Complex is not (the same as) difficult (2)

Pieter Jansen and Fredrike Bannink


Linear and nonlinear systems
In the medical domain research is – not surprisingly –  mainly analytical in nature. In our modern western society, the dominant paradigm is analysis. And this is a very successful approach. But there also seem to be limits to analysis. How do we deal with issues that cannot be properly analyzed? How do we deal with unpredictability?


A 65 kg gymnast jumps down 1 meter. Calculate the forces that his knees must transfer when landing. The same gymnast makes a jump of 2 meters. Recalculate the forces. Then, with 10 meters. He is likely to be injured.

A patient with heart failure shows an improvement of his cardiac output at a dose of 0.5 mg digoxin per day. Will the improvement be 2x as large with 1 mg digoxin? At 10 mg per day there is a serious risk of death. What is 2x grief? Or 3x anger?

The examples above show some limitations of applying linearity to the medical domain. What is linearity? In science and technology, two basic systems are distinguished: linear and nonlinear systems.

  • A linear system has two essential properties: homogeneity and additivity. Similar elements are exactly the same and interchangeable. You can disassemble elements and reassemble them; you can multiply elements and divide them again. The result is always predictable. We only know pure linear systems as theoretical models. Linear models are pleasant for research. They are intuitive, work according to the cause-and-effect principle, are convenient and simple. The world as a clockwork.
  • Other systems are nonlinear. The real world is nonlinear. In the real world, building blocks are not the same. There is always variation. Small irregularities explain the phenomenon that interactions can lead to unpredictable results. The butterfly effect is a well-known metaphor for this unpredictability.


There are conditions that are uniform and stable where a linear approach is feasible. In a more irregular environment one should be careful with interpreting results from research; and even more cautious with extrapolating the outcomes to a situation that is slightly different. What do you know about patients, for example, when they have filled out questionnaires about feelings and thoughts? And can you use that information for situations that are slightly different?

The good news is that there is a simple approach for unpredictable topics: the solution-focused model.

The Complexity Academy has made a series of short videos about linear and nonlinear systems.
They can be found at:

Videos about chaos theory can be found at: