The Shift Towards Structure

Abstract

In this Chap. 1 flesh out the concept of structure and I explain the necessary link between structure and form. Scientists build models and theories that capture, in a more or less accurate way, the regularity of the world. This is possible because nature is structured. Modern physics studies symmetry by discovering the physical laws that remain unchanged when the system is viewed from different perspectives or undergone transformations (Zee A (2007) Fearful symmetry: the search for beauty in modern physics. Princeton Science Library, Princeton). Mathematics provides provable knowledge about the real world and this is due to the fact that mathematical structures deal better than anything else with the structure of the world. That is to say, there is a structure preserving mapping between the mathematical structure that models the world and the world itself. Mathematics aims to provide formal descriptions that capture the general structure in the most economic way. Set theory and category theory are two mathematical languages capable of describing a wealth of interrelationships between structures. Mathematical structures can be modeled themselves as a set of objects with certain distinguished relations and operations within a set or category. The main motivation of this chapter is thus, to formally frame the concept of structure, within a single unified framework.