View source for Sikidy

{{Short description|Malagasy algebraic divination by seeds}}
{{Italic title}}
[[File:Sikidy 1900 01.jpg|thumb|upright=1.15|An {{Lang|mg|mpisikidy}} practices ''{{Lang|mg|sikidy}}'' in 1900]]
'''''Sikidy'''''{{Efn|Also ''sikily'' and ''sikiry''.}} is a form of [[Algebra|algebraic]] [[geomancy]] practiced by [[Malagasy peoples]] in [[Madagascar]]. It involves [[Algorithm|algorithmic operations]] performed on [[Randomness|random]] data generated from tree [[Seed|seeds]], which are ritually arranged in a tableau called a {{Lang|mg|toetry}} and [[Divination|divinely]] interpreted after being mathematically operated on. Columns of seeds, designated "slaves" or "princes" belonging to respective "lands" for each, interact symbolically to express {{Lang|mg|vintana}} ('fate') in the interpretation of the diviner. The diviner also prescribes solutions to problems and ways to avoid fated misfortune, often involving a sacrifice.<ref name=":0" /> 

The centuries-old practice derives from Islamic influence brought to the island by [[Islam in Madagascar#Historical background|medieval Arab traders]]. The {{Lang|mg|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 {{Lang|mg|sikidy}} include the concepts of [[Boolean algebra]], [[symbolic logic]] and [[Parity (mathematics)|parity]].

== History ==
[[File:Sikidy 1895.jpg|left|thumb|upright=1.15|An {{Lang|mg|mpisikidy}} practices ''{{Lang|mg|sikidy}}'' in 1895]]
The practice is several centuries old, and is influenced by [[Arabic geomancy|Arab geomantic]] traditions of Arab Muslim traders on the island.<ref name=":0">{{Cite journal |last=Ascher |first=Marcia |author-link=Marcia Ascher |date=1997 |title=Malagasy Sikidy: A Case in Ethnomathematics |url=https://www.academia.edu/38151275 |journal=Historia Mathematica |volume=24 |issue=4 |pages=376–395 |doi=10.1006/hmat.1997.2159 |issn=0315-0860}}</ref><ref name=":1">{{Cite book |last=Skinner |first=Stephen |author-link=Stephen Skinner (author) |url=https://www.rybn.org/ANTI/ADMXI/documentation/ALGORITHM_DOCUMENTATION/GPS-MANTIC/GEOMANCY/PAPERS/1980_Stephen_Skinner_-_Terrestrial_Astrology_Divination_Geomancy.pdf |title=Terrestrial astrology: Divination by geomancy |date=1980 |publisher=Routledge & Kegan Paul |isbn=978-0-7100-0553-3 |edition=1st |location=London; Boston }}</ref> [[Stephen Ellis (historian)|Stephen Ellis]] and Solofo Randrianja describe {{Lang|mg|sikidy}} as "probably one of the oldest components of Malagasy culture", writing that it most likely the product of an indigenous divinatory art later influenced by Islamic practice.<ref>{{Cite book |last1=Randrianja |first1=Solofo |url=https://www.worldcat.org/title/243845225 |title=Madagascar: a short history |last2=Ellis |first2=Stephen |date=2009 |publisher=University of Chicago Press |isbn=978-0-226-70418-0 |location=Chicago |oclc=243845225}}</ref> Umar H. D. Danfulani writes that the integration of Arabic divination into indigenous divination is "clearly demonstrated" in Madagascar, where the Arabic astrological system was adapted to the indigenous agricultural system and meshed with Malagasy lunar months by "adapting indigenous months, {{Lang|mg|volana}}, to the astrological months, {{Lang|mg|vintana}}".<ref name=":6">{{Cite journal |last=Danfulani |first=Umar H. D. |date=1997 |title=Sixteen Figure Divination in Africa: Its Regional Spread and Relationship with Arab-Islamic Geomancy |journal=Africana Marburgensia |volume=30 |issue=1 |pages=24–45}}</ref> Danfulani also describes the concepts in {{Lang|mg|sikidy}} of "houses" (lands) and "kings in their houses" as retained from medieval Arabic astrology.<ref name=":6" />

Most writers link the practice to the "sea-going trade involving the southwest coast of [[India]], the [[Persian Gulf]], and the east coast of Africa in the 9th or 10th century C.E."<ref name=":0" /> Though the etymology of {{Lang|mg|sikidy}} is unknown, it has been posited that the word derives from the Arabic ''sichr'' ('incantation' or 'charm'). {{Lang|mg|Sikidy}} was of central importance to pre-Christian Malagasy religion, with one practitioner quoted in 1892 as calling {{Lang|mg|sikidy}} "the [[Bible]] of our ancestors".<ref name=":1" /> A missionary report from 1616 describes one form of {{Lang|mg|sikidy}} using tamarind seeds,<ref name=":2" /> and another using fingered markings in the sand.<ref name=":0" /> The early colonial French governor of Madagascar [[Étienne de Flacourt]] documented {{Lang|mg|sikidy}} in the mid-17th century:<ref name=":1" />

