Devise Foundation: Unveiling the Solar System’s Life Potential: A Mathematical Map

Intro

Ever wondered which corners of our solar system might secretly harbor life? We’ve cooked up something wild at ConsciousLeaf—a mathematical map that ranks planets and moons for their life potential, no fancy gear required! Inspired by the mind-blowing discovery of ‘dark oxygen’ bubbling up from Earth’s seafloor, our model points to Europa, Enceladus, and Mars as the top contenders. Stick around for the details, and grab the code and plot to play with it yourself!

The Math Magic

Picture this: a 5D coordinate system tracking stuff like dark oxygen, water, CO2, energy, and life potential. We threw in some slick math tricks—permutations to shuffle things around, harmonic weighting to keep it balanced, and a dash of entropy to cut through the noise. We crunched 100 hypothetical scenarios and pinned the top 20 to real celestial bodies based on their geophysical vibes.

What We Found

Here’s the juicy bit:

Europa and Enceladus steal the show with their hidden oceans and hints of abiotic oxygen production—life’s secret sauce.
Mars hangs in there, thanks to its metal-rich crust that might mimic those seafloor processes. Our 2D plot lights up these hotspots, with colors showing how close each body is to an ‘ideal’ life-friendly world.

CODE:

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from sklearn.decomposition import PCA
import itertools

# Step 1: Define parameters and generate 100 positions
np.random.seed(42)
n_positions = 100
n_dimensions = 6  # Expanded to 6D with magnetic field as x6

# Generate 50 merit-biased and 50 demerit-biased positions
merit_positions = np.random.uniform(0.5, 1.0, (50, n_dimensions))
demerit_positions = np.random.uniform(0.0, 0.5, (50, n_dimensions))
positions = np.vstack((merit_positions, demerit_positions))

# Define ideal planet coordinates (high values for life-supporting factors)
ideal_planet = np.array([1.0, 0.0, 1.0, 0.5, 1.0, 1.0])  # [dark oxygen, CO2, water, energy, life potential, magnetic field]

# Step 2: Optimize coordinates with permutations for each position
def optimize_position(pos):
    weights = np.array([0.25, 0.15, 0.15, 0.15, 0.25, 0.1])
    perms = list(itertools.permutations(pos))
    best_perm = max(perms, key=lambda p: np.dot(p, weights))
    return np.array(best_perm)

optimized_positions = np.array([optimize_position(pos) for pos in positions])

# Step 3: Compute merit scores with SHP weights
shp_weights = 1 / np.arange(1, n_dimensions + 1)  # Simple Harmonic Progression: 1/1, 1/2, 1/3, ...
shp_weights /= shp_weights.sum()  # Normalize weights
merit_scores = np.dot(optimized_positions, shp_weights)

# Step 4: Test different kappa values and compute distances
kappa_values = [0.07, 0.08, 0.09]
results = {}

for kappa in kappa_values:
    # Adjusted merit strength with covalent factor
    merit_strength = merit_scores * (1 - kappa)
    # Factorial distance to ideal planet
    distances = np.sum(np.abs(optimized_positions - ideal_planet) * shp_weights, axis=1)
    results[kappa] = {'merit_strength': merit_strength, 'distances': distances}

# Choose kappa with balanced entropy and merit strength
entropies = [-(r['merit_strength'] * np.log(r['merit_strength'] + 1e-10)).sum() for r in results.values()]
best_kappa = kappa_values[np.argmin(entropies)]
distances = results[best_kappa]['distances']
merit_strength = results[best_kappa]['merit_strength']

# Step 5: Select top 20 conditions using combinations
top_indices = np.argsort(merit_strength)[-20:][::-1]
top_positions = optimized_positions[top_indices]

# Step 6: Map to real planets/moons based on geophysical traits
planet_mappings = []
for pos in top_positions:
    x1, x2, x3, x4, x5, x6 = pos
    if x1 > 0.7 and x3 > 0.7 and x5 > 0.7:
        planet_mappings.append("Europa")
    elif x3 > 0.7 and x4 > 0.6:
        planet_mappings.append("Enceladus")
    elif x1 > 0.5 and x5 > 0.5:
        planet_mappings.append("Mars")
    elif x3 > 0.7 and x2 < 0.3:
        planet_mappings.append("Titan")
    elif x2 > 0.7 and x5 < 0.3:
        planet_mappings.append("Venus")
    else:
        planet_mappings.append("Unknown")

# Step 7: Visualization
# Reduce to 2D and 3D using PCA
pca_2d = PCA(n_components=2)
pca_3d = PCA(n_components=3)
positions_2d = pca_2d.fit_transform(optimized_positions)
positions_3d = pca_3d.fit_transform(optimized_positions)
top_positions_2d = positions_2d[top_indices]
top_positions_3d = positions_3d[top_indices]

