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As Christopher Alexander conceived and defined through his life's work - TheNature of Order - wholeness is a recursive structure that recurs in space andmatter and is reflected in human minds and cognition. Based on the definitionof wholeness, a mathematical model of wholeness, together with its topologicalrepresentation, has been developed, and it is able to address not only why astructure is beautiful, but also how much beauty the structure has. Given thecircumstance, this paper is attempted to argue for the wholeness as thescientific foundation of sustainable urban design and planning, with the helpof the mathematical model and topological representation. We start byintroducing the wholeness as a mathematical structure of physical space thatpervasively exists in our surroundings, along with two fundamental laws -scaling law and Tobler's law - that underlie the 15 properties forcharacterizing and making living structures. We argue that urban design andplanning can be considered to be wholeness-extending processes, guided by twodesign principles of differentiation and adaptation, to transform a space - ina piecemeal fashion - into a living or more living structure. We furtherdiscuss several other urban design theories and how they can be justified byand placed within the theory of wholeness. With the wholeness as the scientificfoundation, urban design can turn into a rigorous science with creation ofliving structures as the primary aim.  Keywords: Beauty, life, scaling law, adaptation, differentiation, and organicworld view

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