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Life is not normally distributed – we live in a world of extreme events that skew what we consider ‘average.’ The chapter begins with a brief explanation of the basic causes of skewed distributions followed by a section on horizontal scalability processes. These are generated by scale-free mechanisms that result in self-similar fractal structures within organizations. The discussion then focuses on one of the most cited mechanisms purported to cause power law distributions: Bak’s (1996) ‘self-organized criticality’. Using three longitudinal datasets of entrepreneurial ventures at different states of emergence, the chapter presents a method to determine whether data are power law distributed and, subsequently, how critical thresholds can be calculated. The analysis identifies the critical point in both founder inputs and venture outcomes, highlighting the threshold where systems transition from linear to nonlinear and from normal to novel. This provides scholars with a conceptual–empirical link for moving beyond loose qualitative metaphors to rigorous quantitative analysis in order to enhance the generalizability and utility of complexity science.

A number of drivers for contemporary research are focusing attention on how to achieve public engagement in research undertaken by Higher Education Institutes (HEIs). In 2008, RCUK funded six ‘Beacons for Public Engagement’. We sought to understand how each Beacon had created the conditions for two-way engagement in the research design and delivery. We undertook an initial scoping study of the organisational culture within each Beacon and, using maximum variation sampling, selected seven projects which were our case studies. The analysis of the findings from these case studies from a complex systems perspective led us to conceptualise an ‘engagement cycle' which has three phases or elements: creating the conditions; co-creation of research; and, feedback loops to inform ongoing and future research. In this chapter, we discuss the approach we used to gather the data, how complexity theory underpins the approach and the interpretation of the findings, and how the results led to the engagement cycle.

The chapter presents a general mathematical framework to study discontinuous change in human interaction dynamics. There are two complementary perspectives: macro and micro. Regarding the macro context, the chapter proposes that levels of ordered structure in complex human organizing can be represented by a category theoretic representation that reflects informational influence acting on individual agents from sources external to the population and those internal to the population. These independent influences interact to change the set of interaction rules that are enacted locally. Regarding micro context, the authors position contagion as the mechanism whereby a common organizing state is adopted across multiple agents. They show that as a general matter, the ordered structure that emerges within a population can be indexed as the number of active degrees of freedom embedded in local rules of interaction that are guiding groups of agents. Category theoretic mathematical approaches should be more used in social science research to suggest deductive hypotheses that can be tested empirically with definitive results.

Understanding the structure of complex networks and uncovering the properties of their constituents has been for many decades at the center of study of several fundamental sciences, especially in the fields of biological and social networks. Given the large scale and interconnected nature of these types of networks, there is a need for tools that enable us to make sense of these structures. This chapter explores how, for a given network, there are a range of emergent dynamic structures that support the different behaviors exhibited by the network’s various state space attractors. We use a selected Boolean Network, calculate a variety of structural and dynamic parameters, explore the various dynamic structures that are associated with it and consider the activities associated with each of the network’s nodes when in certain modes/attractors. This work is a follow-up to past work aiming to develop robust complexity-informed tools with particular emphasis on network dynamics.

In this chapter we discuss and illustrate how network text analysis and social network analysis can be used to investigate complex governance networks. After briefly defining and describing ‘governance networks,’ we discuss the importance of investigating their complex structural properties and the roles actors play in them. Then we describe and illustrate how AutoMap (network text analysis software) and ORA (dynamic network analysis software) can be used in such investigations with two applications in the cases of an urban governance network and that of a statewide policymaking processes. We also discuss the general problems in using archival data sources in network analyses, specific problems and strengths in using AutoMap in network extraction from archival data. We present the protocol we developed for the applications of AutoMap and ORA in the appendix of the chapter.

Making multilevel systems well-defined is essential for the implementation of computer models to investigate the multilevel consequences of policy. This chapter shows that systems thinking can provide practical guidance to those building models of complex multilevel social systems in order to inform policymaking. Part–whole aggregation and taxonomic aggregation are described as methods of representing multilevel structure, and it is shown how they are interleaved in the construction of vocabulary to describe multilevel systems. This enables complex nested structures to be represented as a kind of backcloth that supports patterns of aggregate and disaggregate numbers that describe the day-to-day traffic of people, resources and responsibility that are essential for systems to function.

This gender study exemplifies fields struggling to balance the deeply ingrained desire for logical formalisms and conceptually dynamic models of systems. Gender Studies grounds itself in dynamic models as seen in the popularity of ‘intersectionality theory,’ a notion of experiences as unfolding at the ‘intersections’ of classical taxonomies. This popular theory evades quantitative research because it eschews classical categorical distinctions. The authors introduce multifractal analysis and suggest that cascade dynamics and multifractal analysis provide logical and corresponding statistical frameworks to make intersectionality quantitatively and tractably expressible for gendered experiences. Recent cognitive science advances involve multifractal analysis laying bare key features of the cascades driving cognitive performance. The chapter offers similar demonstration of similar cascades in gender dynamics through multifractal analysis of web-traffic data for gender terms on Wikipedia. It concludes that cascade formalisms and multifractal analysis offer new avenues for gender studies balancing both logical formalisms and dynamic concepts.