Philosophy

Free-will, freedom in fetters, dancing in chains

From the point of view of form, the archetype of all the arts is the art of the musician.-Oscar Wilde ³¹

                   1. Phonetics
                               \
             2. Temperament -> 4. Modes -> 5. NexToken -> 6. Emotion
                               /
                               3. Scales

Dancing in Chains. But these are old conversations about scholarship, politics, and art. The phrase “dancing with chains” (or “dancing in chains”) itself is over a century old: Friedrich Nietzsche used it in 1880 to describe constraining conventions that limit artistic innovation. ¹ The Chinese poet Wen Yiduo used it in the 1930s to suggest that constraints provoke more imaginative art. The entire history of African American literature [and music!] since the enslaved poet Phillis Wheatley is a matter of negotiating real chains as well as metaphorical ones. This was the topic that brought me to China, in fact. ³². The idea of “conditional free-will” came to me as a counterpoint to neuro-endocrine determinism espoused by Sapolsky. ³³ or an idea from William James that the definition of “free-will” is necessarily the definition of an illusion. I woke up this morning and declared that free will as an aesthetic experience, where the agent “dances in chains,” an interplay between freedom and constraint. It suggests that even within the upstream boundaries set by deterministic forces, downstream there’s room for creativity, expression, and agency—much like a dancer who finds elegance and grace within the limitations of choreography. Such constraint implies that true freedom lies not in the absence of constraints but in how skillfully one navigates within them. Just as an artist might create within the boundaries of a medium or genre or a dancer might express themselves within the limits of a routine, free will can be seen as the art of making choices within the confines of external and internal determinants. Viewed this way, an aesthetic autonomy emerges as a form of aesthetic expression. It’s about how we craft our lives, make decisions, and exert influence in the face of limitations. The constraints are not merely obstacles; they are part of what makes the exercise of free will meaningful and beautiful. There is elegance in such agency. Free will lies in the way one harmonizes with the constraints, finding freedom in the rhythm and flow of life’s given conditions. It’s about turning limitations into opportunities for creative and purposeful action, much like a dancer turns a restricted stage into a space for graceful movement - a freedom in fetters, a princely freedom. ³⁵ There is philosophical depth as this view acknowledges that while absolute freedom might be an illusion, the manner in which we navigate relative to our constraints can be profound, purposeful, and even artistic. It transforms the discussion of free will from a binary question of “does it exist or not?” to a richer exploration of how we iteratively live, choose, and express ourselves within the framework we’re given. The beauty of life lies in how we exercise our agency within the bounds we face—an elegant dance within the chains of reality.

(MA-WS-159). Freedom in fetters - a princely freedom . - The last of the modern composers to behold and worship beauty as Leopardi did, the inimitable Pole, Chopin - no one before or after him has a claim to this epithet - Chopin possessed the same princely nobility in respect of convention as Raphael shows in the employment of simplest, most traditional colours - not with regard to colours, however, but in regard to traditional forms of melody and rhythm. These, as born to etiquette, he admits without dispute, but does so playing and dancing in these fetters like the freest and most graceful of spirits - and does so, moreover, without turning them to ridicule.

• The Adjustment Bureau

\(\mu\) Fractals, God

• \(f(t)\) Phonetics: Fractals \(440Hz \times 2^{\frac{N}{12}}\), \(S_0(t) \times e^{logHR}\), \(\frac{S N(d_1)}{K N(d_2)} \times e^{rT}\)

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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)

# Shading the region for normal speaking range (approximately 85 Hz to 255 Hz)
plt.axvspan(500, 2000, color='lightpink', alpha=0.5)

# Annotate the shaded region
plt.annotate('Normal Speaking Range (500 Hz - 2000 Hz)',
             xy=(2000, 0.7), xycoords='data',
             xytext=(2500, 0.5), textcoords='data',
             arrowprops=dict(facecolor='black', arrowstyle="->"),
             fontsize=12, color='black')

