Topological and Dynamic Morphologies in Semiotics

This contribution gives an overview of the evolution of major applications of C.T. (catastrophe theory) in semiotics. The first part describes the historical (and contemporary) context of C.T. applications in linguistics and rival or comparable theories in the field of linguistics and semiotics (generative and cognitive grammar; dynamic models such as chaos theory, fractal geometry, dissipative structures, and “synergetics”). The second part details the use of the elementary catastrophe called “cusp” in catastrophe theoretical semantics. It shows how to understand its geometrical and dynamical properties, to derive linear paths in unfolding the “cusp”, and gives further technical details. Furthermore, it demonstrates that this tool is accessible even for non-mathematicians (presupposing just a high school level of expertise). Two other sections mention applications to visual semiotics and the semiotics of music. Finally, the last part discusses the relevance of this type of mathematical (topological and dynamic) modeling in semiotics/linguistics and its potential for the future.