 To do system innovation, we have to work with the relationships between the parts, and that starts by creating some kind of model for those linkages or connections. An ideal modeling method for this is system dynamics. Over the past several decades, system dynamics has proven to be a very effective and useful tool for mapping out the relationships and basic dynamics within complex organizations. There are plenty of resources on the subject out there, so we will only touch upon it here in giving a brief overview as to how it is of relevance to systems change. System dynamics is a branch of systems theory that tries to model and understand the dynamic behavior of complex systems as they change over time. The basic idea behind system dynamics is that of feedback loops that try to capture the interactions between the parts and how they lead to a certain overall pattern of behavior over time. Diagrams of the primary feedback loops in the system are often converted into computer simulations to model how changes in one part of the system may affect others and the overall pattern of development. System dynamics was created during the mid-1950s by Professor J. Forester at MIT. He talked about the need for system dynamics because of the limitations in our normal modes of reasoning. It is my basic theme that the human mind is not adapted to interpreting how social systems behave. Our social systems belong to the class called multi-loop non-linear feedback systems. In the long history of evolution, it has not been necessary for man to understand these systems until very recent historical times. Evolutionary processes have not given us the mental skill needed to properly interpret the dynamic behavior of the systems of which we have now become a part. In our more traditional ways of thinking, we often look at situations in terms of linear cause and effect. System dynamics helps us to look at and model the feedback loops through which an event may cause another event that then feeds back to create more or less of the same behavior. The basic idea is that of interdependence, that whatever you do does not disappear, but in fact has some effect in the greater system which will over time feedback to affect the cause, with that feedback loop creating certain patterns over time. System dynamics uses what are called causal loop diagrams to do this. A causal loop diagram is a simple map of a system with all its constituent components and their interactions. By capturing interactions and consequently the feedback loops, a causal loop diagram helps to reveal the basic structure of the system. Feedback, in general, is the process in which changing one quantity changes the second variable, and the change in the second variable in turn changes the first. These feedback loops can be of two qualitatively different kinds, either positive or negative. A positive feedback loop means that values associated with the two nodes within the relation change in the same direction. So if the node in which the loop starts decreases, the value associated with the other node also decreases. Similarly, if the node in which the loop starts increases, the other node increases also. For example, the dynamics of the Earth's climate have many feedback loops that work to balance or change the system. One positive feedback loop driving climate change can be identified as such. When ice melts, land or open water takes its place. Both land and open water are on average less reflective than ice and thus absorb more solar radiation. This causes more warming, which in turn causes more melting, and this cycle continues. Another example here is the release of methane in permafrost, as warming is also the triggering variable for the release of carbon, potentially as methane, in the Arctic. Methane released from thawing permafrost, such as the frozen peat bogs in Siberia and on the sea floor, creates a positive feedback. Economics of scale is an example of a positive feedback loop between a business and its customers. The more products a company sells, the more revenue it receives from its customers, giving it more to invest in scaling up production, thus allowing it to reduce costs, which in turn means more customers will purchase the product, and so on. This is also called a virtuous cycle, where one party gains, the other does also. This also works in the opposite direction, giving us a vicious cycle, such as in a trade war, where one's side imposing trade restrictions induces the other side to react with further tariffs. Of course, this cannot go on forever, and that is why positive feedback loops are typically associated with unstable processes that are likely to crash at some time. One thing to note here is how this language of feedback loops lets us look at and talk about nonlinear abrupt processes of change. If, for example, we think about most of our models for climate change, they are very much linear in nature, that if we reduce CO2 by a certain amount, we will reduce warming by a certain amount. This kind of model is obviously not accounting for tipping points and runaway positive feedback. Indeed, it is important to note that most of our formal and informal modeling about the future are based upon this kind of linear projection. If you look at future energy projections, models for the future usage of cars, for food demand, etc., they are generally based upon linear assumptions. Although sometimes they are accurate, those assumptions can also blind us to these nonlinear processes of change, giving us a false sense of security about the future. System dynamics may not give us exact predictions of what will happen, but what it can do is give an overall outline of the dynamics in the system and make us aware of where those points that would drive nonlinear exponential change may lay, and that is critically important when dealing with complexity. Our best delayed plans can go out the window because we have not