# 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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• \(S(t)\) Temperament: Chains Equal temperament, Proportional hazards, Homoskedastic volatility

• \(h(t)\) Scale: Equations ¹ Inherited, Added, Overcome

But you know, I’ve never been able to fall in love. I’ve never been able to find the perfect woman. There’s always something wrong. And then I met Doris. A wonderful woman, great personality, but for some reason I’m just not turned on sexually by her. Don’t ask me why. And then I met Rita. An animal. Nasty, mean, trouble. I love going to bed with her. Though afterward I always wished that I was back with Doris. Then I thought to myself, if only I could put Doris’ brain in Rita’s body, wouldn’t that be wonderful? And I thought, why not? What the hell, I’m a surgeon. ³⁶

That line is classic Woody Allen, capturing his blend of neurotic humor and absurdity. It perfectly encapsulates the human desire for an impossible ideal, and the comedy that arises from the dissonance between our fantasies and reality. The idea of trying to fuse the best qualities of two incompatible people into one perfect partner is as ridiculous as it is relatable. It’s funny because it’s an exaggerated version of what a lot of people feel—the struggle to find a partner who ticks all the boxes. But Allen takes it to the extreme with the surgeon’s ‘solution,’ which is both darkly humorous and a bit unsettling, reflecting his trademark style of intertwining comedy with existential dilemmas. What do you think about how he uses humor to explore these deeper themes?

As we might be able to surmise, Woody Allen has perhaps “danced in chains” in the sense that he accepted life’s hand and stuck to comedy-film and has torutured us with a movie every year for half-century. But otherwise, he’s romanticized everything out of proportion. Whether New York or his three archtypal women.

\(\sigma\) Chains, Neighbor

• \((X'X)^T \cdot X'Y\): Mode: \( \mathcal{F}(t) = \alpha \cdot \left( \prod_{i=1}^{n} \frac{\partial \psi_i(t)}{\partial t} \right) + \beta \cdot \int_{0}^{t} \left( \sum_{j=1}^{m} \frac{\partial \phi_j(\tau)}{\partial \tau} \right) d\tau\) . Accidents mezcal, mezclar, mezcaline. Just a reminder that accidents can mislead one to perceive patterns where there’s no underlying process responsible for them. That said, \(\alpha\) & \(beta\) are emerging as parameters representing the highest hierarchy in this multilevel dataset. They stand for determined (chains) & freewill (wiggle-room)

You’re touching on an intriguing linguistic and cultural trio here:

1. Mezcal: This is the iconic Mexican spirit distilled from the agave plant, known for its smoky flavor and deep connection to indigenous traditions. Unlike tequila, which is a type of mezcal, this spirit can be made from various agave species and is often associated with small-scale, artisanal production methods. Mezcal’s production process, including the roasting of agave hearts in earthen pits, gives it a distinct, rich flavor profile that many connoisseurs appreciate.

2. Mezclar: This Spanish verb means “to mix” or “to blend.” The connection to mezcal is fascinating because the culture around mezcal often involves mixing not just in the literal sense (as in cocktails) but also metaphorically, blending old traditions with new interpretations, artisanal craft with modern consumption, and different agave species to create unique flavor profiles.

3. Mezcalina: This word seems to be a playful combination of “mezcal” and “mescaline,” the psychedelic compound found in certain cacti like peyote. Though not directly related to mezcal, the association hints at the mystical and transformative experiences often linked with both mezcal consumption and the use of mescaline in traditional shamanic rituals. Mezcalina suggests an experience that is both intoxicating and enlightening, a nod to the spirit’s cultural and spiritual significance.

These words together paint a picture of a rich cultural tapestry where traditional practices, linguistic nuances, and the transformative power of mezcal all intertwine. What drew you to this combination? Are you exploring these concepts for a specific reason?

