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 random data generated from tree seeds, which are ritually arranged in a tableau called a toetry and divinely interpreted after being mathematically operated on. Based on their figurations, columns of seeds are designated "slaves" or "princes" belonging to respective "lands" for each, and interact symbolically to express fate in the interpretation of the diviner.

The centuries-old practice derives from Islamic influence brought to the island by pre-colonial Arab traders. The sikidy is consulted for a range of divinatory questions pertaining to fate and the future, including identifying sources of and rectifying misfortune, reading the fate of newborns, and planning annual migrations.

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

History

An mpisikidy practices sikidy in 1895

The practice is several centuries old, and derives from the influence of Arab Muslim traders on the island. 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.

Origin myths

Mythic tradition relating to the origin of 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 Zanahary (the supreme deity of Malagasy religion) giving it to Ranakandriana, who then gave it to a line of diviners (Ranakandriana to Ramanitralanana to Rabibi-andrano to Andriambavi-maitso), the last of whom, the female diviner Andriambavi-maitso, terminated the monopoly 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".

A mythic anecdote of Ranakandriana says that two men observed him one day playing in the sand. In fact he was practicing a form of sikidy worked in sand called sikidy alanana. The two men seized him, and Ranakandriana promised that he would teach them something if they released him. They agreed, and Ranakandriana taught them in depth how to work the sikidy. The two men then went to their chief and told him that they could tell him "the past and the future—what was good and what was bad—what increased and what diminished." The chief asked them to tell him how he could obtain plenty of cattle. The two men worked their sikidy and told the chief to kill all of his bulls, and that "great numbers would come to him" on the following Friday. The chieftain, doubting, asked what would happen if their prediction didn't come true, and the two men promised they would pay with their lives. The chief agreed and killed his bulls. On Thursday, thinking he'd been duped, he prematurely killed the first man of the two who'd told him about the divinatory art. On Friday, however, "vast herds" came amidst heavy rain, actually filling an immense plain in their crowd. The chieftain lamented the mpisikidy's wrongful execution, and ordered for him a pompous funeral. The chieftain took the second man as his close adviser and friend, and trusted the sikidy forever afterwards. The British missionary William Ellis recorded in 1839 two idiomatic expressions used in Madagascar that come from this story: "Tsy mahandry andro Zoma" (lit. 'He cannot wait 'til Friday') is said of someone extremely impatient, and heavy rainshowers falling in rapid succession are called "sese omby" (lit. 'a crowding together of cattle').

Rites and mpisikidy

Seed pods of Entada chrysostachys

The divination is performed by a practitioner called an mpisikidy, ny màsina (lit. 'sacred one'), 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. As part of an mpisikidy's initiation into the art, which includes a long period of apprenticeship, the initiate must gather 124 and 200 fàno (Entada sp.) or kily (tamarind) tree seeds for his subsequent ritual use in sikidy.

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 fàtidra—for example, if the sikidy predicts the death of two men, then two locusts should be killed and thrown away as the fàtidra.

Incantation

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.

As he incants, the mpisikidy turns the seeds on a mat with his right hand.

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 ($\oplus$), 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 for 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 valid in a 1997 paper by American ethnomathematician Marcia Ascher. Verification through the use of Microsoft Excel was achieved and published by Gomez et al. in 2015.

Divination

The sixteen geomantic figures formed by seeds in sikidy

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".

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 directional square showing the placements for the sixteen geomantic figures of the sikidy across the Land of Slaves (northwestern half) and the Land of Princes (southeastern half), including the two migrators in the center square, whose positions depend on the time of day.

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. The migrators are in the east from sunrise to 10 AM, in the north from 10 AM to 3 PM, and in the west from 3 PM to sunset. Sikidy is never performed at night, and thus the migrators are never in the south.

Divination of the sikidy refer to hierarchies of power relating to position and class of figures. "Princes are more powerful than slaves; figures from the Land of Princes are more powerful than those from the Land of Slaves; slaves from the same land are never harmful to one another; and battles between two princes from the Land of Princes are always serious but never end in death."

In divinations relating to illness, the client and creator columns being the same indicates that there will definitely be recovery; if the client and ancestors columns are the same, the illness is due to some discontent on the part of the ancestors; and if the client and house columns are the same, the illness is the same as one that has previously ended in recovery. The relationship between the client and spirit columns is directly referent to illness. If the client is a slave of the east and the spirit is a prince of the south, the client is dominated by the illness, and thus the illness is divined to be serious—but not fatal, because both the east and the south are in the Land of Princes. If the client is a prince of the north (in the Land of Slaves), and the spirit a prince of the south (in the Land of Princes), there would be a difficult battle with a significant chance of the client dying.

The most exceptionally hopeless and severe outcome in a toetry is each value in the first four columns (and thus in the entire tableau) being two seeds. This is called the "red sikidy".

See also

• I Ching