Laterally related topics: The Stone Builders and The Jewish Tradition.
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: Number Words, Logic, Kinship Systems, The Aranda, Ambrym, New Hebrides, The Blackfoot Indians, The Sioux, and The Kpelle of Guinea.Modify notes on this entry Modify bibliography entry Make comment on this entry
D'Ambrosio, Ubiratan. Ethnomathematics: an explanation. Vita mathematica (Toronto, ON, 1992; Quebec City, PQ, 1992), 245--250, MAA Notes, 40, Math. Assoc. America, Washington, DC, 1996. SC: 01A07, MR: 1 391 747.
Discusses the nature of ethnomathematics, where the term is used in a very broad sense. (For a different definition, see Ascher, Marcia and Ascher, Robert, Ethnomathematics.) An interesting example of how the author sees ethnomathematics at work in modern Western mathematics is in the 20 year time lag between the discovery of the Dirac delta function and its acceptance in mathematical circles. The author explains: "In many cases, [an idea] never gets formalized, and the practice continues to be restricted to the culturally differentiated group [e.g., physicists] which originated it." (The reader should be forewarned that the article tends to be a bit abstract.)Modify notes on this entry Modify bibliography entry Make comment on this entry
D'Ambrosio, Ubiratan. On ethnomathematics. Philos. Math. (2) 4 (1989), no. 1, 3--14. (Reviewer: M. P. Closs.) SC: 01A07 (00A30 01A80), MR: 91e:01005.
The author sees ethnomathematics very broadly. (A different notion is in Ascher, Marcia and Ascher, Robert, Ethnomathematics.) To the author, the term "ethno" includes all people, but implies a focus on social and cultural factors, and the term "mathematics" includes many ways of understanding the social and physical environments. Stresses the importance to education of understanding the ethnomathematics of different groups. Closely related topic: Education.Modify notes on this entry Modify bibliography entry Make comment on this entry
Sizer, Walter S. Mathematical notions in preliterate societies. Math. Intelligencer 13 (1991), no. 4, 53--60. (Reviewer: U. D'Ambrosio.) SC: 01A07 (01A12 01A13), MR: 93a:01002.
The author discusses the ethnomathematics of nonliterate societies. There is little detail, as the article is rather brief, but the author does mention the number concept and counting, fractions (very briefly), elementary geometric notions (e.g., that of a line), symmetry, string figures, and games of strategy. One note on the article: there are strong similarities behind the mathematics in different parts of the world. There is a theory that this similarity is due to a common origin. The author credits Cantor for this idea. It was first fully developed, however, by Abraham Seidenberg. Closely related topics: The Number Concept, Fractions, Geometry, Symmetry, Games, and String Figures. Also possibly relevant: Abraham Seidenberg.Modify notes on this entry Modify bibliography entry Make comment on this entry
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