User:Sebastianvattamattam

'Sebastian Vattamattam', is a professor of Mathematics, deeply interested in art, culture and society. Also he does research in Mathematics, as a hobby. Publications: 1. Paristhithi Samskruthi(Ecology & Culture)- Malayalam(Together with S. Kappen) 2. Bhashayum Aadhipathyavum(Language and Hegemony) - Malayalam. 3. Engineering Mathematics – First Year B.Tech Course, Vidyarthimithram, 2006. 4. Prathi-Samskruthiyilekku(On the Thoughts of Sebastian Kappen) Research Papers in Mathematics: 1. “Quadratic Extensions of a Field and their Classification”, presented at the National Seminar on Analysis and Applications, held at U. C. College, Aluva, March 26-28,1999 2. “Associative Algebras via Linear Functionals”, Proceedings of the International Seminar on Mathematical Tradition of Kerala, January 17-19, 2000 3. “A Note on Convolution Algebras”, Chapter 6 in Recent Trends in Mathematical Analysis, Allied Publishers, 2003. 4. ``Non-Commutative Function Algebras", Bulletin of Kerala Mathematics Association, Vol.4, No.2, December 2007. 5.``Transforming Curves by n-Curving, Bulletin of Kerala Mathematics Association, Vol.5, No.2, December 2008. Teaching Experience • Loyola School, Goa, 1972 – 75 [3 years] • St. Berchmans College, Changanachery, 1975 – 82, 1985 – 92, 1993 – 2000 [21 years] • Dutse Teachers College, Kano State, Nigeria, 1982 – 85 [ 3 years] • Pakshama School, Doha, 1992 – 93 . College of Engineering, Kidangoor(CUSAT), 2007-08 Address: Mary Bhavan'' Ettumanoor Kottayam District Kerala, India E-mail ID: vattamattam@dataone.in My Yahoo Group

Sebastian Vattamattam
The Parayas (Sambavas) living in Central Travancore in Kerala, with their distinctive traditions, beliefs, and cultural artifacts, are at the bottom end of the caste hierarchy. In the past the Parayas were traded as slaves by the upper castes. They are noted for their musicality and craftsmanship. Their chief art forms are Kõlam-thullal (mask-dance) as part of their exorcism rituals, and the fertility dance Mudyāttam (hair-dance). This note is based mainly on the Volume Manikkam Pennu (Manusham Publications, Changanacherry, Keralam) of folk songs collected from an eighty-year-old, illiterate woman Mariamma Chedathy (Mrs. Mariamma John). She, belonging to the Paraya community, was converted into Christianity at the age of fifteen. Her former name was Kõtha. As in the case of every organic society of the past, all the collective life experiences of the Parayas found their expression in lyrics, stories, and songs. Myths and symbols, born in this cradle of narratives, became the ‘mythosphere’ from which they breathed the spiritual air that sustained them. An analysis of this mythosphere gives an insight into their systems of beliefs and values. The fertility dance Mudy-ãttam begins with the following hymn: What is there that I shall praise? Who is there that I shall praise? In the East, praise the rising sun; That name, I praise that holy name. In the West, praise the setting sun; That name, I praise that holy name. In the North, praise the Mãvéli;2 That name, I praise that holy name. In the South, praise the Thévéli;3 That name, I praise that holy name. In the High, praise the sky above; That name, I praise that holy name. In the Low, praise the earth below; That name, I praise that holy name. What then is there I shall praise? Who then is there I shall praise? The people of this land I praise The people that have come I praise? [Manikkam Pennu, p. 10] The Parayas found nothing that was unworthy of their praise and admiration; nothing was to them a mere ‘thing’. Everything was invested with a plurality of meanings. Because of this respect as well as concern for all that was, our forbears didn’t allow anything to perish totally. Each tribe preserved and protected its own totem plants and animals. The totem was their god. Theodiversity and cultural diversity went hand in hand. Since gods were mainly plants and animals, theodiversity meant biodiversity as well. Mãranam pidutham is an exorcism ritual. The Paraya shaman who officiates the function is called Velan1. On a plantain leaf he places paddy seeds and ten coins and starts chanting the invocation: 15 The Earth of which I came out, The Earth in which I was, May Earth unite with Earth, May Quarters (dik) unite with Quarters, May land (dè¿am) unite with land, May the unknown (mãyam) unite with the unknown. May the dead (chãv)unite (with me) May my father unite (with me), May my mother unite (with me) May my sisters unite (with me) May Earth shine in unison with Earth, May Quarters shine in unison with Quarters, May land shine in unison with land, The gods shall shine on that land. [Informant: Mariamma Chedathy, but not included in the Book] Velan, representing the whole community, exhorts the four quarters, the unknown spirits, the land, the dead, his  father, mother, and sisters to shine forth in unison with each other. Only in such a land will the gods shine on. Velan knows that the root cause of any malady is the lack of harmony in the social and natural environments. When nations fight with each other one should pray not that his/her land wins but that his land unites with other lands. Here we are reminded of the Brahminic invocation, thamasõ mã jyotir-gamayah, and Newman’s Lead kindly light. Both betray their desire to escape from the surrounding darkness into light. The Parayas do not want to be led from the encircling darkness to light. Instead s/he wants that the darkness be dispelled by the power of the communion of all that is. S/he knows that gods cannot be pleased merely by praising them; they can be pleased only by everything that pleases everything else. The Buddha’s doctrine of universal love and compassion is not likely to have been inspired by the Brahminic philosophy of egoistic unconcern, but by the folk traditions of his times. In the apparent Paraya Advaita, everything merges with everything else, not by losing each one’s identity, but by mutual recognition and concern. Concern not only for fellow beings but also for all beings, living or non-living, gone, born, and to come. In order to appreciate these things we have to give up a number of prejudices. Any religious or scientific claim of monopoly over truth has to be given up. The theologians must realize that the divine (theo) may not  be bottled up in their logical constructs (logos). Scientific rationality must realize the futility of recognizing as real, only what it can manipulate with scientific tools. Many of the Savarna hegemonic interpretations of Indian culture will have thus to be discarded. Marxism, rooted in the hope of the ultimate dis-alienation of Humans and Nature, must recover from the present plague of economic reductionism. Just like the Parayas there are hundreds of other Dalit communities in India, each having its own philosophy of life and system of beliefs. They share certain fundamental  similarities. It is the some total of all these subterranean cultures that truly forms the real core Indian culture, as asserted by Fr. Sebastian Kappen in his Jesus and Cultural Revolution- An Asian Perspective. As an alternative to the predominant capitalist-Savarna culture there should emerge an ecosophic socialist counterculture. We have to look for the constituent elements of this counterculture in the numerous Dalit cultures. 16

