Cultural Symmetry: From Group Theory to Semiotics

This chapter provides an overview of research on symmetry dynamics in cultural creations around the world that shed light on human cognition. This is accomplished first of all by paying attention to a range of historical conceptual developments and their methodologies with an initial focus on the origins of mathematical group theory and group theory’s eventual applications within anthropology for the comparative analysis of symmetrical patterns between (and across) cultures. The chapter presents basic group theoretic classification schemes of finite patterns and tiling plane patterns that are enabled by thinking of symmetry as invariant correspondences related by generative transformations along an axis of translation or across an axis of reflection or rotation. This discussion is followed by a survey of key stages in the development of plane pattern analysis applied to folk art designs from material culture and related socio-cultural dynamics. The chapter then shifts to a range of other perspectives on symmetry dynamics at work in areas traditionally studied by the arts (including the humanities, social sciences, and fine arts). Theories of structural semiotics, rhetoric culture, process semiotics, embodied cognition, cognitive semiotics, and semiotic anthropology provide important leverage for understanding the functions and meanings of symmetry relations at work in everything from brand mark designs and literary structures to neurological lateralization and the evolution of upright posture. Recent research on the chiasmus figure receives special attention, along with the role of symmetry (and symmetry breaking) in ritual contexts. Ultimately the chapter suggests that this under-researched area of human culture and cognition holds much promise for understanding the nature and meaning of both cognitive mathematics and human experience.