Computation and communication theory in Native American culture Ron Eglash, RPI

1. Computation and communication theory in Native American cultureRon Eglash, RPI

2. Anti-essentialist caveat: diverse societies cannot be reduced to a single common core. But we can see a “cluster” of concepts WrongRight

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

4. Consider randomness as a measure of complexity (Kolmogorov-Chaitin measure) Order 9/11 = .818181818181818… Random dice roll = 396158294106538

5. Trickster gods as random: nature is too complex to predict 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).

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

7. 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)

8. The cluster of randomness concepts in Native American cultures

9. Computational significance of genetic diversity in crops The complexity of Nature as Trickster – dry years, cold years, hot years- can only be matched by an equivalent complexity in genetic resources. The native emphasis on “randomness”—gambling games, stochastic divination, and trickster gods—helps to forefront this connection. Monocropping in our factory farms today is an environmentally poor practice. In measuring algorithmic complexity of a pattern, we would need to know the shortest symbol string that can generate the pattern—this too connects to native traditions.

10. What is the shortest symbol string for a set of production rules? Miguel Jiménez-Montaño, University of Veracruz: context free grammar used to measure complexity on amino acids and genetic sequences. A long-time friend of Mario Vazquez, who studies archaeological data on the plants used by the indigenous societies of Mexico. Starting symbol S, production rules, “terminal symbols” which cannot be further replaced. For example, given terminal symbols {a,c,t} and rules {S -> cb, b -> ad, d ->t} we get {cat} as the only permissible string in this grammar. To measure the complexity K, we just sum the number of symbols on the right-hand side of the production rules: K = 2 + 2 + 1 = 5.  Since a string of symbols that repeat should count less, n repetitions of a single symbol is counted as  1+log2n.

11. Suppose corn colors Yellow, Black, Red, and White. Two rows of 32 kernels each, with the following repeating patterns: • YBRW... 2) YBRWBWYB... • Pattern one repeats every four symbols, while pattern two repeats every eight symbols. Intuitively we see pattern two as more complex; but we can confirm that using the complexity measure. The minimum set of production rules can be found by experimentation; they are as follows: • 1) S -> a8 (meaning “aaaaaaaa”) a -> YBRW • The complexity is K = (1+log28) + 4 = 8 • 2) S -> a4 a -> bcb -> YBRW c -> BWYB • The complexity is K = (1+log24) + 2 + 4 + 4 = 13

12. The concept of a production rules of a generative grammar can be seen at work in the native northeast tradition of birch bark scrolls. These scrolls show the progression of a shaman in a series of lodge rituals.

15. Can bead patterns be produced by a generative grammar? W=white, R=red, O=orange WRRRRW WRROOOORRW WRROOOOWWWWOOOORRW WRROOOOWWWWWWWWWWWWOOOORR WRROOOOWWWWWWWWWWWWWWWWWWOOOORRW

16. Communication theory in Native American culture The Apache smoke signal system has three categories: “attention,” “safety,” and “caution,” distinguished by the number of simultaneous fires (from one to three). Lets say that attention signals are sent 55% of the time, safety signals are sent 30% of the time, and caution signals are sent 15% of the time. We can then calculate the average bits per symbol: H = -(  2((.55/2)log2.55/2)) + 2((.30/2)log2.30/2) + ((.15/2)log2.15/2))) = 2.406. If lighting two fires takes twice as long as one, and three fires takes three times as long, what is the optimal assignment of number of fires to categories? Information rate R = (H / average number of signals per second).  F = number of seconds it takes to send the signal. So six possibilities for the information rate: R1 = 2.406/(.55f + .30*2f + .15*3f) = 1.504/f R2 = 2.406/(.55*f + .30*3f + .15*2f) = 1.375/f R3 = 2.406/(.55*2f + .30f + .15*3f) = 1.301/f R4 = 2.406/(.55*2f + .30*3f + .15*f) = 1.119/f R5 = 2.406/(.55*3f + .30*f + .15*2f) = 1.070/f R6 = 2.406/(.55*3f + .30*2f + .15*f) = 1.003/f Code R1 is optimal, and this is the same code assignments as that recorded for the Apache system: “attention” signals use one fire, “safety” signals two, and “caution” signals three.

17. Aliasing in Navajo weaving The 30 degree angle indicates an “up one over one” iteration (warp is about 3 times thicker than weft). She explained that other angles gave a more jagged edge. The same “aliasing” problem occurred in early computer graphics. Do weavers have the equivalent of anti-aliasing algorithms? What might be involved in the curious angles we see in this rug?