Here’s a mathematical expression that captures the dual nature of free will, integrating the absolute (unconscious, deterministic processes) and relative (conscious, iterative control) components:

\[ \mathcal{F}(t) = \alpha \cdot \left( \prod_{i=1}^{n} \frac{\partial \psi_i(t)}{\partial t} \right) + \beta \cdot \int_{0}^{t} \left( \sum_{j=1}^{m} \frac{\partial \phi_j(\tau)}{\partial \tau} \right) d\tau \]

Where:

1. \(\mathcal{F}(t)\): Represents the free will function at time \(t\), encapsulating both absolute and relative components.

2. \(\alpha\): A constant representing the weight of the absolute component—unconscious, deterministic processes (the “chains”). This is fixed and unchangeable, reflecting the impact of factors beyond our control.

3. \(\beta\): A constant representing the weight of the relative component—conscious, iterative control (the “dancing”). This allows for influence and adaptation based on conscious decisions and actions over time.

4. \(\prod_{i=1}^{n} \frac{\partial \psi_i(t)}{\partial t}\): The product of partial derivatives of \(\psi_i(t)\), representing the absolute processes (e.g., genetic, environmental, and other unconscious factors) that evolve over time \(t\). Each \(\psi_i(t)\) corresponds to a deterministic factor contributing to the overall “chains.”

5. \(\int_{0}^{t} \left( \sum_{j=1}^{m} \frac{\partial \phi_j(\tau)}{\partial \tau} \right) d\tau\): The integral of the sum of partial derivatives of \(\phi_j(\tau)\), representing the relative processes—those elements of our existence we can influence over time \(t\). This term captures the cumulative effect of conscious actions, decisions, and iterative adjustments that impact our destiny.

Explanation of Components:

1. Absolute Component (\(\alpha \cdot \prod_{i=1}^{n} \frac{\partial \psi_i(t)}{\partial t}\)):

   • \(\psi_i(t)\): Represents different unconscious, deterministic factors, such as genetic makeup, early life experiences, or environmental influences. These factors change with time but are not within our control.

   • Partial Derivative (\(\frac{\partial \psi_i(t)}{\partial t}\)): Shows how each deterministic factor evolves with time, reflecting the “chains” that bind us.

   • Product (\(\prod_{i=1}^{n}\)): Suggests that these factors together multiply to form a complex web of influences—akin to the fractal patterns you appreciate. The product emphasizes the interconnectedness and cumulative effect of these deterministic processes.

2. Relative Component (\(\beta \cdot \int_{0}^{t} \left( \sum_{j=1}^{m} \frac{\partial \phi_j(\tau)}{\partial \tau} \right) d\tau\)):

   • \(\phi_j(\tau)\): Represents different conscious, iterative decisions or actions we take, which can influence our future. These are the “dancing” elements where we exert control.

   • Partial Derivative (\(\frac{\partial \phi_j(\tau)}{\partial \tau}\)): Captures how these conscious decisions change over time, reflecting our ability to influence the course of events.

   • Sum (\(\sum_{j=1}^{m}\)): Reflects the aggregation of multiple conscious influences over time, recognizing that our will is expressed through a combination of actions.

   • Integral (\(\int_{0}^{t}\)): Shows the cumulative impact of these actions over time, emphasizing the iterative nature of free will—how each action builds upon previous ones.

This expression integrates both the “chains” of deterministic forces and the “dancing” of conscious choice, reflecting your concept of free will as a dynamic interplay between absolute constraints and relative autonomy.

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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-iADL (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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\(\%\) Overcoming, Self

• \(\alpha, \beta, t\) NexToken: Parametrized the processes that are responsible for human behavior as a moiety of “chains” with some “wiggle-room”

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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-Genomics", "Chlorophyll-Transcriptomics", "Flora-Proteomics", "Animals-Metabolomics",
    "Wood-Epigenomics", "Coal-Lipidomics", "Hydrocarbons-Glycomics", "Renewable-Metagenomics", "Nuclear-Phenomics"
]

# 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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• \(SV_t'\) Emotion: Ultimate goal of life, where all the outlined elements converge. It’s the subjective experience or illusion that life should evoke, the connection between god, neighbor, and self. Thus minor chords may represent “loose” chains whereas dom7 & half-dim are somewhat “tight” chains constraining us to our sense of the nextoken

