Ethnomathematician Alban Da Silva explores the complex world of sand drawing in Vanuatu and its mathematical underpinnings.
In the archipelagic nation of Vanuatu, sand drawing is a revered traditional artform that serves as a means of communication and storytelling. Ethnomathematician Alban Da Silva delves into the intricate world of sand drawing, uncovering its mathematical foundations and cultural significance. Through his research, Da Silva reveals that sand drawings can be modeled using mathematical algorithms and operations, shedding light on the relationship between Vanuatu societies and their environment.
1: A Traditional Art
Vanuatu, with its linguistic diversity and unique cultural practices, is home to the art of sand drawing. This practice, known as “sandroing” in the local language Bislama, involves drawing complex figures with a single finger stroke on beaten earth, sand beaches, or ashes. Sand drawing is considered an intangible cultural heritage of humanity and plays a vital role in preserving ritual, religious, and environmental knowledge in Vanuatu.
2: Experts and Rules
From beginners to experts, practitioners of sand drawing follow a set of rules that govern the creation of their intricate designs. These rules include drawing a continuous, closed line without lifting their finger or crossing the same path twice. The drawings are constrained by a composite grid of lines or dots, and each movement from node to node must be made without cutting the grid other than at its nodes. Sand drawing experts, designated as such by their society, have an extensive repertoire of up to 400 drawings.
3: Marcia Ascher’s Intuition
Ethnomathematician Marcia Ascher was a pioneer in recognizing the mathematical nature of sand drawing. She identified the resemblance between the rules of sand drawing and concepts from graph theory, particularly Eulerian graphs. Ascher’s work paved the way for Da Silva’s research, which aimed to refine the mathematical model of sand drawing and explore the process of creating these intricate designs.
4: Decomposition and Graph Theory
Da Silva’s research led him to discover the importance of decomposition in sand drawings. By breaking down the drawings into subdrawings that form the final design, he uncovered the underlying graph structure of the artwork. Each subdrawing returns to the starting point, and when superimposed, they reveal the complete sand drawing. This decomposition process allowed Da Silva to develop a graph model, named G mod, that accurately represents the sand drawing process.
5: Veblen’s Theorem and Cycles
Building upon Oswald Veblen’s theorem, Da Silva found that sand drawings can be broken down into a union of disjoint cycles. These cycles serve as building blocks for sand artists, and their order and arrangement hold significance in the storytelling aspect of the drawings. The focus on graph cycles not only enhances our understanding of sand drawing but also raises questions about the universality of mathematics and its manifestation in different cultures.
Conclusion:
Sand drawing in Vanuatu is not just a visual artform but a complex mathematical practice rooted in cultural traditions. Da Silva’s research has revealed the mathematical foundations of sand drawing and its importance in preserving traditional knowledge. As efforts to decolonize education in Vanuatu continue, incorporating sand drawing into mathematics instruction holds immense potential for bridging the gap between traditional practices and formal education. The study of sand drawing not only enriches our understanding of mathematics but also deepens our appreciation for the diverse ways in which cultures express themselves through art.
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