{{Blockquote|text=[[Matitanana|Matatane]] country in southeastern Madagascar [...] where the [[Antemoro]] [...] live was a center of astrological study as early as the fourteenth century [...]. This area was also the site of early Arab settlements, although strict Islamic observances were lost centuries ago [...]. Historical evidence shows that Antemoro diviners, bearers of the astrological system, infiltrated nearly all the ancient kingdoms of Madagascar beginning in the sixteenth century. [...] Today, although many persons claim to be {{lang|mg|ombiasy}} [diviners], only the Antemoro diviners are considered true professionals. The area is still a famous place of learning where specialists go for training and then return to their home communities with a certain body of knowledge. Now we can better understand the degree of similarity of divination forms found throughout Madagascar. For centuries Matitanana has remained a training center for diviners who have migrated widely, usually attaining important positions in their home communities and with various royal families.|author=[[Étienne de Flacourt]]|title=''l'Histoire de la Grande Isle Madagascar''}}

The "infiltration" of Malagasy kingdoms by Antemoro diviners, and Matitanana's role as a place for astrological and divinatory learning, help to explain the relatively uniform practicing of {{Lang|mg|sikidy}} across Madagascar.<ref name=":6" />

=== Origin myths ===
[[File:Arab geomantic figures classification.jpg|thumb|15th century Arabic classification of the geomantic figures]]Mythic tradition relating to the origin of {{Lang|mg|sikidy}} "links [the practice] both to the return by walking on water of [[Arabs|Arab]] ancestors who had intermarried with [[Malagasy peoples|Malagasy]] but then left, and to the names of the days of the week"<ref name=":0" /> and holds that the art was supernaturally communicated to the ancestors, with [[Zanahary]] (the supreme deity of [[Malagasy mythology|Malagasy religion]]) giving it to Ranakandriana, who then gave it to a line of diviners (Ranakandriana to Ramanitralanana to Rabibi-andrano to Andriambavi-maitso (who was a woman) to Andriam-bavi-nosy), the last of whom terminated the monopoly by giving it to the people, declaring: "Behold, I give you the {{Lang|mg|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".<ref name=":1" /><ref name=":3">{{Cite book |last=Ellis |first=William  |author-link=William Ellis (British missionary) |url=https://books.google.com/books?id=bkpjAAAAcAAJ |title=History of Madagascar |date=1839 |publisher=Fisher |language=en}}</ref>

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 {{Lang|mg|sikidy}} worked in sand called {{Lang|mg|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 {{Lang|mg|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 {{Lang|mg|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 {{Lang|mg|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 {{Lang|mg|sikidy}} forever afterwards.<ref name=":3" /> The British [[Christianity in Madagascar#Background|missionary]] [[William Ellis (British missionary)|William Ellis]] recorded in 1839 two [[Idiom|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}}).<ref name=":3"/>

== Rites and practitioners ==
[[File:Entada chrysostachys Drake.tif|thumb|Seed pods of ''Entada chrysostachys'']]The [[divination]] is performed by a practitioner called an {{Lang|mg|mpisikidy}}, {{Lang|mg|ny màsina}} ({{Lit|sacred one}}),{{Efn|Identified by Lars Dahle as a common name for the {{lang|mg|mpisikidy}} among the [[Betsileo]] and [[Merina]] peoples.|name=Sibree 1892}} {{Lang|mg|ombiasy}}, or {{Lang|mg|ambiàsa}} (derived from the Arabic ''anbia'', meaning 'prophet')<ref name=":1" /> who guides the client through the process and interprets the results in the context of the client's inquiries and desires.<ref name=":4">{{Cite book |last=Ascher |first=Marcia |author-link=Marcia Ascher |url=https://www.jstor.org/stable/j.ctv39x5q7 |title=Mathematics Elsewhere: An Exploration of Ideas Across Cultures |date=2002 |publisher=Princeton University Press|doi=10.2307/j.ctv39x5q7 |jstor=j.ctv39x5q7 }}</ref><ref name=":0" /> As part of an {{Lang|mg|mpisikidy}}'s formal initiation into the art, which includes a long period of apprenticeship, the initiate must gather 124 and 200 {{Lang|mg|fàno}} (''[[Entada]] sp.'') or {{Lang|mg|kily}} ([[tamarind]]) tree seeds for his subsequent ritual use in {{Lang|mg|sikidy}}.<ref>{{Cite book |last=Boiteau |first=Pierre |title=Dictionnaire des noms malgaches de végétaux |date=1999 |isbn=978-2-910717-41-4 |edition=Editions Alzieu |location= |pages=196 |publisher=Alzieu |language=fr}}</ref> 

