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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.