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

Abstract

In a good system, we would expect to find the following conditions: Any identifiable subsystems, we would hope, would be well -that is to say, in good condition. And we would hope that the larger world outside the complex system is also in good order, and well. Thus, the mark of a good system would be that it helps both the systems around it and those which it contains. And the goodness and helping towards goodness is, in our ideal complex system, also reciprocal. That is, our good system, will turn out to be not only helping other systems to become good, but also, in turn, helped by the goodness of the larger systems around it and by the goodness of the smaller ones which it contains. AbstractConceived 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 largeand 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.

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