Dancing in Chains#
Let’s weave the formula \( w = 1/(1 + X/Y) \), where \( X/Y \) represents the noise-to-signal odds, into the five-network framework from the essay, keeping this brief and aligned with Uganda’s and Africa’s identity metaphor. This equation, a form of signal weighting (akin to a logistic function), assigns a value \( w \) between 0 and 1, where a low noise-to-signal ratio (small \( X/Y \)) yields a high \( w \) (strong signal clarity), and a high ratio (large \( X/Y \)) drives \( w \) toward 0 (signal drowned by noise). Applied to the networks: The Pericentral network, handling reflexes, thrives when \( w \) is high—clear “nonself” threats (low noise) trigger sharp responses, but colonial ambiguity -mzungu, not quite the typical enemy in appeance, intent, behavior- might have raised \( X/Y \), muting action. The Dorsal Frontoparietal network, attuned to nonself detection, falters if noise (foreign influence) overwhelms signal (indigenous goals), lowering \( w \) and blurring focus. The Lateral Frontoparietal network, navigating ambiguity, operates in a mid-range \( w \), wrestling with a noisy mix of self and nonself inputs, as Africa did with tribal and colonial signals. The Medial Frontoparietal network, crafting self-identity, seeks a high \( w \) to clarify “self” amidst external noise, but a high \( X/Y \) from historical disruption may have weakened it. Finally, the Cingulo-Insular network, optimizing salience, aims to maximize \( w \) by filtering noise, converging on efficiency—Africa’s potential pivot if it lowers \( X/Y \) through clearer boundaries. The order reflects a progression from raw detection to refined integration, with \( w \) as a lens on how noise (nonself overload) disrupted each stage, stalling convergence.
Fig. 32 Given our deep dive into “nonself” and “self” through biological systems, signal detection, and the metaphor of Uganda’s and Africa’s identity, I’d love to ask you: How do you see the interplay of cultural “noise” and “signal” shaping your own perception of Ugandan identity today—particularly in balancing traditional tribal heritage with the modern, global influences that have woven into its fabric? It ties into our exploration of ambiguity and convergence, and I’m curious about your personal lens on this dynamic.#
The five networks described form a framework for understanding responses to “nonself” versus “self,” mirrored in Africa’s historical and identity struggles. First, the Pericentral network (sensory-motor) drives reflexive reactions, like recoiling from colonial threats, but its effectiveness hinges on clear signals. Second, the Dorsal Frontoparietal network (goal-directed attention) prioritizes nonself detection, ideally rejecting foreign imposition, yet Africa’s fragmented focus suggests distraction. Third, the Lateral Frontoparietal network (flexible decision-making) grapples with ambiguity, as seen in Uganda’s blend of tribal and British systems. Fourth, the Medial Frontoparietal network (self-referential identity) seeks internal coherence, but overemphasis here may have softened nonself defenses. Fifth, the Cingulo-Insular network (salience optimization) balances these, aiming for efficient convergence—a potential unrealized in Africa’s noise-laden past. The order, from reflex to synthesis, suggests a developmental arc, not a strict hierarchy, where stalling at ambiguity or self-focus reflects a missed shift to optimization. Now, enter the formula \( w = 1/(1 + X/Y) \), where \( X/Y \) is the noise-to-signal odds: \( w \) nears 1 with low noise (clear signal, strong response) and drops toward 0 as noise (e.g., colonial disruption) drowns the signal (indigenous clarity). For Pericentral, high \( X/Y \) from unclear threats dulled reflexes; for Dorsal, noisy foreign signals lowered \( w \), weakening nonself rejection; Lateral wrestled with mid-range \( w \), muddling decisions; Medial struggled for high \( w \) against external noise; and Cingulo-Insular’s optimization demands a low \( X/Y \) Africa didn’t achieve. The formula reveals how noise—historical, cultural—disrupted each network’s clarity, with the order showing a path from instinct to integration that faltered, yet hints at convergence as a future efficiency if noise is tamed.
Signal detection theory, rooted in psychology and engineering, models how systems distinguish “signal” (meaningful input, like a “nonself” threat) from “noise” (irrelevant or confounding input). It hinges on four outcomes: hits (detecting a real signal), misses (failing to detect it), false alarms (mistaking noise for signal), and correct rejections (ignoring noise). Sensitivity (\( d' \)), the ability to separate signal from noise, and bias (tendency to favor “yes” or “no” responses), shape performance. In biological terms, the nervous system’s reflexes and the immune system’s PRRs excel when \( d' \) is high—clear nonself signals (pathogens, dangers) trigger hits, while self signals are correctly rejected. The formula \( w = 1/(1 + X/Y) \) aligns here: a low \( X/Y \) (high signal-to-noise ratio) boosts \( w \), enhancing sensitivity and hit rates, while a high \( X/Y \) muddies detection, increasing misses or false alarms.
