How are physical and social spaces related?
– cognitive agents as the necessary “glue”

By: Bruce Edmonds
Date: 23rd May 2005
CPM Report No.: CPM-05-150

Presented at the Agent-Based Modelling topical workshop, Vienna, Decemeber, 2004.  To be published in an edited book resulting from the workshop.


Humans, animals, households, firms etc. exist in physical space.  The way these social entities are distributed in that space is frequently important to us. Some of this distribution can be clearly attributed to economic and environmental factors that are essentially independent to the social interaction between these entities .  However some of the distribution is due to the interaction between these entities – i.e. the spatial organisation of the collection of such entities is (at least partially) self-organised. 
It is difficult to study such self-organisation using statistical techniques.  Statistical techniques are more suited to dealing with aggregate properties where the variation from these properties in particular cases can be considered as due to some essentially random input.  Thus not only is the detail of the spatial organisation lost in the aggregation but also in many social cases the variation is not random.  Furthermore statistical models, in practice, require fairly drastic assumptions in order to make them amenable to such techniques.

Mathematical models (e.g. those expressed as differential or difference equations) have the potential to capture the self-organisation, but only by disaggregating the model into many separate sets of equations for each entity (or place).  This, except in a few special cases where strong assumptions hold, makes any analytic solution impossible.  Thus if one tries to apply such techniques to study self-organised distribution one usually ends up by numerically simulating the results, rather than exploiting the mathematical nature of the formalism. 

The study of such self-organisational processes has been advanced through the use of individual-based computational simulations.  This is a simulation where there are a number of individual entities in the simulation which are named and tracked in the process of the computation.  It is now well established that considerable complexity and self-organisation can result in such models even where the properties and behaviour of the individuals in the models are fairly simple.  Many of these models situate their component individuals within physical space, so that one can literally see the resulting spatial patterns that result from their interaction.  

Some of these individual-based models seek to capture aspects of communicative interactions between actors.  That is, the interaction between the modelled entities goes beyond simple cause and effect via their environment (as in market mechanisms, or extraction of common resources) but tries to include the content or effects of meaningful communication between the actors.  Another way of saying this is that the actors are socially embedded (Granovetter, Edmonds). That is to say that the particular network of social relations is important to the behaviour of the individual – or, to put it another way, a model which “assumes away” these relations will distort the phenomena.  Examples of this might include the spread of new land uses among a community of farmers or a request for households to use less water.  In such models it is often the case that influence or communication occurs between individuals who are spatial neighbours – that is to say that physical space is used as a ‘proxy’ for social space.  In such models communication or influence between individuals is either limited to local neighbourhoods or is totally global.  Thus the topologies of communication are either that of local connectivity or that or total connectivity.

However, the modern world humans have developed many media and devices that, in effect, allow communication at a distance .  For example, farmer may drive many miles to their favourite pub to swap farming tips rather than converse with their immediate neighbours.  Recently there have been some models which seek to explore the effects of other communicative topologies.  There has been particular focus on “small world” topologies, on the grounds that such topologies have properties that are found among the communicative webs of humans, in particular the structure of hyperlinks on the Internet.  However such models are (so far) divorced from any reference to physical space, and focus on the organisation and interactions that can occur purely within the communicative web.

There have been very few models which explicitly include actions and effects within a physical space as well as communication and action within a social space.  This paper argues that such models will be necessary if we are to understand how and why humans organise themselves in physical space.  A consequence of such models will involve a move away from relatively simple individual-based simulations towards more complex agent-based simulations due to the necessary encapsulation of the agents who act in space and communicate with peers. 

To establish the potential importance of the interplay between social and physical spaces, and to illustrate the approach I am suggesting, I exhibit a couple of agent-based simulations which involve both physical and social spaces.  The first of these is an abstract model whose purpose is simply to show how the topology of the social space can have a direct influence upon spatial self-organisation, and the second is a more descriptive model which aims to show how a suitable agent-based model may inform observation of social phenomena by suggesting questions and issues that need to be investigated.

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