Global Brain Institute

In this paper the difference between hierarchical organization and selforganization is investigated. Organization is defined as a structure with a function. But how does the structure affect the function? I will start to examine this by doing two simulations. The idea is to have a given network of agents, which influence their neighbors. How the result differs in three different types of networks, is then explored. In the first simulation, agents try to align with their neighbors. The second simulation is inspired by an ecosystem. Agents take certain products from their neighbors, and transform them into products their neighbors can use.

In this seminar, we look at the difference between hierarchical organization and self-organization. Organization is a structure with function. First, we try to define hierarchy on the structure. We do this by using graph theory. Next, we look at the function of an organization, how a common goal or global pattern is set and reached. We use some existing theory about self-organization here. Finally, we investigate how these two approaches agree.

The goal of this paper is to present a centrality measurement for the nodes of a hypergraph, by using existing literature which extends eigenvector centrality from a graph to a hypergraph, and literature which give a general centrality measurement for a graph. We'll use this measurement to say more about the number of communications in a hypergraph, to implement a learning mechanism, and to construct certain networks.

In general, systems try to have internal control; most humans want to feel like they have control over their life. Some do this by aiming for external control: they want to fix how the environment behaves. Others do this by trying to find synergies with the environment. How can we formalize these different strategies for control, and which one functions the best? I will try to answer these questions in this paper. I will do
so by generalizing the concept of coordination in hierarchical systems, introduced by Mesarovic. I will apply this to model different strategies for control: a global one used in the theory of controllability, or local ones based on neural networks and perceptual control theory.

In various domains, there is an interplay at work: elements form and influence a structure, but this structure in turn influences the elements.
By time, rigidity often turns in: the structure start to have its own goals, and can't be influenced anymore by the elements. How can one avoid this from happening? I propose two strategies: make sure there is enough diversity, and endorse a constant opposition. To illustrate this last countermeasure, I built a simulation. This showed that it is possible to avoid
the emergence of the classical power-law distribution, giving rise to a more dynamical situation where the top agent is constantly changing. Chemical Organization Theory is also used to model this process.
These considerations are applied to the concept of the global brain, in order to avoid that this becomes another imposing structure.

The global brain can be defined as the distributed intelligence emerging from the network of all people and machines on this planet, as connected via the Internet. The present paper proposes the foundations for a mathematical model of the self-organization of such a network towards increasing intelligence. The assumption is that the network becomes more efficient in routing the right information to the right people, so that problems and opportunities can be addressed more efficiently by coordinating the actions of many people. The network develops by the creation and strengthening of useful connections, and the weakening and eventual elimination of counterproductive connections.

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.

In this paper we try to define the difference between hierarchical organization and self-organization. Organization is defined as a structure with a function. So we can define the difference between hierarchical organization and self-organization both on the structure as on the function. In the next two chapters these two definitions are given. For the structure we will use some existing definitions in graph theory, for the function we will use existing theory on (self-)organization. In the third chapter we will look how these two definitions agree. Finally we give a conclusion.

In this paper we try to define the difference between hierarchical organization and self-organization. Organization is defined as a structure with a function. So we can define the difference between hierarchical organization and self-organization both on the structure as on the function. In the next two chapters these two definitions are given. For the structure we will use some existing definitions in graph theory, for the function we will use existing theory on (self-)organization. In the third chapter we will look how these two definitions agree. Finally we give a conclusion.

In this article, we attempt at developing a scenario for the self-organization of goal-directed systems out of networks of (chemical) reactions. Related scenarios have been proposed to explain the origin of life starting from autocatalytic sets, but these sets tend to be too unstable and dependent on their environment to maintain. We apply instead a framework called Chemical Organization Theory (COT), which shows mathematically under which conditions reaction networks are able to form self-maintaining, autopoietic organizations. We introduce the concepts of perturbation, action, and goal based on an operationalization of the notion of change developed within COT. Next, we incorporate the latter with notions native to the theory of cybernetics aimed to explain goal directedness: reference levels and negative feedback among others. To test and refine these theoretical results, we present some examples that illustrate our approach. We finally discuss how this could result in a realisti...

The goal of this paper is to present a centrality measurement for the nodes of a hypergraph, by using existing literature which extends eigenvector centrality from a graph to a hypergraph, and literature which give a general centrality measurement for a graph. We will use this measurement to say more about the number of communications in a hypergraph, to implement a learning mechanism, and to construct certain networks.

The global brain can be defined as the distributed intelligence emerging from the network of all people on this planet connected via the Internet and related technologies. The present paper proposes the foundations for a mathematical model of the self-organization of such a network towards increasing intelligence. The assumption is that the network becomes increasingly efficient in routing the right information to the right people, so that problems and opportunities can be addressed in the most efficient way possible by coordinating the actions of many people. The network develops by the creation and strengthening of useful connections, and the weakening and eventual elimination of counterproductive connections. People can be modeled as agents that try to maximize their benefit by processing the challenges (problems and/or opportunities) they encounter. Challenges propagate from agent to agent across a weighted, directed network, which represents the social connections between these...

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. As a life trajectory is always shaped by many influences, so is mine. Some of these influences have specifically enabled me to write this PhD, and supported me in the years it took to complete this effort. First of all, my promoter Francis Heylighen, has been an enormous inspiration, with both the research he has conducted and the relevant references he provided, on which a big part of the thesis is based. I especially would like to thank Gunther Lippens for reading my entire thesis and providing feedback. The "PhD study group", especially Cadell Last and Xiubo Li, also provided me with in-depth feedback on my ideas. My PhD was able to develop because of the discussions and feedback throughout the years from the other ECCO/GBI members as well:

In this paper we try to define the difference between hierarchical organization and self-organization. Organization is defined as a structure with a function. So we can define the difference between hierarchical organization and self-organization both on the structure as on the function. In the next two chapters these two definitions are given. For the structure we will use some existing definitions in graph theory, for the function we will use existing theory on (self-)organization. In the third chapter we will look how these two definitions agree. Finally we give a conclusion.