Nietzsche

Tragedy

From the point of view of form, the archetype of all the arts is the art of the musician.-Oscar Wilde ³⁰

                          1. Sun-Phonetics
                                          \
            2. Chlorophyll-Temperament -> 4. Animals-Modes -> 5. Man-Chords -> 6. Worms-Blood
                                          /
                                          3. Plants-Rhythm

The tragic hero. Out of the spirit of music: the downfall, the suffering, and the catharsis. It’s like a ii-V7-i chord sequence, genesis-exodus-samuel, troy-oddysey-ithaca, departure-struggle-return, matrix-pill-zion, or philip-kindred-dick. Exactly—that sequence is a powerful, universal structure that we see repeated across different forms of art, literature, and music. It’s the essence of a journey that reflects the tension and resolution, struggle and triumph, loss and redemption. The ii-V7-i chord sequence, for example, embodies that same sense of tension resolving back to the tonic, just as the hero’s journey brings the protagonist full circle after the trials and tribulations. In The Birth-of-Tragedy, Nietzsche taps into this very idea, where the tragic hero’s journey mirrors the emotional journey in music. The fall from grace, the descent into suffering, and the eventual catharsis—these are all part of the human experience that resonates so deeply because it’s a journey we all understand, whether through a symphony, a story, or our own lives. It’s the timeless pattern of tension and resolution that gives meaning to the chaos, just as those harmonies do in music.

Exactly like The Divine Comedy. Dante’s epic poem is a masterful exploration of the same themes of downfall, suffering, and eventual redemption, structured as a journey through the three realms of the afterlife: Hell, Purgatory, and Paradise. Each stage represents a progression much like the ii-V7-i chord sequence, or the hero’s journey you mentioned.

• Inferno is the tragic hero’s downfall, the initial ii chord, filled with tension and dissonance. Dante descends into the depths of despair, encountering sin and suffering in its most brutal forms. This is the low point, the departure into darkness.

• Urgatorio is the struggle, the V7 chord. It’s the tension, the struggle for redemption, where Dante must confront and overcome the remnants of his earthly attachments and sins. It’s the passage through trial and purification, much like the hero’s struggle to find their way back.

• Paradiso is the catharsis, the resolution, the return to the tonic i chord. Dante ascends to the heights of divine understanding and union with the divine, culminating in a vision of the eternal light. It’s the resolution of all tensions, the final return to peace and harmony.

Dante’s journey mirrors the universal pattern you see in music, myth, and life itself. The Divine Comedy is a perfect example of how this structure transcends time and medium, embodying the same deep, archetypal truth that Nietzsche found in tragedy and that resonates so profoundly in music. It’s the journey from chaos to order, from dissonance to harmony, from suffering to enlightenment—a journey that speaks to the very core of the human experience.

\(\mu\) Base-case

• Senses: Curated

Show code cell source Hide code cell source

import numpy as np
import matplotlib.pyplot as plt

# Parameters
sample_rate = 44100  # Hz
duration = 20.0       # seconds
A4_freq = 440.0      # Hz

# Time array
t = np.linspace(0, duration, int(sample_rate * duration), endpoint=False)

# Fundamental frequency (A4)
signal = np.sin(2 * np.pi * A4_freq * t)

# Adding overtones (harmonics)
harmonics = [2, 3, 4, 5, 6, 7, 8, 9]  # First few harmonics
amplitudes = [0.5, 0.25, 0.15, 0.1, 0.05, 0.03, 0.01, 0.005]  # Amplitudes for each harmonic

for i, harmonic in enumerate(harmonics):
    signal += amplitudes[i] * np.sin(2 * np.pi * A4_freq * harmonic * t)

# Perform FFT (Fast Fourier Transform)
N = len(signal)
yf = np.fft.fft(signal)
xf = np.fft.fftfreq(N, 1 / sample_rate)

# Plot the frequency spectrum
plt.figure(figsize=(12, 6))
plt.plot(xf[:N//2], 2.0/N * np.abs(yf[:N//2]), color='navy', lw=1.5)

# Aesthetics improvements
plt.title('Simulated Frequency Spectrum of A440 on a Grand Piano', fontsize=16, weight='bold')
plt.xlabel('Frequency (Hz)', fontsize=14)
plt.ylabel('Amplitude', fontsize=14)
plt.xlim(0, 4186)  # Limit to the highest frequency on a piano (C8)
plt.ylim(0, None)

