The Scales and Structures of Intra-Urban Spaces

Content This project will address the structure of intra-urban spaces from both theoretical and empirical perspectives, and in doing so will provide a foundational reference both for the scales at which urban science may most productively be directed, and for understanding inter-relationships between properties observed across multiple scales. Hypotheses The primary hypotheses addressed by the project are: 1. That similarity between places decays with spatial proximity in a functionally defined manner able to be both theoretically described and empirically quantified; 2. That relationships between proximity and similarity are partly subjective; 3. That spatial interaction models can be improved by considering the full covariance between all spatial points, rather than quantifying each point in terms of simple sums of contributions of all other points; 4. That cities are complex spatial systems in which path dependence implies place dependence, and which must thus manifest discernible spatial discontinuities. Methods Methods developed in this project will build on a novel theoretical foundation to describe how functional relationships between proximity and similarity arise within urban spaces. Resultant theoretical models will inform empirical methods used to quantify empirical proximity--similarity relationships from several large cities of the global north, with both theories and methods incorporating consideration of the potential subjectivity of proximity--similarity relationships. A second component will extend spatial interaction models to describe the statistical properties of spatial covariance matrices, and will use these models to empirically discern spatial discontinuities between urban regions. Discontinuities will be quantified though adapting maximum-entropy descriptions successfully used to quantify the spatial extent of ecosystems. Novel Contributions The first of three primary novel contributions of the project will be to provide a theoretical foundation for the `First Law` of geography, through developing the first fundamental description for the origin of proximity--similarity relationships. Consideration of the potential subjectivity of such relationships forms an equally important and novel aspect. The second component will extend spatial interaction models to enable description of how relationships between any two spatial points will be shared by any pairs of nearby points. Finally, the third component will use these extended models of spatial structure to discern discontinuities between spatial regions, and so allow quantification both of neighbourhood boundaries, and of hierarchical relationships between intra-urban neighbourhoods. 1

This project will address the structure of intra-urban spaces from both theoretical and empirical perspectives, and in doing so will provide a foundational reference both for the scales at which urban science may most productively be directed, and for understanding inter-relationships between properties observed across multiple scales. The primary hypotheses addressed by the project are: 1. That similarity between places decays with spatial proximity in a functionally defined manner able to be both theoretically described and empirically quantified; 2. That relationships between proximity and similarity are partly subjective; 3. That spatial interaction models can be improved by considering the full covariance between all spatial points, rather than quantifying each point in terms of simple sums of contributions of all other points; 4. That cities are complex spatial systems in which path dependence implies place dependence, and which must thus manifest discernible spatial discontinuities. Methods developed in this project will build on a novel theoretical foundation to describe how functional relationships between proximity and similarity arise within urban spaces. Resultant theoretical models will inform empirical methods used to quantify empirical proximity--similarity relationships from several large cities of the global north, with both theories and methods incorporating consideration of the potential subjectivity of proximity--similarity relationships. A second component will extend spatial interaction models to describe the statistical properties of spatial covariance matrices, and will use these models to empirically discern spatial discontinuities between urban regions. Discontinuities will be quantified though adapting maximum-entropy descriptions successfully used to quantify the spatial extent of ecosystems. The first of three primary novel contributions of the project will be to provide a theoretical foundation for the `First Law' of geography, through developing the first fundamental description for the origin of proximity--similarity relationships. Consideration of the potential subjectivity of such relationships forms an equally important and novel aspect. The second component will extend spatial interaction models to enable description of how relationships between any two spatial points will be shared by any pairs of nearby points. Finally, the third component will use these extended models of spatial structure to discern discontinuities between spatial regions, and so allow quantification both of neighbourhood boundaries, and of hierarchical relationships between intra-urban neighbourhoods.