Applied to the networks: The Pericentral network, driving reflexes, relies on high \( d' \) to score hits against nonself threats (e.g., colonial incursions), but Africa’s noisy context—mixed signals of danger and diplomacy—raised \( X/Y \), leading to misses and muted responses. The Dorsal Frontoparietal network, focused on nonself detection, needs sharp sensitivity to tag foreign systems as signals to reject; a low \( w \) from high noise (cultural blending) explains Africa’s integration over expulsion, risking false alarms (overreacting to benign influences). The Lateral Frontoparietal network, handling ambiguity, operates in a gray zone—moderate \( X/Y \) reflects its struggle with Uganda’s hybrid identity, balancing hits (recognizing colonial impact) and false alarms (misjudging tribal tensions). The Medial Frontoparietal network, crafting self, aims for correct rejections of nonself distortions, but a noisy \( X/Y \) from historical upheaval lowered \( w \), missing a unified “self” signal. The Cingulo-Insular network, optimizing salience, seeks peak \( d' \)—high \( w \)—to filter noise and converge on efficiency, a potential Africa could grasp by tuning its bias toward clearer signals.
The order—Pericentral to Cingulo-Insular—mirrors SDT’s progression: from raw detection (hits/misses) to attentional filtering (sensitivity), decision-making (bias adjustment), identity formation (rejection of noise), and optimized integration (maximized \( d' \)). Africa’s “error” of lacking a nonself bias aligns with low sensitivity—high \( X/Y \) drowned signals of threat or identity, stalling at ambiguity rather than converging. Signal detection thus frames the struggle as a detection failure: noise overwhelmed signal, but refining \( w \) through historical lessons could elevate \( d' \), aligning the networks for resilience. Does this deepen the lens you wanted?
Show code cell source
import numpy as np
import matplotlib.pyplot as plt
import networkx as nx
# Define the neural network layers
def define_layers():
return {
'Suis': ['DNA, RNA, 5%', 'Peptidoglycans, Lipoteichoics', 'Lipopolysaccharide', 'N-Formylmethionine', "Glucans, Chitin", 'Specific Antigens'],
'Voir': ['PRR & ILCs, 20%'],
'Choisis': ['CD8+, 50%', 'CD4+'],
'Deviens': ['TNF-α, IL-6, IFN-γ', 'PD-1 & CTLA-4', 'Tregs, IL-10, TGF-β, 20%'],
"M'èléve": ['Complement System', 'Platelet System', 'Granulocyte System', 'Innate Lymphoid Cells, 5%', 'Adaptive Lymphoid Cells']
}
# Assign colors to nodes
def assign_colors():
color_map = {
'yellow': ['PRR & ILCs, 20%'],
'paleturquoise': ['Specific Antigens', 'CD4+', 'Tregs, IL-10, TGF-β, 20%', 'Adaptive Lymphoid Cells'],
'lightgreen': ["Glucans, Chitin", 'PD-1 & CTLA-4', 'Platelet System', 'Innate Lymphoid Cells, 5%', 'Granulocyte System'],
'lightsalmon': ['Lipopolysaccharide', 'N-Formylmethionine', 'CD8+, 50%', 'TNF-α, IL-6, IFN-γ', 'Complement System'],
}
return {node: color for color, nodes in color_map.items() for node in nodes}
# Define edge weights
def define_edges():
return {
('DNA, RNA, 5%', 'PRR & ILCs, 20%'): '1/99',
('Peptidoglycans, Lipoteichoics', 'PRR & ILCs, 20%'): '5/95',
('Lipopolysaccharide', 'PRR & ILCs, 20%'): '20/80',
('N-Formylmethionine', 'PRR & ILCs, 20%'): '51/49',
("Glucans, Chitin", 'PRR & ILCs, 20%'): '80/20',
('Specific Antigens', 'PRR & ILCs, 20%'): '95/5',
