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Dance, Folk

Dance, Folk


Both mathematics and dance are languages that use symbols to convey ideas and expressions. Mathematics uses written symbols to represent abstractions so that users can arrive at a greater understanding of a problem without ambiguity . Dancers use abstract symbols to represent thoughts, feelings, emotions, and ideas, and these symbols may be interpreted in multiple ways. Both disciplines rely to a large extent on pattern recognition.

Many forms of dance, such as classical ballet, involve complex patterns and take years of practice to master. Yet other forms of dance use everyday movements with more simplistic patterns. For example, folk dances have evolved from common movements of work and play.

Although folk dances require concentration and focus, their use of everyday movement invites observers to participate. Similarly, mathematics can be studied at the basic level of arithmetic, which is used to make simple transactions and to understand how things work. More advanced mathematics, such as calculus , chaos theory , or abstract algebra require years to master.

Discreteness in Mathematics and Dance

Many dances are based on a simple method of counting and discrete sequences, which enables participants to recognize and learn a variety of dances. The word "discrete" also has a common, similar usage in mathematics. Discrete mathematics involves counting separate elements, such as the number of arrangements of letters on a license place, or the number of ways that a presidential candidate can visit all fifty states. Solutions in discrete mathematics can be only whole units. Discrete math is therefore one of the most accessible areas of modern mathematics since many of the questions are easy for anyone to understand.

Contradancing. Contradancing is a popular form of folk dance in the United States that illustrates the mathematics of dance. Its origins go back to colonial days, and its roots can be traced to English country dances.

Contradancing, which shares elements of traditional square dancing, is a form of set dancing in which a dancer's position relative to another dancer traces patterns on the dance floor. As in most dancing, timing is crucial, as is the ability to rapidly carry out called instructions.

Music for contradancing is highly structured. Everything occurs in multiples of four. In one common format, the band plays a tune for sixteen beats, repeats the tune, then plays a new tune for sixteen beats and repeats. An eight-beat section is known as a call, during which each block of four dancers executes a called-out instruction.

When contradancers line up in their groups of four to produce a long column "down" the dance floor (extending away from the band), each square block of two couples can be thought of as a mathematical matrix with the dimension 2 × 2. Each dancer, or element of the matrix, is in a specific position within the array. The called instructions correspond to rearrangements of the elements (dancers). After sixty-four beats, for example, the first and second rows of the matrix may be inter-changed. Of course, this could be done in one step, but the fun of dancing comes from performing the various permutations by which groups of four can reach the end result.

There are many called instructions in contradancing, ranging in complexity from simply circling once around to the left or right within each group of four to sequences of moves that involve exchanging partners or stepping one-quarter, one-half, or three-quarters of the way around the ring. With each call, the matrix representing four dancers changes. In the final configuration, the two rows of the original 2 × 2 matrix may be inter-changed, or they may be the same as when the dance started.

Chaos Theory and Dance

Computer scientists have applied the basics of chaos theory to generate variations on dance movement sequences. Special symbols represent human body postures, and positions for each of the body's main joints are encoded by defining an axis and angle of rotation given in the form of a mathematical expression called a quaternion . A motion sequence is then mapped onto a chaotic attractor . Following a new trajectory around the attractor produces a variation of the original motion sequence. To smooth out abrupt transitions introduced by the chaotic mapping, the researchers have developed schemes that capture and enforce particular dance styles.

see also Chaos, Mathematics of.

Marilyn K. Simon

Bibliography

Devlin, Keith. The Language of Mathematics: Making the Invisible Visible. Chicago: W. H. Freeman, 2000.

. Using Chaos to Generate Variations on Movement Sequences." Chaos 8, no. 4 (1998).

Internet Resources

Bradley, Elizabeth. "Chaographer and Motion Mind: Using Mathematics to Generate Choreographic Variations." Chaography Software. <http://www.cs.colorado.edu/~lizb/chaotic-dance.html>.

Contradancing. <http://www.io.com/~entropy/contradance/dance-home.html>.

Country Dance and Song. <http://www.cdss.org/>.

What Is Contra Dance? <http://www.sbcds.org/contradance/whatis/>.


THE COMMUNICATION OF MATHEMATICS AND DANCE

According to Keith Devlin in The Language of Mathematics, mathematics seeks to communicate a sense of what humans experience. The simplicity, precision, purity, and elegance of mathematical expressions and patterns give mathematics an aesthetic value. The mathematical connections to dance similarly give dancers a creative, aesthetic, and interpretive means of expressing the human experience.


