Marc Chemillier's "Les Mathématiques Naturelles" runs just over 200 pages and treats questions of mathetmatics and mathematical reasoning in societies possessing an oral -- but not a written -- tradition. Chemillier proposes the term "natural mathematics" (in analogy to "natural languages") to suggest the great diversity of approach to patterning and formal reasoning present in oral (or preliterate) cultures around the world. And, indeed, the diversity of tradition and place Chemillier visits in "Les Mathématiques ..." is one of the real pleasures of the text -- sand-drawings from Vanuatu and Angola, West African oware, music from the Central African Republic, and fortune-telling or divination from Madagascar.
The body of the book encompasses a chapter each on the visual arts and games of strategy, and a pair of chapters each of music and divination. The examples are gorgeous -- be they sand-drawing black-and-whites, depictions of harp music, or the schematics of sorcery -- and the analyses contained in the text first take apart and then put back together (sometime hypothetically) the different ways in which these different mathematical systems and objects may have developed in preliterate culture.
Cognitive researchers and musicologists will be interested in Chemillier's Big Questions underneath the text, ie, what really counts as formalization, what cognitive categories are required to develop the cultural artifacts that make up body of the book, and whether mathematics without writing is even possible at all. In fact, Chemillier treats these and related points explicitly in the opening and closing chapters of the text and does what is, in my opinion at least, an excellent job of hinting at relationships between certain mathematical properties or phenomena and certain ways of thinking, all without overstepping the bounds of what's really possible to assert at this point in culture (and mathematics) research.
If you're used to thinking of the Western math system as somehow culture-neutral (or even "universal"), then Chemillier's text is as good a place as any to disabuse yourself of such an illusion. There are as many approaches to patterns, process and formalism as there are practioners (no matter where in the world they may be), and the text helps make this point in a direct and engaging way.
One last bit: what initially drew me to "Les Mathématiques Naturelles" was what the text might have to say about music composition (meant in the completely Western way). And, indeed, I was not disappointed -- it's worth reflecting on, say, what it means to "write music" in Wetern way while reading through Chemillier's research on numbers and patterns as they are treated completely outside of any written tradition; how much of Western composition (or painting, or sculpture) is, at some point in the process, likewise a type of "natural mathematics"? And what correspondences (cognitive or otherwise) might be common to both the composer and the fortune-teller, or to both the painter and the artist in the sand?
Recommended.
