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EDMT 3420/MATH3821/MATH7821 Fall 2012 Tuesday, October 16 Divination Systems

EDMT 3420/MATH3821/MATH7821 Fall 2012 Tuesday, October 16 Divination Systems . Divination: Introduction Opening Activity: On the nature of randomness Divination Practices : Knot divination ( Caroline Islands) Sikidy divination ( Madagascar) Exercises Group Activities:

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EDMT 3420/MATH3821/MATH7821 Fall 2012 Tuesday, October 16 Divination Systems

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  1. EDMT 3420/MATH3821/MATH7821 Fall 2012 Tuesday, October 16Divination Systems • Divination: Introduction • Opening Activity: On the nature of randomness • Divination Practices : • Knot divination ( Caroline Islands) • Sikidy divination ( Madagascar) • Exercises • Group Activities: • Knot divination exercises

  2. On the Nature of Randomness • Activity: • Write as many words as you can to explain how you would define the idea of Randomness. • Is there anything mathematical about trying to predict the future? • How often do you think fortune tellers are correct?

  3. Randomness • Closely connected with the concepts of chance, probability , and certainty. • Randomness implies a lack of predictability but admits regularities in the occurrences of events whose outcomes are not certain. • In many cultures various divination practices are attempted to evade randomness and uncertainty in future events.

  4. Divination: Introduction Divination is a decision making process to gain insight into a question or situation by way of a standardized process or ritual. Divination can be seen as a logical method which uses randomizing mechanisms to resolve an issue or an inquiry of interest. Types of Divination: A shared systematic and structured approach intertwined within spiritual and social contexts and which varies by culture. Diviner follows preset procedures and adheres to the rules of the system(Scientific nature). Capitalizes on the supernatural powers of the diviner.

  5. Divination: Main ideas • Divination practices start with randomizing mechanisms eliciting a fixed discrete set of outcomes with different interpretations. • Belief in divination is related to believing that outcomes of particular procedures, carried out under particular circumstances, and usually with particular materials are expressions of specific deities or supernatural forces. • Divination procedures begin with simple randomizing mechanisms but the outcomes can be built upon in various ways.

  6. Divination Practices • Two techniques: • Knot divination of Caroline Islanders. • Sikidy by people in Madagascar . • Purpose: To gain information and understanding about ongoing or future happenings.

  7. Caroline Islanders 1) A group of about 500 small coral islands, east of the Philippines, in the Pacific Ocean.2) The islands were colonized by:Spain, Germany, and Japan before being included in the U.S. Trust Territory of the Pacific Islands after 1947. 3) Now they are the Federated States of Micronesia4) Population=1220005) People remain in close communication with each other and they share common cultural traditions and practices including divination systems.

  8. Knot Divination System: Caroline Islanders Origin of the system: Supunemen god brought to earth 16 destinies in the form of spirits. He had them build a sailing canoe in which they sailed from island to island teaching knot divination. • Each of the spirits has a name and is associated with a pair of numbers (a,b), where a= 1,2,3,4 and b= 1,2,3,4

  9. Knot Divination System: Caroline Islanders Role of diviner: • Sacred and honored person • Well versed with the teachings of the spirits • Consulted on important matters related to real life issues such as fishing, house building, traveling, naming of children, illness, marriage, etc. • Must carefully pass on his knowledge by teaching future diviners.

  10. Knot Divination System: Caroline IslandersRules: • There are 16 spirits: {(1,1), (1,2), (1,3), (1,4),(2,1), (2,2), (2,3), ( 2,4), (3,1), (3,2), (3,3), (3,4),(4,1), (4,2), (4,3), (4,4)} • The order is significant: female if a>b male if a<b • Corresponding pairs are spouses: For ex. (1,3) is the husband of ( 3,1) • (4,4) is the chief; (2,2) is the wife of the chief; ( 3,3) their son; ( 1,1) is a young bachelor. (a,b) =

  11. Knot Divination System: Caroline IslandersProcedure: • The diviner splits the leaves of coconut trees into strips • Client or diviner makes a random number of knotsin each strip • Knotted strips placed in a pile and 4 strips are randomly selected • First strip is placed between thumb and forefinger, second between forefinger and middle finger, third and fourth between the next fingers, etc. • The knots on each strip are counted modulo 4 i.e. returning the count if it exceeds a multiple of 4. Definition: Two integers a and b are congruent modulo n if their difference is a multiple of n. It is written like this: aΞb (mod n) if a-b= k.n for some integer k. For ex. 5=1(mod 4); 9=1( mod 4)

