A Recursive Definition of Goodness of Space for Bridging the Concepts of Space and Place for Sustainability

TL;DR

This paper introduces a recursive, mathematical model of wholeness to evaluate the goodness and sustainability of physical spaces, bridging the concepts of space and place through a holistic perspective.

Contribution

It develops a structural, recursive definition of space's goodness based on wholeness, linking space, place, and sustainability within a mathematical framework.

Findings

A recursive model of wholeness quantifies space goodness.

Spaces are considered more or less sustainable based on their wholeness.

The approach integrates geography and architecture into complexity science.

Abstract

Conceived and developed by Christopher Alexander through his life's work: The Nature of Order, wholeness is defined as a mathematical structure of physical space in our surroundings. Yet, there was no mathematics, as Alexander admitted then, that was powerful enough to capture his notion of wholeness. Recently, a mathematical model of wholeness, together with its topological representation, has been developed that is capable of addressing not only why a space is good, but also how much goodness the space has. This paper develops a structural perspective on goodness of space - both large- and small-scale - in order to bridge two basic concepts of space and place through the very concept of wholeness. The wholeness provides a de facto recursive definition of goodness of space from a holistic and organic point of view. A space is good, genuinely and objectively, if its adjacent spaces are good, the larger space to which it belongs is good, and what is contained in the space is also good. Eventually, goodness of space - sustainability of space - is considered a matter of fact rather than of opinion under the new view of space: space is neither lifeless nor neutral, but a living structure capable of being more living or less living, or more sustainable or less sustainable. Under the new view of space, geography or architecture will become part of complexity science, not only for understanding complexity, but also for making and remaking complex or living structures. Keywords: Scaling law, head/tail breaks, living structure, beauty, streets, cities