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Letters to Abigail

Activation Function, $Q$: 1st, 3rd, 5th, ♭♭7th, 9th

• Hunter-gatherer/War: spiritual teachings (I)
• Peasant/Economics: humanism (B)

Biases, $U()$: 11th, 13th

• Farmer/Calculus: judeo, christian (G)
• Manufacturer/Philosophy: world religions (Y)

Weights, $\frac{dU()}{dQ}$: ♯9,♭9,♯11,♭13

• Electricity/Musick: prophetic utterances (O)
• Railway/Leisure: individual experience (R)

import numpy as np
import matplotlib.pyplot as plt

# Define the total utility function U(Q)
def total_utility(Q):
    return 100 * np.log(Q + 1)  # Logarithmic utility function for illustration

# Define the marginal utility function MU(Q)
def marginal_utility(Q):
    return 100 / (Q + 1)  # Derivative of the total utility function

# Generate data
Q = np.linspace(1, 100, 500)  # Quantity range from 1 to 100
U = total_utility(Q)
MU = marginal_utility(Q)

# Plotting
plt.figure(figsize=(14, 7))

# Plot Total Utility
plt.subplot(1, 2, 1)
plt.plot(Q, U, label=r'Total Utility $U(Q) = 100 \log(Q + 1)$', color='blue')
plt.title('Total Utility')
plt.xlabel('Quantity (Q)')
plt.ylabel('Total Utility (U)')
plt.legend()
plt.grid(True)

# Plot Marginal Utility
plt.subplot(1, 2, 2)
plt.plot(Q, MU, label=r'Marginal Utility $MU(Q) = \frac{dU(Q)}{dQ} = \frac{100}{Q + 1}$', color='red')
plt.title('Marginal Utility')
plt.xlabel('Quantity (Q)')
plt.ylabel('Marginal Utility (MU)')
plt.legend()
plt.grid(True)

# Adding some calculus notation and Greek symbols
plt.figtext(0.5, 0.02, r"$MU(Q) = \frac{dU(Q)}{dQ} = \lim_{\Delta Q \to 0} \frac{U(Q + \Delta Q) - U(Q)}{\Delta Q}$", ha="center", fontsize=12)

plt.tight_layout()
plt.show()

Running this code will generate a visual demonstration of diminishing marginal utility with appropriate calculus notation and Greek symbols.

Here is the generated image:

One needs challenges, a worthy adversary, the embrace of more remote overtones of the harmonic series - Qualities

• Westmalle Dubbel, $7$ %
• Duvel, $8.5$ %
• Truth, $8.7$ %
• Westmalle Tripel, $9.5$ %
• St. Bernardus Abt 12, $10$ %