String Figures as Mathematics?

This book addresses the mathematical rationality contained in the making of string figures. It does so by using interdisciplinary methods borrowed from anthropology, mathematics, history and philosophy of mathematics. The practice of string figure-making has long been carried out in many societies, and particularly in those of oral tradition. It consists in applying a succession of operations to a string (knotted into a loop), mostly using the fingers and sometimes the feet, the wrists or the mouth. This succession of operations is intended to generate a final figure. The book explores different modes of conceptualization of the practice of string figure-making and analyses various source material through these conceptual tools: it looks at research by mathematicians, as well as ethnographical publications, and personal fieldwork findings in the Chaco, Paraguay, and in the Trobriand Islands, Papua New Guinea, which all give evidence of the rationality that underlies this activity. It concludes that the creation of string figures may be seen as the result of intellectual processes, involving the elaboration of algorithms, and concepts such as operation, sub-procedure, iteration, and transformation.

• Analysing String Figure Algorithms
• Analysing String Figure Procedures
• Conceptualization of String Figure-Making
• Cultural and Cognitive Aspects of String Figure-Making
• Double-sided Lozenge String Figures
• Mathematical Activity of Creating String Figures
• Mathematics and String Figures
• Modes of Conceptualization of String Figure
• Names of String Figures
• String Figure-Making
• Thomas Storer and the Concept of Heart-Sequence

“Vandenessche (Paris Diderot Univ., France) divides the volume—which is really many books in one—into four parts: ‘How to Study String Figure-Making,’ ‘Mathematics and String Figures,’ ‘Analysing String Figure Algorithms,’ and ‘String Figures in the Field.’ … Summing Up: Highly recommended. Upper-division undergraduates through faculty and professionals.” (D. V. Feldman, Choice, Vol. 53 (3), November, 2015)

“Vandendriessche gives a mathematical analysis of string figure-making. … The author does recommend that every reader try following his instructions to create some of the string figures. I found his instructions clear and the multicolored pictures helpful. … Anthropologists and ethnomathematicians will benefit from the richness of Vandendriessche’s discussion.” (Joel Haack, MAA Reviews, March, 2015)

• Sciences-Philosophie-Histoire, UMR 7219, CNRS, Université Paris Diderot, Sorbonne Paris Cité, Paris, France

  Eric Vandendriessche

Eric Vandendriessche has obtained the French "Agrégation" of mathematics (1992). In 2010, he received his Ph.D. in History and Philosophy of Sciences from Paris Diderot University. Eric Vandendriessche is a member of the Sciences–Philosophy–History French laboratory (UMR SPHERE 7219 – CNRS & Paris Diderot University). He is currently carrying out research in ethnomathematics, doing fieldwork in Papua New Guinea and Vanuatu (Melanesia, South Pacific). The aim of his work is to study the mathematical rationality that underlies activities involving geometrical and algorithmic practices (such as string figure-making or sand-drawing in Oceania), while attempting to analyze how the practitioners of these activities conceive - or have conceived - them in societies of oral tradition. Eric vandendriessche is in charge of the "String figures: cultural and cognitive aspects of a mathematical practice" research program (2012–2015), financially supported by the city of Paris (program "Emergences" 2011).

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