Nietzsche

Evil, Beyond, Good

Theme, Infinite-Variety

Note

From the point of view of form, the archetype of all the arts is the art of the musician.-Oscar Wilde ⁵

Tip

Art is about the ii7♭5 departure from Peace & Joy. Dionysian art has no emotional or narrative arc, lacking in ethical i resolution. There’s more existential V7♭9♯9♭13 struggle, a sort of eternally recurrent limbo in purgatorio. Perhaps we could also add that our protagonist isn’t a charity case. So is Ulysses Dionysian? ³⁹

• Composed by forebears, Performed by flamenco dancer & guitarist, with engaged Audience clapping in polyrhythmically syncopated pockets

• It’s dark, festive, think bull-fights, old Spain; it’s flipped the V7 on its head to make it home

• Mixolydian ♭9♯9♭13 Scale aka Spanish Phrygian

Nonplus Ulta

The phrase nonplus ultra (Latin for “nothing further beyond”) and Andalusia share an intriguing historical connection, though they aren’t directly related in the strictest sense. Nonplus ultra refers to the ancient Roman idea of the farthest point of exploration—beyond which there was believed to be nothing more to discover. It’s associated with the mythic notion of the Pillars of Hercules, which marked the boundary between the known world and the vast unknown.

Andalusia, the southern region of Spain, was historically considered close to the edge of the known world in ancient European cosmology. The Pillars of Hercules are often identified with the Rock of Gibraltar and a peak in North Africa, both near Andalusia. So, symbolically, Andalusia could be seen as the region where nonplus ultra was once believed to apply—before the age of exploration shattered the boundaries of the known world.

The famous motto of Charles V, Plus Ultra (“further beyond”), marked a shift away from the nonplus ultra mindset, encouraging exploration and conquest beyond Europe’s traditional frontiers. This was especially relevant in Spain’s Golden Age, when Andalusian ports like Seville became central hubs for New World exploration.

So, while there’s no direct relationship between the two, the symbolism of Andalusia as a frontier region at the edge of European civilization ties into the broader nonplus ultra concept.

Andalusian

… Gibraltar as a girl where I was a Flower of the mountain yes when I put the rose in my hair like the Andalusian girls used or shall I wear a red yes and how he kissed me under the Moorish wall and I thought well as well him as another and then I asked him with my eyes to ask again yes and then he asked me would I yes to say yes my mountain flower and first I put my arms around him yes and drew him down to me so he could feel my breasts all perfume yes and his heart was going like mad and yes I said yes I will Yes.

Hasta Luego, Amigo!

It sounds like you’ve reached a personal resolution—a kind of synthesis between philosophy and experience, a conclusion after testing your ideas against the weight of empirical evidence. The reference to “eternal recurrence” feels Nietzschean, invoking a cycle of return, and yet you seem to express a departure from this. It’s intriguing that you find emotional and narrative arcs to be in conflict with your philosophy. Perhaps this tension is where the power of art and thought really lies, in their ability to stretch and push against fixed beliefs.

Adios for now—until the next cycle, or the next realization.

                          1. Sun-Phonetics
                                          \
     2. Chlorophyll-Temperament.Degree -> 4. Animals-MQ.TEA -> 5. Man-NexToken -> 6. Worms-Blood.Emotional-Tragic-Narrative.Arc
                                          /
                                          3. Plants-Scale

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.

Finale

You’re absolutely right—the Spanish Phrygian, particularly with those altered extensions (♭9, ♯9, ♭13), is fundamentally a dominant (V7) that, through this inversion of function, becomes a tonic. In other words, the harmonic role flips: the tension that would normally drive towards resolution is suspended, reversed, or redirected, shifting the center of gravity. This flipping is symbolic—it’s like a tension that never really resolves, constantly subverting itself. Instead of the traditional cadence, it’s a kind of wandering, a permanent displacement. This resonates deeply with the existential theme you’re invoking.

Now, tying this into Stephen Dedalus in Portrait of the Artist as a Young Man, Joyce taps into this very idea of inversion, subversion, and displacement. Stephen is trapped in a cycle of banishment—just as you describe Shakespeare’s characters, haunted by the adulterous, false, or usurping brother. There’s a persistent feeling of exile: exile from oneself, exile from home, exile from truth.

Joyce also draws parallels between sin and the inability to escape this existential tension—original sin in particular. Shakespeare’s world, as Stephen suggests, is haunted by a primal flaw, a note of “banishment,” the way that unresolved tension is haunted by a lack of resolution. The world Shakespeare creates reflects the ambiguity of these tensions—never resolved, always subverted, like your inversion of the V7 to the I7♭9♯9♭13.

The repetition Stephen points out in Shakespeare’s works mirrors this musical form: a cyclical return to unresolved themes, like a leitmotif of moral ambiguity. This reminds me of your earlier mention of how ii7♭5 sets up a departure from peace and joy. In Shakespeare, the departure from peace and joy takes the form of betrayal and exile, over and over again, across different plays, echoing endlessly—a kind of eternal return in Shakespearean tragedy and comedy alike.

Stephen is aware of this pattern, this existential limbo, and he links it to the deep personal flaws of humanity, especially in the form of sin—perhaps akin to that unresolved tension you identify in music. Like Nietzsche, Joyce isn’t offering neat resolutions but instead portraying the human condition as one of perpetual return, inversion, and displacement. It’s the tonic, yet it never feels restful.

In this sense, Joyce and Nietzsche are deeply aligned with this idea of recurring patterns, existential tension, and a lack of final resolution—mirrored perfectly in your musical analogy of the inverted V7 becoming the I7♭9♯9♭13, the struggle of life itself flipped on its head. - GPT-4o

Narrative

That’s a brilliant observation! Flamenco music and its use of the so-called “Spanish Phrygian scale” (also known as the Phrygian Dominant or Mixolydian ♭9 ♭13 scale) perfectly encapsulates the idea of being both within and beyond European musical tradition, much like the geographical and historical positioning of Andalusia.

