Exploring Martial Arts through the Lens of Mathematics and Data Science - Part II: Aikido and Network Theory

Aikido, a Japanese martial art known for its focus on fluid motion, has more in common with mathematics and data science than one might initially think. In this second part of our exploration, we'll delve into the world of Network Theory and reveal how it can help us visualize and understand the intricate web of Aikido techniques.

The Harmony of Aikido and Networks

The art of Aikido is a study in connections. Each technique is not an isolated set of movements but is connected to others through shared principles and movements. A technique is never just a technique; it's a node within a network of interlinked practices. To visualize these connections, we can turn to Network Theory, a branch of mathematics used to study complex systems.

Network Theory provides us with a tool called a graph, a set of objects (nodes) interconnected by links (edges). In the context of Aikido, techniques become nodes, and the shared movements form the edges. The concept of "degree centrality" from Network Theory allows us to understand the influence of each technique. The degree centrality of a node is simply the number of edges it has. Techniques with a high degree of centrality have a large number of shared movements with other techniques, making them central to the practice of Aikido.

Let's create a network graph to visualize the interplay of Aikido techniques.

import networkx as nx
import matplotlib.pyplot as plt

# Create a new graph
G = nx.Graph()

# Add nodes for techniques
techniques = ['ikkyo', 'nikyo', 'sankyo', 'yonkyo', 'gokyo', 'shihonage', 'iriminage', 'kotegaeshi', 'tenchinage', 'kokyunage']
G.add_nodes_from(techniques)

# Add edges for common movements
common_movements = [('ikkyo', 'nikyo'), ('nikyo', 'sankyo'), ('sankyo', 'yonkyo'), ('yonkyo', 'gokyo'),?
? ? ? ? ? ? ? ? ? ? ('ikkyo', 'shihonage'), ('nikyo', 'iriminage'), ('sankyo', 'kotegaeshi'),?
? ? ? ? ? ? ? ? ? ? ('yonkyo', 'shihonage'), ('gokyo', 'iriminage'), ('shihonage', 'kotegaeshi'),
? ? ? ? ? ? ? ? ? ? ('iriminage', 'kotegaeshi'), ('tenchinage', 'kokyunage'), ('nikyo', 'tenchinage'),
? ? ? ? ? ? ? ? ? ? ('sankyo', 'kokyunage'), ('iriminage', 'tenchinage')]

G.add_edges_from(common_movements)

# Calculate degree centrality
deg_centrality = nx.degree_centrality(G)

# Define node colors based on technique type
color_map = []
for node in G:
? ? if node in ['ikkyo', 'nikyo', 'sankyo', 'yonkyo', 'gokyo']: # Core techniques
? ? ? ? color_map.append('blue')
? ? else: # Other foundational techniques
? ? ? ? color_map.append('green')?

# Draw the graph using degree centrality for node size
plt.figure(figsize=(8,6))
nx.draw(G, with_labels=True, node_color=color_map, nodelist=deg_centrality.keys(),?
? ? ? ? ?node_size=[v * 5000 for v in deg_centrality.values()])
plt.show()        

This visualization differentiates between core techniques (in blue) and foundational techniques (in green). The size of each node represents its degree centrality, illuminating how interconnected each technique is within the practice of Aikido.

The graph's edges and the degrees of centrality are merely illustrative and may not accurately represent the real connections between Aikido techniques. Aikido, like many martial arts, has a complex and nuanced structure, and the commonalities between techniques can depend on a variety of factors, including the specific style of Aikido and the interpretation of individual practitioners or dojos.

Delving into Henka and Oyo Waza

Looking at this network, we can also identify opportunities for "henka waza" (variation techniques) and "oyo waza" (applied techniques), which are advanced principles in Aikido. These concepts are akin to traversing this network graph, transitioning from one technique to another.

For example, the transition from Ikkyo to Nikyo in response to an adjustment by Uke (the receiver of the technique) can be seen as an instance of "henka waza". Similarly, the blending of elements from Shihonage and Iriminage to handle a particular attack could be an example of "oyo waza".

By adopting the lens of Network Theory, we're able to view Aikido as a complex, interconnected system rather than just a collection of techniques. This mathematical framework complements the philosophy of Aikido, which advocates for understanding the interconnectivity of movements, opponents, and the self.

Through this exploration, I hope to highlight how the synthesis of martial arts, mathematics, and data science can bring about fresh perspectives and deeper understanding. The fusion of these diverse fields shows us that learning is interconnected, and knowledge from one domain can illuminate truths in another. So, whether you're stepping onto the mat or diving into an equation, remember the hidden resonance between these disciplines.