On Perceptual Geometry, Homology, and other things I know that I know nothing about

This journal issue proposes reflections on the central role of geometry within the science of representation, tracing its cultural and disciplinary developments from the Florentine school to contemporary debates. The editorial highlights how geometry, often perceived as an elitist and inaccessible knowledge, is a connective discipline linking mathematics, drawing, and perception. It retraces its evolution from descriptive and projective methods to digital transformations involving photogrammetry, parametric modelling, and ontological systems, showing how geometry persists as an invariant and a dynamic language. Particular attention is given to perceptive geometry and homology, explored as tools for interpreting distortion, transformation, spatial continuity, and the renewed dialogue between theory and practice. References to past and present research underline the importance of opening geometry to wider academic exchange, integrating historical depth with technological innovation. In this perspective, geometry emerges as a technical foundation and a cognitive and interpretative framework capable of guiding design, research, and teaching. The volume reflects on geometry as a space where passion and rationality converge in pursuing beauty, form, and knowledge, reaffirming its role as the enduring core of representation.