{{Ill|Raymond Decary|fr}} writes that, at least among the [[Sakalava people|Sakalava]], a man must be 40 years old before learning and practicing {{Lang|mg|sikidy}}, or he risks death. Before beginning to study, a student practitioner must make incisions at the tips of his index finger, his middle finger, and his tongue, and put within the incisions a paste containing [[Chili sauce and paste|red pepper]] and crushed [[wasp]]. This paste impregnates the fingers that will move the seeds of the {{Lang|mg|sikidy}} and the tongue that will speak their revelations with the power to decipher the {{Lang|mg|sikidy}}. Once this is done, he leaves at dawn to search for a {{Lang|mg|fano}} (''Entada chrysostachys'') tree. Upon finding it, he throws his [[spear]] at its branches, shaking the tree and causing its large seed pods to fall. During this act, some {{Lang|mg|mpisikidy}} say: "When you were on the steep peak and in the dense forest, on you the crabs climbed, from you the crocodiles made their bed, with their paws the birds trod on you. Whether you are suspended in the trees or buried, you are never dried up nor rotten." In 1970, Decary reported that the salary paid by an apprentice to his master is "not very high": up to five [[Malagasy franc|francs]], plus a red [[rooster]]'s [[feather]].<ref name=":2" />

Some {{Lang|mg|mpisikidy}} are considered specialists, dealing only with areas of inquiry and resolution within their expertise.<ref name=":0" /> In the process of divination, the {{Lang|mg|mpisikidy}} relates interactively to the client, asking new questions and discussing the interpretation of the seeds.<ref name=":4" /> [[Alfred Grandidier]] estimated in the late 19th century that roughly one in three Malagasy people had a firm grasp on the art; by 1970 Raymond Decary wrote that the number of {{Lang|mg|mpisikidy}} was now more limited, and the common knowledge of how to operate and read the {{Lang|mg|sikidy}} was now more basic, with masters of {{Lang|mg|sikidy}} becoming more rare.<ref name=":2" />

=== {{Lang|mg|Faditra}} and {{Lang|mg|sōrona}} ===
[[File:Ceremony of the fati-drà, Madagascar.webp|thumb|upright=1.15|1913 painting by Henri Ratovo depicting the ceremony of the {{Lang|mg|fati-drà}} ({{Lang|mg|faditra}})]]
{{Lang|mg|Mpisikidy}} also provide guidance on how to avoid the misfortune divined in the subject's fate. Solutions include offerings, sacrifices, charms (called {{Lang|mg|[[sampy|ody]]}}), stored remedies, or observed {{Lang|mg|[[fady (taboo)|fady]]}} (taboos).<ref name=":5">{{Cite book |url= |title=African Divination Systems: Ways of Knowing |date=1991 |publisher=Indiana University Press |isbn=978-0-253-20653-4 |editor-last=Peek |editor-first=Philip M. |edition=First |language=en}}</ref> The resolution often comes in the form of the ritual disposal of a symbolic object of misfortune, called the {{Lang|mg|faditra}}:{{Efn|also {{lang|mg|fàtidra}}}} for example, if the {{Lang|mg|sikidy}} predicts the death of two men, then two [[Locust|locusts]] should be killed and thrown away as the {{Lang|mg|faditra}}.<ref>{{Cite journal |last=Sibree |first=James |author-link=James Sibree |date=June 1862 |title=Divination among the Malagasy, Together with Native Ideas as to Fate and Destiny |url=http://www.tandfonline.com/doi/abs/10.1080/0015587X.1892.9720105 |journal=Folklore |language=en |volume=3 |issue=2 |pages=193–226 |doi=10.1080/0015587X.1892.9720105 |issn=0015-587X}}</ref> William Ellis compares this practice to the ancient Jewish [[scapegoat]].<ref name=":3" /> Other {{Lang|mg|faditra}} objects can be trivial, such as "a little grass", some earth, or the water with which the patient rinses his mouth. If the {{Lang|mg|faditra}} is ashes, they are blown from the hand to be carried off by the wind; if it is cut money, it is thrown to the bottom of deep waters; if a [[sheep]], it is "carried away to a distance on the shoulders of a man, who runs with all his might, mumbling as he goes, as if in the greatest rage against the {{Lang|mg|faditra}}, for the evils it is bearing away." If it is a [[pumpkin]], it is carried away a short distance and then thrown on the ground with fury and indignation.<ref name=":3" /> The disposal of a {{Lang|mg|faditra}} may be as simple as a man standing at his doorway, throwing the object a few feet away, and saying the word "{{Lang|mg|faditra}}".<ref name=":3" /> Ellis reports the following {{Lang|mg|faditra}} for various sources and manifestations of evil:<ref name=":3" />
{| class="wikitable"
|+
!Evil's origin
!{{Lang|mg|Faditra}}
|-
|Heaven
|An herb called {{Lang|mg|tsikobon-danitra}} (''[[Portulaca oleracea]]'')
|-
|The earth
|A water-flower
|-
|Cattle
|A grasshopper called {{Lang|mg|tsiavaramonina}}
|-
|Sheep
|A small fish called {{Lang|mg|ondrindrano}}, {{Lit|water-sheep}}
|-
|Money
|A grasshopper called {{Lang|mg|tsimbolavola}}
|-
|The mouth; speaking
|The mouth or brim of a small basket
|-
|The north
|A tree called {{Lang|mg|tsiavaramonina}}, {{Lit|not residing northward}}
|-
|The south
|An herb called {{Lang|mg|antsiontsiona}}
|-
|The west
|A [[Cyperaceae|rush]] called {{Lang|mg|harefo}}
|-
|The east
|An herb called {{Lang|mg|anantsinahy}}
|-
|Fire
|A red flower called {{Lang|mg|songo songo}} (''[[Euphorbia splendens]]'')
|-
|{{Lang|mg|Tsingy}} (the reproach or blame of parents or friends)
|A broken fragment of the {{Lang|mg|sing}} (water vessel)
|}
{| class="wikitable"
!Foretold danger or misfortune
!{{Lang|mg|Faditra}}
|-
|Sickness
|A piece of a tree that has been injured by accident, cutting, or maiming ({{Lang|mg|hazomarary}}, {{Lit|sick-tree}})
|-
|Death
|An object without life; or a piece of a stone, especially granite, in incipient degradation ({{Lang|mg|vato maty}}, {{Lit|dead-stone}})
|-
|Partial danger of witchcraft (some person's partial inclination to bewitch the offerer)
|The kernel or gland in a bullock's fat, called the {{Lang|mg|mosavin-kena}}, {{Lit|bewitching meat}}
|-
|Danger from persons collecting together (foretells burial)
|A grass called {{Lang|mg|ahidratsy}} or {{Lang|mg|atobahoaka}}, together with some earth, thrown away from a point measured eight to ten feet away
|}
A divine offering, called a {{Lang|mg|sōrona}}, is also prescribed by the {{Lang|mg|mpisikidy}}. The {{Lang|mg|sōrona}} may consist of a combination of beads, silver chains, ornaments, meats, herbs, and the singing of a child. Other {{Lang|mg|sōrona}} objects include "a young bullock which just begins to bellow and to tear up the earth with his horns", fowl, rice mixed with milk and honey, a [[Cooking banana|plantain]] tree flush with fruit, "slime from frogs floating on the water", and a groundnut called {{Lang|mg|voanjo}}. {{Lang|mg|Sōrona}} amulets and bracelets may continue to be worn after the cause of their prescription, effectively becoming {{Lang|mg|ody}}.<ref name=":3" />

