Self-organization versus hierarchical organization: a mathematical investigation of the anarchist philosophy of social organization

In combining anarchist theory with mathematics, this thesis wishes to better understand what power and hierarchy are in order to explore how we can live without coercion. My motivation to study these concepts stems from observing a lack of freedom in contemporary society despite a lack of obvious coercion or clear hierarchical structure. I divide this issue into three main research questions. What are, on the one hand, authority and hierarchy, and, on the other hand, what are freedom and autonomy? How does hierarchy evolve in social systems? And how can we shift from hierarchical control to a more free social organization? To answer these questions, I make use of social theory, anarchist theory, complex systems theory, mathematics and computer simulations. I distinguish several aspects of power: control, coercion, constraint, determination and hierarchy. Defining these aspects leads to different understandings of freedom. Internal control refers to control over your own situation, while external control is directed towards the (whole) environment. Coercion forces a person to do something he does not want to do, while constraint limits a person’s possibilities. External determination, wherein one is completely influenced by an external force, makes one vulnerable to coercion. Determination and coercion are associated with a hierarchical structure. In a hierarchy, each element has no more than one influence and this influence works in only one direction. These concepts are described using mathematical tools such as graphs and entropy in cybernetic models. Self-organization can lead to the development of a controller. Working together to reach your goals can lead to a higher-level system. This system can acquire goals of its own, which can become disconnected from the goals of the entities that created the system. The rise of such a controller can be avoided by constantly opposing any seed of hierarchy or coercion. In this manner, no power can grow too big. This mechanism of constant opposition is illustrated in a simulation. Overall, this thesis illustrates how to think in a less hierarchical way by focusing on local coherence. In this way, there can be jointly related ideas rather than a single, primary concept with several sub-concepts. The tension between hierarchy and local coherence recurs throughout the thesis—in the difference between Marxism and anarchism, in internal versus external control, in the structural component of hierarchy, in hierarchical models versus their non-hierarchical variants, and in human agency versus determination.