Updated: Jul 9, 2021

Managing Complexity - The butterfly effect

To manage complexity, we need first to understand it, or at least define it, and understand where it comes from.

*Defining complexity*

A vital property of a complex system is not the difficulty of understanding it but the difficulty of predicting how it evolves. A good starting point to define complexity is looking at how it differs from complication. A mechanical clock is an example of a complicated piece of equipment. Building one requires excellent skills, a lot of time and very focused attention. Its behaviour, on the other hand, is very predictable. Relying on its predictability is actually the whole point of having a high-precision watch.

Quite differently, a dish of spaghetti is straightforward to describe and prepare: anyone can do it. Predicting the position of each spaghetto in the bowl, however, is no easy task. It would require a powerful computer running and advanced simulation program and exact knowledge of the position of each spaghetto before you toss them.

In other words, complexity is not related to the difficulty to build or describe a system:

an elementary system can display an extraordinarily unpredictable and complex behaviour. As shown in the figure, consider a pendulum, constituted by a rod free to rotate at one tip. The pendulum behaviour is fully described by the angle of the rod. The free end is constrained to be on the circumference defined by the length of the rod. For small oscillations, a simple formula available in an introductory textbook to classical mechanics describes the movement in terms of the mass and size of the rod and the gravitational pull at its location. For large oscillations, it's a bit more complicated, but classical mechanics can sort it out quite simply. There is, however, always a difference between a theoretical model and reality. Imagine that you build such a pendulum and want to predict its position given an initial starting point. You just need to use the classical formula and plug in your length, weight, and gravitational pull values. Of course, you are bound to make errors in the measurements, resulting in errors in the calculated position of the pendulum versus the actual one. Reality will, however, not be way off your calculation. A small mistake in the measurement will result in a small error in the calculated position. Suppose your estimate of the initial starting point is a bit off. In that case, the actual amplitude and period of the pendulum oscillation will be somehow different than calculated but still relatively close.

Now let's make just a little, simple addition to the set-up and add a second pendulum attached to the first. The double pendulum’s behaves in an infinitely more complex way than the regular one. The tip of the pendulum can be anywhere within the circle, not just on the circumference, and its actual position can vary significantly for minor variations of an initial starting point. Predicting the motion of a double pendulum is exceptionally challenging. Minor errors in the measurement of the length or the weight mean the pendulum may at a given time suddenly move to a position that is opposite to the one predicted.

The double pendulum is actually a textbook example in an introduction to chaos theory. It is a good, if simplistic, illustration of the challenges of managing complexity. Managing in a complex environment means that no matter how precise our assumptions are, the behaviour of the system we are interacting with can be astonishing.

This type of chaotic behaviour gives rise to what is often called the butterfly effect: the flap of a butterfly's wings in the Amazon can influence the weather in China. One possible implication for organizations is that managerial focus may have to move away from planning, command and control. It becomes crucial to sense and react quickly to emerging conditions and develop resilience to unexpected and unpredictable situations.

Currently, the worldview that we adopt to understand the surrounding environment, whether in economics or management, is heavily inspired by a classical explanation of the world. A deterministic, mechanical world where an action corresponds to a simple opposite reaction that has its roots in the works of Isaac Newton. This approach has proved highly effective for highly predictable systems, like the simple pendulum. Still, it tends to fail in real life when one adds just a single layer of complexity. The theory is still correct. It becomes impossible, in real life, to obtain the precise information that allows us to apply it. To manage in a complex world, we need e new worldview, one that considers the possibility that unexpected events emerge from the dynamic interaction of the different components of the system. We will see that modern physics can be the inspiration of this worldview like Newtonian Mechanics was the inspiration of the mechanistic worldview that is still predominant.

In the case of the double pendulum, complexity arises from the simple modification of adding another pendulum to the initial pendulum. In future posts, we will explore the sources of complexity and start to design a worldview that can help us manage the complexity.

Image credits

Butterfy effect Image by __Gerd Altmann__ from __Pixabay__

Pendulum licensed under the Creative CommonsAttribution-Share Alike 3.0 Unported license. **Attribution: ****JabberWok**