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folk dance

folk dance, primitive, tribal, or ethnic form of the dance, sometimes the survival of some ancient ceremony or festival. The term is used also to include characteristic national dances, country dances, and figure dances in costume to folk tunes. Many children's games, such as "London Bridge" and "The Farmer in the Dell," are traditional folk dances. More elaborate examples are the Spanish fandango, the Bohemian polka, the Hungarian czardas, the Irish jig, the Scottish Highland fling, the Hawaiian hula, and the English morris dance, sword dance, and Maypole dance. American barn dances, such as the Virginia reel, are largely derived from European sources. Early in the 20th cent. Cecil James Sharp, founder of the English Folk Dance Society, made a notable collection of English folk songs and dances. The American Folk Dance Society has done much to preserve the knowledge of old American country dances, and a similar interest has developed in other countries. A popular form of recreation, folk dancing is often taught in schools.

See M. D. Lidster and D. H. Tamburini, Folk Dance Progressions (1965, repr. 1978); A. S. Duggan et al., Folk Dance Library (5 vol., 1948, repr. 1980).

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folk dance

folk dance • n. a popular dance, considered as part of the tradition or custom of a particular people: well-known folk dances | ballet steps complicated by borrowings from folk dance. DERIVATIVES: folk danc·er n. folk danc·ing n.

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Folk Dance

FOLK DANCE

FOLK DANCE Dance plays an important role in celebrating South Asian life-cycle events and calendrical rituals, as well as religious beliefs, and appears to have done so for millennia. Every Indian language and social group has its own words for dance, emphasizing the local and unique over the national and common. Indeed, no single word can commonly translate the idea of dance, and no single encyclopedia entry could hope to discuss every dance form, classical or folk. Moreover, dance provides numerous examples of the codification of "folk" tradition into classical praxis. When aristocrats brought regional dances into their courts (as with kathak) and when temples standardized village dance dramas (as with kathakali), they helped link cosmopolitan and rural India. Thus, dance illustrates a continuum between the folk and the classical in South Asian performance traditions. Dancers in "folk" traditions may spend many hours perfecting their choreography with the assistance of teachers, learning patterns and techniques passed down from previous generations. However, these dance contexts can also spawn improvised and spontaneous gestures that can take on choreographic lives of their own.

In many cases, folk dance seems to begin as stylized gestures illustrating either daily routine or episodes of religious stories. If, for example, during devotional singing an individual stands up and demonstrates how a character in the song walked or behaved, then the careful execution of those movements becomes dance. When, in the context of music, individuals reenact daily chores such as carrying a water pot on the head, or illustrate their ability to handle weapons such as swords, the careful execution of those movements becomes dance. And, when these actions are isolated, abstracted, and socialized, dance is a consequence. Sometimes, children's games are the source of dances. For example, in the hikat of Jammu and Kashmir (and found widely in similar forms throughout South Asia), pairs of dancers cross and extend their arms, clasping their partner's wrists, leaning backward and spinning in time with the music. The dance ends when one of the dancers becomes too dizzy or the rate becomes too fast. Notably, the dance teaches a participant to rely on a partner—whose counterbalance keeps you from falling during the dance and who will hold you if you fall. In an agrarian society where success and survival are linked with mutual dependence, the lesson is not frivolous.

Regional genres, such as Gujarati garbā, can function both in the contexts of life-cycle events (such as weddings) and calendrical rituals associated with religious festivals (such as Navarātrī, in which it is the preferred form of worship for mother goddesses). However, at the core of this musico-choreographic form is a celebration of fertility, both etymologically (garbā derives from garbhā, "womb") and symbolically. For example, one of the most common central points of this circular and repetitive dance is a perforated earthen pot (garbhā dīpā), which represents life within the womb. Other representations in this tradition can be a pot of water with a coconut stopper or a basket of seedlings. Women gather in the evening during Navarātrī (nine nights of autumnal celebration) wearing long embroidered skirts with inset mirrors, short blouses similarly decorated, and long scarves. As they dance in a circle, they bend, clap, and repeat the pattern, while singing songs praising the mother goddesses and asking for their blessings. The twirling dancers, with the light of the garbhādīpā reflecting off their skirts, illustrate the reality of dance, not as entertainment, but as a cathartic experience that, combined with fasting, brings the goddess into their midst as a fellow dancer. The genre also has gendered versions: garbo (masculine) for women and garbī (feminine) for men. (Garbā is the plural form.) Regional variants include Punjabi giddhā, performed at festivals or in connection with wheat, both during sowing and harvesting. This dance can also mark the arrival of rain or of a new baby and has a rich musical tradition.

