Geometría, diagramas y movimiento en la física matemática de Leibniz

Abstract

In this paper, we examine the general guidelines that allow us to understand how Leibniz transitioned from pure mathematics (algebra and geometry) to natural science, with the aim of mathematizing the latter. To this end, we first summarize how Leibniz conceived of physical space from the perspective of his dynamic concepts, especially in relation to abstract or mathematical space. Within this framework, we also propose some guidelines for differentiating between physical and abstract time. Third, we address issues of universal or general mathematics and analysis situs, with the objective of proposing an intermediate discipline, the tornatoria, or the science of the traces of movement, as a link that allows the application of geometric forms to different aspects of physical motion. In this sense, the tornatoria can be conceived as static aspect of motion. We then propose some concrete examples for generating geometric forms through compositions of movements. Finally, in the conclusions, we project the general guidelines to delve deeper into this analysis through the theory of ductus or “transport”.