The idea of discretisation
In this chapter, I discuss the history and the evolution of the tension between the notion of the continuous and the discrete, identifying a number of milestones in the form of breakthroughs and discoveries that represented radical shifts in the understanding of the world as a discrete environment. This chapter stems from the idea that the world is neither truly continuous nor utterly discrete; and that the two positions have been equally valid at different times and when applied to different scenarios. Overall, there are two views that are cast onto the world’s phenomena that suggest that any object can be considered as part of the realm of continua or that of discreteness. The general idea underpinning this section is that the discrete vision of the world becomes increasingly relevant and helpful in analysing, understanding and designing as the complexity of the phenomenon observed increases.
This chapter examines the notions of continuity and discretisation from different points of view, starting from Democritus and the atomists, and including the idea of discrete and set theory in mathematics, geometry and philosophy. The evolution of this concept is then considered along with the contribution of several key algorithmic techniques and logics, including cellular automata, voxels and fractals. The idea of this chapter is to provide a series of notional and theoretical coordinates that support the observations, hypotheses and the projects that follow in the next chapters.