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Mathematical Aspects of Sikidy | OMICS International
ISSN: 1736-4337
Journal of Generalized Lie Theory and Applications
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Mathematical Aspects of Sikidy

Anona F. M.*

Department of Mathematics and Computer Sciences, Faculty of Sciences, University of Antananarivo, Antananarivo 101, BP 906, Madagascar

Corresponding Author:
Anona FM
Department of Mathematics and Computer Sciences
Faculty of Sciences, University of Antananarivo
Antananarivo 101, BP 906, Madagascar
Tel: +261202232639
E-mail: [email protected]

Received Date: January 29, 2016; Accepted Date: March 02, 2016; Published Date: March 04, 2016

Citation: Anona FM (2016) Mathematical Aspects of Sikidy. J Generalized Lie Theory Appl S2: 008. doi:10.4172/1736-4337.S2-008

Copyright: © 2016 Anona FM. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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It emphasizes the mathematical aspects of the formation of sikidy. The sikidy as an art of divination is transmitted by oral tradition, the knowledge of these mathematical relationships allows for a more consistent language of sikidy. In particular, one can calculate systematically all ”into sikidy” special tables of Sikidy used in the ”ody” (kind of talismans).


Sikidy; Divination; Into; Abelian groups


Divination held a special place for all peoples and all times. In Madagascar, the sikidy is an enough precise art of divination and a remedy to avert the fate of the consultant. The present paper is the English version of an unpublished paper [1] translated by Randriambololondrantomalala. Only, introduction and bibliography of the original paper are modified. I’m a differential geometer and Lie theory specialist in this previous domain as [2-6] show. But, this Malagasy art of divination which has mathematical practices has fascinated me and paid my intention in quality of mathematician. So, I made this paper as a first step of long studies about the powerful of mathematics in another fields like divinations. The original paper had plenary lecture in a scientific conference at the University of Fianarantsoa, Madagascar. Next, I think that publication of my paper [1] will be useful as well as several authors have cited my results cf. [7-11]. This article is the first step of my research in this area and mainly, my motivation is to build an algorithm about Sikidy’s practice in my next paper.

Formation of Sikidy and Mathematical Relations

Generally, we use seeds of ”kily” (Tamarind), the total number of seeds must be even and large enough to make all desired combinations, at least a hundred seeds. We awakens the sikidy by an invocation that expresses a certain oral tradition of Sikidy and, formulates at the end the questions that we want to have the answers, while turning in circles and always with the right hand the seeds of kily on a mat. Then we take a handful of seeds from the pile at random. It would be at this level the intervention of the Hereafter. We compute the seeds in pairs, if the handle is even number, we align two seeds; in the odd case, we align one seed.

This forms a table from right to left, said mother-sikidy:


Each variable aij is composed of one seed or two depending on the result obtained by the above method. The index i indicates the position of the line, j that of the column ranging from 1 to 4. The quadruplet Equation designates Tale (Consultant); next Equation Maly (Wealth), Equation Fahatelo (A third person); next one Equation Blady (Earth); Equation Fianahana (Child); Equation Abily (An elderly person); next EquationAlisay (Woman); Equation Fahavalo (Enemy).

We build eight other figures below the mother-sikidy left to right derived from the above quadruplets respecting the following law:

• One seed and one seed yield two seeds,

• Two seeds and one seed give one seed,

• Two seeds and two seeds yield two seeds.

So the law of inner composition of Abelian group Equation ; two seeds represent the identity element Equation, one seed is Equation . The combining operation is done in Equation (quadruplets of Equation ). Thus, we obtain:

• Fahasivy (9, ninth or talisman) = Alisay (7) + Fahavalo (8);

• Haja (11, honor or food) = Fianahana (5) + Abily (6);

• Asorita (13, spirits of deads, or authorities) = Fahatelo (3) + Blady (4);

• Lalana (15 Road) = Tale (1) + Maly (2).

Then combined the above results to have:

• ombiasa (10, soothsayer) Fahasivy = (9) + Haja (11);

• Sely (14 people) = Asorita (13) + Lalana (15);

• Aky (12, god) = ombiasa (10) + Sely (14).

The last figure is:

• Kiba (16, house) = Aky (12) + Tale (1).

Then, an array of sikidy is written:

Equation Equation

As a result, the number of sikidy’s tables is determined by the mother-sikidy or 216 = 65536.

There are two categories of sikidy’s figures, princes whose number of seeds is even, and slaves to the odd number of seeds.

The tradition imposes this rule:

”A sikidy can not be interpreted if the Aky (12) is not a prince.”

