International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 11, Issue 8, August 2020, pp. 53-62, Article ID: IJARET_11_08_007 Available online at http://iaeme.com/Home/issue/IJARET?Volume=11&Issue=8 ISSN Print: 0976-6480 and ISSN Online: 0976-6499 DOI: 10.34218/IJARET.11.8.2020.007
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EXISTENCE OF GRAPH THROUGH MALAY TRADITIONAL DANCE
Wan Muhammad Afiq bin Wan Muhamad Fauzan Laboratory of Ethnomathematics and Didactics, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia.
Sharifah Kartini Said Husain Laboratory of Ethnomathematics and Didactics, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia. Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
Mohd Rohaizat Abdul Wahab Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia Laboratory of Archaeology and Archaeometry, Institute of the Malay World (ATMA), Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia
ABSTRACT Ethnomathematics refers to the mathematics that was created based on culture and the value system of an ethnic. The Malay ethnomathematics is the mathematics inherited from the Malay civilization that was taught, uttered, applied, and developed in the language and follows the Malay values. The definition of a graph is a set consisting of vertices connected to one another through the group of edges. In creating choreography in the Malay traditional dance, it must follow several general principles of choreography and almost all traditional Malay dance apply the concept of symmetrical balance that focuses on strength and harmony. The concept of symmetry is also applied to the whole dance pattern that begins and ends with the same floor patterns and movement. Malay traditional dance involves steps that are simultaneous repetition in the shape of mapping that is matching, serial, transformation, shifting and flexible. If it is defined in dance, edges are the location of positions of the dancers and vertices refer to movement between one position to another. This study also determines every unique graph pattern derived from every type of Malay dance. Key words: Malay Traditional Dance, Graph Theory, Ethnomathematics.
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Cite this Article: Wan Muhammad Afiq bin Wan Muhamad Fauzan, Sharifah Kartini Said Husain and Mohd Rohaizat Abdul Wahab, Existence of Graph through Malay Traditional Dance, International Journal of Advanced Research in Engineering and Technology, 11(8), 2020, pp. 53-62. http://iaeme.com/Home/issue/IJARET?Volume=11&Issue=8
1. INTRODUCTION In early 1986, the term of ethnomathematics was introduced by D’Ambrosio as a technical art of understanding, informing, clarifying, learning, dealing, and managing the life of humans in a certain way that suits the society [1]. Besides, ethnomathematics is also defined as a branch of mathematics or related thinking that is derived based on culture and value system of an ethnic [2]. Ethnomathematics is not specifically owned by certain ethnic, but the uniqueness of ethnomathematics is rather outstanding based on the difference in culture that exists within the society itself. For the Malay community, Malay ethnomathematics refers to mathematics inherited from Malay civilization taught, mentioned, written, and developed in the Malay value system [3]. Culture is not isolated in one’s life because without it, the identity of the people will be lost. A great civilization will have an equally great culture. Culture also has varied definitions. According to Kamus Dewan (2015), culture is a way of life as well as the advancement of thoughts, manners, behavior, and so on [4]. Edward B Taylor defines culture as the whole complexity consisting of knowledge, facts, beliefs, arts, manners, laws, customs other abilities, and behaviors owned by the member of society [5]. Whereas arts refer to branches of culture, it is a wonderful and vast field to be digested because it is a combination of socio-culture such as beliefs, moral and ethics, creativity, custom and life rules [6]. The values of certain arts did not merely lie on the external beauty but it must be through its contribution to the society. Abdul Samad bin Ahmad (Asmad) stated in his book, Kesenian Tarian, the art of dance will only be acknowledged once it fulfills three main features; beauty, truth, and goodness to people and society [7]. The arts in focus in this article is the art of dance. The fineness of arts depends on the fineness of the artist who creates it and the fineness depends on his level of manner. Islam does not forbid its followers from being involved in arts neither forbids its followers to abandon anything than Arabic culture, but Islam acknowledges the diversity of arts that exists in every society as long as it does not violate the law of Islam. In Muhammad Qutb’s work cited by Adnan M Wazzan, explains that Islamic art as [6]: “Islamic art is not of necessity an art which speak of Islam, and it is certainly not preaching guidance and enjoying virtue. Equally it is not barely facts of faith crystallized in philosophical form. It is an art which portrays the form existence from an Islamic point of view of this world, it is an eloquent expression of the Universe, Life and Man through Islam and human life, it is an art which paves the way of the complete integration of beauty and truth, for the beauty is reality of this universe while truth is the summit of beauty, and so they meet at the peak at which all the realities of existence come together” Islam highlights the concept of harmony regardless of race and origins and therefore enables Islam to be accepted by the whole world. However, the discussion on the definition of Islamic art requires different discourse and research. This research focuses on the connection between mathematics and Malay traditional dance. Malay traditional involves repetitious steps that simultaneous repetition in the shape of mapping that is matching, serial, transformation, shifting, revolving, and flexible mapping [8]. This article aims at observing graph shapes created in certain types of different traditional dance.
