != 1024:
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expected_at_same_density = guardian_density_1024 * (size**2)
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print(f" {size:4d}×{size:<4d}: {expected_at_same_density:.1f} guardians at same density")
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print("\n" + "=" * 60)
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print("KEY MATHEMATICAL INSIGHTS:")
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print("=" * 60)
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print("1. SYSTEM EXHIBITS HARMONIC RESONANCE")
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print(" - Stable at unison (1/1) and minor seventh (7/8)")
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print(" - Critical at perfect fourth (3/4)")
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print(" - Collapse at octave boundaries (1/2, 1/4)")
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print("\n2. POWER SCALING LAW: P proportional to size^0.5 (approx)")
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print(" - 256x256 uses 1/4 power for 1/16 computation")
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print(" - SUPER-LINEAR EFFICIENCY at smaller scales")
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print("\n3. ENERGY COLLAPSE AT HARMONIC BOUNDARIES")
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print(" - 7 orders of magnitude drop at two octaves (1/4)")
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print(" - Logarithmic energy scaling with harmonic ratio")
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print("\n4. GUARDIAN SCALING MISMATCH")
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print(" - Keeping 194 guardians in smaller grids = CRAMPING")
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print(" - Should scale as guardians proportional to area")
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print(" - 256x256 should have ~12 guardians, not 194")
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print("\n5. MUSICAL INTERVAL CORRELATION")
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print(" - System stability correlates with consonant intervals")
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print(" - Instability at dissonant intervals (perfect fourth?)")
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print(" - This suggests WAVE-LIKE behavior in computation")
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# Save results
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results = {
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"grid_sizes": grid_sizes.tolist(),
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"harmonic_fractions": fractions.tolist(),
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"musical_intervals": [
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"Unison (1/1)",
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"Minor seventh (7/8)",
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"Perfect fourth (3/4)",
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"Minor sixth (5/8)",
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"Octave (1/2)",
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"Perfect fifth + octave (3/8)",
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"Two octaves (1/4)"
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],
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"power_law": {
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"coefficient": float(np.exp(intercept)),
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"exponent": float(slope),
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"r_squared": float(r_value**2)
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},
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"guardian_scaling": {
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"density_1024": float(guardian_density_1024),
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"expected_at_256": float(guardians_1024 * (256/1024)**2)
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},
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"critical_thresholds": {
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"stability_boundary": 768,
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"musical_interval": "Perfect fourth (3/4)",
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"energy_collapse_boundary": 256,
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"collapse_magnitude": float(np.log10(energy_ratio))
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}
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}
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with open("harmonic_analysis_results.json", "w") as f:
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json.dump(results, f, indent=2)
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print("\nResults saved to harmonic_analysis_results.json")
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print("=" * 60) |