Chapter 13: Towards a Generic Methodology
13.1 INTRODUCTION This study aims to enhance our understanding of social dynamics in a complex and turbulent world. It does so in part as a contribution to knowledge, but also as the basis for an improved policy analytics. Part 1 was concerned with the conceptualisation – the ontology – of social dynamics. Our ontology centred on the evolution of connections – technological and institutional – in a struggle for positional advantage: what we have described as ‘deepen-widen-warp’. It is with the search for models and methods appropriate to this ontology that Part 2 has been concerned. We began with the mathematical modelling of linear and non-linear systems. This included some treatment of specific models – for example, logistic growth – which have been widely applied in the social sciences; and others – including Turing instabilities – which have not. We saw that depending on the model, we may be able to solve the mathematics, in terms, for example, of the model’s eigenvectors and eigenvalues; alternatively, a computational approach may offer an approximate solution. Even where mathematical solutions are not possible, and it is not possible to predict the state that the system will attain at any given moment, its trajectory or orbit can often be described in general terms, saying whether it is confined to the region of particular ‘attractors’ and the extent to which it is dependent on the initial conditions. We extended this discussion to chaotic dynamics, fractals and strange attractors. This then served as a mathematical representation of some of the dynamics discussed in Part...
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