Anglican

Religion

From the point of view of form, the archetype of all the arts is the art of the musician.-Oscar Wilde ⁴⁶

                1. f(t)
                       \
            2. S(t) -> 4. y:h'(t)=0;t(X'X).X'Y -> 5. b -> 6. SV'
                       /
                       3. h(t)

What happened to Free Will?. Who said anything about Free Will? You know, we actually tried Free Will before. After taking you from hunting and gathering to the height of the Roman Empire we stepped back to see how you’d do on your own.You gave us the Dark Ages – for five centuries – until finally we decided we should come back in. From the ii-V7-i theme of a character arc, What variations might we perceive here? What departure-struggle-return? For our protagonist its politics vs love \(f(t)\) - duty vs impulse \(S(t), h(t)\) - determinism vs. freewill \(\beta, SV_t'\).

• The Adjustment Bureau

• The tension between emotion, impulse, and action \(h(t)\) versus

• Duty, rules, and tradition \(S(t)\)

• A classic struggle that defines much of human experience \(f(t)\). It’s the stuff of great drama, literature, and philosophy—a war within the self that pits personal desires and instincts against the expectations and obligations imposed by society.

• This conflict is often portrayed in narratives where characters are forced to choose between following their heart and adhering to the norms of the group, be it a family, community, or institution. The “Adjustment Bureau” you mentioned, whether metaphorical or literal, represent the forces that attempt to maintain order by curbing individuality and ensuring conformity in line with the categorical imperative. They’re like the unseen hands of fate, working to suppress or redirect those impulses that threaten the stability of the collective unconscious \((X'X)^T \cdot X'Y\).

• In many ways, this struggle reflects the larger theme of free will \(SV_t'\) versus

• Determinism \(\beta\). Are we free to act on our emotions and impulses, or are we bound by the duties and traditions we’ve inherited? The beauty and tragedy of this conflict lie in the fact that there’s no simple resolution—it’s an eternal push and pull, where the outcome is never certain. Characters who wrestle with this dilemma are often the most compelling because they embody the human condition in its rawest form. They challenge the status quo, disrupt the carefully maintained order, and force a reckoning between personal authenticity and societal expectations. And in this clash, there’s often no clear winner, just a deeper understanding of the costs and consequences of choosing one path over the other.

\(\mu\) Base-case

• Senses: Kasubi View

• Patterns

  • \(440Hz \times 2^{\frac{N}{12}}\)

  • \(S_0(t) \times e^{logHR}\)

  • \(\frac{S N(d_1)}{K N(d_2)} \times e^{rT}\)

• Chains

  • Equal temperament

  • Proportional hazards

  • Homoskedastic volatility

• Formulae ³

  • Inherited

  • Added

  • Overcome

• Unconscious. Absolute pitch, also known as perfect pitch, is not a myth, but it is a somewhat misunderstood and often romanticized phenomenon. Absolute pitch refers to the ability to identify or produce a specific pitch without an external reference tone. People with absolute pitch can name the notes they hear or sing a note on command, seemingly without effort. This ability is rare, with estimates suggesting that only about 1 in 10,000 people possess it. The “myth” aspect comes into play when people assume that absolute pitch is some kind of magical or universally superior musical skill. While it’s true that those with absolute pitch often have a strong affinity for music, this ability doesn’t necessarily make someone a great musician. In fact, some argue that relative pitch—the ability to discern intervals between notes—is more valuable for musicians, as it underpins essential skills like harmony, melody, and musical improvisation.

• Moreover, absolute pitch can be a double-edged sword. For some, it can become a burden, making transposing music or dealing with slight pitch variations difficult. Imagine being able to hear every note out of tune, even if the difference is minuscule—it could drive someone with absolute pitch to distraction.

• There is also an ongoing debate about whether absolute pitch can be developed through training or if it’s solely an innate ability. While early musical training in a pitch-naming environment (especially before the age of 6) seems to increase the likelihood of developing absolute pitch, most research suggests that there is a significant genetic component to it. In summary, absolute pitch is real but not as mystical or essential as it’s sometimes made out to be. It’s a fascinating ability that can be both a gift and a challenge, depending on the context.

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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: St. Francis Chapel

• Emotions: I’m not Your Superwoman

\(\sigma\) Varcov-matrix

• Becoming: A Man ¹⁷

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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

• Cravings: 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

Nihilism defeated!

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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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                1. Exposure
                           \
               2. Role ->  4. Categorical.Imperative -> 5. Determinism -> 6. Freewill
                           /
                           3. Impulse

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