O número no espectro arquetípico: psicogênese do imaginário matemático

Abstract

This work proposes an explanation guided by the theoretical framework of Analytical Psychology, specifically the archetypal spectrum theory, about how mathematical products derive from an instinct of grasp and discrimination of quantities and become a symbolic and well-formulated language that intertwines with cultural images. Taking mathematics as a product of archetypal nature, a psychological investigation is traced here starting from animal mathematics and moving towards anthropological studies of the imaginary, aiming to delineate the relationships between mathematical products and human culture. Three movements are also proposed as explanatory devices for the relationships between mathematics, humanity, and culture, namely, the first one, called "dextrogyrus movement" which addresses the relation between cultural materiality and the understanding and making of mathematical ideas; The second, called "sinistrogyrus movement", refers to the relationship between the unconscious dynamics of archetypal images and mathematical knowledge, and finally, the "prorsus movement" which specifies how new mathematical knowledge is assimilated into the vast cultural framework. The educational possibilities that stem from the understanding of these movements and the rescue of mathematics as a human thing, treasuring its poetic and imaginary identity, are also approached.