  12. Knot Divination System: Caroline Islanders 6. From the first two strips a pair (a, b) is obtained and from the third and fourth another pair (a’, b’) is obtained. 7. Pair the different numbers to get possible set of outcomes ** Class Exercises • Exercises

  13. Sikidy Divination System: Madagascar • Madagascar, an island in the Indian Ocean off the southeastern coast of Africa, is the fourth-largest island in the world. • Madagascar was colonized by France from 1890 to 1960 when the current Republic of Madagascar became independent. • Around 20 different ethnic groups. The main religions are Malagasy mythology and Christianity but there are Islamic minorities as well. • Malayo- Polynesian language, the Malagasy language with traces of Arabic

  14. Sikidy: A Malagasy Divination System Role of diviner: • The ombiasy is a diviner who is expert in sikidy and specializes in guiding people. • He has a long apprenticeship, a formal initiation, knowledge of formal divining practices and an interactive approach in the use of divining material to interpret outcomes. • Questions for consultation include: finding a spouse, finding lost objects, identifying thieves, causes of illness, etc. • As part of the initiation process, the ombiasy gathers between 124 to 200 dried fano seeds for his subsequent use.

  15. Sikidy: A Malagasy Divination System • Underlying mathematical ideas: • Boolean systems: • Symbols represent classes of objects ( 2-valued numerical symbols of 0 &1) • Apply rules, operations, and combinations of operations on the symbols (AND, OR, Exclusive or)

  16. Sikidy: A Malagasy Divination System • In sikidy, we will use these 2 –valued logic symbols and operation: • Exercise: Generate a rule to help you understand the operation.

  17. Sikidy: A Malagasy Divination System • Procedure: • Ombiasy takes seeds from his bag and randomly lumps them into 4 piles. • Each pile is reduced by deleting two seeds at a time until one or two seeds are left in each pile. For ex. If he took 4 piles of 21, 16, 19, 13 then the remaining seeds after counting mod 2 will be 1,2,1,1. • He repeats the process four times until he has 4 columns each to the left of the other with 4 entries listed from top to bottom.

  18. Sikidy: A Malagasy Divination System Procedure: 4. Hence the overall array is made up of four randomly generated columns (c1,c2,c3,c4) of four entries each starting from right to left. 5. This randomly generated set of data is called the mother-sikidy. 6. Taking entries from the rows, moving right to left will generate 4 more columns(c5,c6,c7,c8) 6. Using XOR operation, an additional 8 columns are generated position by positions as follows:

  19. Sikidy: A Malagasy Divination System C9 = C8 C7 C10= C6 C5 C11= C4 C3 C12= C2 C1 C13= C9 C10 C14= C11 C12 C15= C13 C14 C16= C15 C1

  20. Sikidy: A Malagasy Divination System Interpretation: • Each column in the tableau has a referent as follows:

  21. Sikidy: A Malagasy Divination System Interpretation (Cont’d) • 16 outcomes have particular connotations related to spatial positioning(ex. North-East is good; South West lacks in virtue) • The eight possible outcomes that contain an even number of seeds are categorized as princes, the odd ones are slaves. • Each of the 16 columns is conceived by the diviner as associated with a particular place in a square.

  22. Positions associated with the outcomes Power relations: P more powerful than S S(or P) from the land of P are more powerful than S (or P) from the land of S S from the same land are not harmful to each other Battles between Ps from the Land of P are always serious but never end in death Migrators

  23. Positions associated with the outcomes N Sikidy unique: is a tableau that has the four regions represented : east, West, North, South and it holds special interest. E W Migrators : Position of the sun S

  24. Sikidy: A Malagasy Divination System • Summary of procedure: 1. The client asks a question 2. Draws 16 random piles, 4 piles at a time 3. Extracts the tableau 4. Specifies the Princes/Slaves 5. Specifies the directions 6. Interprets the result

  25. Knot and Sikidy divinations • Influenced by ilmal-raml practiced by Arabs during 10th century • Modular arithmetic • Systematic process with a fixed number of known outcomes, generated at least in part, by some random process.

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