 In this module, we will be discussing the role of feedback loops with respect to self-organization by looking at how they work to promote or depromote synchronization of states between elements within complex adaptive systems. We will start by talking about the different types of feedback loops while also discussing a number of examples. We will then look at positive and negative externalities and finish by talking about the effects of combining both feedback loops and externalities. A feedback loop defines a relationship of interdependency between two or more components where the change in state of one element affects that of another, with this effect then in turn feeding back to alter the source element. This dynamic, captured by feedback loops, plays a fundamental role in the self-organization of elements within complex systems. When the state of elements within a system is independent from each other, then we can use statistics to model the synchronization of states between elements. For example, say we have a hundred people in a town with just two banks, A and B. If all other things are equal then, we can model whether two people are customers of the same bank using simple statistics where approximately 50% of the people will be using any one of the banks. But if the usage of each bank is not independent, it is instead interdependent, then it will no longer simply be statistics governing the dynamics. It will now be these feedback loops of interdependencies. To illustrate this, say more people are using Bank A and this leads to overcrowding in the bank. This may then feedback to affect the users as they decide to go to Bank B, which is now quicker and easier to use, and likewise if Bank B, after some time then becomes overcrowded, people may move back to Bank A. This is an example of a negative feedback where the state of one element affects the other in the opposite direction. We can see how the net result of this would be a stable system. If we had a hundred banks in this town governed by this rule, the result would be a very evenly distributed and stable system where the agents occupy a wide variety of states with respect to the banks that they use. But imagine one day Bank A starts a marketing campaign, putting up a big billboard saying for every customer we have, we will give you 1% extra interest on your savings. The result of this would be that for every new customer the bank had, it would present itself as a more attractive option for any other prospective customer. This is an example of a positive feedback where the more elements that adopt this state, the stronger the attraction placed upon any other element is to also synchronize its state with this pattern of organization. Something to take away from this banking example is that in both the first and the second example, that is when we had random correlations or negative feedback between the elements, both of these dynamics led to an overall stable state where the system tended towards an equilibrium. Systems governed by these dynamics are linear, additive. We can create closed formula solutions to model them and they are the focus of most of our scientific framework. In these first two systems, there is a dynamic that is working to maintain a distribution amongst the states between the elements that results in equilibrium. But this is not always the case. As we saw, positive feedback can drive the system far from equilibrium. Stock market crashes, outbreaks of war, political movements, growth and decay of ecosystems, traffic jams and many biological processes are the product of positive feedback that takes place far from equilibrium. Take for example a social riot. As the rioting breaks out, your chance of going to jail decreases and the social benefit of joining in increases. This creates an attractor attracting more elements to align themselves with this new organization. Positive feedbacks are non-linear and they are often a signal of a system shifting into a new regime. Whereas feedback refers to dependencies between the same actions, externalities refer to dependencies between different actions. An example of an externality might be the relationship between the usage of personal transportation and air quality. The more cars, the lower the air quality. This is a negative externality. A positive externality might be one between the temperature on a given day and the sale of ice creams. The higher the temperature, the higher the ice cream sales are likely to be. In contrast to a positive feedback loop, positive externalities can reinforce desynchronized states and diversity as two or more different states or classes of things are reinforcing and sustaining each other. This is essentially what we call a synergy. If we have more flowers, we can have more bees. If we have more bees, we can have more flowers. Thus, they endorse and sustain the diversity of states between them. Positive feedback, combined with negative externalities, can be a powerful force for synchronizing the state of elements within a system as it both places a strong attraction on elements of the same class to synchronize their states while also depleting a different class. We might think about the rise of the Third Reich in pre-war Germany as an example. Every time a new member adheres and promotes the ideology of a sociopolitical organization like the Nazi Party, it has a positive feedback effect amplifying this attractor. But also, this social system was having a negative externality on other ethnic minority groups. Thus, it was both reducing the variety within the social group and external to it as all elements became aligned in this sociopolitical regime. The net result of this was totalitarianism as the social system moved far from its equilibrium, ultimately resulting in a phase transition as it collapsed into a post-war economic and social crisis. In contrast to this, negative feedback, combined with positive externalities, will create a strong mechanism for maintaining equilibrium through endorsing a diverse set of desynchronized states within the system. This will clearly add to a system's robustness and long-term sustainability, with mature ecosystems exemplifying this. In summary then, we've been talking about how feedback loops work to synchronize the state of elements within complex adaptive systems. We have looked at how negative feedback works to maintain a desynchronized set of states between components as they interact through an inverse relationship that promotes diversity of states and a stability. While positive feedback works to synchronize the different states between elements as it creates an attractor that exerts a force aligning elements into a single regime. Finally, we talked about externalities as interdependencies between different activities and saw how, when we combined feedback with externalities, they can work to complement and amplify each other's effect.