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This article is organized as follows: The definitions of ethnomathematics and Malay culture are given in Section 1. Section 2 contains the brief information about Malay traditional dances. While Section 3 focuses on the relationship between mathematics and dance, here some previous researches are stated. The methodology and findings are presented in Section 4, and Section 5 provides the conclusion of the research.
2. MALAY TRADITIONAL DANCE The art of dance is a branch of unique art. This form of art emerges from the observation of movements and the swaying of nature such as leaves and so on. This observation is later displayed in the form of dance and choreographed as a story to be presented to the audience. Besides, this art also adapts the daily life of the people. To illustrate, if the society’s life focuses on the fishery, then the elements of fish and sea will be embedded in the dance, such as Ulek Mayang in Terengganu. If the life of the society revolves around agriculture, then the movement that depicts agricultural life will be included in their dance, such as Belotah Dance in Perak The high degree of courtesy in the Malay society is manifested in its traditional dance. The dance is generally not performed singly, but rather in groups or pairs, be it the same or different genders. Even though the genders are different during the performance but it does not involve physical touching which is parallel to Islamic teaching that forbids touching between mahram (marriageable) couples. If necessary, shawls or mufflers are used as holders between the couples. As far as structure is concerned, dance needs to consider the organization of socio- economy, religion, and politics. Since the Malay society loves peace, courteous, and mutual respect, all these show in their dance that are performed slowly, gracefully and gently. The choreography of traditional dance focused on the Malay features itself that were set during the creation of the dance and later descended to the following generations in its original form. Secular dance, on the other hand, shows differences and additions in the choreography in line with the modern era. In contrast, ritual dance does not have any addition to its original form because it is believed that it will trigger spiritual anger. However, the addition took place in secular dance is not that prevalent since it attempts to sustain the original message of the dance. There are several variations of Malay dance, which is caused by the different purposes of the creation of the dance. There are three forms of Malay dance; the one for events or celebrations, namely Seni Tari Pertunjukan. The one for social and entertainment, Tarian Pergaulan or Hiburan. The last one, Seni Tari Pemujaan or Persembahan is for rituals or the ones practiced during the pre-Islamic era that later transformed into entertainment [7]. The art of dance is defined as a form of human movement that symbolizes the basics of culture which is based on courtesy, manner, and characters of a certain races. The richness of Malay arts has given birth to various forms and patterns of dance and therefore dances that are ethnic and regional in nature also exist. There are four types of dances that are not regional; Joget, Inang, Zapin, and Asli dance. These four types have been acknowledged as original Malay dances. According to Asmad (1991), the special feature of these dances is that it has its own rhythms and tempos [7].
3. MATHEMATICS AND DANCE Mathematics is a vast and comprehensive knowledge. Mathematics is originally a connector between other knowledge’s but currently, it is being viewed upon as calculations on paper. The diversity of branches that exist in mathematics today such as calculus, number theory,
http://iaeme.com/Home/journal/IJARET 55 [email protected] Existence of Graph through Malay Traditional Dance graph theory, and others originates from five main divisions; arithmetic, astronomy, music, logic, and geometry [9][10]. The early studies that set human movement as the focus have been done by Rudolf Laban in 1920. The finding from this research has produced a technique to record human movement, known as labanotation. It refers to a notation system to record and analyze human movement [11]. The symbols in Figure 1, are generally used to show: Direction and level of movement The parts of the body involved in the movement The duration of the movement. The quality of dynamic movement
Figure 1 The Part of Body’s symbol that used by Laban Consequently, studies on mathematics and dances were continued, especially in European countries. Among the studies on traditional dances that have been done is “court and country” or contra dance. The initial study on contra dance started with the one on the tempo of the dance and from that, it has been successfully proven that the concept of symmetry is the base of the contra dance [12]. Hence, contra dance was further studied by establishing its connection to the matrix [13]. In 2016, a study has produced mathematical representation of the contra dance that is simultaneous to contra dance [14]. In this study, an analysis of the existence of the graph has been conducted to three traditional dances; Joget, Inang, and Zapin. There are several definitions of mathematics used to analyze a graph; among them are eccentricity, diameter, radius, degree of edges, and chromatic number. Generally, a graph contains the elements that can be divided into two sets; the set of vertices, V and the set of edges, E. The cardinality or the number of vertices is the order of graph and the cardinality of edges give the size of the graph. A graph is said to be connected if there is a path in every pair of vertices. The graph is called a rotation graph if it has at least one revolving graph. The graph that has a direction is called direction graph or digraph. Loop is an edge that is connected to the same vertex. Multiple edges, also is the one with two edges that are connected between two similar vertices. Its eccentricity is the maximum distance that can be formed from one vertex to another in the related graph. Based on this value of eccentricity
http://iaeme.com/Home/journal/IJARET 56 [email protected] Wan Muhammad Afiq bin Wan Muhamad Fauzan, Sharifah Kartini Said Husain and Mohd Rohaizat Abdul Wahab of each vertex, the highest eccentricity value is the diameter of the graph while the value of the lowest eccentricity is the radius. The degree of a vertex for the simple graph is the number of edges for each vertex but for digraph, the degree of a vertex is divided into two types; indegree and outdegree. Indegree is the number of edges point towards the vertex whereas outdegree means the number of edges that is a point away from the vertex. The chromatic number refers to the maximum number of colouring the vertices that can be used if the same colours are not side by side [15][16][17][18].
