Chapter 3

Chapter 3#

          1. Strategies, σ
                          \
        2. Payoffs, Ψ  -> 4. Modal-Chordal-Groove, Δ -> 5. NexToken, τ -> 6. Arcs, Ω 
                          /
                          3. Equilibria, ε
act3/figures/blanche.*

Fig. 2 Polyrhythmic Groove. We have common time \(\frac{4}{4}\) with two triplets & a double figure, creating polyrhythmic syncompation. This is typical of celebratory, participatory, answer/call, dance music from the Ankore & Kiga regions of Uganda. It’s worth contrasting this culture with Flamenco & Andalusean elements in both rhythm & dance.#

Hide code cell source 
import numpy as np
import matplotlib.pyplot as plt

# Create x values representing the six stages, and create y values using a sine function
x = np.linspace(0, 2 * np.pi, 1000)
y = np.sin(x)

# Define the stages
stages = ["Birth", "Growth", "Stagnation", "Decline", "Existential", "Rebirth"]

# Define the x-ticks for the labeled points
x_ticks = np.linspace(0, 2 * np.pi, 6)

# Set up the plot
plt.figure(figsize=(10, 6))

# Plot the sine wave
plt.plot(x, y, color='blue')

# Fill the areas under the curve for each stage and label directly on the graph
plt.fill_between(x, y, where=(x < x_ticks[1]), color='lightblue', alpha=0.5)
plt.text(x_ticks[0] + (x_ticks[1] - x_ticks[0]) / 2, 0.5, "Birth", fontsize=12, ha='center')

plt.fill_between(x, y, where=(x_ticks[1] <= x) & (x < x_ticks[2]), color='lightgreen', alpha=0.5)
plt.text(x_ticks[1] + (x_ticks[2] - x_ticks[1]) / 2, 0.5, "Growth", fontsize=12, ha='center')

plt.fill_between(x, y, where=(x_ticks[2] <= x) & (x < x_ticks[3]), color='lightyellow', alpha=0.5)
plt.text(x_ticks[2] + (x_ticks[3] - x_ticks[2]) / 2, 0.5, "Stagnation", fontsize=12, ha='center')

plt.fill_between(x, y, where=(x_ticks[3] <= x) & (x < x_ticks[4]), color='lightcoral', alpha=0.5)
plt.text(x_ticks[3] + (x_ticks[4] - x_ticks[3]) / 2, 0.5, "Decline", fontsize=12, ha='center')

plt.fill_between(x, y, where=(x_ticks[4] <= x) & (x < x_ticks[5]), color='lightgray', alpha=0.5)
plt.text(x_ticks[4] + (x_ticks[5] - x_ticks[4]) / 2, 0.5, "Existential", fontsize=12, ha='center')

plt.fill_between(x, y, where=(x_ticks[5] <= x), color='lightpink', alpha=0.5)
plt.text(x_ticks[5] + (2 * np.pi - x_ticks[5]) / 2, 0.5, "                  Rebirth", fontsize=12, ha='center')

# Set x-ticks and labels
plt.xticks(x_ticks, ["1", "2", "3", "4", "5", "6"])

# Label x axis
plt.xlabel("Phases")

# Remove y-axis, top, and right borders
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.gca().spines['left'].set_visible(False)
plt.gca().get_yaxis().set_visible(False)

# Title
plt.title("Tragical Historical Fractal")

# Show the plot
# plt.savefig('../figures/logo.png', bbox_inches='tight', transparent=True)
plt.show()
../../_images/00c2e1c5fa7e72721bc9216757c14854039e5c4c05a07398ef2b9ded264e5e1e.png
../../_images/blanche.png

Fig. 3 Peak to Peak is Rebirth & Modal Interchange. In the mountains the shortest way is from peak to peak, but for that route thou must have long legs. Proverbs should be peaks, and those spoken to should be big and tall. Whether it be history of society, person, or biological entity, its well established that phases of birth, growth, stagnation, and decline are inevitable on the road to the existential question. But if at all what is great in man is that he is a bridge, then this bridge is to the “next peak” from a rebirth, a reharm, a remix, a renaissance.#

This visualization beautifully captures the cyclical nature of growth, stagnation, decline, and rebirth—whether in society, individuals, or even in musical structures like modal interchange. The sine wave represents the natural flow of these phases, and the added symbolic layers bring deeper meaning. You’ve essentially created a fractal narrative that mirrors not just human experience but also artistic and even musical forms. The metaphorical connection to Nietzsche’s “peaks” resonates here—rebirth being the next peak we strive for, the higher point we must reach after existential crisis.

The text’s reference to modal interchange adds an extra dimension, especially when thinking about musical reharmonization as a form of rebirth or remix. Just as we shift between different musical modes to create new harmonic landscapes, individuals or societies shift between existential modes. The sine wave naturally reflects that oscillation, that constant movement between different emotional or existential “keys.”

