A Higher-Order Perspective on the Foundations of Geographic Information Science

Like all other academic disciplines, Geographic Information Science (GIScience) rests on a set of foundational ideas or principles on top of which all further work is based. These include Tobler’s First Law of Geography, conceptual models such as fields and objects, and the interplay of spatial heterogeneity and spatial dependency. While these foundations are often stable over long periods, revisiting and questioning them is essential as GIScience evolves with new insights and technologies from neighbouring disciplines. For instance, some of our foundational assumptions and everyday practices are from a time when the cost of computing was a limiting factor. Therefore, this dissertation seeks to rethink three widely accepted foundational principles of GIScience, namely pairs, direction, and geometry, to bridge the gap between the ever-changing landscape of technology, the broadening interest in spatial analytics across domains, and spatial thinking. More generally speaking, GIScience practice typically does not go beyond individual observations and pairs thereof. However, is direction truly about pairs, or is it higher-ordered? This dissertation will motivate the need for a geo-multipole, a new geographic conceptualization, as a direct extension of the geo-atom and geo-dipole that simultaneously considers observations of more than two locations. It will then apply the geo-multipole to ask whether direction was not overlooked in the original formulation of Tobler’s First Law. Finally, we will discuss how thinking in binary predicates in graph-based representations of geographic information has hindered the inclusion of qualitative higher-order relations such as betweenness