Recovery without adherence to divined prescription and {{Lang|mg|faditra}} is believed "almost impossible". William Ellis recorded in 1838 that, though the application of indigenous remedies was most common, some patients had lately been instructed as part of the {{Lang|mg|sikidy}} resolution to ask the local foreign missionaries for medicine.<ref name=":3" />

=== Occasions and questions for {{Lang|mg|sikidy}} ===
[[File:Un mpisikidy.jpg|thumb|An {{Lang|mg|mpisikidy}} c. 1900–1905]]
Problems and questions for divined resolution via {{Lang|mg|sikidy}} include the selection of a day on which to do something (including taking a trip, planting, a wedding,<ref name=":3" /> and [[Famadihana|the exhumation of ancestral corpses]]), whether a newborn child's destiny is compatible with its parents and thus whether it ought to be [[Adoption|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 (physiology)|sterility]].<ref name=":0" />

Raymond Decary writes that the {{Lang|mg|sikidy}} is consulted "in all circumstances", but especially:

# In cases of illness, which are understood to be either punishments or warnings from supernatural powers due to the transgression of a {{Lang|mg|fady}} (taboo), or poisonings or curses (called {{Lang|mg|tolaka}}) from other humans.
# Before undertaking a journey, in order to divine an auspicious day for travel.
# To acquire wealth or foresee the growth of herds (gold prospecting and panning must take place on a day selected by the {{Lang|mg|sikidy}}).
# For all questions relating to women, including whether a potential bride has a fate aligned with her suitor's.
# In order to cast a bad spell on someone.
# To search for or track down thieves.<ref name=":2" />

The kind and color of sheep to be sacrificed in a wedding procession is also divined by {{Lang|mg|sikidy}}.<ref name=":3" /> Among the forest-dwelling [[Mikea people|Mikea]] people, {{Lang|mg|sikidy}} is used "to direct the timing of residential movements to the forest ({{Lang|mg|mihemotse}})".<ref>{{cite book |title=The Cambridge Encyclopedia of Hunters and Gatherers |chapter=I.IV.8 The Mikea of Madagascar |last=Rabedimy |first=Jean-François |editor-first=Richard B. |editor-last=Lee |editor1-link=Richard Borshay Lee |editor2-first=Richard Heywood |editor2-last=Daly |date=2006 |orig-date=1999 }} Cited from ''[https://search.credoreference.com/articles/Qm9va0FydGljbGU6OTAxNjYy?aid=237298 Credo Reference]'' version.</ref>