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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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import matplotlib.pyplot as plt
import numpy as np
from matplotlib.cm import ScalarMappable
from matplotlib.colors import LinearSegmentedColormap, PowerNorm

def gaussian(x, mean, std_dev, amplitude=1):
    return amplitude * np.exp(-0.9 * ((x - mean) / std_dev) ** 2)

def overlay_gaussian_on_line(ax, start, end, std_dev):
    x_line = np.linspace(start[0], end[0], 100)
    y_line = np.linspace(start[1], end[1], 100)
    mean = np.mean(x_line)
    y = gaussian(x_line, mean, std_dev, amplitude=std_dev)
    ax.plot(x_line + y / np.sqrt(2), y_line + y / np.sqrt(2), color='red', linewidth=2.5)

fig, ax = plt.subplots(figsize=(10, 10))

intervals = np.linspace(0, 100, 11)
custom_means = np.linspace(1, 23, 10)
custom_stds = np.linspace(.5, 10, 10)

# Change to 'viridis' colormap to get gradations like the older plot
cmap = plt.get_cmap('viridis')
norm = plt.Normalize(custom_stds.min(), custom_stds.max())
sm = ScalarMappable(cmap=cmap, norm=norm)
sm.set_array([])

median_points = []

for i in range(10):
    xi, xf = intervals[i], intervals[i+1]
    x_center, y_center = (xi + xf) / 2 - 20, 100 - (xi + xf) / 2 - 20
    x_curve = np.linspace(custom_means[i] - 3 * custom_stds[i], custom_means[i] + 3 * custom_stds[i], 200)
    y_curve = gaussian(x_curve, custom_means[i], custom_stds[i], amplitude=15)
    
    x_gauss = x_center + x_curve / np.sqrt(2)
    y_gauss = y_center + y_curve / np.sqrt(2) + x_curve / np.sqrt(2)
    
    ax.plot(x_gauss, y_gauss, color=cmap(norm(custom_stds[i])), linewidth=2.5)
    median_points.append((x_center + custom_means[i] / np.sqrt(2), y_center + custom_means[i] / np.sqrt(2)))

median_points = np.array(median_points)
ax.plot(median_points[:, 0], median_points[:, 1], '--', color='grey')
start_point = median_points[0, :]
end_point = median_points[-1, :]
overlay_gaussian_on_line(ax, start_point, end_point, 24)

ax.grid(True, linestyle='--', linewidth=0.5, color='grey')
ax.set_xlim(-30, 111)
ax.set_ylim(-20, 87)

# Create a new ScalarMappable with a reversed colormap just for the colorbar
cmap_reversed = plt.get_cmap('viridis').reversed()
sm_reversed = ScalarMappable(cmap=cmap_reversed, norm=norm)
sm_reversed.set_array([])

# Existing code for creating the colorbar
cbar = fig.colorbar(sm_reversed, ax=ax, shrink=1, aspect=90)

# Specify the tick positions you want to set
custom_tick_positions = [0.5, 5, 8, 10]  # example positions, you can change these
cbar.set_ticks(custom_tick_positions)

# Specify custom labels for those tick positions
custom_tick_labels = ['5', '3', '1', '0']  # example labels, you can change these
cbar.set_ticklabels(custom_tick_labels)

# Label for the colorbar
cbar.set_label(r'♭', rotation=0, labelpad=15, fontstyle='italic', fontsize=24)


# Label for the colorbar
cbar.set_label(r'♭', rotation=0, labelpad=15, fontstyle='italic', fontsize=24)


cbar.set_label(r'♭', rotation=0, labelpad=15, fontstyle='italic', fontsize=24)

# Add X and Y axis labels with custom font styles
ax.set_xlabel(r'Principal Component', fontstyle='italic')
ax.set_ylabel(r'Emotional State', rotation=0, fontstyle='italic', labelpad=15)

