Geometries of the gaze and the invisibility

  • Jorge Cruz Pinto Universidade de Lisboa


This research lies between the visible and the latent structures of invisibility, and is supported by my theory of the Space-Limit. It integrates a set of original geometric analysis carried out on a well-known work of a Italian Renaissance painting and several historical buildings, in Portugal and in Spain. The matrix identification of sacred geometry, and the systems of forces and vector fields between the visible and the invisible recognized by the Gestalt theory become fundamental for our research. These latent structures define the DNA of the works that crosses different architectural cultures. The specific theme of the Geometry of the Gaze is based on my geometric analysis of the famous Renaissance fresco "La Trinità" by Masaccio (1428), where "perspective as a symbolic form" (Panovsky, 1991) constitutes the device for representing the interior architectural space. Underlying the representation is a vector tracing based on the matrix principles ad triangulum and ad quadratum that unites the eyes of the various characters represented through the geometries of the gaze. Vector lines of forces construct the "frame of the visible". Geometry constructs the plot that deepens the gaze beyond the imagery of Christian iconology, allowing access to the symbolism of the Tree of Life of Jewish Kabbalah that reveals itself as the structure from the latent plane. The same matrix geometric principles are present in the successive phases of the construction of the Mosque- Cathedral in Cordoba. The “ad triangulum”, “ad quadratum” and “ad circulum” principles are also recognized in other buildings of other religious cultures, which will illustrate the discourse. Similar principles of the geometries of the gaze and the invisibility are applied in my contemporary architectural and pictorial production, such as portraits and para-architectural works, between painting, architecture and installation, developed under the theme of in praise of emptiness.

How to Cite
Cruz Pinto, J. (2018). Geometries of the gaze and the invisibility. ARCC Conference Repository.