William Ellis describes two ritual occasions for {{Lang|mg|sikidy}} relating to infants: the declaring of the child's destiny, and the "scrambling" ceremony.<ref name=":3" />

As one of the "first acts" following a child's birth, the child's father or close relative consults the local {{Lang|mg|mpisikidy}}, who works the {{Lang|mg|sikidy}} in order to read the child's destiny. When a child's destiny is declared to be favorable, "the child is nurtured with that tenderness and affection which nature inspires, and the warmest gratulations are tendered by the friends of the parents."<ref name=":3" /> 

The "scrambling" ceremony, which only occurs with firstborn infants, takes place two or three months after the child's birth on a day divined by the {{Lang|mg|sikidy}} to be lucky or good. The child's friends and family gather, and the child's mother is decorated with silver chains on her head. If the infant is a boy, the father carries him, along with some ripe bananas, on his back. In a rice pan, a mixture is cooked, consisting of the fat from a [[zebu]] ox's hump, rice, milk, honey, and a grass called {{Lang|mg|voampamoa}}. One lock, called the {{Lang|mg|sonia ratsy}} ('evil lock') is cut from the left side of the child's head and thrown away, "in order to avert calamity". A second lock, called the {{Lang|mg|sonia soa}} ('the fortunate lock'), is cut from the right side, and added to the mixture in the rice pan. The mélange is mixed well and held up in its pan by the youngest girl of the family, at which point the gathered (especially the women) make a rush for its contents. It is believed that those who obtain a portion of the mixture are bound to become mothers. The scramble also takes place with bananas, lemons, and sugarcane. The rice pan is then considered sacred, and cannot be removed from the house for three days, "otherwise the virtue of those observances is supposed to be lost".<ref name=":3" />

=== Incantation ===
[[File:Mpisikidy tandroy.jpg|thumb|[[Antandroy]] diviners]]
To "awaken" the seeds in his bag as well as his own verbal powers, the {{Lang|mg|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.<ref name=":0" /> As he incants, the {{Lang|mg|mpisikidy}} turns the seeds on a mat eastward<ref name=":2" /> with his right hand.<ref name=":1" /> One [[Merina people|Merina]] incantation<ref name=":2" /> quoted by Norwegian [[Christianity in Madagascar|missionary]] Lars Dahle reads:<ref name=":1" />

{{Blockquote|text=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.}}When practicing the {{Lang|mg|sikidy}}, Sakalava diviners work with a fragment of [[hyaline]] [[quartz]] in front of their seeds, which is set out before the seeds are produced from their sack.<ref name=":2" />

== Arranging the seeds ==
After his incantation, the {{Lang|mg|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 {{Lang|mg|toetry}} (tableau). The process is repeated three more times, with each new column of seeds being placed on the {{Lang|mg|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 {{Lang|mg|renin-sikidy}} ({{Lit|mother-{{lang|mg|sikidy}}}}). There are 65,536 possible {{Lang|mg|renin-sikidy}} arrays.{{Efn|1=2<sup>16</sup>=65,536}} From the {{Lang|mg|renin-sikidy}} data, four additional "columns" are read as the rows across the {{Lang|mg|renin-sikidy}}'s columns, and eight additional columns are generated algorithmically and placed in a specific order below the four original columns.<ref name=":0" />
[[File:Sikidy example diagram.png|thumb|upright=2.25|A diagrammed example of a 16-column {{Lang|mg|toetry}} with a valid arrangement of seeds|center]]
=== Algorithmically-generated columns ===
Columns 9–16 of the {{lang|mg|toetry}} are generated using the [[XOR gate|XOR logical operation]] (<math>\oplus</math>), which determines a value based on whether two other values are the same or different. In {{lang|mg|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):<ref name=":0" /> 

<math display="block"> \begin{align}
 o \oplus o &= oo \\ 
 oo \oplus oo &= oo \\
 o \oplus oo &= o \\
 oo \oplus o &= o
\end{align} </math> 

The first 12 columns are generated algorithmically from pairs of adjacent columns in the randomly-generated {{Lang|mg|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 {{lang|mg|toetry}} are derived from the algorithmically-generated columns, with column 16 operating on the first and fifteenth column as a pair.<ref name=":0" />

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.<ref name=":0" /><ref name=":1" />

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).<ref name=":0" />

=== Checks ===
{{see also|Error detection and correction}}
The {{Lang|mg|mpisikidy}} performs three algorithmic and logical checks to verify the {{Lang|mg|toetry}}'s validity according to its generative logic: one examining the whole {{lang|mg|toetry}}, one examining the results of combining some particular columns, and one [[parity check]] examining only one column.<ref name=":0" /> First, the {{Lang|mg|mpisikidy}} checks that at least two columns in the {{Lang|mg|toetry}} are identical. Next, it is ensured that the pairs of columns 13 and 16, 14 and 1, and 11 and 2 (called "the three inseparables"{{Efn|The pairs of columns 2 and 16, 11 and 13, and 12 and 15 are also called "three inseparables".}}) all yield the same result when combined via the XOR operation. Finally, it is checked that there is an even number of seeds in the 15th column—the only column for which parity is logically certain.<ref name=":0" />