A variation of this dance style is kummi of Tamil Nadu, Andhra Pradesh, and Kerala, the songs of which sometimes describe everyday tasks such as chores, while others are dedicated to specific gods. Women perform kummi as a counterpart to men's dances, and it can take multiple forms, even within the same region. In Tamil Nadu, for example, the kummi is both a "flower dance," extolling the beauty of flowers, and a "housewife's dance," to name just two of many. The dance is also performed during Dīvālī, when cattle (the animals considered sacred to Shiva and Krishna) are decorated and led in a procession accompanied by music and dance. New rice is cooked and girls dance—stepping, jumping, pirouetting, and clapping to form circles.

In northwestern India, a rāsa or rāso can be a legend set in verse and sung about kings or warriors (such as the Prithvirāj Rāso), suggesting that perhaps the widespread dance of the similar name might have begun as an enactment of scenes in these stories. These dances share movements and perhaps origins with dances that have distinctly military associations, such as the katthak of the Pathans. In this case, male dancers perform a series of stylized military motions with swords and shields, complete with feints, turns, and pivots. Similarly, in eastern India, men perform versions of the chau dance-drama, particularly the puruliā chau of West Bengal and Bihar, in the spring. This last version includes mock reenactments of fights between the principal characters, in which dancers strike their "weapons" against each other in a stylized battle. Serāikela chau in Bihar also uses stylized martial movement, but today prominently includes rural and rustic themes. Chau dancers also wear masks in most (but not all) traditions and depict episodes from the Mahābhārata and the Rāmāyaṇa, as well as other religious stories. Another martial and religious themed dance is the parāsa (after parāsu, "battle ax") dance of Sirmur in Himachal Pradesh, where male dancers wield clubs and reenact the story of Parashu-Rāma (an incarnation of Vishnu) defeating Renuka.

Stick dances occur in various forms throughout India and celebrate deities, agriculture, marriage, and life-cycle events and, while they may vary in specific features and functions, the fundamental elements remain the same. The defining characteristics are the use of two sticks and, like garbā, choreographic patterns of one or more counterrevolving concentric circles (or sometimes, two parallel lines). Rs̄a stick dances share the characteristic of dancer pairings; dancers beat their own sticks together and with those of other dancers in time with the music. Stories of Krishna are often themes in stick dances, though some regions, such as Travancore and Cape Comorin, pay homage to other deities, such as Shiva and St. Francis Xavier. Stick dances can be found throughout India and commonly have connections with agriculture, the dance movements often reflecting this association as dancers pat the earth, imitating the sowing of seeds. Some social groups use stick dances to celebrate life-cycle events. For example, Rajasthani Bhils perform a version of rāsa called jhorīā (referring to the pair of wooden sticks) at weddings. Performances of rāsa in northern India typically occur on festivals such as Vasant Pancamī, Navarātra, and Sharada Purnima, which celebrate harvests. But while rāsa commonly has links with agricultural cycles, individual societies ultimately dictate the content of the dance. The rāsas of some communities, such as those found in Manipur, are less related to agriculture, while in many of Saurashtra's villages, dandīārāsa ("stick" rāsa) dances are nearly synonymous with harvests. Communities throughout Gujarat, Saurashtra, and Maharashtra perform dances of this type, maintaining the fundamental traits of rāsa, while imprinting the movements with regional stylistic features.

Variations of the rāsa exist even within regions. Some dances replace sticks with stylized swords, others remove vocals and dance only to the accompaniment of drums, and the sticks vary in size and style. Rās līlā in Manipur is generally elaborate and thematic, with different varieties such as basant rāsa ("spring" rāsa, depicting the amorous quarrels of Rādhā and Krishna), kunj rāsa (the love of Rādhā and Krishna), mahārāsa (the separation of Krishna and Rādhā), divārāsa ("daytime" rāsa), nitya rāsa ("everyday" rasa), nātnārāsa (Krishna playing with the milkmaids), and others. Some of these are in the form of a circle (such as the mahārāsa and the nātnārāsa), while others are more dramatic representations. In Sirmur of the Himalayan region, rāsa performances occur during the Maghi or Bisu festivals and, unlike the dance in Graj and Manipur, use many instruments and focus less on deities and more on stories of mortal love. One variation, the rās līlā, found particularly in Uttar Pradesh, reenacts Krishna legends in various celebrations, and some local variants have sophisticated patterns of foot stamping and flowing arm movements. In the Punjab, jhummar seems to be a variation on bhangṛā (see below), but is performed by women with sticks during festivals like Navarātra. Again, women move in circles, often pirouetting (as in other Indian circle dances) and striking pairs of sticks together and against those of other dancers.

