An Ethnomathematics Comparison of African and Native American Divination Systems

1. Dr. Ron Eglasheglash@rpi.eduPaper delivered at “Realities Re-viewed/Revealed: Divination in Sub-Saharan Africa.” National Museum of Ethnology, Leiden. July 4-5. An Ethnomathematics Comparison of African and Native American Divination Systems Many material and conceptual aspects of Native American cultures are connected to randomness: gambling games, random events in trickster stories, and diversity in crop genetics all share some version of this theme. The presence of random movement in several Native American divination practices fits well into this portrait. Several forms of African divination, on the other hand, are better characterized in terms of “deterministic chaos” in the sense of nonlinear dynamics, and provide a similar fit to their cultural contexts.

2. Thesis • Many Native American cultures share a cluster of connected ideas around themes of randomness • Many African cultures share a cluster of connected ideas around themes of deterministic chaos.

3. “Cluster” • Anti-essentialist caveat: diverse societies cannot be reduced to a single common core. WrongRight

4. This analysis concerns only indigenous North American tribes

5. The cluster of Native American randomness concepts • Genetic diversity in crops • Trickster stories featuring random events • Gambling and games of chance • Divination by random movement

6. Religious significance of genetic diversity in crops “Do you select only the biggest corn kernels of all one color?” “It is not a good habit to be too picky... we have been given this corn -- small seeds, fat seeds, misshapen seeds -- all of them.  It would show that we are not thankful for what we have received if we plant just certain ones and not others” (Nabham 1983 pp. 7)

7. Trickster gods as random First Man placed the Star Which Does Not Move [polaris] at the top of the heavens. ...Then he placed the four bright stars at the four quarters of the sky. ...Then in a hurry, Coyote scattered the remaining mica dust so it did not fall into exact patterns but scattered the sky with irregular patterns of brilliance (Burland 1968 pp. 93).

8. Gambling and Games of Chance

9. Divination and randomness • Zuni: shuttlecock (also a gambling game of chance) • Ojibway shaking tent • Navajo hand trembling

10. The cluster of randomness concepts in Native American cultures

11. Anthropology of the strange tribe called “mathematicians” • 300 B.C. to 19th century: chaotic = random • 20th century: chaotic, unpredictable behavior can be caused by deterministic equations

12. R = 3.0 Deterministic chaos example: logistic equation P(n+1) = R*Pn (1 - Pn) (population each year) Population repeats every 2 years Population repeats every 4 years R = 3.5 R = 3.7 Population never repeats: deterministic chaos!

13. The cluster of African deterministic chaos concepts • Fertility as recursive expansion • Tricksters unpredictable by self-reference • Pseudorandom chaos in games • Pseudorandom chaos in divination

14. Bamana Sand Divination The first four symbols are generated by random process

15. But the next 12 symbols are generated by a deterministic “loop” – a pseudo-random number generator

16. The same pseudorandom effect forms the basis of Owari, Mancala, and related African games To settle into a “marching formation” requires 13 iterations, a “chaotic transient”

17. The African Trickster also makes use of the chaos of recursion • Ashanti stories of Ananse: “Hates-to-be-contradicted” is tricked into contradicting himself. • “Thus Ananse rejects truth in favor of lying, but only for the sake of speech; temperance in favor of gluttony for the sake of eating; chastity in favor of lasciviousness for the sake of sex....” • “Whose Talking” (Nupe of Nigeria)

18. Fertility and fecundity as positive feedback loop

19. The cluster of deterministic chaos concepts in African cultures

20. Conclusion