Ethnomathematician Alban Da Silva explores the intricate mathematics behind the ancient practice of sand drawing in Vanuatu, shedding light on the cultural significance and the universal nature of mathematics.
In the remote archipelago of Vanuatu, nestled in the South Pacific, lies a traditional art form that has captivated locals and visitors alike for thousands of years. Sand drawing, a practice that involves creating intricate figures with a single finger stroke on beaten earth, sand beaches, or ashes, has not only served as a means of artistic expression but has also revealed a fascinating connection to the world of mathematics. Ethnomathematician Alban Da Silva’s groundbreaking research has unveiled the mathematical patterns and algorithms that underpin this ancient art, shedding light on the cultural significance of sand drawing and its universal nature.
A Traditional Art
Vanuatu, an archipelago with a population of 315,000 people spread across 83 islands, boasts a rich cultural diversity and linguistic density. The practice of sand drawing is concentrated in the central islands of the country, particularly in the Penama province, where Da Silva conducted his field surveys. Recognized as part of Vanuatu’s intangible cultural heritage by UNESCO, sand drawing serves as a visual language that helps preserve and transmit ritual, religious, and environmental knowledge.
Experts and Rules
Sand drawing encompasses a wide range of expertise, from beginners who practice simple drawings to expert artists with an impressive repertoire of up to 400 designs. While the tradition was once reserved for men, women in Vanuatu have also embraced the art form and demonstrated a high level of expertise. The practice follows a set of rules, with drawings beginning with a grid that provides support and defines nodes and lines. Artists must navigate the grid without crossing the same path or cutting it, returning to the starting point without lifting their finger. These rules, reminiscent of concepts from mathematics, form the foundation of Da Silva’s research.
Marcia Ascher’s Intuition
Da Silva’s work builds upon the pioneering research of American mathematician Marcia Ascher, who recognized the connection between sand drawing and graph theory in the 1980s. Ascher’s observations led her to propose that sand drawings could be described as graphs, with vertices representing dots and edges representing lines. These graphs were also Eulerian, meaning that the sand artist had to visit each edge only once and return to the starting point. Ascher’s work challenged the assumption that mathematical knowledge was exclusive to societies with writing, opening doors to the study of mathematics in oral traditions.
A Theorem Discovered in Drawings
Building upon Ascher’s work, Da Silva refined the graph model of sand drawing and introduced a new perspective. By considering the direction of movement between nodes, Da Silva created a modified graph in which each node of the grid is treated as two vertices assigned to different diagonals. This new graph, named G mod, retains the Eulerian property and allows for the decomposition of sand drawings into cycles. These cycles, or sequences of consecutive edges, serve as building blocks for sand artists and provide insights into their creative process and the stories that accompany the drawings.
Conclusion:
The study of sand drawing in Vanuatu has revealed a profound connection between art and mathematics, demonstrating the universal nature of mathematical principles and their manifestation in diverse cultural practices. Da Silva’s research has not only deepened our understanding of sand drawing but has also opened up new possibilities for mathematics education in Vanuatu and beyond. As the art form continues to evolve and adapt, it serves as a testament to the enduring beauty and relevance of mathematics in our world.
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