In fact, if we sum all elements of Aky, we have


Even if the Aky couldn’t be a prince, we were wrong calculation.

For clarification on the interpretation, we continue to combine the figures that appear on the table [12]. Thereupon, we must take into account the mathematical links of the sikidy, otherwise we may give different meanings for the same thing [12]:

”The ninth (9) and the healer (10) give the leaves or plants to be used as medicines, ravin’ody”.

In fact, given the binary operation of the group, the combination of Fahasivy (9) and Ombiasa (10) gives Haja (11), that is to say a figure that already exists on the table (the relationship (9) + (11) = (10) is equivalent to (9) + (10) = (11)).

There are other examples of contradictions.

Into Sikidy

The sixteen figures of Sikidy are classified according to the cardinal directions. The classification below is used mainly in the southern region of Madagascar. Subscripted letters above each figure will be used to identify the respective figures.

1. Group of the east:


2. Group of the north:


3. Group of the West:


4. Group of the South:


Naturally, these figures have specific meanings [12].

If we denote by Pk, k = 1, … , 16, Tale’s locations (1) at Kiba (16) in an array of sikidy; we call ”Into” the case where one and only one representative of a group appears only once on sixteen seats, P1 to P16.

Example: Adabara ”Into” to the Tale.


In this example, Adabara, E1 one member of the group of the East is located at P1, the other E1, l = 1,2,3 don’t take place at Pk, 2 ≤ k ≤ 16.

In that table of Sikidy, we say that the Sikidy gives a formal advice (mitoka vava). The consultant would be successful.

To calculate these ”Into”, we use the following Table 1 of inner law of composition:

+ E1 E2 E3 N1 N2 N3 N4 O1 O2 O3 O4 O5 S1 S2 S3 S4
E1 S1 O1 O2 O3 S4 O5 O4 E2 E3 N1 N4 N3 E1 S3 S2 N2
E2 O1 S1 N4 S3 N3 N2 E3 E1 O4 S2 O2 S4 E2 O3 N1 O5
E3 O2 N4 S1 N2 N1 S3 E2 O4 E1 S4 O1 S2 E3 O5 N3 O3
N1 O3 S3 N2 S1 E3 N4 N3 S2 S4 E1 O5 O4 N1 O1 E2 O2
N2 S4 N3 N1 E3 S1 E2 S3 O5 O3 O2 S2 O1 N2 O4 N4 E1
N3 O5 N2 S3 N4 E2 S1 N1 S4 S2 O4 O3 E1 N3 O2 E3 O1
N4 O4 E3 E2 N3 S3 N1 S1 O2 O1 O5 E1 O3 N4 S4 N2 S2
O1 E2 E1 O4 S2 O5 S4 O2 S1 N4 S3 E3 N2 O1 N1 O3 N3
O2 E3 O4 E1 S4 O3 S2 O1 N4 S1 N2 E2 S3 O2 N3 O5 N1
O3 N1 S2 S4 E1 O2 O4 O5 S3 N2 S1 N3 N4 O3 E2 O1 E3
O4 N4 O2 O1 O5 S2 O3 E1 E3 E2 N3 S1 N1 O4 N2 S4 S3
O5 N3 S4 S2 O4 O1 E1 O3 N2 S3 N4 N1 S1 O5 E3 O2 E2
S1 E1 E2 E3 N1 N2 N3 N4 O1 O2 O3 O4 O5 S1 S2 S3 S4
S2 S3 O3 O5 O1 O4 O2 S4 N1 N3 E2 N2 E3 S2 S1 E1 N4
S3 S2 N1 N3 E2 N4 E3 N2 O3 O5 O1 S4 O2 S3 E1 S1 O4
S4 N2 O5 O3 O2 E1 O1 S2 N3 N1 E3 S3 E2 S4 N4 O4 S1

Table 1: Inner law of composition.

Compute these ”Into” using this table is elementary. The total of the ”Into” for one figure in the place Pk takes its value from 0 to a hundred. For example, Alohotsy ”Into” to Ombiasa (who means the Great Divine), searched by the Mpisikidy, doesn’t exist, but Alohotsy ”Into” to Sely which has total number 8. Adabara ”Into” to Tale has 132,...etc.

These ”Into” Sikidy have particular significations and truthfully considered. We use them to get talismans.


In the present paper, Anona investigated mainly the mother- Sikidy. In a next paper in the same topic, he will make the Sikidy more precise in order to check daughter-Sikidy and so on. The language of the Sikidy is very large. Frequently, the data obtained from the Mpisikidy are contradictory. Certainly, make a coherent language of the Sikidy throughout different collects of data is very interesting.


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