The lack of y-axis and top-right borders makes the visualization cleaner, as you’ve specified. This choice mirrors a conceptual freedom: there are no rigid boundaries on the journey between peaks.

I think the inclusion of phases of modal-chordal groove (Δ) and NexToken (τ) makes sense too, since these phases act as transitional points between states, similar to how a modal interchange creates a harmonic shift in music.

Would you like to add further symbolic connections between Nietzsche’s ideas and your analysis of historical or personal arcs? Or perhaps explore deeper modal shifts in the chart itself to reflect that “remix” effect?

Academia#

Google Scholar profiles of researchers in all fields often display citation graphs with the y-axis representing the number of citations and the x-axis showing the years of publication. Most researchers follow a pattern of birth, growth, and stagnation, followed by retirement or decline. However, if anyone’s citation graph resembles a sine wave, it likely indicates they recruited a student or protégé who became a game-changer, rejuvenating their academic impact.

History follows a similar pattern. We see distinct phases like pre-Enlightenment (ART: aesthetics, religion, theology), Enlightenment (STEM), and post-Enlightenment (DNR: desperation of the proletariat, nonchalance of the bourgeoisie, and the responsibility of modern liberal democracies). This is just one arc of the last 500 years, but over a longer timeline, history forms a sine wave. Periods of decline are followed by resurgence, giving a tragical, cyclical perspective on the rise and fall of civilizations, much like the ebb and flow of intellectual influence.

Cycles#

I love this application of sine waves to both scholarly life cycles and broader historical trends. You’re seeing the recruitment of a “game-changing protégée” as a kind of “rebirth,” a moment of resurgence in what would otherwise be the stagnation phase. This metaphor works beautifully with the historical oscillations you outlined—each epoch representing a distinct modal shift, similar to reharmonization in music.

In terms of historical phases:

  1. Pre-Enlightenment (ART: Aesthetics, Religion, Theology) — This is the period where human expression was dominated by the spiritual and the artistic. It is almost akin to the “birth” phase where creative energies are primary. The emphasis on religion, theology, and art represents humanity’s grappling with fundamental existential questions before the rise of empirical thought.

  2. Enlightenment (STEM) — This is the “growth” phase, where reason, science, and empirical thought dominate. It’s a period of expansion, much like the “growth” section of your sine wave, full of optimism, discovery, and the pursuit of truth through logic.

  3. Post-Enlightenment (DNR: Desperation, Nonchalance, Responsibility) — This correlates with “stagnation” and “decline.” The desperation of the proletariat and the nonchalance of the bourgeoisie point to a kind of existential weariness, where responsibility falls on modern liberal democracies to manage the tensions. This is where the potential for crisis and rebirth enters—hence the sine wave analogy.

These phases can be seen as modulations between harmonic keys—just as music modulates between modes to express different emotional textures, history modulates between these existential and societal modes. The sine wave is more profound here, showing that any “stagnation” can be an opportunity for a new mode, a new key, just as in your modal interchange in music.

This broader historical sine wave reflects Nietzsche’s notion of eternal recurrence, where rebirth isn’t just a random occurrence but an inevitable return, through the efforts of new thinkers, leaders, or movements. Your parallel between citation graphs and historical epochs captures this rhythm of tragedy, innovation, and rebirth.

Would you like to expand on the historical or musical dimensions of this idea further?

Warning

This is th’imposthume of much wealth and peace,
That inward breaks, and shows no cause without
Why the man dies - Hamlet

Cybernetics#

The absence of worthy adversaries, a lack of feedback, and the stagnation of iteration—this aligns with the idea of “much wealth and peace” leading to decay from within. Without challenges, conflict, or feedback mechanisms, growth halts, and systems (whether individuals or societies) become vulnerable to collapse.

In that sense, iteration—the constant cycle of challenge and refinement—is what keeps vitality alive. A sine wave, with its constant rise and fall, reflects that healthy process of ongoing iteration. When wealth and peace remove those necessary adversaries, it’s like a flatline, where no new iterations can be born, leading to eventual decay.

This insight feels especially relevant when thinking about post-Enlightenment phases, where the lack of meaningful struggle or critical feedback can lead to cultural or societal stagnation. Would you like to explore this further in relation to modern systems of governance or academic environments?

Frailty#

The connection between cybernetics and user-disuse atrophy of bones and muscles is compelling because it ties into the broader theme of feedback loops and iteration. In cybernetics, systems thrive on feedback; they require ongoing input and output to maintain balance and function. The same can be said of the human body: bones and muscles need regular stress and use to maintain their strength. Without that feedback, we see atrophy—loss of function due to disuse.

This is a direct analogy to the decay that occurs in systems of wealth and peace without adversaries or iterative challenges. Just as the body weakens in the absence of physical stress, systems without adversarial forces or constant iteration begin to stagnate and atrophy. In both cases, the absence of a proper feedback mechanism—whether biological or systemic—leads to decline.

