The Rationalism of Leonardo Da Vinci and the Dawn of Classical Science

Extract

The fundamental concept of classical science is the differential representation of movement. Classical science studies movement between two points or between two instants of time. Peripatetic physics is based on a static scheme of natural positions, and it only considers movement from the point of view of its limiting points. Its theory of movement does not take account of the local state of moving bodies at every intermediate point of their path. Classical science, on the other hand, deals with instantaneous local states, which, in the special case of a body left to itself, do not change; in the general case, the interactions of bodies consist in acceleration that is proportional to the force applied. Thus, the basic concepts for classical science are the limiting relations between the distance traversed and the time taken, and between speed and time; and these lose their meaning in the absence of an integral concept of moving bodies. Classical science appeared when the differential concept of movement became a system of differential laws, and found its essential mathematical formulation in the infinitesimal calculus. There had already existed a vague and unformed concept of a unitary local event, state, or relationship, which could be subjected to scientific analysis to the extent that it was conditioned by preceding events, states and relationships and itself determined subsequent ones. This concept had not yet been connected to the study of movement, it was sometimes applied to areas very remote from mechanics, while at other times it approached very close to physics, mechanics and mathematics, to the ideas of classical science. It approached very close—but it had not yet entered into these ideas. This was the dawn of classical science.