Interview: Doing mathematics without knowing it
Why did you choose to study cat’s cradle games?
My interest in cat’s cradle is part of an ongoing personal project. The thesis I defended in 2010 was on the mathematical aspects of these cat’s cradle games.
I then met Céline Petit, who defended a thesis on the social role of cat’s cradle for the Inuit and Ana Guevara, who is completing her thesis on the anthropology of memory in Patagonia.
They had both had the opportunity to collect information on the practice of cat’s cradle in these societies. By comparing our ethnographical data and our respective questions, we thought it would be relevant to study this practice using an approach which combined anthropology and mathematics.
So the innovate element of your research project is that it combines mathematics and anthropology?
Yes. Some anthropologists have been interested in cat’s cradle games, more specifically wondering about their spread through different societies at the end of the 19th century. At the same time, mathematicians have developed tools for analysing cat’s cradle games as ways of crossing string to make shapes. The aim of our study is to get a better understanding of how cat’s cradle games are mathematical and how far this mathematical activity covers different social and symbolic functions in the societies in question.
Which societies are most involved in your project?
Our research is focused on societies with a so-called “oral tradition”, such as the Trobrianders (in Papua New Guinea), the Inuit (in the Arctic) and the Mapuche in Patagonia. We realised that in these societies, the practice of cat’s cradle was often accompanied by the use of a specific vocabulary.
To which period of history does cat's cradle correspond?
It is very difficult or even impossible to date the appearance of cat’s cradle in these societies according to a Western historical perspective. The origin of these games is, however, the subject of mythical tales among several of these peoples.
Oral statements by those who play them lead us to understand that the practice of cat’s cradle goes back to ancient times and is secular in nature. And we can see that this practice is still alive and well in the societies involved in our study.
What are your working methods?
We began by carrying out ethnographical surveys, following both the practices and the terms involved in the creation of string shapes. We are also attempting to develop new conceptual tools which will allow us to collect and analyse these games using an ethno-mathematical approach.
Cat’s cradle games can in fact be considered as mathematical algorithms and studied as such. These procedures can be broken down into simple gestures which I call elementary operations: taking hold of the string, rotating a finger or wrist, etc. These elementary operations have been organised into sub-procedures, meaning ordered sequences of elementary operations which are identical in several cat’s cradle games within the same corpus or iterated within the same game.
We have noticed that these corpuses of cat’s cradle games differ considerably from one society to another in their use of sub-procedures.
How important is the Emergence(s) funding?
The funding has allowed us to recruit Céline Petit and Ana Guevara and therefore to start to put together a true research team, particularly with the creation of post-doctoral contracts for ethnologists and mathematicians. Without this, we would not have managed to make a connection between mathematics and anthropology. We are also collecting data on the different cat’s cradle games and the funding helps us with travel and research costs.
How has the research project progressed since it started?
We signed the contract in December 2011, so we are still at the start of the project. At the moment, we are concentrating on collecting ethnographical data, i.e. information on the cat’s cradle games practised today in the societies I have mentioned; we are also considering the creation of new methodological tools.
And we are looking to extend our research to other mathematical games practised in some of these societies, such as the sand drawings made by the inhabitants of Vanuatu. Here, we are looking at the existence of similarities in the mental operations or procedures involved in these games.
How do you think the research project will progress in the future?
For the “mathematical” element I am studying, I have managed to create a language for reducing all cat’s cradle games to a simple formula. I would like to be able to computerise this and the conceptual tools, so that the computer is able to break down each cat’s cradle game into sub-procedures and gestures.
We are also looking to collaborate with ethnologists, linguists and mathematicians, which would allow us to develop the project internationally; this would then help us to collect information in the societies we are interested in.
How have you presented your project to the scientific community?
First of all we organised two seminars, one on the anthropology of memory, with the aim of studying how far and in which ways cat’s cradle can play a role in fixing the memory of certain social rules, events or mythical tales belonging to these societies; the other seminar was on the history of mathematics and the elementary operations involved in cat’s cradle. The premises of the project were also presented at the Université Paris Diderot on 24 May, with the screening of a film outlining our approach and questions regarding this “traditional” mathematical activity.
Title of the research: Cat’s cradle: cultural and cognitive aspects of a mathematical practice.
Team: Eric Vandendriessche, Professor of Mathematics/Doctor of Epistemology and History of Sciences (French), Céline Petit, Ethnologist/Doctor of Ethnology (French) and Ana Guevara, Anthropologist (Chilean – Argentinean)
Emergences December 2010
Université Paris Diderot/CNRS (National Centre for Scientific Research)