Relational logics and diagrams: 'No-scale conditions'

Abstract

The paper investigates logics of relational thinking and connectivity, rendering particular correspondences between the elements of representation and the things represented in drawings, diagrams, maps, or notations, which either deny notions of scale, or work at all scales without belonging to any specific one of them. They include ratios and proportions (static and dynamic, geometric, arithmetic and harmonic progressions) expressing symmetry and self-similarity principles in spatial-metric terms, but also principles of nonlinearity and complexity by symmetry-breakings within non-metric systems. The first part explains geometric and numeric relational figures/sets as taken for "principles of beauty and primary aesthetic quality of all things" in classical philosophy, science, and architecture. These progressions are guided by certain rules or their combinations (codes and algorithms) based on principles of regularity, usually directly spatially reflected. Conversely, configurations representing the main subject of the following sections, could be spatially independent, transformable, and unpredictable, escaping regular extensive definitions. Their forms are presented through transitions from scalable to no-scale conditions showing initial symmetry breakings and abstractions, through complex forms of dynamic modulations and variations of matter, ending with some of the relational diagrammatic and topological ways of architectural data-processing outside of the spatial constraints and parameters - all through diagrams as ultimate tools of relational thinking and inference.