To expand search, see Mathematics and Mysticism. Laterally related topics: Numerology, Magic Squares, The Pentagram, Astrology, and Pseudoscience.
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.
Manansala, Paul. Sungka mathematics of the Philippines. Indian J. Hist. Sci. 30 (1995), no. 1, 13--29. (Reviewer: J. S. Joel.) SC: 01A29 (01A13), MR: 96g:01009.
The author discusses the Sungka Board, which may once have been used as a kind of abacus. The word sungka is from the Philippines, but the author tells us that a similar board is "known over a wide area of the Malayo-Polynesian world from Madagascar to Polynesia, and also through Southeast Asia, India, and even mainland Africa." As the author notes, "documentation for this usage is very hard to come by". The arithmetical algorithms that the author advances for the sungka board have few surprises to someone familiar with abacus systems, but the article has some interesting remarks about other uses of the sungka board and about some number systems from India, the Philippines, and elsewhere in Asia that used mixed number bases. The author is particularly interested in eight-based counting systems, and believes that the Sungka board is particularly relevant in this regard: "The board has two large wells at each end, with each large well having a corresponding row of seven smaller wells. These two rows of seven are parallel and thus the board has a total of 16 wells divided into two groups of eight." The wells were apparently once filled with various numbers of things such as cowrie shells. In the examples given, the wells are used for powers of 10. Apparently the sungka board is now used at least as much for divination. As the author explains, "Its main purpose in modern times is to serve as a sedentary game. In the Philippines, and probably elsewhere, the Sungka Board is also still occasionally used for popular divination, especially by elders enquiring on whether travel by youths is auspicious on a certain day, or by girls interested in finding out whether and when they will get married." Closely related topics: The Philippines, The Abacus, Indo-Malay Archipelago, Polynesia, and Africa.
Martzloff, Jean-Claude. Pi in the Sky. Unesco Courier (Nov., 1989), 22--28.
Very brief. Includes a bit on the influence of divination, astronomy/astrology, Confucianism, and Taoism on the development of Chinese mathematics. The emphasis on the answer rather than the proof shows a Taoist influence, "on the grounds that the fallacious arguments of the sophists showed its limits". Also a bit on how mathematics and mathematicians fit into Chinese society. Appears in edited form in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: China, Astronomy, Astrology, Confucianism, and Taoism.