Preface

Preface#

We outline a structure for analyzing events or systems in three distinct stages:

  1. History (agent, principal): 1 This could represent the foundational relationships and roles in any system. The agent refers to the one acting on behalf of another (the principal), suggesting an origin in legal, economic, or philosophical thought. For example, in finance, the agent manages assets for the principal, and in history, it could refer to leaders (agents) executing the will of the people or sovereigns (principals). The key here is the nature of the relationship and the motivations behind action: i.e., adversarial training & reinforcement learning. This step lays out the power & game dynamics. (Think Alexei & The General in The Gambler). Strategy

  2. Experience (amateur, professional): This stage highlights the growth or development within a system, where experience determines the evolution of the actors involved. The amateur is learning, experimenting, and taking risks, while the professional operates with a deeper understanding, possibly more constrained by rules or market expectations. This could be applied to many areas—musicians, traders, or scholars all evolve through this dichotomy. (Think Tight-Rope Walker in Thus Spoke Zarathustra). Payoff

  3. Reconciliation (market makers): This final stage involves the synthesis or balancing act between different actors in a market. Market makers suggests a focus on liquidity and equilibrium, where those who understand both sides (agent/principal and amateur/professional) create systems that allow for continuous trade, exchange, or balance. This could be interpreted economically, socially, or even artistically, as a way to resolve tensions between different players or perspectives. (Think United Workers in Communist Manifesto) Nash

The whole progression from historical roles, through the development of experience, to a final stage of reconciliation is quite balanced and mirrors many evolutionary processes. How would you apply this structure in your work or thinking?

Theme & Variation#

\( \begin{bmatrix} \textcolor{gray}{\text{Friendship}} & \textcolor{gray}{\text{Character}} & \textcolor{gray}{\text{Ethics}} \\ \text{Raw} & \text{Filtered} & \text{Transcendental} \\ \text{ART} & \text{STEM} & \text{DRE} \\ \text{History} & \text{Experience} & \text{Reconciliation} \\ \text{Phonetics} & \text{Temperament} & \text{Mode} \end{bmatrix} \begin{bmatrix} \textcolor{gray}{x, y: Emotional} \\ z: Tragic \\ t, m: Narrative \end{bmatrix} \)

\( \begin{bmatrix} \textcolor{gray}{\text{Friendship}} & \textcolor{gray}{\text{Character}} & \textcolor{gray}{\text{Ethics}} \\ \text{Raw} & \text{Filtered} & \text{Transcendental} \\ \text{ART} & \text{STEM} & \text{DRE} \\ \text{History} & \text{Experience} & \text{Reconciliation} \\ \text{Phonetics} & \text{Temperament} & \text{Mode} \end{bmatrix} \begin{bmatrix} \textcolor{gray}{x, y: Animal} \\ z: Man \\ t, m: God \end{bmatrix} \)

\( \begin{bmatrix} \textcolor{gray}{\text{Friendship}} & \textcolor{gray}{\text{Character}} & \textcolor{gray}{\text{Ethics}} \\ \text{Raw} & \text{Filtered} & \text{Transcendental} \\ \text{ART} & \text{STEM} & \text{DRE} \\ \text{History} & \text{Experience} & \text{Reconciliation} \\ \text{Phonetics} & \text{Temperament} & \text{Mode} \end{bmatrix} \begin{bmatrix} \textcolor{gray}{x, y: Dostoevsky} \\ z: Nietzsche \\ t, m: Marx \end{bmatrix} \)

\( \begin{bmatrix} \textcolor{gray}{\text{Friendship}} & \textcolor{gray}{\text{Character}} & \textcolor{gray}{\text{Ethics}} \\ \text{Raw} & \text{Filtered} & \text{Transcendental} \\ \text{ART} & \text{STEM} & \text{DRE} \\ \text{History} & \text{Experience} & \text{Reconciliation} \\ \text{Phonetics} & \text{Temperament} & \text{Mode} \end{bmatrix} \begin{bmatrix} \textcolor{gray}{x, y: Strategy} \\ z: Payoff \\ t, m: Nash \end{bmatrix} \)

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

def draw_triangle(ax, vertices, labels, color='black'):
    """Draws a triangle given vertices and labels for each vertex."""
    triangle = plt.Polygon(vertices, edgecolor=color, fill=None, linewidth=1.5)
    ax.add_patch(triangle)
    for i, (x, y) in enumerate(vertices):
        ax.text(x, y, labels[i], fontsize=12, ha='center', va='center')

def get_triangle_vertices(center, radius):
    """Returns the vertices of an equilateral triangle centered at `center` with a given `radius`."""
    angles = np.linspace(0, 2 * np.pi, 4)[:-1] + np.pi/2  # angles for vertices of an equilateral triangle
    return np.column_stack([center[0] + radius * np.cos(angles),
                            center[1] + radius * np.sin(angles)])

# Create the plot
fig, ax = plt.subplots()
ax.set_aspect('equal')

# Define the layers of the fractal with vertices and labels
centers = [(0, 0)]
radii = [1, 2, 3, 4]
triads = [
    ['Betrayal', 'Power', 'Survival'],
    ['Loyalty', 'Empathy', 'Resilience'],
    ['Faith', 'Love', 'Hope'],
    ['Friendship', 'Character', 'Ethics'],

]
colors = ['blue', 'green', 'orange', 'purple']

# Draw the triangles with increasing radius and different colors
for radius, triad, color in zip(radii, triads, colors):
    vertices = get_triangle_vertices(centers[0], radius)
    draw_triangle(ax, vertices, triad, color=color)

# Set limits and hide axes to fit the frame
ax.set_xlim(-3.7, 3.7)
ax.set_ylim(-3.7, 3.7)
ax.axis('off')

# Display the plot
plt.savefig('figures/apmmpa.png')
plt.show()
_images/79a4ba14c1db414570139dec006527244f310979cffe75cc1653cc97bd03e754.png

Structured#

Contents