Philosophy#
Free-will, freedom in fetters, dancing in chains#
Tip
Fisher information, \(I(\theta)\), is defined as:
where \(f(X; \theta)\) is the likelihood function of the data \(X\) given the parameter \(\theta\).
The Cramér-Rao lower bound provides a relationship between Fisher information and the variance of an estimator:
Thus, the variance of any unbiased estimator \(\hat{\theta}\) is at least the reciprocal of the Fisher information.
P.S. Data in the digital age has the greatest variance since publishing isn’t in the hands of a few regulated publishers, but in the hands not only of every human, but also countless bots. The variance of data & its informativeness are inversely correlated; but who would know that?
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. 9 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. 14. The idea of “conditional free-will” came to me as a counterpoint to neuro-endocrine determinism espoused by Sapolsky. 13 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. 16 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.#
\(\mu\) Fractals, God#
\(f(t)\) Phonetics:
Fractals\(440Hz \times 2^{\frac{N}{12}}\), \(S_0(t) \times e^{logHR}\), \(\frac{S N(d_1)}{K N(d_2)} \times e^{rT}\)
Show 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)
# 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()
Show code cell output
Inherited Constraints. 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. 9 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. 14. The idea of “conditional free-will” came to me as a counterpoint to neuro-endocrine determinism espoused by Sapolsky. 13 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. 16 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.#
\(S(t)\) Temperament:
ChainsEqual temperament, Proportional hazards, Homoskedastic volatility\(h(t)\) Scale:
Equations9 Inherited, Added, Overcome
\(\sigma\) Chains, Neighbor#
\((X'X)^T \cdot X'Y\): Mode: \( \mathcal{F}(t) = \alpha \cdot \left( \prod_{i=1}^{n} \frac{\partial \psi_i(t)}{\partial t} \right) + \beta \cdot \int_{0}^{t} \left( \sum_{j=1}^{m} \frac{\partial \phi_j(\tau)}{\partial \tau} \right) d\tau\) .
Accidentsmezcal, 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)
Show 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-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()
Show code cell output
Added Constraints. Art & Religion (the same thing, really) mirror life but with a focus on the emotional arcs rather than mere representation. Various modern day activities & rituals recapture the above phases in the history of the human race & invoke primeval emotional arcs. Olympics, country-home, retreates, etc.#
\(\%\) Overcoming, Self#
\(\alpha, \beta, t\) NexToken:
Parametrizedthe processes that are responsible for human behavior as a moiety of “chains” with some “wiggle-room”
Show 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-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()
Show code cell output
\(SV_t'\) Emotion:
Ultimategoal 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.Thusminor chords may represent “loose” chains whereas dom7 & half-dim are somewhat “tight” chains constraining us to our sense of thenextoken
Show 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
Overcoming constraints. Modal interchange overcomes the biological and psychological constraint of diminishing marginal utility. With modal interchange, the “Q” is reset to zero and utility is infinite – like the very first time!#
Show code cell source
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()
Show code cell output
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 (♯, ♭) 13#
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. 22 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.#