There is a great prevalence of Euclidean geometry in Western culture. For example, we are taught linear geometry as the singular or primary type of geometry in school. When cities are planned, they are often laid out in a grid pattern. When the United States expanded into the West, it split some states and counties into squares and rectangles. This prevalence has caused problems in agriculture; before the Dust Bowl, American farmers would sow their seeds in a linear pattern (and didn’t rotate crops), so their crops became susceptible to wind erosion and eventually the Midwest fell victim to the Dust Bowl.
While linear, Euclidean math is prevalent in Western culture, other cultures may have different forms of mathematics. This class focused on Native American and African cultures. Native American cultures share a cluster of connected ideas around themes of randomness. There is enormous diversity among these many cultures, and cannot be boiled down to a single, all-encompassing characteristic. See Figure 1, taken from Ron’s paper “An Ethnocomputing Comparison of African and Native American Divination Systems,” shows how a cluster of principles works.
Some Native American cultures share a cluster of connected ideas centered around themes of randomness. These cultures emphasize genetic diversity in crops, trickster stories featuring random events, gambling and games of chance, and divination by random movement. Genetic diversity in crops helps tribes cope with environmental uncertainty. They choose all types of seeds to show that they are grateful for what they have received (Eglash 2013). In many Native American cultures, the Coyote is a prevalent trickster character. In the Navajo story of creation, human put down Polaris and then four ordered stars, and then in a hurry Coyote scattered mica dust into irregular patterns, creating the constellations. The Shoshoni attribute the bountifulness and irregularity of salmon presence in their rivers to Coyote; Coyote put salmon in the river by breaking a basket, and the regularity of the basket is contradicted by the irregularity of fish flow. The Cayuga game of Dish exemplifies games of chance:
In the Cayuga version of the game six peach stones, blackened on one side, are tossed and the total numbers landing black side or brown side recorded as the outcome. The traditional Cayuga point scores for each outcome are proportionate to the exact values calculated by probability theory. (Eglash, 2013)
Gambling is used quite often, and is used as a wealth distribution tool in order to guard against injustice. Three examples of divination by random movement include Navajo hand trembling, Ojibway shaking tents, and the Cherokee suspended stone on a string.
Many African cultures also share a cluster of connected ideas, though these are connected by themes of deterministic chaos. They view fertility as recursive expansion, tricksters as unpredictable due to self-reference, pseudorandom chaos in games, and pseudorandom chaos in divination. Fertility is viewed as a positive feedback loop, such as in the Baule door that depicts fecundity as such. African tricksters act in an unpredictable fashion, but still have a deterministic characteristic due to their recursive nature. The Ashanti story of Ananse and contradiction is an example of this; a man that hates to be contradicted was forced to contradict himself. Mancala is a pseudorandom game that has become popular in Western culture as well as African culture. Bamana sand divination is a great example of pseudorandom chaos in divination. I have included a picture of my own sand divination in Figure 2. The interpretations done in class come from medieval-era geomancy, and may not be pertinent to this essay, so I will not include it.
Math and culture often influence each other. The linearity of Western culture leads to the grid system of cities like New York City. The Ashanti in central Ghana see logarithmic spirals in everything, from snails to water droplets to rope coils. The Ashanti create Adinkra cloth, which is stamped with Adinkra symbols. Spirals and loops are an integral part of Adinkra designs. There are three stages in making an Adinkra symbol: observing an object from nature or culture, artistically representing this object, and abstracting the art into geometric forms to make stamps easier to reproduce and recognize. The Sankofa symbol is a good example as it depicts the logarithmic curve of a bird bending its neck. The Dwennimmen symbol shows four spirals, and emulates a ram’s horn. This symbol is based on the proverb, “It is the heart, and not the horns, that leads a ram to bully,” meaning that one must take responsibility for their own actions. The Dwennimen symbol will be shown later in this paper. Adinkra symbols can be found everywhere, not just on Adinkra cloth. They are found on fences, sculptures, and even chocolate bar wrappers. Many companies have incorporated Adinkra symbols into their logos.
Educational achievement in the United States shows a stark gap between the performance of white students and African-American students. In Los Angeles, white students are, on average, an entire grade level ahead of their African-American peers; the gap is 2.3 grade levels in New York City (Lyles et al., 2016). This gap could be due to many factors, including teacher and student expectancy, “a lack of economic access, failing public infrastructure, and the deindustrialization of urban centers.” This leads to the alienation of students, which further decreases their academic performance.
Culture is included in the way we teach science, technology, engineering, and math (STEM) to students. The prevalence of multiculturalism in humanities and the absence of multiculturalism in STEM education sends the implicit message that STEM fields are only for those of European descent (Eglash, 1997). There is a lack of diversity in STEM fields, and fixing the lack of diversity in STEM education may alleviate the lack of diversity in STEM fields. The C-STEM researchers at RPI are trying to attack the lack of diversity in STEM education through Culturally Situated Design Tools. These tools show how different cultures use math, and how to create a small program to emulate that math; Adinkra is used in one of these tools. The Dwennimmen symbol can be emulated using the script and giving the result shown in Figure 3.
The prevalence of Euclidean geometry in Western culture is pervasive, entering into every part of culture from agriculture to architecture to education. However, this is not the only way to do math. In some Native American cultures, math is based on randomness. In some African cultures, math is based on deterministic chaos. Both of these examples use math for divination, have trickster stories that exemplify their mathematical bases, and use math for games. The education gap is quite large, and by broadening the diversity in STEM education we can decrease the alienation of students from underrepresented groups in STEM. One way to broaden diversity in STEM is to use CSDTs, which highlight the mathematical bases for cultural phenomenon such as cornrows or Adinkra symbols.
Culturally Situated Design Tools, Adinkra: Cultural Background https://community.csdt.rpi.edu/cms/application-contexts/adinkra/cultural-background/
Eglash, R. (2013). An ethnocomputing comparison of African and Native American divination systems. pp. 295-312 in Beek, Walter E. A. van, and Philip M. Peek. /Reviewing reality: dynamics of African divination./
Eglash, R. (1997). When Math Worlds Collide: Intention and Invention in Ethnomathematics. Science, Technology, & Human Values, 22(1), 79-97. Retrieved from http://www.jstor.org/stable/689967
Lyles, D., Lachney, M., Foster, E., & Zatz, Z. (2016). Generative Contexts: Generating value between community and educational settings. Teknokultura. Journal Of Digital Culture And Social Movements, 13(2), 613-637. doi:10.5209/rev_TEKN.2016.v13.n2.52845