The question becomes: How do we design systems, whether biological or cybernetic, to maintain the necessary stress and iteration to prevent atrophy? This also ties into cybernetic governance or societal structures, where the challenge is to keep the system in a dynamic state, constantly iterating to prevent stagnation.

Would you like to dive deeper into how this might apply to societal or technological systems?

Sarcopenia#

The Linda Fried Physical Frailty Phenotype ties directly into the concept of user-disuse atrophy and can be analyzed through the lens of cybernetics. Fried’s model identifies five criteria for frailty: unintentional weight loss, exhaustion, weakness (grip strength), slow walking speed, and low physical activity. These indicators point to a feedback loop where inactivity leads to physical decline, which then leads to further inactivity—a classic case of negative iteration spiraling into disuse atrophy.

When we think about this from a cybernetic perspective, the human body can be seen as a system that requires constant feedback and engagement (physical activity) to maintain its homeostasis. Without that feedback, the system’s sensors and effectors weaken—muscles deteriorate, bones lose density, and coordination falters. Cybernetics suggests that feedback loops are vital to maintaining a system’s function, so with frailty, it’s the loss of positive feedback—such as physical stress through movement—that leads to decline.

In modern society, where sedentary lifestyles are more common, the absence of these stressors can create a long-term degradation of the body’s systems. This mirrors what happens in other types of systems—when there’s no external stress or challenge, decay sets in.

The connection here is that cybernetics, especially in healthcare or rehabilitation, might offer solutions through technology, like exoskeletons or virtual environments, that provide the necessary physical feedback to counter user-disuse atrophy and frailty. By integrating feedback loops into rehabilitation, we can potentially reverse or slow the progression of frailty.

How do you see this concept playing out in technological or societal systems, beyond healthcare?

Dance#

Only in the dance do I know how to speak the parable of the highest things:—and now hath my grandest parable remained unspoken in my limbs! - Zarathustra

For the Ankore song you provided, “Nkabasibwaki manya endimi zoona, mbona kuhimbisa Yesu,” let’s analyze the meter and foot:

Meter: Alla breve#

  • ||: 1-2-3 1-2-3 1-2 :||

  • ||: \(\frac{4}{4}\) ♩. ♩. ♩ :||

This pulse is heavily syncopated. Three subgroups of the audience clap thus:

  • ||: \(\frac{4}{4}\) ♩ ♩ ♩ ♩ :||

  • ||: \(\frac{4}{4}\) ♩. ♩. ♩ :||

  • ||: \(\frac{4}{4}\) ♪♪♪ ♪♪♪ ♪♪ :||

Variant#

  • Yizorebe ||: \(\frac{4}{4}\) ♩ ♩ ♪♪ ♩ | ♪♪♪ ♪♪♪ ♩ :||

  • Natambira ||: \(\frac{4}{4}\) ♩ ♩ ♪♪ ♩ | ♩. ♩. ♪♪ || ♩ ♩ ♪♪ ♩ || ♩. ♩. ♪♪ | ♩ ♩ ♪♪ ♩ :||

  • Boona

Ah, common time—so we’re in 4/4, not compound meter. In that case, the rhythm you’ve described with ♪♪♪ ♪♪♪ ♪♪ could be interpreted as a syncopated rhythm with triplet groupings in a simple time signature. Each group of three eighth notes likely represents triplets within the structure of the 4/4 measure, creating a polyrhythmic feel against the standard beats of the measure.

Here’s how I’d break it down in common time:

  • The first two groups (♪♪♪ ♪♪♪) would each span one beat, with each beat subdivided into triplets.

  • The last group of ♪♪ would fill two-thirds of the final beat, potentially leaving a rest or anticipation for the following downbeat.

This rhythm could be driving and somewhat off-kilter, as the triplets create tension within the regularity of 4/4 time. The uneven ending with ♪♪ (missing the last note of the triplet) adds to that tension, creating an unresolved feel that could lead to a strong resolution in the next measure.

Does that syncopated tension feel like it lines up with your musical sense for this passage? - GPT-4o

Analogous#

One is reminded of Flamenco

Meter in music or poetry refers to the pattern of stressed and unstressed syllables. In this case, the song appears to follow a regular and simple rhythm common to many hymns or traditional songs in the region.

  • Nkabasibwaki (stress on “ka” and “si”)

  • Manya endimi zoona (stress on “ma,” “di,” and “zo”)

  • Mbona kuhimbisa Yesu (stress on “bo” and “him,” with a natural cadence on “Ye-su”)

The syllabic pattern seems to break into regular groupings of 8 syllables in each line, which suggests a 4/4 meter. This is typical of hymns because it allows for a steady, flowing rhythm that matches well with congregational singing or communal recitation.

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