Foreword: On Grids and Networks

Abstract

The “grid” and the “network” have become pivotal notions in a wide variety of areas of research and creation. The present volume constitutes indisputable evidence of this trend. It is truly amazing that the same structural concepts are shared by such an abundance of fields as modern art, urban planning, the creator’s role in aesthetics, music, computer-aided design and production, acting, cinema art, verbal interaction, and virtual reality. This collection of essays will most probably challenge many researchers to fine-tune the grid aspects common to the varied multiplicity of fields, and will open new venues to promote them. It corresponds, though not directly or too strictly, with the international conference entitled “The Multidisciplinary Grid 2020” that took place in November 2020 at HIT – Holon Institute of Technology (an institution of which both the Editors and I are members). The conference, organized by the Department of Multidisciplinary Studies, was aimed at exploring the “grid” as a cross-disciplinary theme. It strove to explore a new horizon of relationships and fusion of the “grids”, and to foster a fruitful dialogue concerning gridded interpretations among researchers, practitioners, and artists.1 Although a distinction between the grid and the network may not be mandatory-and the present collection further blurs and softens the boundaries between them – it is still tempting to somewhat elaborate on potentially different emphases. These varied emphases, or focal points, may promote a better understanding of the foundations and the discovery of new potential directions, which might be of interest to experts in many diverse areas. The following remarks point to this path in conversation between exact sciences, applied science, fine arts, and humanities. As a mathematician, I admit to a slight and quite expected bias towards the first two of these areas. Mathematicians seem to have started dealing with these structures in the seventeenth century, specifically through ideas expressed by Gottfried Wilhelm Leibniz –a world-renowned mathematician, contemporary of Isaac Newton. Many consider Leonhard Euler’s 1736 paper, “The Seven Bridges of Königsberg” (which provided a systematic solution to a popular puzzle), to be the starting point of what is presently known as “Graph Theory.” In the formal, abstract-cum-precise language of mathematics, a graph is a set of objects referred to as “vertices”, together with a prescribed set of pairs from among these vertices, referred to as “edges.” Many would realize this notion as a set of points in a plane with lines connecting a number of pairs from among those points. A “graph” is therefore an abstract notion: more than what is actually considered in a graph are the aspects that are not of issue; essentially, it has nothing to do with graphics. The location of vertices is not significant, and so are the geometrical properties – straight or curved – of the edges connecting some of them;