Dr. Ron Eglasheglash@rpi.edu

Paper delivered at “Realities Re-viewed/Revealed: Divination in Sub-Saharan Africa.” National Museum of Ethnology, Leiden. July 4-5.

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.

An Ethnomathematics Comparison of African and Native American Divination Systems

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.

“Cluster”• Anti-essentialist caveat: diverse societies cannot

be reduced to a single common core.

Wrong Right

This analysis concerns only indigenous North American tribes

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

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)

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).

Gambling and Games of Chance

Divination and randomness

• Zuni: shuttlecock (also a gambling game of chance)

• Ojibway shaking tent

• Navajo hand trembling

The cluster of randomness concepts in Native American

cultures

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

Deterministic chaos example: logistic equation

P(n+1) = R*Pn (1 - Pn) (population each year)

R = 3.0

R = 3.5

R = 3.7

Population repeats every 2 years

Population repeats every 4 years

Population never repeats: deterministic chaos!

The cluster of African deterministic chaos concepts

• Fertility as recursive expansion

• Tricksters unpredictable by self-reference

• Pseudorandom chaos in games

• Pseudorandom chaos in divination

Bamana Sand DivinationThe first four symbols are generated by random process

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

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”

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)

Fertility and fecundity as positive feedback loop

The cluster of deterministic chaos concepts in African cultures

Native Am.

Divination by random movement

Fertility as random genetic diversity

Games as probability

Trickster unpredictable due to random behavior

African Divination by pseudo-random calculation

Fertility as recursive fecundity

Games as pseudo-random calculation

Trickster unpredictable due to recursive behavior

Conclusion