thought about the possibility of a financial crisis, that paradigm shift in technology, that collapse in an ecosystem's services, that political regime shift. Those things happen, but if you are not using nonlinear models, you will be blinded to them, and your best late intentions will simply get overwritten by those broader processes of change. This happens time and time again, and it is another way in which we end up simply going round in circles. A negative causal link means that the two nodes change in opposite directions. If the node in which the link starts increases, then the other node decreases and vice versa. Negative feedback is what works to hold the system in its current state, whereas positive feedback tends to lead to instability via exponential growth, oscillation, or chaotic behavior. Negative feedback generally promotes stability. The core supply and demand mechanism within a market is an example of negative feedback. When demand goes up, this creates more demand than supply, meaning producers can set higher prices, which then feeds back to affect consumers to purchase less, which then induces suppliers to produce production. This feedback stays playing out until the system reaches some equilibrium, where supply and demand are matched, and the system will stay close to that until there is some change. Negative feedback is what makes the system sustainable, because it means that the system is paying its own bills, so to speak. What is being gained from the action that you take is feeding back to be taken from you again, like when you purchase an item. You get what you want, but the consequence of that is that you have to pay for it. For example, take the small town in northern France that was having such trouble with the rubbish being dumped in an unused public space outside the village. The culprits were many, but primarily the local building contracting companies that were trying to reduce costs by simply offloading their waste building materials into the public space. Although the local authorities knew who was to blame, the national laws restricted their capacity to deal with the issue. Disillusioned with waiting for the national policy to change, they eventually took the situation into their own hands by implementing a policy where locals could report those who dumped rubbish illegally. The local authorities would then collect the waste, track who it belonged to, and then go and dump it on their doorstep. This worked to solve the issue. We can understand the dynamics of what is going on here in terms of feedback loops. Firstly, there was a positive feedback loop that worked to let the system get out of hand. Every time someone dumped rubbish and was not prosecuted, this made it more acceptable for others to do likewise, as the rubbish built up over time. Then came the negative feedback loop where people who were dumping were reconnected with the cost of their actions by having it put inside their property, where they would have to suffer the consequences of it instead of that being borne by others in the common space. The underlying dynamic here is one of negative externalities. Positive feedback is always unsustainable because it is drawing in resources to fuel itself from somewhere external to the system. This will, however, only last for a brief period of time and then it will be over. The solution to negative externalities and unsustainability is to close the positive feedback loop and convert it into a negative loop which makes the system self-sustaining. As this is a key part to developing sustainable solutions, we will talk further about it in a coming module. To perform a more detailed quantitative analysis, a causal loop diagram is transformed to a stock and flow diagram, which helps in studying and analyzing the system in a quantitative way, typically through the use of computer simulations. A stock is a term for any entity that accumulates or depletes over time. A flow, in contrary, is the rate of change in a stock, so an example of a stock might be a water reservoir. It is a store of water and we can ascribe a value to the volume it contains. Now, if we put an outlet on the side of our reservoir and started pouring water out of it, this would be an example of a flow. Whereas a stock variable is a measure of some quantity, a flow variable is measured over an interval of time. By using these tools of system dynamics, we may get a qualitative and or quantitative idea of how a system of interest is likely to develop over time. For example, if we create a simple two-dimensional graph with time on the horizontal axis, we will see how the different feedback loops create different types of graphs. Graphs for positive feedback loops typically reveal an initial exponential growth as they shoot upwards rapidly, but then reach some environmental-bounded condition where they crash back down again. A financial bubble and ensuing crash could be an example of this. Whereas the net result of a negative feedback loop will be a wave-like graph that will likely be bounded within an upper and lower limit over a prolonged period of time, with relatively smooth fluctuations during the system's development that enable it to sustain an overall stable state in the long term. System dynamics not only helps us to understand the dynamics deriving the behavior of the system, but this also gives us insight into where to best intervene in the system. It helps to identify leverage points. Identifying positive and negative feedback within a system is critical to systems analysis because it tells you about the system's potential for change. In general, complex systems do not change when there is a lot of negative feedback. The only chance for systems change is when there is a large amount of positive feedback. It is this period of exponential change driven by positive feedback that we can call phase transitions, and we will pick this topic up again in the next section.