This chapter offers responses to the question ‘why regulate?’ and ‘why do regulatory regimes emerge in a particular form?’ by examining ‘theories of regulation’. While chapter 1 introduced the readers to the economic justifications of regulation, this chapter delves into the different theories that explain why we need regulation and how public and private actors interact to shape the content of regulation. These theories refer to a set of propositions or hypotheses about why regulation emerges, which actors contribute to that emergence, and typical patterns of interaction between regulatory actors. It discusses theories from several disciplinary approaches, classifying these theories into four kinds: public interest, private interest theories, systems and institutionalist approaches and ‘hybrid’ theories.

In this final chapter, we take on an issue that perhaps precedes all the others: how and why did language evolve? Linguistic theory has recently pivoted to amass considerable research on these questions. As we’ve seen over and over in the book, simpler structures have been posited across frameworks to account for the need to explain how language evolved. However, in this book, we’ve seen many distinct approaches to understand human language. A view of language evolution that permits the pluralism of the book would be consistent with the broad approach of this work. Therefore, in this chapter, I want to turn the minimalist research agenda on its head with an alternative thesis: natural language is a complex system and its emergence is likely to have been prompted by multiple interacting factors. First, we assess the current state of the art in biolinguistics and the strong saltation claim that goes with it. Then, we challenge the assumptions that’ve resulted in the saltation picture of language evolution on evolutionary grounds. Lastly, a radical approach to language evolution in terms of complexity science is proffered based on a unique connection with systems biology.

This chapter describes the Better Strangers/Shakespeare Reloaded project, which is a collaborative education research partnership between the University of Sydney and Barker College (Sydney). The project’s initial design and its philosophical grounding in complexity theory are discussed before a detailed account is given of one teacher’s long-term involvement in project activities. The chapter describes many research and teaching initiatives and outputs generated during the life of the project and explains how they represent a pursuit of educational ardenspaces. Such ardenspaces are argued to be a necessary response to overly constraining educational systems because they allow imagination, creativity and freedom to flourish in teaching and learning.

We live an unpredictable unrepeatable yet creative existence. Revealing the underlying patterns of our thoughts and behavior, nonlinear dynamics provides models to understand our lives and our creativity as ever-evolving human beings in a constantly changing universe. As the writer James Baldwin said, “the artist must know, and he must let us know, that there is nothing stable under heaven.” The creative trance, modeled as a creative chaos, brings forth new work and personal transformation. With its disciplines of chaos theory and complexity theory, nonlinear dynamics explains processes like creativity that do not progress in a straight line, cannot be predicted, never exactly repeat themselves, and yet have the capacity for originality and transformation. There are aspects of nonlinear dynamics such attractors, fractals, self-organization, emergence, the butterfly effect, and self-organized criticality that strongly correlate with the creative process, insights, the power of memories, global transformation, catharsis, and transforming panic attacks into creativity.

Trials, legal systems, governments, and market economies are all complex adaptive systems. Viewing them in that light opens up new avenues for research, and leads to a possibly unprovable supposition that human flourishing well be enhanced at the intersection of societies with a commitment to the rule of law that embrace free elections, market economies and responsive legal systems of which the common law is the paradigmatic example. These complex adaptive systems have the advantage of feedback mechanisms that may facilitate the intelligent exploitation of the vast amount of information contained in each of the systems.

This chapter discusses key questions to provide a foundation for understanding why quantum computers are different from classical computation: What is computation? How is computation different from calculation? What kinds of tasks can computers perform? What is complexity theory? This chapter discusses the early design and government patronage of computing. Critically, this chapter dispels the commonly-held belief that quantum computers have magical, universal powers to solve problems.

Chapter 6 covers global flat foldability.This includes determining how we can tell if a crease pattern with multiple vertices will fold flat without forcing the paper to self-intersect, as well as discovering properties that all such crease patterns have, beyond what was covered in the previous chapter.Justin’s Theorem, which is a generalization of Kawasaki’s and Maekawa’s Theorems and whose proof uses elements of basic knot theory, is covered, as are Justin’s non-crossing conditions that provide necessary and sufficient conditions for a general crease pattern to fold flat.The matrix model from Chapter 5 is developed further to create a formal folding map for flat origami.Finally, Bern and Hayes’ seminal proof that determining flat foldability of a given crease pattern is NP-Hard is presented and updated with more recent results on box pleating.

The final chapter considers more theoretical aspects of rigid origami.The first section outlines a proof that deciding whether or not an origami crease pattern can be rigidly folded from the unfolded state using some subset of the creases is NP-hard.Then configuration spaces of rigid origami crease patterns are discussed in more depth than in the previous chapter, including a proof that the germ of single-vertex rigid origami configuration spaces is isomorphic to the germ of a quadratic form.Examples of disconnected rigid origami configuration spaces are also included.The chapter, and book, ends with an introduction to the theory of self-folding, where we imagine that a crease pattern is rigidly folded using actuators on the creases, and we wish for these actuators to fold the crease pattern to a target state and not to some other rigid origami state.The aim is to characterize when simple actuating forces can do this, and we present the current theory behind this as well as its limitations.

The field of algorithmic randomness studies the various ways to define the inherent randomness of individual points in a space (for example, the Cantor space or Euclidean space). Classically, this quest seems quixotic. However, the theory of computing allows us to give mathematically meaningful notions of random points. In the past few decades, algorithmic randomness has been extended to make use of resource-bounded (e.g., time or space) computation. In this survey we survey these developments as well as their applications to other parts of mathematics.