In Kerala and Karnataka, another variation on rāsa is the kōlāṭṭam, a ribbon and braid dance that originally was a fertility dance, but which has also come to symbolize the triumph of the goddess Mohini over the demon Basmasura. Although the dance has developed agricultural associations throughout the decades, the kōlāṭṭam's popularity has spread to homes, schools, and cities, making the dance primarily social today. Some communities, however, still maintain the earlier principles of the kōlāṭṭam. In Tamil Nadu, for example, girls perform the kōlāṭṭam by moving around the circle or square and hitting sticks high and low as they bend from side to side. Opposing dancers hit sticks as they dance around the circle, moving forward and backward, leaping onto and away from their toes. Kōlāṭṭam can also focus on religious, philosophical, or musical ideas through song, and may celebrate deities such as Rāma.

Dances celebrate many occasions in the Punjab, but by far the best-known Punjabi dance is bhangrā, originally performed by farmers after a harvest but now widely performed by men in public contexts. Again, this dance is gendered. Women sometimes perform bhangrā, but only in private contexts, such as in the home or with family. However, when men perform bhangrā, they commonly engage in intensely kinesthetic movement meant to illustrate the physical prowess of the dancers. They may even engage in gymnastics and activities such as human pyramids. The jumps, spins, bends, and other exaggerated movements in time with the drumming are usually accompanied by the dancers holding their arms above their heads, often snapping their fingers, with the head either slightly downturned or bent back, suggesting a kind of self-absorption. Bhangrā became one of the most popular dance forms in twentieth-century popular Indian films and, because of this identity, bhangrā and its variations have spread internationally, especially in British club settings. Today, bhangrā-like dances can be seen in wedding processions in Bengal, Gujarat, Himachal Pradesh, and Kerala.

Some folk dances have become the subject of elaborate urban and suburban competitions that attract thousands of people. Bhangrā, garbā, and dandīārāsa are the choreographic fields upon which dance clubs and teams compete; they are judged not only on the intricacy and execution of the dances, but also for their costumes and stage props. One part of the strategy for a successful performance in these competitions is to evoke historical or regional variations. Bhangrā dancers might swing a farmer's stave (lāthī) as part of their choreography, attempting to evoke an authenticity to their dance (the presumption being that a rural performance would be more "authentic" than an urban or suburban performance), but also demonstrating the virility of the men dancing (the lathi being a formidable weapon in the right hands). In garbā competitions, women and girls will often dance with pots on their heads, sometimes with lamps burning inside, and, in the most elaborate situations, some performers may dance with a mandapikā (lamp tree). Dandīārāsa competitions may have the most elaborate choreographies. The essential dance pattern itself is already complex: an inner circle moves counterclockwise, an outer circle moves clockwise, and dancers are paired with a different partner after each set of gestures and one partial rotation of each of the circles. The gestures can be simple (the commonest consisting of about eight strikes against your partner's sticks and your own) or much more elaborate (e.g., dancers twirl before, during, and after the strikes, perhaps also kneeling and striking the floor). Dance teams can come from such diverse sources as neighborhood associations and police academies. Universities in Gujarati-speaking western India commonly have dandīārāsa clubs. All will purchase or create elaborate costumes that attempt to be both colorful and authentic, sometimes to the point of being too flamboyant and only romantically authentic.

A contributing factor to the codification of folk dance in India has been the central government, whose annual Independence Day celebrations in Delhi have regularly featured troupes of dancers from the different states. Performed in a large stadium, only those dances that involve the most people in the brightest costumes, making the grandest gestures, have an impact. The intimacy and contextual importance of the local art form is lost.

Gordon ThompsonKasha RybczykShelley Smith

See alsoDance Forms

BIBLIOGRAPHY

Thompson, Gordon. "Music and Values in Gujarati-speaking Western India." Ph.D. diss., University of California at Los Angeles, 1987.

Vatsyayan, Kapila. Traditions of Indian Folk Dance. New Delhi: Indian Book Company, 1976.

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