The young infant's triangular communication in the family : access to threesome intersubjectivity ? Conceptual considerations and case illustrations

During these last decades, the notion of primary intersubjectivity has gained acceptance among developmentalists and clinicians. But a new challenge is put out to our models by recent findings on the triangular competence of the very young infant, or her capacity to simultaneously communicate with two partners at a time. This discovery raises the question of a collective form of intersubjectivity. Findings on the triangular competence of the 3- to 4-month-old interactions with father and mother in different contexts of the Lausanne trilogue play situation are reviewed and illustrated, with a view to examine whether it is based on a dyadic or triangular program and whether conditions for a threesome form of primary intersubjectivity are fulfilled. The discussion focuses on the revisions of the theory of intersubjectivity, of developmental theory, and of clinical practice these findings call for, pointing toward a three -person psychology too.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.