Each of these three checks are mathematically proven valid in a 1997 paper by American [[Ethnomathematics|ethnomathematician]] [[Marcia Ascher]].<ref name=":0" /> Verification through the use of [[Microsoft Excel]] was achieved and published by Gomez et al. in 2015.<ref>{{Cite journal |last1=Gomez |first1=Cristina |last2=Oppenheim |first2=H. |last3=Yúrekli |first3=O. |date=March 27, 2015 |title=Divination: Using Excel to explore ethnomathematics |url=https://sie.scholasticahq.com/article/4636-divination-using-excel-to-explore-ethnomathematics.pdf |journal=Spreadsheets in Education}}</ref>

== Divination ==
Once the {{Lang|mg|mpisikidy}} has checked the {{Lang|mg|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 {{Lang|mg|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".<ref name=":0" />

[[File:Sikidy Lands.png|thumb|upright=1.8|center|The directional square showing the placements for the sixteen geomantic figures of the {{Lang|mg|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.]]

Each column making up the {{Lang|mg|toetry}} has a distinct divine referent:<ref name=":0" /><ref>{{Cite book |last=Jaovelo-Dzao |first=Robert |url= |title=Mythes, rites et transes à Madagascar - Angano, Joro et Tromba, Sakalava |date=1996 |publisher=Karthala |isbn=978-2-86537-666-7 |edition= |location=Antananarivo; Paris |pages=273–292 |language=French |trans-title=Myths, Rites, and Trances in Madagascar |chapter=Le divin, le guérisseur, et le sorcier |trans-chapter=The diviner, the healer, and the sorcerer}}</ref>
{| class="wikitable"
|+Columns of the {{Lang|mg|toetry}} and their symbolic meanings
!Column number
!Malagasy name
!Symbolic meaning
!Notes
|-
|1
|{{Lang|mg|Tale}}
|The client or patient
|From [[Arabic]] طلع {{Transliteration|ar|bgn/pcgn|talah}}, meaning 'to rise'.
|-
|2
|{{Lang|mg|Mady}} or {{Lang|mg|Maly}}
|Material goods; riches; [[zebu]]
|From Arabic المال {{Transliteration|ar|bgn/pcgn|al-mal}}, meaning 'goodness', 'richness', 'property'.
|-
|3
|{{Lang|mg|Fahatelo}}
|A male evil-doer ({{Lit|the third}})
|
|-
|4
|{{Lang|mg|Bilady}}
|The domicile; the country; the Earth
|From Arabic بلد {{Transliteration|ar|bgn/pcgn|bilad}}, meaning 'country' or 'land'.
|-
|5
|{{Lang|mg|Fianahana}}
|The fifth child; descendants; children; youth
|
|-
|6
|{{Lang|mg|Abidy}} or {{Lang|mg|Abily}}
|Slaves
|From Arabic عبد {{Transliteration|ar|bgn/pcgn|abid}}, meaning 'slaves'.
|-
|7
|{{Lang|mg|Betsimisay}}, {{Lang|mg|Betsilisay}}, or {{Lang|mg|Alisay}}
|The wife of the house
|From Arabic بيت {{Transliteration|ar|bgn/pcgn|beit}}, meaning 'house', and النساء {{Transliteration|ar|bgn/pcgn|al-nisaa}}, meaning 'wife'.
|-
|8
|{{Lang|mg|Fahavalo}}
|The sorcerer; illness; the enemy ({{Lit|the eighth}})
|
|-
|9
|{{Lang|mg|Fahasivy}}
|The spirits ({{Lit|the ninth}})
|
|-
|10
|{{Lang|mg|Omasina}} or {{Lang|mg|Ombiasa}}
|Nourishment; the healing diviner
|From Arabic محسن {{Transliteration|ar|bgn/pcgn|mihsan}} or {{Transliteration|ar|bgn/pcgn|mihsin}}, meaning 'the beneficient' and 'the generous'
|-
|11
|{{Lang|mg|Haja}}
|Everything that can be eaten
|
|-
|12
|{{Lang|mg|Haky}}
|The Creator
|
|-
|13
|{{Lang|mg|Sorotany}} or {{Lang|mg|Solotany}}
|The chiefs and elders
|
|-
|14
|{{Lang|mg|Saily}} or {{Lang|mg|Saly}}
|The road
|
|-
|15
|{{Lang|mg|Safary}} or {{Lang|mg|Lalana}}
|The road
|
|-
|16
|{{Lang|mg|Akiba}}
|The house or its inhabitants
|
|}
There are sixteen possible configurations of {{Lang|mg|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 {{Lang|mg|mpisikidy}}, the formations are associated with directions.{{Efn|This relates to Malagasy cultural connotations ascribing values to different directions: the northeast is good, the southwest lacks virtue, and the directions between "vary in religious and moral value". These same associations also prescribe house and tomb orientations, as well as the positioning and orientation of visitors based on social status (with the most important standing to the northeast and the least important to the southwest).}}<ref name=":0" /> 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 direction|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 {{Lang|mg|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. {{Lang|mg|Sikidy}} is never performed at night, and thus the migrators are never in the south.<ref name=":0" />{{Efn|Some diviners associate migrators with the west regardless of time.}}

