Sikidy

An mpisikidy practices sikidy in 1900

Sikidy is a form of algebraic geomancy practiced by Malagasy peoples in Madagascar. It involves algorithmic operations performed on data generated randomly from seeds of the fàno (Entada chrysostachys) tree, which are ritually arranged in a tableau called a toetry and interpreted after being mathematically operated on.

The divination is performed by a practitioner called an mpisikidy, ny màsina (lit. 'sacred ones'), ombiasy, or ambiàsa (derived from the Arabic anbia, meaning 'prophet') who guides the client through the process and interprets the results in the context of the client's inquiries and desires. Problems and questions for divined resolution via sikidy include the selection of a day on which to do something (including taking a trip, planting, and exhumation of ancestral corpses), whether a newborn child's destiny is compatible with its parents and thus whether it ought to be cared for by another family, the finding of a spouse, the finding of lost objects, the identification of a thief, and the explanation for a misfortune, including illness or sterility. Among the forest-dwelling Mikea people, sikidy is also used "to direct the timing of residential movements to the forest (mihemotse)". Some mpisikidy are considered specialists, dealing only with areas of inquiry and resolution within their expertise. Mpisikidy also provide guidance on how to avoid the misfortune divined in the subject's fate. The resolution often comes in the form of the ritual disposal of a symbolic object of misfortune, called the fàditra—for example, if the sikidy predicts the death of two men, then two locusts should be killed and thrown away as the fàditra.

History

An mpisikidy practices sikidy in 1895

The origin myth for sikidy "links [the practice] both to the return by walking on water of Arab ancestors who had intermarried with Malagasy but then left, and to the names of the days of the week" and holds that the art was supernaturally communicated to the ancestors, with God giving it to Ranakandriana, who then gave it to a line of diviners, the last of whom terminated the succession by giving it to the people, declaring: "Behold, I give you the sikidy, of which you may inquire what offerings you should present in order to obtain blessings; and what expiation you should make so as to avert evils, when any are ill or under apprehension of some future calamity".

The practice is several centuries old, and derives from the influence of Arab traders. Though the etymology of sikidy is unknown, it has been posited that the word derives from the Arabic sichr ('incantation' or 'charm'). Sikidy was of central importance to pre-Christian Malagasy religion, with one practitioner quoted in 1892 as calling sikidy "the Bible of our ancestors". The early colonial French governor of Madagascar Étienne de Flacourt documented sikidy in the mid-17th century.

Rites

Seed pods of Entada chrysostachys

As part of an mpisikidy's initiation into the art, the initiate must gather 124 and 200 fàno seeds for his subsequent use.

To "awaken" the seeds in his bag as well as his own verbal powers, the mpisikidy incants to the gods or earth spirits in attempt to constrain the gods/spirits to tell the truth, with emphasis on "the trickiness of the communicating entities, who misle[a]d if they [can]", and orates the practice's origin myth. One incantation quoted by Norwegian missionary Lars Dahle reads:

Awake, O God, to awaken the sun! Awake, O sun, to awaken the cock!

Awake, O cock, to awaken mankind! Awake, O mankind, to awaken the sikidy, not to tell lies, not to deceive, not to play tricks, not to talk nonsense, not to agree to everything indiscriminately; but to search into the secret; to look into what is beyond the hills and on the other side of the forest, to see what no human eye can see. Wake up, for thou art from the long-haired Mohammedans from the high mountains, from [Anakandriananahitra, the almost mythical founder of the art in Madagascar, whose name is followed by those authorities who passed the art on to the people and their present diviners, thereby establishing an historical line of legitimacy] ... Awake! for we have not got thee for nothing, for thou art dear and expensive. We have hired. thee. in exchange for a fat cow With a large hump, and for money on which there was no dust [i.e. good value]. Awake! for thou art the trust of the sovereign [the ruling house of pre-colonial Madagascar used court diviners literally dozens of times a day to decide the advisability of even the most everyday actions, from matters of state to the timing of matters of personal hygiene] and the judgement of the people. If thou art a sikidy that can tell, a sikidy that can see, and does not [only] speak about the noise of the people, the hen killed by its owner, the cattle killed in the market, the dust clinging to the feet [i.e. uninteresting commonplaces], awake here on the mat!

But if thou art a sikidy that does not see, a sikidy that agrees to everything indiscriminately, and makes [false statements, as if] the dead [were] living, and the living dead, then do not arise here on the mat.