# Add musical modes as X-axis tick labels
# musical_modes = ["Ionian", "Dorian", "Phrygian", "Lydian", "Mixolydian", "Aeolian", "Locrian"]
greek_letters = ['α', 'β','γ', 'δ', 'ε', 'ζ', 'η'] # 'θ' , 'ι', 'κ'
mode_positions = np.linspace(ax.get_xlim()[0], ax.get_xlim()[1], len(greek_letters))
ax.set_xticks(mode_positions)
ax.set_xticklabels(greek_letters, rotation=0)

# Add moods as Y-axis tick labels
moods = ["flow", "control", "relaxed", "bored", "apathy","worry", "anxiety", "arousal"]
mood_positions = np.linspace(ax.get_ylim()[0], ax.get_ylim()[1], len(moods))
ax.set_yticks(mood_positions)
ax.set_yticklabels(moods)

# ... (rest of the code unchanged)


plt.tight_layout()
plt.show()

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Emotion & Affect as Outcomes & Freewill. And the predictors \(\beta\) are MQ-TEA: Modes (ionian, dorian, phrygian, lydian, mixolydian, locrian), Qualities (major, minor, dominant, suspended, diminished, half-dimished, augmented), Tensions (7th), Extensions (9th, 11th, 13th), and Alterations (♯, ♭) ³³

• Marginal utility is that “wiggle-room” within the “chain” of cumulative utility

• How might we “make the most” of each extra year of life ?

• The general answer is: by remaining independent in activities of daily living

• And the philosophyical answer is “by exercizing freewill”, viewed as a little wiggle-room within chains of your fate

• Let’s hold-off frailty onset as long as we possible can

• Inevitability of our outcomes doesn’t mean we have no say in the details of the journey: nihilism loses!

“I think that yesterday was a crisis in my life,” James wrote to his father. “I finished the first part of Renoir’s second Essais and see no reason why the definition of Free Will- ‘the sustaining of a thought because I choose to when I might have other thoughts’, need be the definition of an illusion. At any rate, I will assume for the present-until next year-that it is no illusion. My first act of free will should be to believe in free will.” So, again, nihilism loses!

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

China | Sizing up the ticket. China’s rulers are surprised by Kamala Harris and Tim Walz. One has never been to China, the other has visited 30 times. hinese officials and analysts are struggling. A woman who has never visited China and who has only briefly met its leader, Xi Jinping, has suddenly emerged as a serious contender in the race for the White House. The Democratic Party will gather this week to celebrate the nomination of Kamala Harris as its presidential candidate and her selection of Tim Walz as her running mate. For China’s rulers the ascent of the Harris-Walz ticket creates two difficulties. It challenges China’s nihilistic interpretation of American politics as racist and decrepit. And it has triggered a scramble to assess how a Harris administration might approach China relations, not least because Ms Harris’s credentials on dealing with China are limited, while Mr Walz has more experience of China than any vice-presidential candidate in decades. ⁴¹ Cynicism about American politics abounds in China. The shake-up in the presidential race since June illuminates the limitations of China’s understanding of its superpower rival. When Barack Obama was elected in 2008, his appeal upset the widely held belief in China, reinforced by relentless official propaganda, that America was so profoundly racist that a black person could not become president. China’s latest report on human rights in America, published in May, says racism is getting worse, while gender discrimination is “rampant”. But America could elect its second black president, and its first female one. For much of this year the Biden-Trump contest was a boon for Chinese propagandists, allowing them to portray American democracy as a fight between two men past their cognitive prime, whose attacks were redolent of playground bickering. By bowing out Mr Biden has unsettled that narrative and encouraged some Chinese to wonder about their own system, in which Mr Xi, 71, appears set on remaining leader for life. Last month a blogger on Netease, a Chinese internet platform, wrote “for some people, the greatest contribution they can make to the party, the country and the people is to hand over power, step down from the stage and go home to play with their grandchildren”. The next sentence—“That’s right, I’m talking about you, Biden”—did not calm China’s censors, who scrubbed the post.