To expand search, see Social Science. For material on related topics, see Anthropology, General. Laterally related topics: Taxation, Warfare, Anthropology, General, 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 and Ascher, Robert. Ethnomathematics. Hist. of Sci. 24 (1986), no. 64, part 2, 125--144. (Reviewer: Jens Høyrup.) SC: 01A10 (92A20), MR: 88a:01005.
Discusses the danger of identifying non-literate mathematics with "primitive" mathematics. Warns against assuming that because a group has two sets of number words (as in the Blackfoot Indians, who are said to use different sets of numbers for the living and the dead), the group therefore doesn't understand the underlying identity between the different words. Regarding logic, when asked the question "All Kpelle men are rice farmers. Mr Smith is not a rice farmer. Is he a Kpelle man?", one Kpelle respondent answered "If you know a person, if a question comes up about him you are able to answer. But if you do not know the person, if a question comes up about him, its hard for you to answer." The authors emphasize that a response like this doesn't show a lack of ability in logical reasoning, but just differences in views in talking about people you don't know and about 'playing along' with a questioner. The authors discuss how the Sioux viewed the circle as a more natural shape than the (western) line. Kinship systems of the Aranda of Australia, and in Ambrym in the New Hebrides. How elders in Ambrym used diagrams to elucidate the kinship systems, and explicitly explained the patricycles of degree 2 and the matricycles of degree 3. An interesting question for a student might be to investigate if the Aranda system (with six groups) is optimal in ruling out certain types of marriages that are too close. Closely related topics: Ethnomathematics General, Number Words, Logic, The Aranda, Ambrym, New Hebrides, The Blackfoot Indians, The Sioux, and The Kpelle of Guinea.
Seidenberg, A. The ritual origin of the circle and square. Arch. Hist. Exact Sci. 25 (1981), no. 4, 269--327. (Reviewer: M. P. Closs.) SC: 01A10 (51-03), MR: 83h:01008.
Abraham Seidenberg advances a theory that the circle first arose in the context of the ritual enactment of a creation myth. In many cases, stars seem to play an important role in these myths. Seidenberg's research suggests that participants in these myths generally moved in a circle in imitation of the stars in the heavens. It is interesting that individuals in these societies often move in the same direction as the stars, and movement in the opposite direction is often considered unlucky. The fact that the Aztec god Tezcatlipoca is missing is right foot, forcing him to walk clockwise in a circle may be related. Seidenberg suggests that the creation myth is the origin for the dance around the may pole, which is for example observed near the summer solstice in northern Scandinavia today. Analogous rituals may play (or have played) a role in a wide variety of other cultures as well; examples are found in the Aztecs, ancient Indians, American Indians, and Greeks. (Spinning tops may have a ritual significance as well.) Special support is given to Seidenberg's these through the fact that in some cases, a pole may have been set up at an angle so as to point towards the pole star. Seidenberg notes that the moon might have motivated the circle rather than the stars, but the sun is unlikely to. His investigations tend to confirm this, and also suggest that lunar culture is older than solar culture. Seidenberg believes that the square arose from the circle, through the process of dividing a group into a dual organization, where for example members of one group marry someone in the other group and also (as he notes) play complementary roles in ritual. If a society divides a second time, one can think of it dividing the tribal circle into four parts. He finds some evidence of this as well. The four parts naturally define a square. His theory therefore implies that the circle arose first and that the square arose as a dual form of the circle; there is some other evidence (e.g., architectural) that may tend to confirm this. Seidenberg mentions several interesting dualities involving the circle and the square. The Altar of Heaven in Peking, for example, exhibits the equations Heaven : Earth = circle : square = three : two = South : North = White : Yellow. In Sinhalese art he finds the equation circle : square = standing : sitting. In the Omaha tribe he finds the equations that Sky : Earth = superior : inferior = one : two. He also notes the equations Heaven : Earth = Male : Female and Male : Female = one : two. The former is well known, and the latter is extensively discussed in Seidenberg, A., The ritual origin of counting The ancient Egyptians appear to be an exception as they associated the square with the earth and the circle with the sky. A fascinating paper. Closely related topics: Myth and Ritual, Religion, Anthropology, General, The Circle, The Square, and Abraham Seidenberg.