4. METHODOLOGY AND FINDINGS In analyzing the existence of graph in Malay traditional dance, the methodology applied is: Every data of certain dance is translated into mapping or known as floor pattern. Here, the mapping or floor pattern is observed from the position as a group of dancers. This position is later translated as a vertex and denoted with the numbers {1, 2, 3, 4, …} while the shift from one position to another forms an edge symbolized with {a, b, c, d, …}. The features of the graph created is analyzed in Table 1. The data in this research is obtained from a collection of old videos from the Youtube channel, Museum of Malay Ethnography, Academy of Malay Studies, Universiti Malaya (Figure 2), and direct recordings in collaboration with Dance Club Universiti Putra Malaysia, Adimasturi UPM (Figure 3).
Figure 2 Trip to Museum of Malay Ethnography, Academy of Malay Studies, Universiti Malaya
Figure 3 With the Dancers of Adimasturi UPM
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Through the sources gained, the observation can be done in various ways. Among them are: Group observation Pair observation Individual observation ( movements of the sole) Individual observation ( movements of the body) In every observation, if scrutinized, it is able to generate a certain graph that can give a new perception on Malay traditional dance. The concept of this dance, however, must be understood to determine the common and uncommon factors in Malay Dance. These factors play a big role in future studies. In this study, the data gained from group observations on three types of Malay traditional dances; Joget, Inang, and Zapin. The observation on Joget and Inang dances were done in collaboration with Adimasturi UPM, while the observation on Zapin Dance was done based on videos from of Malay Ethnography, UM in CD entitled “Citra Budaya Malaysia: Johor”. Figures 4, 5, and 6 show the mapping of the three dances.
5 1
2 6
3 7
4 8
Figure 4 Mapping of Joget Dance
1 3
2 4
Figure 5 Mapping of Inang Dance
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1 5
2 6
3 7
8 4
Figure 6 Mapping of Zapin Dance
Figure 7 Graph of Joget Dance Whereby, Figures 7, 8 and 9 show graphs pattern derived from each mapping.
Figure 8 Graph of Inang Dance http://iaeme.com/Home/journal/IJARET 59 [email protected] Existence of Graph through Malay Traditional Dance
Figure 9 Graph of Zapin Dance
The similarities that exist among the three graphs are that the graph is connected graph, digraph and each has a cyclic graph. The difference between the graphs can be observed in the table below.
Table 1 The Differences between the Graphs. Graph of Joget Dance Graph of Inang Dance Graph of Zapin Dance Order, 8 , 4, 8, Set of vertices Size, 11, 7, 13, Set of edges Multiple edges None Exist Exist The number of 2 3 5 loops Chromatics number 3 2 2 Eccentricity Diameter 7 3 6 Radius 4 0 0 Indegree of a vertex Vertex Degree Vertex Degree Vertex Degree 1 2 1 2 1 1 2 1 2 2 2 2 3 1 3 1 3 2 4 1 4 2 4 3
5 2 5 1 6 2 6 1 7 1 7 2 8 1 8 1 Outdegree of a Vertex Degree Vertex Degree Vertex Degree vertex 1 3 1 3 1 2 2 1 2 2 2 2 3 1 3 1 3 2 4 1 4 1 4 3
5 1 5 1 6 2 6 1 7 1 7 2
8 1 8 0 The table above shows that each dance produces different graph features and this shows that different dances created different graphs. This proves that there is a connection between dance and Mathematics.
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5. CONCLUSION The study on the connection between science and arts has still not been given serious attention in Malaysia, particularly in mathematics. Mathematics and arts have an inseparable connection but it has yet been proven because of the scarcity of the study on it, especially in Southeast Asia. This leads to our tendency to abandon this culture and eventually we will lose our identity and value. The thought that says culture and customs will make us left behind must be eradicated since we are created as peoples and we have our strengths. It is hoped that studies like this will be a starting point to reconnect mathematics and the arts of dance so that Malaysians will value their culture that has been existing in this Malay world.
ACKNOWLEDGEMENT Appreciation was given to Associate Professor Dr. Hanafi bin Hussin, Dean of Faculty of Art and Social Science at Universiti Malaya who assisted in this study. It is also noteworthly to Universiti Putra Malaysia for funding this study under the IPS Putra Grants Putra numbered GP-IPS/2018/9645600. Also to Universiti Kuala Lumpur for funding this study under FRGS 201-1 numbered FRGS/1/2016/STG06/UNIKL/02/1
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