Ethnomathematician Alban Da Silva explores the intricate relationship between mathematics and the ancient practice of sand drawing in Vanuatu.
In the remote archipelago of Vanuatu, nestled in the South Pacific, lies a centuries-old tradition that marries art and mathematics in a mesmerizing way. Sand drawing, a practice steeped in cultural significance, has captivated the imagination of ethnomathematician Alban Da Silva. Through years of research and observation, Da Silva has uncovered the hidden algebraic secrets behind these intricate drawings. His work not only sheds light on the mathematical nature of sand drawing but also offers insights into the complex relationship between Vanuatu societies and their environment.
A Traditional Art
Vanuatu, with its rich linguistic diversity and unique cultural heritage, provides the perfect backdrop for exploring the art of sand drawing. The practice is widespread in central islands such as Maewo and Pentecost and has been recognized as part of the intangible cultural heritage of humanity by UNESCO. Sand drawing is a multidimensional art form that serves as a vessel for storytelling, religious and environmental knowledge, and social commentary. Each drawing, created with a single finger stroke, is an ephemeral masterpiece that is erased once completed.
Experts and Rules
Sand drawing encompasses a range of expertise, from beginners to highly skilled artists. These artists follow a set of rules that govern the creation of their drawings. The process begins with a grid, which provides support and defines nodes and lines. The artists must navigate the grid, moving from node to node without crossing the same path or cutting the grid, and ultimately return to the starting point without lifting their finger. These rules ensure the creation of continuous, closed lines, reminiscent of Eulerian graphs in mathematics.
Marcia Ascher’s Intuition
Da Silva’s research builds upon the groundbreaking work of American mathematician Marcia Ascher, who recognized the mathematical nature of sand drawing. Ascher drew connections between sand drawings and graph theory, particularly Eulerian graphs. She observed that each sand drawing could be represented as a graph, with vertices and edges. These graphs were Eulerian, meaning that the sand artist had to traverse each edge exactly once and return to the starting point. Ascher’s work challenged the assumption that only societies with written languages could practice mathematics.
Experts and Rules
Da Silva’s research takes Ascher’s insights further by refining the graph model and exploring the role of movement and direction in sand drawing. He discovered that the direction of movement is as crucial as the nodes in the grid. By creating a new graph model, named G mod, Da Silva captures the essence of sand drawing. The G mod graph represents the movement from one node to another, with each movement corresponding to an edge between vertices. This graph is still Eulerian and offers a deeper understanding of the sand drawing process.
A Theorem Discovered in Drawings
Building upon the work of mathematician Oswald Veblen, Da Silva identified another characteristic of Eulerian graphs in sand drawings. Veblen’s theorem states that a graph is Eulerian if and only if it can be broken down into a union of disjoint cycles. Da Silva found that sand drawings could be decomposed into cycles, providing insights into the artistic process. These cycles serve as building blocks for sand artists and play a fundamental role in their storytelling. The focus on graph cycles also mirrors the way Vanuatu societies understand their relationship with the natural world.
Conclusion:
The marriage of art and mathematics in Vanuatu’s sand drawing tradition is a testament to the universality of mathematical principles and the diverse forms they can take in different cultures. By uncovering the algebraic secrets of sand drawing, Alban Da Silva has not only deepened our understanding of this ancient practice but also opened up new possibilities for teaching mathematics. As efforts to decolonize education in Vanuatu gain momentum, the integration of sand drawing into the mathematics curriculum holds great promise. The beauty and complexity of sand drawing serve as a powerful reminder of the interconnectedness of art, mathematics, and culture.
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