('PRR & ILCs, 20%', 'CD8+, 50%'): '20/80',
('PRR & ILCs, 20%', 'CD4+'): '80/20',
('CD8+, 50%', 'TNF-α, IL-6, IFN-γ'): '49/51',
('CD8+, 50%', 'PD-1 & CTLA-4'): '80/20',
('CD8+, 50%', 'Tregs, IL-10, TGF-β, 20%'): '95/5',
('CD4+', 'TNF-α, IL-6, IFN-γ'): '5/95',
('CD4+', 'PD-1 & CTLA-4'): '20/80',
('CD4+', 'Tregs, IL-10, TGF-β, 20%'): '51/49',
('TNF-α, IL-6, IFN-γ', 'Complement System'): '80/20',
('TNF-α, IL-6, IFN-γ', 'Platelet System'): '85/15',
('TNF-α, IL-6, IFN-γ', 'Granulocyte System'): '90/10',
('TNF-α, IL-6, IFN-γ', 'Innate Lymphoid Cells, 5%'): '95/5',
('TNF-α, IL-6, IFN-γ', 'Adaptive Lymphoid Cells'): '99/1',
('PD-1 & CTLA-4', 'Complement System'): '1/9',
('PD-1 & CTLA-4', 'Platelet System'): '1/8',
('PD-1 & CTLA-4', 'Granulocyte System'): '1/7',
('PD-1 & CTLA-4', 'Innate Lymphoid Cells, 5%'): '1/6',
('PD-1 & CTLA-4', 'Adaptive Lymphoid Cells'): '1/5',
('Tregs, IL-10, TGF-β, 20%', 'Complement System'): '1/99',
('Tregs, IL-10, TGF-β, 20%', 'Platelet System'): '5/95',
('Tregs, IL-10, TGF-β, 20%', 'Granulocyte System'): '10/90',
('Tregs, IL-10, TGF-β, 20%', 'Innate Lymphoid Cells, 5%'): '15/85',
('Tregs, IL-10, TGF-β, 20%', 'Adaptive Lymphoid Cells'): '20/80'
}
# Define edges to be highlighted in black
def define_black_edges():
return {
('PRR & ILCs, 20%', 'CD4+'): '80/20',
('CD4+', 'TNF-α, IL-6, IFN-γ'): '5/95',
('CD4+', 'PD-1 & CTLA-4'): '20/80',
('CD4+', 'Tregs, IL-10, TGF-β, 20%'): '51/49',
}
# Calculate node positions
def calculate_positions(layer, x_offset):
y_positions = np.linspace(-len(layer) / 2, len(layer) / 2, len(layer))
return [(x_offset, y) for y in y_positions]
# Create and visualize the neural network graph
def visualize_nn():
layers = define_layers()
colors = assign_colors()
edges = define_edges()
black_edges = define_black_edges()
G = nx.DiGraph()
pos = {}
node_colors = []
# Create mapping from original node names to numbered labels
mapping = {}
counter = 1
for layer in layers.values():
for node in layer:
mapping[node] = f"{counter}. {node}"
counter += 1
# Add nodes with new numbered labels and assign positions
for i, (layer_name, nodes) in enumerate(layers.items()):
positions = calculate_positions(nodes, x_offset=i * 2)
for node, position in zip(nodes, positions):
new_node = mapping[node]
G.add_node(new_node, layer=layer_name)
pos[new_node] = position
node_colors.append(colors.get(node, 'lightgray'))
# Add edges with updated node labels
edge_colors = []
for (source, target), weight in edges.items():
if source in mapping and target in mapping:
new_source = mapping[source]
new_target = mapping[target]
G.add_edge(new_source, new_target, weight=weight)
edge_colors.append('black' if (source, target) in black_edges else 'lightgrey')
# Draw the graph
plt.figure(figsize=(12, 8))
edges_labels = {(u, v): d["weight"] for u, v, d in G.edges(data=True)}
nx.draw(
G, pos, with_labels=True, node_color=node_colors, edge_color=edge_colors,
node_size=3000, font_size=9, connectionstyle="arc3,rad=0.2"
)
nx.draw_networkx_edge_labels(G, pos, edge_labels=edges_labels, font_size=8)
plt.title("OPRAH™: Nonself & the Salient Network", fontsize=18)
plt.show()
# Run the visualization
visualize_nn()
Fig. 33 G1-G3: Ganglia & N1-N5 Nuclei. These are cranial nerve, dorsal-root (G1 & G2); basal ganglia, thalamus, hypothalamus (N1, N2, N3); and brain stem and cerebelum (N4 & N5).#