Ethnomathematician Alban Da Silva uncovers the intricate mathematical patterns and cultural significance behind Vanuatu’s traditional sand drawings.
In the archipelago of Vanuatu, nestled in the South Pacific, lies a centuries-old tradition of sand drawing. These intricate designs, created with a single stroke of a finger, have captivated both locals and visitors alike. But what lies beneath the surface of these ephemeral artworks? Ethnomathematician Alban Da Silva embarked on a journey to unravel the mathematical secrets and cultural significance hidden within Vanuatu’s sand drawings. His research reveals a fascinating connection between graph theory, Eulerian graphs, and the artistic expressions of the island’s inhabitants.
A Traditional Art
Vanuatu, with its 83 islands and diverse linguistic landscape, is a treasure trove of cultural traditions. Sand drawing, known as “sandroing” in the local Bislama language, is a practice unique to certain central islands of Vanuatu. This ancient art form, recognized as part of the intangible cultural heritage of humanity by UNESCO, involves drawing continuous, closed lines on surfaces like beaten earth, sand beaches, or ashes. These drawings are often constrained by a grid of lines or dots, providing a framework for the artist’s creativity.
Experts and Rules
Sand drawing encompasses a wide range of expertise, from beginners to seasoned experts. While the practice was once believed to be reserved for men, women in Vanuatu have also honed their skills and achieved a high level of proficiency. The artists follow a set of rules, including moving from node to node without crossing the same path or cutting the grid, and returning to the starting point without lifting their finger. These rules create a sense of structure and consistency within the sand drawings, allowing for the exploration of complex patterns and narratives.
Marcia Ascher’s Intuition
Alban Da Silva’s research builds upon the pioneering work of American mathematician Marcia Ascher, who recognized the mathematical underpinnings of sand drawings in the 1980s. Ascher drew parallels between sand drawings and graph theory, specifically Eulerian graphs. These graphs consist of vertices (dots) connected by edges (lines), and in sand drawings, the continuous line traced in the sand can be represented as an Eulerian graph. Ascher’s groundbreaking perspective challenged the notion that mathematical knowledge could only exist within written traditions.
Graphs and Decomposition
Da Silva’s research takes Ascher’s work a step further by refining the graph model and exploring the concept of decomposition. He observed that sand drawings could be broken down into subdrawings, which, when combined, formed the final design. Each subdrawing returned to the starting point, adding layers of complexity and storytelling to the artwork. By modeling sand drawings as graphs, Da Silva discovered a connection to Veblen’s theorem, which states that a graph is Eulerian if and only if it can be broken down into a union of disjoint cycles.
Cultural Significance and Teaching Potential
Sand drawings in Vanuatu hold profound cultural significance. They serve as a means of preserving ritual, religious, and environmental knowledge, as well as supporting narratives that reflect the ethical and political dimensions of society. Furthermore, the practice of sand drawing is now being integrated into Vanuatu’s education system, aiming to decolonize education and promote traditional knowledge. Da Silva’s research paves the way for incorporating sand drawing into mathematics instruction, exploring the intersection of art, culture, and mathematics in the classroom.
Conclusion:
Vanuatu’s sand drawings are not merely beautiful works of art; they are mathematical expressions deeply rooted in the cultural fabric of the islands. Alban Da Silva’s research sheds light on the intricate patterns and structures that underpin these ephemeral creations, revealing the universality of mathematics and its diverse forms across cultures. As the practice of sand drawing continues to evolve and find its place in education, it serves as a testament to the rich heritage and ingenuity of Vanuatu’s people.
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