The digital business and the world has become over-complex and hyper-connected, some thought linear thinking is a type of logical thinking and non-linear thinking is an out-of the-box thinking. But dig deeper, non-linear thinking is an emerging type of systems thinking to understand such complexity and craft a good strategy. Linear thinking vs. Non-linear thinking, what are they about, and how to differentiate them?
In the real, physical world or business world, most relationships are non-linear: Linear thinking is viewed by many as being simply the opposite of closed loop thinking (thinking in a straight line rather than circularly). In the real, physical world, most relationships are non-linear. As an object grows in one dimension, its surface area grows as the square and its mass by the cube. Most things have limits to their scale, network connections grow non-linearly with nodes etc. Linearity has very little to do with predictability but rather describes the connection of two points; where linear is traditionally by the shortest path, a straight line and non-linear by any other path, geometric progression, exponential, step functions with variety. People vastly underestimate the complexity and non-linearity of the human cognition processes they rely on in all business systems. At linear often implies cause & effect with no feedback, A -> B, and non-linear implies feedback where A -> B -> A with the admission that there may be numerous other elements in the loop. So there is a linear structure - in other words, A causes B causes C. Structurally lots of business stuff is nonlinear - A may cause B, which may cause C, but then C also causes A and whenever there are circular relationships of this type, the outcomes do tend to be unpredictable.
The linear thinking implies the whole is equal to the sum of its parts, which is not effective from a business perspective as well: Linear systems are those that follow a generalized superposition principle (doubling the input doubles the output, adding two inputs together leads to adding their two outputs.) This attribute leads to powerful analysis tools that allow you to break any input into simple pieces and compute the output due to each piece separately, then add the results. The whole is equal to the sum of its parts, the concept of reductionism. The reason linear thinking is in many cases, not so effective for solving the complex problem, because there is always a temptation to use simple linear models to understand highly complex, nonlinear scenarios. So just one example is strategic decision making. If you design this as a linear process, it almost always fails. So from a design point of view, it's critically important to be able to design nonlinear structures as well as linear processes if you want your business to survive and ultimately thrive.
Reductionism vs. holism: The positive approach comes from attempting to isolate and understand the dynamics of the individual functions in the enterprise, some of which for the time frame will be as good as linear, but more often, the organization as a whole has to function more holistically and coherently. There are two different philosophical approaches for managing businesses; one is called reductionism (break a problem into parts, solve each part separately, add up results) vs holism (the whole is different from the sum of the parts.) When systems are not linear, they are defined as nonlinear. And ultimately, organizations need to ensure the business as a whole is superior to the sum of pieces. So the holistic thinking rules in modern business and society.
Nonlinear thinking is a type of integral thinking: Linear models are usually about simplifications. They are valid only within limited conditions. Simplifications can lead to errors and incorrect results, especially when moving from the modeled world to the real world because there are many interdependent components in the business. Then it is necessary to integrate their interdependencies if they exist because it is here that Emergence becomes apparent, the concept of "non-linear" behavior as a concept is representative of what we term emergent properties. The criticism is used for people who apply tools like linear extrapolation, based on linear models when the system is not operating linearly.
The applying of non-linear thinking has to do with COMPLEXITY: It just turns out that, as human society gets more and more complex, the very natural attempt of humans to take the very powerful techniques of mathematics, such as techniques of linear mathematics or non-linear mathematics, and apply it to the world very quickly come up against insurmountable difficulties, such as...
(1) you can't measure the initial conditions precisely with small variation.
(2) you can't measure the transformations on initial conditions precisely
(3) the phenomena aren't even deterministic (that is, you can only characterize the phenomena through manipulation of "random variables", which are used to infer characteristics of an entire population based on a sample, using statistics)
(4) even when deterministic, the equations that would describe the phenomena are so complex that you cannot discover what they are.
From linear to non-linear thinking could be evolutionary. At the beginning, you often make a one-dimensional, linear, list of things to do. At the end when you have gone through the mufti-dimensional analysis or process, when everything else is in place you again have a list of what you need to do. One characteristic of nonlinear systems is that small changes can have large impacts. A small error, inconsistency or change in a system specification can totally ruin its performance. Similarly, achieving the desired impact can sometimes be as the result of a very small initiative or decision. this is the magic of non-linear systems thinking. If you pick the right thing to alter, you can sometimes achieve enormous outcomes at little or no expenditure of effort on your part. This approach requires great insights and knowledge.