АЛГЕБРАЇЧНІ МОДЕЛІ СИМЕТРІЇ БАЛТО-СЛОВ’ЯНСЬКИХ ФОЛЬКЛОРНИХ ТЕКСТІВ

Abstract

The present article suggests a tool for describing and analyzing the folklore texts' symmetry by introducing basicconcepts of abstract algebra: set theory, group theory, function, equation, and symmetry. The mathematical model showsthe internal homogeneity of folklore texts composition that is valid across the genre boundaries. The compositionallymeaningful entities of different language levels that constitute the core of a compositional pattern can be divided intotwo sets connected by a function of symmetrical reflection. Each element of the first set A is projected onto the elementof the second set B. The set A can be called input, the symmetrical set B – output. On the metrics and rhyme level, it isa constant reiteration of the same pattern reflected ad infinitum. On the level of syntactic order, this function connectssentences that constitute parallelistic structures. Thus, the composition and perception of folklore texts resemblea succession of linguistic equations: a singer introduces independent variables that should be given a specific dependentvariable, which can be chosen only from the thesaurus of elements accepted by a specific folklore tradition. The functionthat associates elements of the input set with the output set is the folklore poetics itself, so it can be defined in a seriesof elementary equations that show the connection between the number of compositionally significant elements and otherproperties of the texts, mainly the type of symmetry that is inherent to a particular text. Though all main types of symmetrycan be detected in the folklore texts, they can be reduced to a basic operation of reiterating a small number of elements belonging to one set, connected by an operation of symmetrical reflection constituting a group of symmetry. Compositionpatterns of seemingly different genres (riddles, ritual songs, cumulative fairytale, magical fairytale) have one fundamentalfeature in common that underlies them: when the enumeration of the input set A is over, the level of freedom for the choiceof the output set B is highly restricted, as each of the linguistic equations (L. Zadeh) should be solved: the hero, onceborn, should be either married or killed, the riddle should be answered traditionally, set of images of human life shouldbe confronted with the set of corresponding images of nature (in ritual songs), etc., thus giving the recipient pleasureof constant reiteration and decipherment of already known patterns. In this case, the new meaning of folklore texts canbe revealed. By introducing repetitive patterns of composition, they introduced elementary classification and logic tools.In this case, phenomena like I Quing turned out to be not an exception but rather a logical continuation of binary logicof folklore text composition, so overtly represented in the Balto-Slavic area but valid for a much broader realm of folkloretraditions.