The Transformations of Physico-mathematical Visual Thinking: From Descartes to Quantum Physics

After the Copernican revolution, it was clear that the experience of vision could no longer be considered a completely reliable source of knowledge due to the optical relativity of motion. Furthermore, new optical instruments (telescope, microscope) pointed out the epistemological problem of the limits of human vision. However, the spatial-visual representation of physical phenomena by geometry remained a stalwart scientific practice and the source of certain conclusions. But, as is known, the algebraization of geometry by Descartes’s analytic geometry broke the correspondence between arithmetic or algebra and its intuitive geometric meaning. In mathematical semiotics, we passed from iconic symbols to arbitrary signs. The change led to a reduction of geometry to algebraic calculus and the abandonment of visual geometric thought. The analytical geometry of Descartes, on the other hand, involved a new geometric visualization of physico-mathematical relations. The birth of non-Euclidean geometries, the special and general relativity theories, and the four-dimensional representation of space–time inspired a new chrono-geometric graphic representation. Quantum physics and quantization of space–time required a completely new mathematical creative imagination to understand Nature.