Modélisation des savoirs

SIKIDY : Divination in Madagascar

Abstract : SIKIDY (Malagasy word meaning "divination", pronounced s'kid') is a Web site in French presenting field works and analyses on Malagasy divination conducted by a group of French and Malagasy researchers in 2001-2007. It deals with the status of Malagasy diviners, the rules of their divination system and the underlying mathematical knowledge embedded in it, and some psychological experimentations involved in the study of this knowledge. The main feature of this Web site is a database of notebooks used by diviners to keep particular arrangements of seeds used in divination (see below).

The starting point of these works is an article by Marcia Ascher on Malagasy divination published in 1997 in Historia Mathematica, vol. 24, p. 376-395. More details can be found in the book by Marc Chemillier (in French), Les Mathématiques naturelles, Paris, Odile Jacob, 2007, or in the chapter "Fieldwork in Ethnomathematics" of the Oxford Handbook of Linguistic Fieldwork, edited by Nick Thieberger, Oxford University Press, 2011, p. 317-344.


  • The status of diviners in Malagasy society
  • The diviner, called mpisikidy or ombiasy, is an expert with an important place in Malagasy society. Whereas everybody knows the basic rules of the divination system (which is exactly the old Arabic divination practice called "geomancy"), the professional diviner has a specific knowledge. His is a specialist in guiding people, and his position is related to three main features :

    • He owns specific sacred horns of zebu, called mohara,
    • He is an expert in the knowledge of medicinal plants and woods, called volohaza (for instance retsara on the right picture above taken at the market place of Ambovombe)
    • He knows elaborated properties of a system of computation with seeds, which is designed by the word sikidy.

    cornes mohara     bois au marche     bois retsara


  • The computation with seeds
  • The most important aspect of the system of computation with seeds used by diviners is the construction of tableaux. Each of the entries in the tableau can be one seed or two seeds as can be seen on this picture :

    tableau de graines

    Mother-sikidy = the upper part of the tableau with four rows and four columns (the rows are considered from right to left, thus 2 2 1 1 is the first row above).
    Daughter-columns  = the lower part of the tableau with eight columns of four entries each.

    The daughters are deduced from the mother-sikidy by applying a simple mathematical rule :

    • 1 + 1 = 2
    • 2 + 2 = 2
    • 1 + 2 = 1

    The order of generation of daughter-columns is illustrated by the following animated picture. The mother-sikidy is different from the picture above, but one can verify that the computation rule is the same on both pictures :

    construction des filles

    There are 16 possibles outcomes, which are classified in different ways :

    Princes / Slaves : The 8 outcomes with an even number of seeds are called princes, for instance (2 2 1 1) with 6 seeds, and the others are called slaves, for instance (1 1 1 2) with 5 seeds.

    Cardinal directions  : There exists a classification of the 16 outcomes according to the 4 cardinal directions :

    • North  = (1 2 2 2), (2 2 1 2), (1 1 1 2), (1 2 1 2)
    • West  = (2 2 2 1), (1 2 1 1), (1 2 2 1), (2 1 2 1), (2 1 1 1)
    • East  = (2 1 2 2), (2 2 1 1), (2 1 1 2)
    • South  = (2 2 2 2), (1 1 1 1), (1 1 2 2), (1 1 2 1)

    Some tableaux with particular positions of the outcomes are considered as strongly powerful at the symbolic level. The diviner put dust on some of the outcomes occurring in the tableau, and then, the dust is used as a strong talisman able to cure an illness. These particular tableaux are :

    Toka (or tokan-tsikidy)  = tableaux such that one of the cardinal directions is represented only once, by a unique outcome (among the four rows and columns of the mother-sikidy and the eight daughter-columns). The following tableau is a double toka (East and South) :

          w  w  e  s  
          .  .. .. .  w  
          .. .  .  .  n  
          .. .  .  .  n  
          .  .  .. .  w  
    .. .. .. .. .  .. .  .  
    .  .. .  .  .  .  .. .. 
    .. .  .  .. .  .  .. .  
    .  .. .  .  .. .  .  .. 
    w  n  w  w  n  w  w  n  

    Fohatse  = tableaux such that an outcome is repeated at least eight times in the tableau (among the four rows and columns of the mother-sikidy and the eight daughter-columns). The picture of the tableau above shows a fohatse with (2 2 1 1) repeated exactly nine times (2 rows and 2 columns in the mother-sikidy and 5 columns among the daughters)

    Another way to use the tableaux is related to the divining practice itself. In this case, the mother-sikidy is chosen randomly, by taking 16 piles of seeds and reducing them to one or two seeds by deleting them two at a time.

    tirage aleatoire


  • A database of notebooks used by diviners
  • During field works made on the subject of divination in Madagascar, it appeared that diviners use notebooks to keep particular tableaux of seeds considered as powerful (mostly toka or fohatse). Here is a page from a diviner's notebook (only the mother-sikidy are written) :

    une page de carnet

    We have collected some of these notebooks and they are stored in the following database. You can test some aspects of the search engine on a small sample of a notebook made available without restriction in this Web site.

    Name of the notebook Diviner Number of pages Number of tableaux
    ANO01 Anonymous557

    The access to the full database is restricted to academic researchers by entering a login ("Utilisateur") and a password ("Mot de passe") on the sample page (comments are in French).

    For registration, please send an email indicating the academic context of your research to :