How are physical and social spaces related--论文代写范文精选

因此空间组织的细节不仅可以迷失在聚合的过程,在许多社会情况下也不是随机的。此外在实践中的统计模型需要一定的假设为了让他们服从。数学模型有可能捕获自我组织。下面的essay代写范文继续进行详述。

Introduction 
Even social entities such as: humans, animals, households, firms etc. exist in physical space. The way these 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 of the social interaction between these entities1 . However it is overwhelmingly likely that 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 via processes of social interaction. It is difficult to study such self-organisation using purely statistical techniques. 

Statistical techniques are more suited to dealing with aggregate properties where the deviation from these properties in particular cases can be considered as essentially random. Thus not only can the detail of the spatial organisation be lost in the process of aggregation but in many social cases the distribution of the deviations are 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 analytic nature of the formalism. It is for these reasons that the study of such self-organisational processes has been advanced primarily through the use of individual-based computational simulations. 

These are simulations 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 (Axtell and Epstein). Some of these individual-based models seek to capture aspects of communicative interaction between actors. That is, the interaction between the modelled entities goes beyond simple cause and effect via their environment (as in market mechanisms, or the 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 important aspects of 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. However, in the modern world humans have developed many media and devices that, in effect, allow communication at a distance2 . For example, farmer may drive many miles to their favourite pub to swap farming tips rather than converse with their immediate neighbours. Thus the network represented by the communication patterns of the actors may be distinct from the spatial pattern. 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 human entities 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. Thus some sort of cognitive agency will be necessary to connect the communication with the action of the individuals. This parallels Carley’s call for social network models to be agentified (Carley). Thus this paper argues that such agency will be unavoidable in adequate models of the spatial distribution of human-related actors and, further, that the spaces within which action and communication occur will have to be, at least somewhat, distinct. 

Thus the burdon of proof is upon those modellers who omit such aspects. 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.

The Schelling model of racial segregation
To illustrate the interplay of social and physical spaces, I go back to Schelling’s pioneering model of racial segregation (Schelling 1969). This was a simple model composed of black and white counters on a 2D grid. These counters are randomly distributed on the board to start with (there must be some empty squares left). There is a single important parameter, c, which is the ratio of counters of its own colour among the counters in its immediate neighbourhood (see the first diagram in Figure 1 below) below which the counter will seek to move. Each generation of this game, each counter is considered and if the ratio of same coloured counters in its neighbourhood is less than c then it randomly selects an empty square next to it (if there is one) and moves there.

It is interesting to note that, even in Schelling’s model the social topology (in this case the neighbours each counter considers in the decision to move or not) can have an effect. Figure 4 shows the corresponding graph to Figure 3 for runs of the Schelling model with a neighbourhood of distance 3. Since each counter has many more neighbours (in the later case 56 of them) it is more likely that one is satisfied with a random mix at the beginning for low values of c. In other words, it is much less likely that a counter will find itself attached to a monolithic clump of the other colour at the beginning and so will not ever move. This “flattening” of segregation for low levels of c (i.e. c < 0.35) depends upon the random initialisation of the model. If one started from an already segregated pattern then increasing the size of neighbourhoods would have a less significant effect.

I have extended this model by adding an explicit “social structure” in the form of a friendship network. That is a directed graph between all counters to indicate who they consider are their friends. The topology of this network is randomly determined at the start according to three parameters: the number of friends, the local bias and the racial bias. The number of friends is how many friends each counter is allocated. 

The local bias controls how many of a counter’s friends come from the local neighbourhood – a value of 1 means all its friends come from its initial neighbourhood, and a value of 0 means that all counters are equally likely to be a friend. The racial bias controls the extent to which a counter's friends have its own colour – a value of 1 means that all its friends have the same colour as itself and a value of 0 that it is unbiased with respect to colour and friendship. In this model this structure is then fixed for the duration of the run. This network has several functions: firstly, influence only occurs from a counter to a friend, secondly, if it has sufficient friends in its neighbourhood a counter is unlikely to seek to move and, thirdly, (depending on the movement strategy set for the run) if a counter has decided to move it may seek to move nearer to its friends (even if this move is not local).

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