The seminar given on the 5th December by Professor Mike Worboys was entitled: ‘A Fresh Look at the Object-Field Dichotomy’. In Mike’s own words, this was a ‘fairly abstract’ talk that looked at the mathematical structures lying behind geographical objects and fields, as well as introducing a fresh look at their definitions.

Professor Worboys, an Honorary Professor in the School of GeoSciences here at Edinburgh, is a mathematician by trade, and throughout his career has tried to bridge the gap between GIS and the mathematical theory behind it.

The talk started by outlining the well-known ‘object-field’ model of the world, and the functional relationships joining entities to their attributes (object model), or specific locations with attributes (field model). These are simple ‘timeless’ models of the world, and can be stored in mathematical structures using set theory.

The location of an object or field however, can be expressed spatially (S), temporally (T), or spatio-temporally (SxT) i.e. the product of the spatial and temporal location. Space and time can be represented in several ways, such as on a Cartesian plane, graphs, in 3D (space), or in simultaneous temporal dimensions.

Bringing in this spatio-temporal dimension requires objects and fields to be expressed differently, and some ways of doing this have been suggested, such as Goodchild’s ‘geo-atom’. According to Prof. Worboys this is more of a field-based approach as it begins with the location of the point, followed by its property at that location.

Prof. Worboys introduced the concept of viewing entities as ‘Continuants’ (i.e. things that exist such as a house, a person, a table), or ‘Occurents’ (i.e. events that happen in space-time). This is known as the ‘Snap-Span’ approach. A temporal snapshot is a series of continuants that may differ at each snapshot (‘Snap’ approach), whereas the ‘Span’ approach views the world as a collection of events, with objects existing or changing as a result of these events.

Prof. Worboys then introduced the work of two mathematicians, Leonhard Euler and Joseph-Louis LaGrange, and how their two different models of physical processes can be used to explain geographical entities, much like the object-field approach. Both models were originally developed to explain motions in fluid, and so can be explained as such.

The Eulerian approach imagines that one stands on the bank of a river, and focuses on one spot in the water, of which several attributes may change through time (such as flow rate, temperature, etc.). This is a pure field approach, where the value of an object is found as a product of its location in space and time. This can be done by beginning with the spatial location, followed by the time to find the value (a time series approach), or beginning with the time followed by the spatial location to find the value (snapshots of spatial patterns).

The LaGrangian approach is the opposite. It imagines that one sits on a boat and follows the water (entity) downstream, noting how the attributes of the entity change through time. This can be a mixed or pure object approach, where the value of the entity (which can include its location) is found by combining the entity with time. Starting with time, and then finding the entity to find the value is a mixed approach (snapshots of entity patterns), whereas beginning with the entity and adding the time to find the value is a pure object approach (which produces ‘trajectories’ of the entity through time).

A case study was then used to explain this. When measuring pedestrian movement in a city, the Eulerian approach would be to set up checkpoints and measure the number of pedestrians passing through a certain point or area in a certain time. The LaGrangian approach would be to follow each pedestrian and map their movement through time, to create ‘trajectories’.

Prof. Worboys finished by highlighting the difficulties that may arise when trying to move between the Eulerian and LaGrangian approaches, similar to the difficulties found moving between object and field approaches.

Duncan Kinnear

(MSc in GIS at the University of Edinburgh)