The power to see into the past or future is greater in {{Lang|mg|toetry}} in which all four directions are represented, and most powerful in {{Lang|mg|toetry}} with four directions represented but with one direction having only one representative. These {{Lang|mg|toetry}} are called {{Lang|mg|tokan-sikidy}} ('{{Lang|mg|sikidy}}-unique'). Beyond being powerful arrangements for divination, {{Lang|mg|tokan-sikidy}} represent a particular abstract interest to {{Lang|mg|mpisikidy}}, who seek to understand them and the data which generate them as an unsolved intellectual challenge. Knowing many {{Lang|mg|tokan-sikidy}} leads to personal prestige for the {{Lang|mg|mpisikidy}}, with discovered examples being posted on doors and spread among diviners by word of mouth.<ref name=":0" />

Divination of the {{Lang|mg|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."<ref name=":0" />

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.<ref name=":0" /> 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.<ref name=":0" />

If the ninth and fifteenth columns are the same, a bead must be offered as a {{Lang|mg|sōrona}}, called {{Lang|mg|vakantsileondoza}} ({{Lit|overcoming the calamity}}). If the first and fourth are the same, then a piece of a tree that grows in the villages (not in the fields) must be offered.<ref name=":3" /> If the values of the tenth and fifteenth columns added together and subtracted by two equal the values of the first, a stone (called {{Lang|mg|vato-tsi-very}}, {{Lit|stone-not-lost}}) is thrown, retrieved, and carefully preserved by a friend or relation, and so not lost.<ref name=":3" />

The most exceptionally hopeless and severe outcome in a {{Lang|mg|toetry}} is each value in the first four columns (and thus in the entire tableau) being two seeds. This is called the "red {{Lang|mg|sikidy}}".<ref name=":0" />

A study [[Computer simulation|computer-simulating]] the algorithmic generation and objective initial interpretation (according to [[Sakalava people|Sakalava]] tradition) of the 65,536 possible arrangements of {{Lang|mg|sikidy}} found that, assuming a male client and an inquiry about an illness' cause, the divined cause of illness would be sorcery 21.1% of the time, witchcraft 16.5% of the time, {{Lang|mg|haky}}{{Efn|A term which "covers such ideas as spirit possession, god, feature of nature, and surprise." Gardenier observes that "if there is any reason to let it stand for spirit possession, the other possibilities are ignored".}} for 9.6%, the village chief for 2.6%, the contamination of food with dirt (which may involve carelessness or evil intentions) for .8%, ancestors for .7%, and undetermined for 48.7%.<ref>{{Cite book |last=Gardenier |first=William J. G. |title=Madagascar: society and history |date=1986 |publisher=Carolina Academic Press |isbn=978-0-89089-252-7 |editor-last=Kottak |editor-first=Conrad Phillip |location=Durham, N.C |pages=337–351 |language=en, fr|chapter=Divination and Kinship Among the Sakalava of West Madagascar |editor-last2=Wenner-Gren Foundation for Anthropological Research}}</ref><ref name=":0" />

