Jean Petitot Knihy

Exploring the rich field of semiotics, this book delves into the ways signs and symbols shape meaning across various European cultures. It examines theoretical frameworks and practical applications, highlighting the contributions of key thinkers in the field. By analyzing diverse texts and visual media, the work reveals how semiotic principles inform our understanding of communication, identity, and cultural narratives. The text serves as both an academic resource and an insightful commentary on the interplay between language, culture, and society in Europe.

Focusing on the mathematical modeling of the primary visual cortex, this book presents an original geometrical framework for understanding its neural architecture. It explores how visual neurons filter optical signals through wavelet analysis and illustrates the relationship between the contact structure of curves in the retinal plane and cortical architecture. Additionally, it models the visual algorithms that integrate contours from incomplete sensory data using sub-Riemannian geometry, providing insights into the neurogeometry underlying visual perception.

This book – written in collaboration with René Doursat, director of the Complex Systems Institute, Paris – adds a new dimension to Cognitive Grammars. It provides a rigorous, operational mathematical foundation, which draws from topology, geometry and dynamical systems to model iconic «image-schemas» and «conceptual archetypes». It defends the thesis that René Thom’s morphodynamics is especially well suited to the task and allows to transform the morphological structures of perception into Gestalt-like, abstract, proto-linguistic schemas that can act as inputs into higher-level specific linguistic routines. Cognitive Grammars have drawn upon the view that the deep syntactic and semantic structures of language, such as prepositions and case roles, are grounded in perception and action. This study raises difficult problems, which thus far have not been addressed as a mathematical challenge. Cognitive Morphodynamics shows how this gap can be filled.