Alexander's Wholeness as the Scientific Foundation of Sustainable Urban Design and Planning

TL;DR

This paper proposes a mathematical model of wholeness rooted in Christopher Alexander's concept, arguing it as a scientific foundation for sustainable urban design by guiding the transformation of spaces into living structures.

Contribution

It introduces a formal mathematical and topological model of wholeness, linking it to urban design principles and justifying existing theories within this new framework.

Findings

Developed a mathematical model of wholeness.

Linked wholeness to urban design principles.

Justified urban theories through the wholeness framework.

Abstract

As Christopher Alexander conceived and defined through his life's work - The Nature of Order - wholeness is a recursive structure that recurs in space and matter and is reflected in human minds and cognition. Based on the definition of wholeness, a mathematical model of wholeness, together with its topological representation, has been developed, and it is able to address not only why a structure is beautiful, but also how much beauty the structure has. Given the circumstance, this paper is attempted to argue for the wholeness as the scientific foundation of sustainable urban design and planning, with the help of the mathematical model and topological representation. We start by introducing the wholeness as a mathematical structure of physical space that pervasively exists in our surroundings, along with two fundamental laws - scaling law and Tobler's law - that underlie the 15 properties for characterizing and making living structures. We argue that urban design and planning can be considered to be wholeness-extending processes, guided by two design principles of differentiation and adaptation, to transform a space - in a piecemeal fashion - into a living or more living structure. We further discuss several other urban design theories and how they can be justified by and placed within the theory of wholeness. With the wholeness as the scientific foundation, urban design can turn into a rigorous science with creation of living structures as the primary aim. Keywords: Beauty, life, scaling law, adaptation, differentiation, and organic world view