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String Figures as Mathematics? An Anthropological Approach to String Figure-making in Oral Tradition Societies

Eric Vandendriessche
Publication Date: 
Number of Pages: 
Studies in History and Philosophy of Science 36
[Reviewed by
Joel Haack
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What are string figures? It may be easiest to think of the example of cat’s cradle, a relatively familiar activity from many of our childhoods, in which a closed loop of string is manipulated by fingers or other body parts to create a variety of patterns.

Eric Vandendriessche’s String Figures as Mathematics? An Anthropological Approach to String Figure-making in Oral Tradition Societies has a wide spectrum of goals. First, he examines the question of whether making string figures is mathematics or at least an example of ethnomathematics, arguing that it is. He then gives a history of the study of string figure-making. After this, Vandendriessche gives a mathematical analysis of string figure-making. Next, he presents his anthropological work among the Guarani-Ñandeva of the Paraguayan Chaco and, more extensively, among the Trobriand Islanders of Papua-New Guinea. He concludes by returning to the question of whether string figure-making can be seen as mathematical, concluding that some portions of it can; “some phenomena reflect intellectual processes that can be regarded as mathematical.” [8]

Let us see how the author fares on the mathematical issues. That mathematical ideas can be used to study string figure-making is demonstrated by Vandendriessche in this book. His history of such studies includes a discussion of the work of many anthropologists, including Alfred and Kathleen Haddon, William H. R. Rivers, Guy Mary-Rousselière, Thomas Thomson Paterson, G. Landtman, Diamond Jenness, and Knud Rasmussen. Vandendriessche also examines popular books by Caroline Furness Jayne and W.W. Rouse Ball, and he includes a discussion of the disappearance of the topic of string figures from later editions of Rouse Ball’s Mathematical Recreations and Essays (H. S. M. Coxeter chose to remove it, directing readers to Rouse Ball’s An Introduction to String Figures, causing some anxiety among those who would argue for string figure-making as mathematics!). Finally, Vandendriessche includes a discussion of the studies of string figure-making by mathematician Ali Rina Amir Moez, computer scientists Yameda Masashi, Burdiato Rahmat, Itoh Hidenori and Seki Kirohisa, and, in some detail, mathematician Thomas Storer.

The question of whether string figure-making is mathematical of course requires a discussion of what mathematics is. In Vandendriessche’s view, the case for string-figure making as a mathematical activity relies on a description of the activity as composed of a number of elementary operations acting on the string (and the pattern formed by the string), which are then organized into procedures, sub-procedures, iterative processes, etc. I found it particularly interesting that there is no word for “mathematics” in Kilivila, one of the languages of the Trobriand Islanders. The Islanders would instead include mathematics in a term translated as “writings,” that is, “what one learns in school.” At least some of the Islanders who knew from school what (western) mathematics is were comfortable with the idea that “string figure-making is not only connected to mathematics, but is ‘actually mathematical.’“ [256-7]

It is always a pleasure to note that not only can mathematics be used to assist in the studies of other disciplines, but the other disciplines can also offer suggestions for interesting mathematical problems. Vandendriessche outlines a few mathematical questions that are motivated by the study of string figure-making, including the topological study of punctured diagrams and (n,n)-tangles. [356-357]

Vandendriessche mentions that the study of several activities similar to string figure-making could benefit from a mathematical analysis, including bag-weaving and mat-making, noting the successes in studying other ethnomathematical topics such as sand drawings. [366-367]

I should also mention that the publisher Springer has made available an extensive collection (342MB) of supplementary digital material, including a number of videos showing Trobriand Islanders and Guarani-Ñandeva making string figures, instructions for constructing many string figures, and a summary of the nomenclature. These supplemental materials greatly enrich the reader’s experience.

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. Of course, the reader has to provide the coordination to carry it off!

A casual reader with an interest in string figures would enjoy much of this book but would likely choose to skip some of the more technical details. Anthropologists and ethnomathematicians will benefit from the richness of Vandendriessche’s discussion.

Joel Haack is Professor of Mathematics at the University of Northern Iowa.