Abstract
The Cambridge mathematician Walter William Rouse Ball (1850–1925) devoted a chapter to “String Figures” in his popular book Mathematical Recreations and Essays. This may be the first ever attempt by a mathematician to demonstrate the connection between mathematics and procedural activities such as string figure-making. The epistemological stake of such a connection is not explicitly addressed by Ball. However, this chapter shows that he has selected some string figures within ethnographical publications and has conceived the structure of his chapter in order to shed light on the mathematical aspect, dealing with concepts such as classification, operation and transformation.
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Notes
- 1.
In 1888, Ball published a book entitled A Short Account of the History of Mathematics (Ball 1888) which has been republished several times. In 1889, he published another book, History of the Study of Mathematics at Cambridge (Ball 1889). He was interested in the works of Newton and he published, in 1891, a paper entitled “A Newtonian Fragment relating to Centripetal Forces” in the Proceedings of the London Mathematical Society (Ball 1891), followed by the book An Essay on Newton’s Principia in 1893 (Ball 1893).
- 2.
See the article Singmaster (2005) for further details in the historical background.
- 3.
As Singmaster pointed out, “Several major mathematical works have devoted much space to problems that are now considered recreational, […]” (Singmaster 2005, p. 654). Singmaster gives the example, among others, of the “Nine Chapters”, “The Aryabhata”, etc. It shows that there can sometime be a movement from mathematics to Recreational Mathematics. The opposite can also happen. Problems raised in a recreational context sometimes become a mathematical field. This is demonstrated by historian of mathematics Mitsuko Mizuno who brought to light the relationship between the mathematical recreations of mathematician König Dénes (1884–1944) and his work in graph theory (Wate-Mizuno 2010).
- 4.
The subject of “Cryptography”, that Ball suggested to be indirectly connected to mathematics raised afterwards some fundamental mathematical questions throughout the twentieth century. See for instance: Oded Goldreich, Foundations of Cryptography, in two volumes, Cambridge University Press, 2001 and 2004.
- 5.
For each string figure described in the book, Jayne precisely mentions her informants. A total of 28 procedures were collected by Jayne in the United States on the occasion of the St. Louis Universal Exposition in September 1904. Twenty two procedures from the book had been taught to Jayne by Haddon, of which five were being published for the first time. Jayne’s brother, anthropologist William Henry Furness, allowed her to include 16 string figures he had collected himself in the Caroline Islands. John Lyman Cox collected 16 string figures for her from the Indian School at Hampton, Virginia (Sherman 2003). Finally, Jayne refers to Gray and Boas about two other figures. The interest of Furness and Cox in string figures suggests that besides the few articles published in the period of 1902–1906, some anthropologists or enthusiasts, interested in string figures, devoted some time to this activity even though they did not publish any articles.
- 6.
- 7.
- 8.
Cf. Alexandre-Bidon and Lett (2004).
- 9.
As far as I know, the expression “string figure” seems to be due to Haddon and Rivers (1902, p. 147). The name “Cat’s Cradle” is still in use nowadays, particularly in the USA, as a generic reference to “string figures”.
- 10.
- 11.
- 12.
See Ball (1920a, pp. 361–362). The same procedure is known under the name Meta (trap) in the Trobriand Islands. The reader will find the instructions for making this string figure in the accompanying website (kaninikula Corpus).
- 13.
Jaynes describes this figure as Ten Men. See Sect. 3.2.2.1 See also the procedure 52. Salibu (kaninikula corpus) in the accompanying website.
- 14.
The reason put forward by Ball for choosing the Navaho method is rather obscure to me. According to him, the Oregon method would be more artistic because of its simultaneous and symmetrical movements. But Haddon and Jayne have described the Navaho “Many Stars” with a succession of operations performed by both hands most of the time simultaneously and symmetrically. The one hand is used “to arrange the string on the other hand” only for performing Movement T (Navahoing). Furthermore, Ball modified Jayne and Haddon’s description by substituting a few non-simultaneous operations to symmetrical and simultaneous ones (see the description of Many Stars).
- 15.
See above Sect. 4.2.2.1 (Classification and transformation).
- 16.
It was first republished in 1920 in a small booklet entitled An introduction to string figures which was to be republished, with some additions, several times under different titles (Ball 1920c). The 1920 lecture was also republished in 1960, in a book entitled String Figures and other Monographs (Ball 1920b).
- 17.
Some comments have been added in square brackets in the text of the lecture published in the Proceedings of the Royal Institution of Great Britain. They show that Ball repeatedly illustrated his talk by demonstrating the making of string figures to the audience.
- 18.
In the 1920 lecture and the Appendix published in the Proceedings of the Royal Institution of Great Britain, Ball refers to Haddon and Rivers (1902), Jayne (1962 [1906]), Compton (1919), Landtman (1914), Gordon (1906), Haddon (1911), and also his own sister A. E. Hodder, who collected some string figures in Asia. In the booklet An Introduction to String Figures, Ball refers mostly to Jayne and Kathleen Haddon—and sometimes to Compton. He justified his choice by writing: This works by Jayne and Haddon, both excellent, mentioned in my lecture, are more accessible than the articles in which the discoveries of these figures were first announced, and accordingly, I refer, by choice, to these books (in which the sources of information are quoted) rather than to the original memoirs (Ball 1920c, p. 21).
- 19.
See Sect. 4.3.2.
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Vandendriessche, E. (2015). W.W. Rouse Ball’s Mathematical Approach to String Figures. In: String Figures as Mathematics?. Studies in History and Philosophy of Science, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-319-11994-6_4
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