Knowledge as Ecological Cosmopoiesis: From Euclidean Geometry to Geometrical Bioinspiration

The paper aims to outline a historical-epistemological trajectory that highlights the processes of ecologization of the mappings and geometric-mathematical models produced by Western civilization, thus developing a path in four stages. The first is marked by Euclidean geometry, whose metric rigor reduced the complexity of natural patterns to pure, ideal forms. However, the belief that Euclidean geometry constitutes the ontology of reality has been challenged by non-Euclidean geometries and by the reflections of the mathematician Imre Toth, according to whom geometry is not the ontological language of the world but, conversely, an activity of the human mind that implies a cosmopoiesis, the construction of infinite possible cognitive worlds. From this perspective, the fractal world is an exceptional case. Benoît Mandelbrot, for the first time in the history of Western mathematics, marks the end of the a priori application of models to reality, to observe the intrinsic patterns and forms of nature itself. Finally, we now witness a tendency, in biological avant-gardes, not only to observe the fractal forms of nature but also to relate natural geometry to the cognitive faculties of ecosystems, as shown by the studies of Stefano Mancuso. In this case, the biological geometry of nature becomes the reflection of the mind of ecosystems and, above all, can become a source of Bioinspiration: the possibility of rethinking social, urban, and digital systems looking at the organization of the natural world.