In the interpretation of myths, woman and nature are often identified. There is a beautiful lyric representation of this identity in the Paraya Folklore: Father dug up the ground, Mother cleared the pits. In that pit and in this pit, Kochèri-kanni4 planted a Kõtheri-plantain. One shoot for our Kõtheri-plantain, One month for our Kochèri-kanni. Two shoots for our Kõtheri-plantain, Two months for our Kochèri-kanni. Three shoots for our Kõtheri-plantain, Three months for our Kochèri-kanni. Four shoots for our Kõtheri-plantain, Four months for our Kochèri-kanni. Five shoots for our Kõtheri-plantain, Five months for our Kochèri-kanni. Six shoots for our Kõtheri-plantain, Six months for our Kochèri-kanni. Seven shoots for our Kõtheri-plantain, Seven months for our Kochèri-kanni. Eight shoots for our Kõtheri-plantain, Eight months for our Kochèri-kanni. Nine shoots for our Kõtheri-plantain, Nine months for our Kochèri-kanni. A big bunch for our Kõtheri-plantain, A little baby for our Kochèri-kanni. [Informant: Mr. C. J. Kuttappan] These lines reflect the belief that a plantain tree and a woman have the same period of pregnancy. Both are treated with the same care and concern. The boundary line between the human and the non-human, vanishes. It is this holistic view of all creatures on earth that we have lost sight of, in our historic march to ‘progress.’ According to the Creation Myth of the Parayas, everything started from Pooyinkal Tharavad5, the primal family of the Parayas. The earth and then Pooyinkal Tharavadu came to be as follows: Once when there was no Pooyinkal house, Fluttering flew up seven6 dragonflies. From the south-west7 corner (Kanni-ma-kõne) of the sea, Did they take seven balls of clay, And moulded the earth, the dragonflies. Two trees there sprouted, Chittãl8 and Pèral.9 What was next, the next to be? Darbha10 grass was the next to be. What was next, the next to be? Poovan-kurunnal11 was the next to be. What was next, the next to be? 17 Munda-varikka12 was the next to be. What was next, the next to be? Then came Pooyinkal house, all of its own, Pooyinkal house for Pooyinkal-amma. Pooyinkal-amma lived with Pooyinkal-appan. Then began Pooyinkal-amma to speak: Why no cock to herald the dawn? Why no chatter-birds to wake up the world? Cock came to herald the dawn, Chatter-birds came to wake up the world; Perched they on the branches of the trees. [Manikkam Pennu p. 11-12] The earth was created not by some god beyond and above Nature. It is seven dragonflies that made the earth with clay collected from the south-west corner of the sea. Then everything just started emerging from the earth. The last of them was Pooyinkal house for Pooyinkal-amma to live. But from where did Pooyinkal-amma come? She might be the primordial Mother of everything that is, the Mother Goddess of all the primitive societies. Though Pooyinakl-appan is likewise mentioned; nothing more is said about him. It is significant that a powerful primordial father figure is absent in Paraya mythoshere. It is such a conception of a Father-God, that paved the way for all authoritarian social formations such as the Jewish community and the Catholic Church. It is that God who gave Man (Woman was yet to be created ) dominion over the Earth and everything in it (Genesis: 1.26) Man uses this to legitimize his destructive practices leading to the ecological disaster we are in today. If the earth is the handiwork of the dragonflies that flew up from the corners of nothingness, then who is its real owner? If humans have the sole ownership of the earth then they alone have the right and duty to worship God. In the Paraya folklore we can hear the parrots praying to Parama-Siva, a prominent god of the Parayas: Thitharo thiki-tharo thaka-thiki-thara Thitharo thiki-tharo thaka-thiki-thara Give us two eyes to see and eat, Give us two beaks to peck and eat, Give us two legs to scratch and eat, Give us two wings to fly above. [Manikkam Pennu, p. 16] The parrots do not ask for their ‘daily bread’, but only for the capacity to work for it. Never did the Parayas cherish the selfish belief that humans were the only children of God, and among humans they  were specially chosen by God. Is it not such an exclusive belief that made the West conquer all other peoples with the Word of their God and their Sword? There is an interesting interaction between a girl and the fishes in a brook. The girl wants to collect some water from a shallow stream. Then starts the trouble: She broke a twig, and  dug a pool; She waited till the water was clean. 18 Vatton fish came and dirtied the water; She waited till the water was clean. Pallathy fish came and called her names; Stunned she waited till the fish vanished. Karingana fish looked at her with burning eyes; Stunned she waited till the fish vanished. Kolachi fish came with an angry look; Stunned she waited till the fish vanished. [Manikkam Pennu, p. 28] These lines show the recognition that the humankind have no exclusive control over the resources of this planet. Taking water from a brook by violently digging a hole in it is an aggression on the brook and its natural inhabitants. If so what about the big dams that we build with no concern even for the humans around? In the Paraya mythology there is no authoritarian God who has absolute power and control over everything. But they find a tinge of the divine in everything that they come into contact with – on the tree they are going to climb, on the sword they are going to fight with. In everything they find a spark of the Unutterable, and show respect and reverence to it. All their forbears, the gone and the killed, would come to their help in their need, they believe. That is why whenever their great heroes like Chengannur-athi and Kamacha-velan, were about to leave the house for a fight or a mate, they prayed: May the Churika-god abide in my churika (sword), May the Paricha-god abide in my paricha (shield). May the killed forbears abide in my hair, May the dead and the departed come to my help. Theology and scientific rationality have gathered all the elements of the divine and the sacred from all in Nature, and cast  them out. [This unholy alliance between the two avowed antagonists can be symbolized by the White Man with the Bible in one hand and the Sword in the other.] This has paved the way for the human, to enter every nook and corner of this world as an elephant does into a plantain grove. The search for a new Echo, Dalit, or Feminist theology ought to be a sort of remorseful attempt to retrace the steps.  	May be the Velluvan (Paraya) priest at the court of the Pallava kings. [Sharad Patil, Dasa-Sudra Slavery, p. 85]  The Mahãbali, a mythical benevolent ruler.  	Sree-devi, an ancient Mother Goddess  	A newly married girl  A matrilineal joint family  The mother goddesses are said to be seven in number. [Sharad Patil, Dasa-Sudra Slavery, p. 30]  Nirurti, the ancient mother goddess, is supposed to be in the south-west region. [Sharad Patil, Dasa-Sudra Slavery, p. 86]. South-west direction has a synonym Kanni-disa, in Malayalam, where kanni means unmarried or newly married  girl. Kannyakumari is at the south-west region.  Chit-arayãl: A tree smaller than Arayãl (Pipal tree), having medicinal powers. 19  Banian tree  	A kind of sacred and medicinal grass, Poa cynosuroides.  One of the ten sacred and medicinal flowers, associated with the goddess Sree-devi of prosperity.  Jack fruit tree 

