Gestaltungsmetrik : Parallel transport in arts and culture for topological and holonomical activity

Abstract

This treatise introduces Gestaltungsmetrik as a con¬ceptual framework for studying and designing infor¬mal spaces, from image and Gestaltung to anatomy and materials. In mathematics and physics, the nexus between movement and space can be described by parallel transport on a metric space. This nexus may define analogue activity related to nontrivial geome¬tries such as anholonomy effects due to transport on geometries, leading to holonomic computing and topological nonreciprocity or filtering. Yet the notion of metric spaces for activity design, particularly in the context of cultural and material sciences, is far from widespread. This prompts a rethinking of broadly defined parallel transport along nontrivial metric spaces with the aim of clarifying and improving the design of geometric activity. Gestaltungsmetrik emerges as the study of informal spaces by focusing on the intended anholonomy of parallel transport on an underlying latent Riemannian metric, imbuing agents with geometric activities in physical, artistic, societal and cultural spaces.