Foreword: On Grids and Networks

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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;
前言:论网格与网络
“网格”和“网络”已经成为各种研究和创造领域的关键概念。目前的数量是这一趋势的无可争辩的证据。现代艺术、城市规划、创作者在美学中的角色、音乐、计算机辅助设计和制作、表演、电影艺术、口头互动和虚拟现实等众多领域都有着同样的结构概念,这真是令人惊讶。这本论文集很可能会挑战许多研究人员对网格方面进行微调,以适应不同领域的多样性,并将开辟新的场所来推广它们。它与2020年11月在哈工大-霍伦理工学院(编辑和我都是该学院的成员)举行的题为“多学科网格2020”的国际会议相对应,尽管不是直接或过于严格。这次会议由多学科研究部门组织,旨在探索“网格”作为一个跨学科主题。它努力探索“网格”的关系和融合的新视野,并促进研究人员,从业者和艺术家之间关于网格解释的富有成效的对话尽管网格和网络之间的区别可能不是强制性的——而且目前的集合进一步模糊和软化了它们之间的界限——但对潜在的不同重点进行详细阐述仍然是诱人的。这些不同的重点或焦点可能促进更好地理解基础和发现新的潜在方向,这可能是许多不同领域的专家感兴趣的。下面的评论在精确科学、应用科学、美术和人文科学之间的对话中指出了这条道路。作为一名数学家,我承认对前两个领域有轻微的偏见,这是意料之中的。数学家们似乎在17世纪开始研究这些结构,特别是通过戈特弗里德·威廉·莱布尼茨(Gottfried Wilhelm Leibniz)——一位与艾萨克·牛顿同时代的世界著名数学家——所表达的思想。许多人认为莱昂哈德·欧拉1736年的论文“Königsberg的七座桥”(为一个流行的谜题提供了系统的解决方案)是现在被称为“图论”的起点。在形式化的、抽象而又精确的数学语言中,图是一组被称为“顶点”的对象,以及这些顶点之间的一组规定的对,被称为“边”。很多人会把这个概念理解为平面上的一组点,这些点之间用直线连接一些对。因此,“图”是一个抽象的概念:在图中实际考虑的不仅仅是无关紧要的方面;从本质上讲,它与图形无关。顶点的位置并不重要,连接其中一些顶点的边缘的几何性质(直线或弯曲)也不重要;
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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