“Minds do not naturally work in straight lines. Rather they consist of associations radiating out (or in) from many different connection points” -Flemming Funch, 1995.-

Cause & Effect

A line is often defined as the shorts path from one point to another, linear thinking then describes how we interpret events or act in terms of direct cause and effect means. When we use linear thinking to describe something we create a direct logical connection from one cause to one effect, if A then B, resulting in a linear sequential logic. When we apply this linear thinking to acting in the world it means we look for the simplest means that will create the desired outcome or solution, for example there are many different means one could take to get to work each day, but when we think about it in a linear fashion we will search for the most direct method to get from A to B, in this way the process of getting from one state to another is simply a means to achieving a desired end and of course this can be very effective and efficient at producing results. Important to this method of reasoning is the idea that you already know what the outcome is at the inception of the process and getting there means merely filling in the gaps between where you are and this end result.

Non-linearity then describes how we get from point A to point B by not taking a straight line that represents the shortest most direct path, but instead explore multiple different paths or means to an end. In terms of describing things this means there can be many different causes behind some given phenomena and we will try to explore how these different effects interact in a parallel or networked fashion in order to produce the end result, it is seeing how events and solutions emerge out of many different interacting parts without there being one right method, configuration or path to follow. In contrast to linear thinking that sees getting from A to B as simply a means to be executed, with nonlinear thinking the end product is a composite of many different parts, it is created out of the different stages in the process of getting there, like the old saying “the journey is the destination”. Thus nonlinear thinking is an exploratory endeavor where one is continuously wandering off the shortest path to explore different options and possibility and then as you get near the end of the process one pulls all these different ideas back together to create the end solution.

“What I would argue and what you really need to kind of begin with is this idea that an idea is a network on the most elemental level. I mean, this is what is happening inside your brain. An idea — a new idea — is a new network of neurons firing in sync with each other inside your brain. It’s a new configuration that has never formed before”
-Steven Johnson-

Small Causes – Large Effects

One of the key features to non-linearity in general is a dis-proportionality between input and output, linear systems have a well defined proportionality between input and output, we know if we hit a ball with a bat at a certain force then the ball will move off in the opposite direction with a velocity that is directly proportional to the force that we hit the ball with. With linear thinking where we predefine the end point before beginning and then follow a linear sequence of well-defined steps to get there we end up getting predictable and standardized results like a production process, and at times this may be exactly what is required but not always. When we see getting from A to B as simply a means then we will typically chose some known and proven solution, with the result being what we expect it to be, the outcome will be little more than what we put in. The dis-proportionality that is characteristic of non-linear systems often arises from the interaction between the parts, where the parts may be working together to produce a combined outcome that is much greater than the simple sum of the part that we put in, like an orchestra playing a symphony it is out of all the parts working together that we get what are called synergies that add extra value to the whole arrangement. Inversely all the parts might bet working against each other creating interference with the net result being a combined effect that is less than what we put in, like nations at war.

With nonlinear thinking where we explore the whole space or environment between the start and the end result, we create many different possibilities and solutions that can be combined to form the end result, this is how a lot of innovation happens by taking many different ideas or solutions and simply seeing what happens when we put them together, we are becoming increasingly aware that great ideas don’t happen in isolation but are the product of combinations, remixes of things that already exist, by creating a space for them to interact and mix we can try to find what works together in a synergistic way to create the end solution. By creating this space between the inception and end product we allow a process to take place whereby many different things can interact with new synergistic combinations emerging as the finished solution. In this way we can start with something small and end with something disproportionally larger, but equally we might fail altogether and end up with nothing, failure is a part of the process of succeeding, we shouldn’t then think of non-linearity as a good thing or bad thing it simply widens the spectrum of possibilities.

“It used to be thought that the events that changed the world were things like big bombs, maniac politicians, huge earthquakes, or vast population movements, but it has now been realized that this is a very old-fashioned view held by people totally out of touch with modern thought. The things that really change the world, according to Chaos theory, are the tiny things. A butterfly flaps its wings in the Amazonian jungle, and subsequently a storm ravages half of Europe”
– Neil Gaiman

Feedback & Iteration

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.

“The premise of a feedback loop is simple: provide people with information about their actions in real time, then give them a chance to change those actions, pushing them toward better behaviors. Why does putting our own data in front of us somehow compel us to act? In part, it’s that feedback taps into something core to the human experience, even to our biological origins. Like any organism, humans are self-regulating creatures, and feedback loops are how we learn, whether we call it trial and error or course correction. In so many areas of life, we succeed when we have some sense of where we stand and some evaluation of our progress.” -Wired Magazine


The concept of an attractor is one of the big ideas to come out of nonlinear systems theory and it has a lot of general applications, an attractor simply put is a set of states towards which something naturally evolves, as an example we might think of someone who is a couch potato, it don’t matter in what state we find them they will sooner or later naturally gravitate back towards sitting on the couch and this is the same for many things that cycle through a set of states in a periodic fashion like an economy that goes from boom to bust and back to boom and so on. These basins of attraction usually represent some source of energy that a person or thing receives and then dissipates, like Earth going around the sun or a person consuming food and then dissipating it during exorcise and then consuming more food and so on. Many of the things we see around us are held in their current pattern of behavior because they are in some set of attractors, we might think about our periodic cycle of going to work everyday in order to pay the bills, this holds us in some set of states or routine that is often not so easy to get out of.

Seeing the attractors is about seeing the environment within which things take place, the lines or contours of least resistance along which things naturally flow. When we can see these landscapes of attractors that shape and influence things around us we can begin to think about how to alter their fabric not so much through manipulation and force but more by creating new possibilities new sources of innovation, that represent new basins of attraction. When we create pathways that are easier for people to follow they often will do so, if we create a mobile phone that has more functionality, a better organized business or a production process that is faster, these are all forms of attractors and by creating them we get to create the landscape along which things flow, we get to create the future. Attractors are another way to try and understand how things go (or flow) from A to B and how by changing this landscape we can change the outcome to events.

“(An attractor is) a set of states of a dynamic physical system toward which that system tends to evolve, regardless of the starting conditions of the system… For example, a marble rolling in a smooth, rounded bowl will always come to rest at the lowest point, in the bottom center of the bowl; the final state of position and motionlessness is a point attractor” -Dictionary.com


Linear and nonlinear thinking are really to sides of the same coin or we might say two stages in the same process. Nonlinear thinking is a way of reasoning that describes phenomena as the product of many different interacting parts, it helps us to explore a wide set of possibilities in order to look for unknown solutions, it is a cyclical and oscillatory process that helps us to look at many different paths and different options and try to find different combinations of these in order to create synergistic outcomes. But once we have explored the full set of possible outcomes and have some general idea for the overall solution we can us linear thinking to narrow things down and define them more accurately. Linear thinking looks for the simplest most direct cause for any given effect it is a way of seeing the world in terms of the most direct means to achieving some end, it describes a well known and predictable set of procedures we can undertake in order to effect a predefined and predictable outcome. Untimely it is a synthesis of both methods of reasoning that result in a fuller picture of the world.