Arranging the seeds

After his incantation, the mpisikidy takes a fistful of awakened seeds from his bag and randomly divides the seeds into four piles. Seeds are removed two at a time from each pile until there is either one seed or two seeds remaining in each. The four remaining "piles" (now either single seeds or pairs) become the first entries in the first column of a toetry (tableau). The process is repeated three more times, with each new column of seeds being placed on the toetry to the left of the previous. At the end of this, the array consists of four randomly-generated columns of four values (each being either one seed or two) each. The generated data represented in this array is called the renin-sikidy (lit. 'mother-sikidy'). There are 65,536 possible renin-sikidy arrays. From the renin-sikidy data, four additional "columns" are read as the rows across the renin-sikidy's columns, and eight additional columns are generated algorithmically and placed in a specific order below the four original columns.

A diagrammed example of a 16-column toetry with a valid arrangement of seeds

Algorithmically-generated columns

Columns 9-16 of the toetry are generated using the XOR logical operation, which determines a value based on whether two other values are the same or different. In sikidy, the XOR operation is used to compare values in sequence across two existing columns and generate corresponding values in a third column: two seeds if the corresponding values are identical across the pair, and one seed if the values are different. The rules for generating a column from the XOR operation are (with o representing one seed, and oo representing two):

$o\oplus o=oo$

$oo\oplus oo=oo$

$o\oplus oo=o$

$oo\oplus o=o$

The first 12 columns are generated algorithmically from pairs of adjacent columns in the randomly-generated renin-sikidy (the four-by-four grid of seeds representing eight datasets across its four columns and four rows). The last four columns (12-16) of the toetry are derived from the algorithmically-generated columns, with column 16 operating on the first and fifteenth column as a pair.

For example, the first value of column 9 is determined by comparing the first values of columns 7 and 8. If they are the same (both one seed or both two seeds), the first value of column 9 will be two seeds. If they are different, the first value of column 9 will be one seed. This operation iterates for each pair of corresponding values in columns 7 and 8, creating a complete set of values for column 9. Column 10 is then generated by applying the XOR operation between the values in columns 5 and 6. Similarly, column 11 is generated from columns 3 and 4, and column 12 from columns 1 and 2.

Columns 13-16 are generated in the same manner, performing the XOR operation on ascending pairs of the algorithmically-generated columns, starting with columns 9 and 10 (to generate column 13) and ending with columns 15 and 1 (to generate column 16).

Checks

The mpisikidy performs three algorithmic and logical checks to verify the toetry's validity according to its generative logic: one examining the whole toetry, one examining the results of combining some particular columns, and one parity check examining only one column. First, the mpisikidy checks that at least two columns in the toetry are identical. Next, it's ensured that the pairs of columns 13 and 16, 14 and 1, and 11 and 2 (called "the three inseparables") all yield the same result when combined via the XOR operation. Finally, it's checked that there is an even number of seeds in the 15th column—the only column for which parity is logically certain.

Each of these three checks are mathematically proven as valid in a 1997 paper by American ethnomathematician Marcia Ascher.

Divination

Once the mpisikidy has checked the toetry, his analysis and divination can begin. Certain questions and answers rely on additional columns beyond the prepared sixteen. Some of these columns are read spatially in patterns across the existing toetry's data, and some are generated with additional XOR operations referring to pairs of columns within the secondary series. These new columns can involve "about 100 additional algorithms".

There are sixteen possible configurations of sikidy seeds in each column of four values. These formations are known to the diviner and identified with names, which vary regionally. Some names relate to names of months. For many mpisikidy, the formations are associated with directions. The eight formations with an even number of seeds are designated as "princes", while the eight with an odd number of seeds are "slaves". Each slave and prince has its place in a square whose sides are associated with the four cardinal directions. The square is divided into a northwestern "Land of Slaves" and a southeastern "Land of Princes" by a diagonal line extending from its northeastern corner to its southeastern corner. Despite their names, each "Land" contains both slaves and princes, including one migrating prince and one migrating slave that move directionally with the sun, such that the migrators belong to different lands depending on the time of day at which the sikidy is performed. It is never performed at night.

Each column has a distinct divine referent:

1. The client
2. Material goods
3. A male evil-doer (lit. 'the third')
4. The earth
5. The child
6. The bad intentions
7. A woman
8. The enemy (lit. 'the eighth')
9. The spirit (lit. 'the ninth')
10. Nourishment
11. Ancestors
12. The road
13. The diviner
14. The people
15. The creator
16. The house

The arrangement of seeds making up each column is symbolically interpreted.

Mathematics

The mathematics of sikidy include the concepts of Boolean algebra, symbolic logic and parity.