Ethnomathematician Alban Da Silva reveals the intricate mathematical patterns behind Vanuatu’s ancient sand drawings.
In the remote archipelago of Vanuatu, nestled in the South Pacific, lies a unique art form that has captivated locals and researchers alike for centuries: sand drawing. These complex and ephemeral drawings, created with a single stroke of a finger, have long been regarded as a traditional graphic art that reflects the beliefs, cosmogonies, and social organization of the Vanuatu societies. However, it wasn’t until ethnomathematician Alban Da Silva embarked on a six-year journey to study sand drawing that the hidden mathematical beauty of this ancient art form was unveiled.
Unraveling the Mystery of Sand Drawing:
Da Silva’s fascination with sand drawing began during a kava-drinking session in a French high school in Port Vila, Vanuatu. As he watched a trainee meticulously draw a fish hiding under a stone in the sand, he couldn’t help but wonder about the mathematical principles behind this intricate art form. This encounter sparked a deep curiosity that led him to conduct extensive field surveys, study the methods of expert sand artists, and delve into the history of sand drawing.
A Mathematical Model of Sand Drawing:
Through his research, Da Silva developed a mathematical model of sand drawing that revealed the underlying algorithms and operations of an algebraic nature. He discovered that sand drawings could be described as graphs, with vertices representing the nodes of the grid and edges representing the movements of the artist’s finger. These graphs turned out to be Eulerian, meaning that the artist had to visit each edge only once and return to the starting point. Da Silva’s work demonstrated that mathematical language is not only suitable for describing sand drawing but also offers insights into the relationship between Vanuatu societies and their environment.
The Cultural Significance of Sand Drawing:
Sand drawing holds immense cultural significance in Vanuatu. The practice is deeply intertwined with the beliefs, cosmogonies, and social organization of the Vanuatu societies, collectively known as kastom. Each drawing has a vernacular name and can evoke narratives, ethical considerations, or political dimensions. Sand drawings serve as a means of recalling ritual, religious, and environmental knowledge, and the artists themselves act as spokespeople for the land and its silent voices.
Experts and Rules:
Sand drawing encompasses a range of expertise, from simple drawings known by some to the impressive repertoire of expert sand artists. While the art form was traditionally reserved for men, Da Silva discovered that several women had achieved a high level of expertise. All sand drawers follow a set of rules, including drawing a grid as a foundation, 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 ensure the creation of continuous, closed lines in the sand.
Marcia Ascher’s Influence:
Da Silva’s work builds upon the groundbreaking research of American mathematician Marcia Ascher, a pioneer of ethnomathematics. Ascher recognized the connection between sand drawing and graph theory, particularly Eulerian graphs. Her insights challenged the prevailing notion that only societies with writing could engage in mathematics, highlighting the mathematical knowledge embedded in oral traditions. Da Silva’s research expands upon Ascher’s findings, refining the mathematical model and exploring the decomposition of sand drawings into subdrawings.
A Theorem Discovered in Drawings:
Da Silva’s study of sand drawing led him 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. He found that sand drawings could indeed be decomposed into cycles, shedding light on the artistic process and the significance of cycles in the narratives accompanying the drawings. This discovery raises questions about the universality of mathematics and its manifestation in different cultures, offering new perspectives for teaching mathematics and decolonizing education in Vanuatu.
Conclusion:
The intricate sand drawings of Vanuatu have long fascinated both locals and researchers. Thanks to the pioneering work of ethnomathematician Alban Da Silva, the mathematical beauty of these ancient artworks has been unveiled. By developing a mathematical model and exploring the underlying algorithms, Da Silva has shed light on the complex relationship between mathematics, art, and culture. Sand drawing not only serves as a testament to the rich traditions of Vanuatu but also offers a unique window into the universal language of mathematics.
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