=== Figures ===
[[File:Sikidy malagasy.jpg|thumb|The sixteen geomantic figures of the {{Lang|mg|sikidy}}, arranged from seeds of the {{Lang|mg|fàno}} (''Entada africana'') tree]]
The following are the most common names and meanings for the sixteen geomantic figures of the {{Lang|mg|sikidy}}.<ref name=":5" /> Names that also refer to lunar months are marked with a '☾'.
{| class=wikitable
!Figure
!Malagasy name
!Meaning
|-
|[[File:Geomantic via.svg|frameless|24x24px]]
|{{Lang|mg|Taraiky}}
|Emaciation; path, road
|-
|[[File:Geomantic caudadraconis.svg|frameless|24x24px]]
|{{Lang|mg|Karija}}
|Slave; cool speech
|-
|[[File:Geomantic caputdraconis.svg|frameless|24x24px]]
|{{Lang|mg|Alakaosy}} ☾
|Child; evil thoughts
|-
|[[File:Geomantic fortunamajor.svg|frameless|24x24px]]
|{{Lang|mg|Adabara}}
|[[Zanahary]]; most sacred
|-
|[[File:Geomantic puer.svg|frameless|24x24px]]
|{{Lang|mg|Alikasajy}}
|Charm; mourning
|-
|[[File:Geomantic laetitia.svg|frameless|24x24px]]
|{{Lang|mg|Alahijana}}
|Woman; death
|-
|[[File:Geomantic tristitia.svg|frameless|24x24px]]
|{{Lang|mg|Alikisy}}
|Earth; auspicious
|-
|[[File:Geomantic populus.svg|frameless|24x24px]]
|{{Lang|mg|Asombola}} ☾
|Abundance
|-
|[[File:Geomantic acquisitio.svg|frameless|24x24px]]
|{{Lang|mg|Alohotsy}} ☾
|Money; unhappiness, misfortune
|-
|[[File:Geomantic amissio.svg|frameless|24x24px]]
|{{Lang|mg|Adalo}} ☾
|Chief or child; tears
|-
|[[File:Geomantic conjunctio.svg|frameless|24x24px]]
|{{Lang|mg|Alatsimay}}
|Slave; evil thoughts
|-
|[[File:Geomantic carcer.svg|frameless|24x24px]]
|{{Lang|mg|Alokola}}
|House; food
|-
|[[File:Geomantic albus.svg|frameless|24x24px]]
|{{Lang|mg|Alabiavo}}
|Water spirit; joy
|-
|[[File:Geomantic rubeus.svg|frameless|24x24px]]
|{{Lang|mg|Alahamora}}
|Diviner; crowd, mob; grief, trouble
|-
|[[File:Geomantic fortunaminor.svg|frameless|24x24px]]
|{{Lang|mg|Alahasady}} ☾
|Food; anger, wrath
|-
|[[File:Geomantic puella.svg|frameless|24x24px]]
|{{Lang|mg|Alakarabo}} ☾
|Robbers, rogues; unhappiness, misfortune
|}

== Related traditions ==
Other Malagasy methods of divination include [[astrology]], [[cartomancy]], [[ornithomancy]], [[extispicy]], and [[Necromancy|necromantic]] [[Dream interpretation|dream-interpretation]].<ref name=":2">{{Cite book |last=Decary |first=Raymond |url=https://gallica.bnf.fr/ark:/12148/bpt6k3344625j |title=La divination malgache par le Sikidy |date=1970 |publisher=P. Geuthner |location=Paris |language=FR |trans-title=Malagasy divination by the Sikidy}}</ref>

=== African sixteen-figure divinatory traditions ===
Aside from Arabic geomancy, a number of [[African divination]] methods using sixteen basic figures have been studied, including Yoruba ''[[Ifá]]'' [[cowrie]]-[[Seashell|shell]] divination, also known by its [[Fon language|Fon]] name ''Fa'' and the [[Ewe language|Ewe]] and [[Igbo language|Igbo]] name ''Afa''. African diasporic populations in Latin America have retained the practice, with the tradition being called ''Ifa'' among [[Afro-Cubans]], [[Afro-Brazilians]], and [[Afro-Haitians]]. Umar H. D. Danfulani records a breadth of sixteen-figure divinatory traditions across Africa:<ref name=":6" />

* ''Ifá'' – from [[Yoruba people|Yoruba]] culture
* ''Fa'' – from [[Fon people|Fon]] culture; same tradition as ''Ifá''
* ''Afa'' – from [[Igbo people|Igbo]] and [[Ewe people|Ewe]] cultures; same tradition as ''Ifá''
* ''Pa''; ''Pe'' – from [[Chadic languages|Chadic]] speakers of the [[Jos Plateau]]
* ''Noko'' – from [[Jukun people (West Africa)|Jukun]] and [[Kuteb people|Kuteb]] cultures
* ''Eba'' – from [[Ekoi people|Ekoi]] culture
* ''Agbigba'' – from [[Igbira]] and [[Okun people|Okun]] cultures
* ''Efa'' – from [[Ekoi people|Ekoi]] culture
* ''Eva'' – from [[Isoko people|Isoko]] culture
* ''Ominigbon''; ''Ogwega''; ''Iha Ogwega'' – from [[Bini people|Bini]] (Edo) culture
* ''Hakata'' – "from [[Zaire]] and [[Angola]] to [[South Africa]]"; "bone casting/throwing"; originating from the court circles of [[Mwene Mutapa]] (present-day [[Zimbabwe]]) and "in the southern [[Congo River Basin|Congo river-basin]] empires"
* ''{{Lang|mg|Sikidy}}'' – from Malagasy culture

== See also ==
{{portal|Madagascar}}
* ''[[I Ching]]''

== References ==
{{Reflist}}

== Notes ==
{{Notelist}}{{Madagascar topics}}{{Divination}}
[[Category:Geomancy]]
[[Category:Culture of Madagascar]]
[[Category:Divination]]
[[Category:Algebra of random variables]]
[[Category:Mathematics and culture]]
[[Category:Mathematics and mysticism]]
[[Category:Algorithms]]
[[Category:Boolean algebra]]
[[Category:Logic]]
[[Category:Islam in Madagascar]]