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================ Curves in the Complex Plane Let C denote the field of Complex numbers. A continuous function γ from the closed interval [0, 1] of real numbers to the field C is called a curve. The complex numbers γ(0) and γ(1) are, respectively, the initial and terminal points of the curve. If they coincide, the curve is called a loop. The set C[0, 1] of all the curves is a vector space over C.

We can make this vector space of curves into an algebra by defining multiplication as above. Choosing $$e(t) = 1 $$ for all t in [0, 1] we have for α,β in C[0, 1],
 * $$ {\alpha} \cdot {\beta} = {\alpha}(0){\beta} + {\beta}(1){\alpha} - {\alpha}(0){\beta}(1)e $$

Then, C[0, 1] is a non-commutative algebra with e as the unity.

We illustrate this with an example.

Example Let us take (1) the unit circle with center at the origin and radius one, and (2) the line segment joining the points (1, 0) and (0, 1). As curves in C[0, 1], their equations can be obtained as
 * $$u(t)=\cos(2\pi t)+i\sin(2\pi t)$$ and $$ f(t)=1-t +it $$

Since $$ u(0)=u(1)=1$$ the circle u is a loop. The line segment f starts from $$f(0)=1 $$ and ends at $$f(1)= i $$

Now, we get two f-products u\middot f and f\middot u given by
 * $$(u\cdot f)(t)=[1-t - \sin (2\pi t)] +i[t-1+\cos(2\pi t)]

$$ and
 * $$(f\cdot u)(t)=[-t+\cos (2\pi t)]+i[t+\sin(2\pi t)]$$



Observe that $$ u\cdot f \neq f\cdot u$$ showing thet multiplication is noncommutative.