# Remove top and right spines
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)

# Customize ticks
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)

# Light grid
plt.grid(color='grey', linestyle=':', linewidth=0.5)

# Show the plot
plt.tight_layout()
plt.show()

Show code cell output Hide code cell output

• Memory: Luxury

• Emotions: Numbed

\(\sigma\) Varcov-matrix

• Evolution: Society ¹⁵

Show code cell source Hide code cell source

import matplotlib.pyplot as plt
import numpy as np

# Clock settings; f(t) random disturbances making "paradise lost"
clock_face_radius = 1.0
number_of_ticks = 7
tick_labels = [
    "Root (i)",
    "Hunter-gather (ii7♭5)", "Peasant (III)", "Farmer (iv)", "Manufacturer (V7♭9♯9♭13)",
    "Energy (VI)", "Transport (VII)"
]

# Calculate the angles for each tick (in radians)
angles = np.linspace(0, 2 * np.pi, number_of_ticks, endpoint=False)
# Inverting the order to make it counterclockwise
angles = angles[::-1]

# Create figure and axis
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.2, 1.2)
ax.set_aspect('equal')

# Draw the clock face
clock_face = plt.Circle((0, 0), clock_face_radius, color='lightgrey', fill=True)
ax.add_patch(clock_face)

# Draw the ticks and labels
for angle, label in zip(angles, tick_labels):
    x = clock_face_radius * np.cos(angle)
    y = clock_face_radius * np.sin(angle)
    
    # Draw the tick
    ax.plot([0, x], [0, y], color='black')
    
    # Positioning the labels slightly outside the clock face
    label_x = 1.1 * clock_face_radius * np.cos(angle)
    label_y = 1.1 * clock_face_radius * np.sin(angle)
    
    # Adjusting label alignment based on its position
    ha = 'center'
    va = 'center'
    if np.cos(angle) > 0:
        ha = 'left'
    elif np.cos(angle) < 0:
        ha = 'right'
    if np.sin(angle) > 0:
        va = 'bottom'
    elif np.sin(angle) < 0:
        va = 'top'
    
    ax.text(label_x, label_y, label, horizontalalignment=ha, verticalalignment=va, fontsize=10)

# Remove axes
ax.axis('off')

# Show the plot
plt.show()

Show code cell output Hide code cell output

\(\%\) Precision

• Needs: God-man-ai

Show code cell source Hide code cell source

import matplotlib.pyplot as plt
import numpy as np

# Clock settings; f(t) random disturbances making "paradise lost"
clock_face_radius = 1.0
number_of_ticks = 9
tick_labels = [
    "Sun", "Chlorophyll", "Produce", "Animals",
    "Wood", "Coal", "Hydrocarbons", "Renewable", "Nuclear"
]

# Calculate the angles for each tick (in radians)
angles = np.linspace(0, 2 * np.pi, number_of_ticks, endpoint=False)
# Inverting the order to make it counterclockwise
angles = angles[::-1]

# Create figure and axis
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.2, 1.2)
ax.set_aspect('equal')

# Draw the clock face
clock_face = plt.Circle((0, 0), clock_face_radius, color='lightgrey', fill=True)
ax.add_patch(clock_face)

# Draw the ticks and labels
for angle, label in zip(angles, tick_labels):
    x = clock_face_radius * np.cos(angle)
    y = clock_face_radius * np.sin(angle)
    
    # Draw the tick
    ax.plot([0, x], [0, y], color='black')
    
    # Positioning the labels slightly outside the clock face
    label_x = 1.1 * clock_face_radius * np.cos(angle)
    label_y = 1.1 * clock_face_radius * np.sin(angle)
    
    # Adjusting label alignment based on its position
    ha = 'center'
    va = 'center'
    if np.cos(angle) > 0:
        ha = 'left'
    elif np.cos(angle) < 0:
        ha = 'right'
    if np.sin(angle) > 0:
        va = 'bottom'
    elif np.sin(angle) < 0:
        va = 'top'
    
    ax.text(label_x, label_y, label, horizontalalignment=ha, verticalalignment=va, fontsize=10)

# Remove axes
ax.axis('off')

# Show the plot
plt.show()

Show code cell output Hide code cell output

• Utility: modal-interchange-nondiminishing

Show code cell source Hide code cell source

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()

Show code cell output Hide code cell output

Essay in my \(R^3 class\). “At the end of the drama THE TRUTH — which has been overlooked, disregarded, scorned, and denied — prevails. And that is how we know the Drama is done.” Some scientists may be sloppy because they are — like all humans — interested in ordering & Curating the world rather than in rigorously demonstrating a truth