A measurement theory for time geography

Hagerstrand's time geography is a powerful conceptual framework for understanding constraints on human activity participation in space and time. However, rigorous, analytical definitions of basic time geography entities and relationships do not exist. This limits abilities to make statements about error and uncertainty in time geographic measurement and analysis. It also compromises comparison among different time geographic analyses and the development of standard time geographic computational tools. The time geographic measurement theory in this article consists of analytical formulations for basic time geography entities and relations, specifically, the space-time path, prism, composite path-prisms, stations, bundling, and intersections. The definitions have arbitrary spatial and temporal resolutions and are explicit with respect to informational assumptions: there are clear distinctions between measured and inferred components of each entity or relation. They are also general to n-dimensional space rather than the strict two-dimensional space of classical time geography. Algebraic solutions are available for one or two spatial dimensions, while numeric (but tractable) solutions are required for some entities and relations in higher dimensional space.