Linear thinking results in a sequential set of stages to a process which are predefined and it is then expected that we follow these stages in a uni-directional step by step process, A is followed by B then C etc. This is like the waterfall model in project management where everything is seen to flow downhill in one long progression from start to finish never going back up stream. This has may advantages such as predictability and the fact that it is very orderly means we can do rigorous planning, but one of the main disadvantages is that everything gets locked into a predefined cause and effect chain from inception and this is characteristic of linear thinking. If we start from one point we get easily locked into some logical sequence of steps to some end conclusion, salespeople use this type of logic to start from a simple trivial statement (that it is difficult to argue with) and use a predefined set of logical steps to lead you to the conclusion that you must by whatever product they are selling and it can be difficult to try and breakout of this chain reaction without seeming irrational.
A key characteristic of non-linearity is what are called feedback loops, this is the idea that the result of some action taken now will feedback to effect us in the future, these feedback loops lead to what is called path dependency meaning that because we have this cyclical interaction between the actions we have taken and the effect they have on the environment (with this then feeding back to effect future actions), the overall long-term trajectory of things will be a product of the path created by these actions and the feedback loops. This path would then be clearly very difficult to predict at inception and in this way events and ideas evolve, something in the present can effect the state of things in the future or the past and this can feedback to effect the present. Thus we need to do something and then assess how that has changed the context or where we want to go and then do another cycle. Part of nonlinear thinking is then seeing these feedback loops, looking at how some action may have multiple effects within the environment that it takes place within and how these effects will then alter the future context within which we act. In this way getting from A to B becomes not linear, a cyclical process of continuous iteration.
Thinking in feedback loops is about seeing the effect than actions have and trying to close those loops so that they come back to their source because when they do they can be a very effective means of self-regulations, when some one knows that they will have to bear the cost of their actions they will be more prone to regulate themselves. It is only when these feedback loops become broken and we get what are called externalities (where people don’t have to pay for the consequences of their actions) that we then need to use top down regulation, which is never the best solution. Seeing the feedback loops that regulate our world both in nature, technology and social organizations is a powerful lens with which to understand the world and learn how to build self regulating systems.