To expand search, see Language and Literature. Laterally related topics: Mathematics in Language, The Development of Writing, Literature, Shakespeare, Language and Linguistics, and Myth and Ritual.
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Ascher, Marcia. Graphs in cultures. II. A study in ethnomathematics. Arch. Hist. Exact Sci. 39 (1988), no. 1, 75--95. (Reviewer: M. P. Closs.) SC: 01A10, MR: 90d:01003.
Discusses the cultural background and mathematical properties of the continuous graphs traced by the Booshong and Tshokwe, who live in the Angola/Zaire/Zambia region of Africa. The Bushoong are a subgroup in the Kuba chiefdom, and exchange their art for food and raw materials. They have interesting ways of classifying designs, which are touched on by the author. The problems in continuous tracing among the Bushoong are primarily the domain of children. Ascher discusses the tracing algorithms used. In the Tshokwe, continuously traced graphs play an important role in the story-telling tradition. The author gives examples of how some diagrams are used to discuss a rite of passage and in connection with the muyombo trees representing the village ancestors. In some cases, the notion of inside/outside is important (an aspect of the Jordan curve theorem). Ascher discusses geometric characteristics of the graphs (for example, many are regular of degree 4), and algorithms for drawing the curves. Closely related topics: Continuous Tracing Problems, The Bushoong, and TheTshokwe.
Ascher, Marcia. Graphs in cultures: a study in ethnomathematics. Historia Math. 15 (1988), no. 3, 201--227. (Reviewer: M. P. Closs.) SC: 01A10, MR: 90d:01002.
As the author observes, the philosopher Wittgenstein pointed to the problem of tracing graphs or figures as one that everyone can recognize as mathematical. Related problems have occurred in a variety of cultures. In western Europe, problems of tracing graphs or figures have occurred in Danish folk puzzles, where they were used as an alternative to dancing. Two patterns that are traced out are said to be similar to those on an artifact from Viking times, and are said to have mystical significance; and two others are said to be useful in witchcraft. Similar problems occur in other cultures as well. The article focuses on the context of the puzzles and the methods used to solve them in New Ireland and the Republic of Vanuatu, especially on the island of Malekula. A number of designs from Vanuatu have mythic significance. There is a tradition that one must complete a certain diagram to enter the Land of the Dead; failure results in being eaten. The methods used to draw the diagrams are also very interesting. In many cases, Ascher shows how individual drawing elements are transformed by processes such as reflection and rotation and are combined in systematic ways to draw the figure. Other types of mathematical ideas from Malekula include a drum signaling system with rhythms for each clan, rank, grade of pig, and special phrases, and a six-class marriage system which the elders explained with diagrams in the sand. Closely related topics: Continuous Tracing Problems, The Malekula of Vanuatu, New Ireland, The Philosophy of Mathematics, and Denmark Folk Tradition.
Seidenberg, A. The ritual origin of counting. Arch. Hist. Exact Sci. 2 (1962b), 1-40.
It is common to argue that counting and other elementary mathematics arose spontaneously throughout the world in response to a practical, or perhaps psychological, need. Abraham Seidenberg argues instead for a diffusion theory, that counting arose only once, and then spread throughout the world. In fact, many common associations with numbers suggest such a common origin. One such association that Seidenberg is the idea that odd numbers are male and even numbers are female; this is certainly well known from the Pythagoreans, but turns out to be nearly universal. Seidenberg proposes that counting in fact originally arose in a ritual context. Seidenberg draws from a wide variety of anthropological sources for rituals and myths that hint at what this common origin might have been. He finds that counting "was frequently the central feature of a rite, and that participants in ritual were numbered." He focuses more specifically on creation rituals. He suggests that in the enaction of creation myths, men and women may have come onto the scene alternately, easily explaining the odd/male even/female association. He finds that his ideas clarify "pure 2-counting, which is the oldest stratum of counting we can detect." In pure-2 counting, there are separate words for one and two and these are used to form all other number words. He illustrates this with number words from diverse languages such as the Gumulgal of Australia, the Bakairi of South America, and the Bushmen of South Africa. He sheds additional light on his hypothesis with discussions of the possible origin of counting taboos (and connections with ritual sacrifice), of ancient one-one-correspondence "tally" systems (e.g., counting people with stones), of taxation systems, of money, and of gematria. Seidenberg also gives us some fascinating examples of counting in world religions. These include the analogy The Lord : His people = the shepherd : his sheep, the analogy The shepherd : his sheep = the moon : the stars. These two lead one to expect the moon to count the stars; and Seidenberg in fact finds evidence of this in ancient Babylonia. He argues from the equation The Lord's people = the stars of the heaven to The Lord's people = the sand upon the seashore that one would expect to find a ritual counting of sand. In fact, he finds the notion of Counter of the Sands both in Buddhism and among the Ancient Greeks. The equation The Lord = The Counter seems to be confirmed in two of the ninety-nine beautiful names of Allah, namely The Counter and the Reckoner; and there is further confirmation in Chapter's XV and XIX of the Qu'ran. This is a fascinating article, connecting mathematics with a wide variety of disciplines. Closely related topics: Myth and Ritual, Anthropology, General, Counting, TallySystems, Taxation, Number Words, The Pythagoreans, Gematria, Religion, The Islamic World, and Abraham Seidenberg.