Reach Us
+44-1522-440391

**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.

**Visit for more related articles at** Journal of Generalized Lie Theory and Applications

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 The present paper is the English version of an unpublished paper [1] translated by Randriambololondrantomalala.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.

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 a_{ij} 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 designates Tale (Consultant); next Maly (Wealth), Fahatelo (A third person); next one Blady (Earth); Fianahana (Child); Abily (An elderly person); next Alisay (Woman); 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 ; two seeds represent the identity element , one seed is . The combining operation is done in (quadruplets of ). 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:

As a result, the number of sikidy’s tables is determined by the mother-sikidy or 2^{16} = 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.

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 P_{k}, 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, P_{1} to P_{16}.

Example: Adabara ”Into” to the Tale.

In this example, Adabara, E_{1} one member of the group of the East is located at P_{1}, the other E_{1}, l = 1,2,3 don’t take place at P_{k}, 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 P_{k} 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.

- Anona FM (2001) Aspects of Mathematics sikidy. Antananarivo University, Department of Mathematics and Computer Science.
- Anona FM (1980) Sur la
*dL*-cohomologie. CRAS, Paris Sér A-B 290: 649-651. - Randriambololondrantomalala P, Ravelonirina HSG, Anona M (2015) Of the Lie algebra associated with a connection. Canadian Mathematical Bulletin 58: 692-703.
- Randriambololondrantomalala P, Ravelonirina HSG, Anona M (2010) The Lie algebra of a distribution and a generalized foliation. African Diaspora Journal of Mathematics 10: 135-144.
- Ravelonirina HSG, Randriambololondra ntomalala P, Anona M (2012) The Lie algebra of a system of swappable field vectors. Italian Journal of Pure and Applied Mathematics 29: 163-174.
- Ravelonirina HSG, Randriambololondrantomalala P, Anona M (2010) The Lie algebra of vector fields polynomial. African Diaspora Journal of Mathematics 10: 87-95.
- Chemillier M (2012) The evidence in divination in Madagascar.
- Chemillier M (2007) Natural mathematics. Odile Jacob, Paris.
- Chemillier M (2007) Mathematics oral traditions. Math Sci Hum Mathematics and Social Sciences, 45th year 2: 11-40.
- Chemillier M (2001) Mathematics and cognitive modeling of musical structures. HDR memory, Paris.
- Chemillier M, Jacquet D, Randrianary V, Zabalia M (2007) Mathematical and Cognitive Aspects of sikidy Divination on Madagascar. L’Homme 1: 7-39.
- Decary R (1970) The Malagasy divination by sikidy. University Centre for Modern Oriental Languages. 6th Series IX Imprimerie Nationale. Librairie Orientalist Paul Geuthner, Paris.

Select your language of interest to view the total content in your interested language

- Adomian Decomposition Method
- Algebra
- Algebraic Geometry
- Analytical Geometry
- Applied Mathematics
- Axioms
- Balance Law
- Behaviometrics
- Big Data Analytics
- Binary and Non-normal Continuous Data
- Binomial Regression
- Biometrics
- Biostatistics methods
- Clinical Trail
- Combinatorics
- Complex Analysis
- Computational Model
- Convection Diffusion Equations
- Cross-Covariance and Cross-Correlation
- Deformations Theory
- Differential Equations
- Differential Transform Method
- Fourier Analysis
- Fuzzy Boundary Value
- Fuzzy Environments
- Fuzzy Quasi-Metric Space
- Genetic Linkage
- Geometry
- Hamilton Mechanics
- Harmonic Analysis
- Homological Algebra
- Homotopical Algebra
- Hypothesis Testing
- Integrated Analysis
- Integration
- Large-scale Survey Data
- Latin Squares
- Lie Algebra
- Lie Superalgebra
- Lie Theory
- Lie Triple Systems
- Loop Algebra
- Matrix
- Microarray Studies
- Mixed Initial-boundary Value
- Molecular Modelling
- Multivariate-Normal Model
- Noether's theorem
- Non rigid Image Registration
- Nonlinear Differential Equations
- Number Theory
- Numerical Solutions
- Operad Theory
- Physical Mathematics
- Quantum Group
- Quantum Mechanics
- Quantum electrodynamics
- Quasi-Group
- Quasilinear Hyperbolic Systems
- Regressions
- Relativity
- Representation theory
- Riemannian Geometry
- Robust Method
- Semi Analytical-Solution
- Sensitivity Analysis
- Smooth Complexities
- Soft biometrics
- Spatial Gaussian Markov Random Fields
- Statistical Methods
- Super Algebras
- Symmetric Spaces
- Theoretical Physics
- Theory of Mathematical Modeling
- Three Dimensional Steady State
- Topologies
- Topology
- mirror symmetry
- vector bundle

- Total views:
**8943** - [From(publication date):

specialissue-2016 - Aug 21, 2019] - Breakdown by view type
- HTML page views :
**8768** - PDF downloads :
**175**

**Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals**

International Conferences 2019-20