Geometry as a Persisting Backbone Metalanguage to Architecture

Abstract

Albeit Architecture is not mere Geometry, much of Architecture is about Geometry. Either in real shapes, or in representational models, or in theoretical terms. Three simple questions should suffice to illustrate the point. What would a cathedral be, without its geometric feature? What would a BIM model collapse in, without its geometric framework? 
What would architectural theory be based on, without its reference to geometry of space? That is, looking through an ideal infrared lens, Geometry is revealed everywhere in the architectural field, from the dawn of time, and throughout the different
technological eras. And not only in the architectural field, as René Descartes officially highlighted, establishing Geometry at the base of the nexus between logical (λόγος) and visual (γραφή) thinking1, in the last decades widely reconfirmed, also at the computational test. This dual nature, making Geometry working as a metalanguage2, so beneficial in agglutinating the multi-disciplinary field of Architecture, is even more to be considered when facing the challenges promised by AI (fig. 1), either in research or in the professional world, and especially in Geometry education, which is still our priority mission. Then, a further question seems to emerge. What would AI based architectural design be without Geometry? This paper aims at discussing some of the implications related to these topics, including some simple generative tests made with Midjourney and ComfyUI, and an instant tip from Chat GPT.