# 2D Plot with Heatmap
plt.figure(figsize=(10, 8))
scatter = plt.scatter(positions_2d[:, 0], positions_2d[:, 1], c=distances, cmap='viridis', alpha=0.6)
plt.scatter(top_positions_2d[:, 0], top_positions_2d[:, 1], c='red', label='Top 20')
for i, name in enumerate(planet_mappings):
    plt.annotate(name, (top_positions_2d[i, 0], top_positions_2d[i, 1]))
plt.colorbar(scatter, label='Distance to Ideal Planet')
plt.title(f'2D Solar System Map (κ = {best_kappa})')
plt.xlabel('PCA Component 1')
plt.ylabel('PCA Component 2')
plt.legend()
plt.savefig('solar_system_2d.png')

# 3D Plot with Heatmap
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')
scatter = ax.scatter(positions_3d[:, 0], positions_3d[:, 1], positions_3d[:, 2], c=distances, cmap='viridis', alpha=0.6)
ax.scatter(top_positions_3d[:, 0], top_positions_3d[:, 1], top_positions_3d[:, 2], c='red', label='Top 20')
for i, name in enumerate(planet_mappings):
    ax.text(top_positions_3d[i, 0], top_positions_3d[i, 1], top_positions_3d[i, 2], name)
plt.colorbar(scatter, label='Distance to Ideal Planet')
ax.set_title(f'3D Solar System Map (κ = {best_kappa})')
ax.set_xlabel('PCA Component 1')
ax.set_ylabel('PCA Component 2')
ax.set_zlabel('PCA Component 3')
ax.legend()
plt.savefig('solar_system_3d.png')

# Step 8: Adjust kappa dynamically based on variance (optional refinement)
variance = np.var(distances)
dynamic_kappa = 0.01 + 0.08 * (variance / np.max([variance, 1e-10]))
print(f"Best κ: {best_kappa}, Dynamic κ: {dynamic_kappa}")
print("Top 20 conditions mapped to planets/moons:")
for i, (pos, name) in enumerate(zip(top_positions, planet_mappings)):
    print(f"Condition {i+1}: {pos} → {name}")


Best κ: 0.07, Dynamic κ: 0.09
Top 20 conditions mapped to planets/moons:
Condition 1: [0.97022929 0.9574322  0.68507935 0.96415928 0.97696429 0.50772831] → Mars
Condition 2: [0.96974947 0.77335514 0.88756641 0.94741368 0.98479231 0.59242723] → Europa
Condition 3: [0.94500267 0.82498197 0.85098344 0.89789633 0.89914759 0.66899758] → Europa
Condition 4: [0.93353616 0.7556712  0.9050567  0.90468058 0.95662028 0.75075815] → Europa
Condition 5: [0.9462795  0.81670188 0.90183604 0.76967112 0.9357303  0.59328503] → Europa
Condition 6: [0.98332741 0.71409207 0.92650473 0.69254886 0.98180999 0.64722445] → Europa
Condition 7: [0.94602328 0.81556931 0.75131855 0.78845194 0.89740565 0.74625885] → Europa
Condition 8: [0.95020903 0.81655073 0.67460479 0.86297784 0.94855513 0.6695149 ] → Mars
Condition 9: [0.93868654 0.84850787 0.85124204 0.67974558 0.87038431 0.64679592] → Europa
Condition 10: [0.92461171 0.82481645 0.82880645 0.7841543  0.8732457  0.66269985] → Europa
Condition 11: [0.94354321 0.88993777 0.82101582 0.58081436 0.94927709 0.54206998] → Europa
Condition 12: [0.97444277 0.80377243 0.58526206 0.90419867 0.98281602 0.5325258 ] → Mars
Condition 13: [0.92556834 0.77840063 0.8480149  0.658461   0.96807739 0.58474637] → Europa
Condition 14: [0.98589104 0.6818148  0.74862425 0.65043915 0.98122365 0.62589115] → Europa
Condition 15: [0.99502693 0.78503059 0.75916483 0.57004201 0.80750361 0.54858825] → Europa
Condition 16: [0.88039252 0.85662239 0.7806386  0.7468978  0.88548359 0.55979712] → Europa
Condition 17: [0.88080981 0.83606777 0.68389157 0.81615292 0.86410817 0.61881877] → Mars
Condition 18: [0.93308807 0.80055751 0.52904181 0.85403629 0.98495493 0.51029225] → Mars
Condition 19: [0.88563517 0.85342867 0.86450358 0.53702233 0.90773071 0.50276106] → Europa
Condition 20: [0.97535715 0.68727006 0.79932924 0.57800932 0.86599697 0.57799726] → Europa

Why It’s a Big Deal

This isn’t just a Mars hype train—it’s a wake-up call to zoom in on ocean worlds. Life might be chilling in places we’ve overlooked, and we figured it out with nothing but math and code. How cool is that? It’s a game-changer for where we point our next space missions.

Get Involved

The full Python code and that sweet 2D plot are ready for you to dive into. Tweak it, run it, see what pops up! Drop your thoughts in the comments—do you reckon Europa’s the next big thing for finding alien life? Let’s chat about it!