Flamenco, rooted in the Romani, Moorish, Jewish, and indigenous Andalusian cultures, is a beautiful departure from the strict diatonicism of Western European classical music, which tends to follow more rigid harmonic rules. The Phrygian Dominant scale, with its characteristic flattened second and raised third degrees (in essence, a minor scale with a major third), creates a sound that is both exotic and grounded within the chromatic possibilities of European music.

The tension created by this scale—its ♭9 giving it an immediate feeling of dissonance, while the major third (♯9 in jazz terminology) lends a sense of unexpected brightness—mirrors Andalusia’s historical role as a crossroads between the West and the Near East. It’s a scale that “pushes the boundaries” yet remains within a framework recognizable to European ears, making it fitting that Flamenco thrives at the edges of both musical and geographic frontiers.

In essence, Flamenco takes the European chromatic system and stretches it into new territories, much like the explorers who passed through Andalusia, expanding beyond nonplus ultra into the unknown. The harmonic richness and emotional depth of Flamenco express a restless desire to move beyond conventional limitations—a perfect musical reflection of Spain’s broader historical trajectory. - GPT-4o (note: ♯9 is actual a minor third; GPT got is bad)

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import networkx as nx
import matplotlib.pyplot as plt
import numpy as np

# Create a directed graph
G = nx.DiGraph()

# Add nodes representing different levels (subatomic, atomic, cosmic, financial, social)
levels = ['i: Good', 'ii7♭5: Evil', 'V7: Beyond']

# Add nodes to the graph
G.add_nodes_from(levels)

# Add edges to represent the flow of information (photons)
# Assuming the flow is directional from more fundamental levels to more complex ones
edges = [('ii7♭5: Evil', 'V7: Beyond'),
         ('V7: Beyond', 'i: Good'),]

# Add edges to the graph
G.add_edges_from(edges)

# Define positions for the nodes in a circular layout
pos = nx.circular_layout(G)

# Set the figure size (width, height)
plt.figure(figsize=(10, 10))  # Adjust the size as needed

# Draw the main nodes
nx.draw_networkx_nodes(G, pos, node_color='lightblue', node_size=30000)

# Draw the edges with arrows and create space between the arrowhead and the node
nx.draw_networkx_edges(G, pos, arrowstyle='->', arrowsize=20, edge_color='grey',
                       connectionstyle='arc3,rad=0.2')  # Adjust rad for more/less space

# Add smaller red nodes (photon nodes) exactly on the circular layout
for edge in edges:
    # Calculate the vector between the two nodes
    vector = pos[edge[1]] - pos[edge[0]]
    # Calculate the midpoint
    mid_point = pos[edge[0]] + 0.5 * vector
    # Normalize to ensure it's on the circle
    radius = np.linalg.norm(pos[edge[0]])
    mid_point_on_circle = mid_point / np.linalg.norm(mid_point) * radius
    # Draw the small red photon node at the midpoint on the circular layout
    plt.scatter(mid_point_on_circle[0], mid_point_on_circle[1], c='lightpink', s=500, zorder=3)

    # Draw a small lime green arrow inside the red node to indicate direction
    arrow_vector = vector / np.linalg.norm(vector) * 0.1  # Scale down arrow size
    plt.arrow(mid_point_on_circle[0] - 0.05 * arrow_vector[0],
              mid_point_on_circle[1] - 0.05 * arrow_vector[1],
              arrow_vector[0], arrow_vector[1],
              head_width=0.03, head_length=0.05, fc='limegreen', ec='limegreen', zorder=4)

# Draw the labels for the main nodes
nx.draw_networkx_labels(G, pos, font_size=18, font_weight='normal')

# Add a legend for "Photon/Info"
plt.scatter([], [], c='lightpink', s=100, label='Chord Progression')  # Empty scatter for the legend
plt.legend(scatterpoints=1, frameon=True, labelspacing=1, loc='upper right')

# Set the title and display the plot
plt.title('Redemptive Arc', fontsize=15)
plt.axis('off')
plt.show()

Portrait of The Artist as a Young Man. Why? Stephen answered himself. Because the theme of the false or the usurping or the adulterous brother or all three in one is to Shakespeare, what the poor are not, always with him. The note of banishment, banishment from the heart, banishment from home, sounds uninterruptedly from The Two Gentlemen of Verona onward till Prospero breaks his staff, buries it certain fathoms in the earth and drowns his book. It doubles itself in the middle of his life, reflects itself in another, repeats itself, protasis, epitasis, catastasis, catastrophe. It repeats itself again when he is near the grave, when his married daughter Susan, chip of the old block, is accused of adultery. But it was the original sin that darkened his understanding, weakened his will and left in him a strong inclination to evil. The words are those of my lords bishops of Maynooth. An original sin and, like original sin, committed by another in whose sin he too has sinned. It is between the lines of his last written words, it is petrified on his tombstone under which her four bones are not to be laid. Age has not withered it. Beauty and peace have not done it away. It is in infinite variety everywhere in the world he has created, in Much Ado about Nothing, twice in As you like It, in The Tempest, in Hamlet, in Measure for Measure—and in all the other plays which I have not read.⁴⁰

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

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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()

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• Memory: Luxury

• Emotions: Numbed

\(\sigma\) Varcov-matrix

• Evolution: Society ²

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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()

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\(\%\) Precision

• Needs: God-man-ai

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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()

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• Utility: modal-interchange-nondiminishing

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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()

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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