Simple Thoughts
on Complexity

The Chaos Theory
in five easy pictures:
an informal attempt
to simplify complexity

by Giancarlo Livraghi
November 2004
(English translation August 2005)

anche in italiano   –   también en español

For over twenty years I have been trying to understand what we can learn from the Theory of Chaos and the many elaborate analyses of complexity, turbulence etcetera. It isn’t easy, but it’s intriguing. It’s a matter of understanding that things called “chaos” aren’t chaotic, but follow laws that we can’t easily understand or define; and that complexity is actually simple, but our way of thinking makes it appear complicated.

This is how Mitchell Waldrop explained it in his book Complexity (1992): «The edge of chaos is where life has enough stability to sustain itself and enough creativity to deserve the name of life. The edge of chaos is where new ideas and innovative genotypes are forever nibbling away at the edges of the status quo, and where even the most entrenched old guard will eventually be overthrown».

The edge of chaos is where we are. But what does that mean in everyday practice?

One day, in October, 1997, a question kept popping up in my mind. Was it possible to explain some points on complexity in an extremely simple manner? Silly as it sounds, I tried. I wrote these short comments and asked the opinion of people who, from different angles, had been studying chaos and complexity quite seriously. Had I made any mistakes? Was it oversimplified, superficial or nonsense? They were somewhat embarrassed – but, much to my surprise, they grudgingly agreed that it made sense.

Three years later, I still wasn’t quite sure. In December 2000 I printed a few copies of this text in a tiny book, that I gave to friends and acquaintances. Their comments encouraged me to place it in another book, that was published in 2001. Again, I had several encouraging inputs from readers – and I was again surprised that none of them found it simplistic, superficial or unreasonable.

I believe that understanding complexity is one of the ways of reducing the risk of being stupid. So in November, 2004 this was published once more, in Italian, as an appendix to a book on The Power of Stupidity.

Here it is, for the first time, in English. I hope readers won’t think it’s stupid – and maybe more people will find it practically useful.

A small update: in May, 2009 this was published again
The Power of Stupidity in English.

In the meantime I have had fewer comment on these “simple thoughts”
than on my general work on stupidity – but the same trend continues.
For some readers the simplicity may be embarrassing,
but nobody seems to think that it’s silly.

If any people reading these short notes are competent in mathematics, physics, statistics, ecology, biology or management theory, I beg their pardon for the childish simplification of the reasoning and the pictures. I am not trying to offer scientifically strict or philosophically accurate models or patterns, but only a few hints for practical thinking.

I am not trying to get into the elaborate analyses of the Chaos Theory, turbulent systems and complexity. There is abundant literature on these subjects – and for many years it has been clear (at least in theory) that it doesn’t concern only physics, meteorology or engineering, but also human behavior – and, therefore, organizations, society, the economy, politics and culture.

Let’s begin with an observation that may appear simplistic. But “obvious” facts are often a good starting point.

When we are planning to go from A to B, the concept appears in our mind as a straight line:


In a real world there are no straight lines. Between A and B there are obstacles, interferences, indirect routes, so that even if the task is extremely simple, such as going out for a cup of coffee, our actual behavior is likely to take this sort of shape:


In a task as simple as this, that takes a few minutes, it’s unlikely that in the meantime we shall forget where we are going and why.

But the problem takes a different shape when it involves an organization, with much greater complexities, unexpected events, constant change of the situation and the environment, etcetera.

Any group of people doing something together is, de facto, an organization. Even four or five people meeting for a cup of coffee. And even in the simplest case reality is more complex than is shown in these flat pictures. Going to the coffee house involves a three-dimensional route, because there are probably stairs or elevators. In an organization, even when it’s small, the model is obviously multi-dimensional. The “flat” diagrams that I am using to summarize the picture are necessarily less complex that the situation in actual experience. But I hope simplification can help to understand the basic nature of the problems, that would be hard to detect in an analytical “topology”.

So it becomes possible (it actually happens quite often) that some parts of the organization forget the original direction...


... and the entire system loses sight of the objective, with the added complication that several people or groups think that they are heading for C, D, E or F and therefore they work in disharmony with each other and with the organization as a whole. This is, in any case, a serious problem – but it’s to be noted that people heading for C or F are shifting, though on a lateral course, toward B, while those heading for D or E are moving in the opposite direction – and in order to return to a route leading to B they will need a complex, cumbersome (and often expensive) detour. It’s quite easy, observing the behavior of organizations, to notice how often this sort of thing is happening.

In an environment that isn’t changing, or where evolution is predictable and controllable, there is (if only in theory) a simple solution. Everybody should have a compass. That is to say, nobody should be left to carry out a task without understanding a broader perspective. All parts of the organization should know that the objective is B, and the process should be continually monitored so that the (unavoidable) deviations return as soon as possible to the right direction. The system, therefore, would behave like this:


But in a complex and turbulent environment the process could evolve quite differently. The situation is mutating and unpredictable. Heading only toward objective B may turn out to be a mistake.

If we look back a the third picture, with diverging directions, we notice that (for instance) two “spontaneous” deviations (C and D) are converging in an unforeseen direction. It may be useful to find out why. We could discover that this is the situation:

new direction

In this example the “turbulent” evolution of the system has led us to discover a new objective N – and to understand that it’s convenient to concentrate our energies in that direction, while not losing sight of other “branches” that could reveal unexpected opportunities.

We notice that some of those “branches” have directions relatively close to our “old” objective B, some don’t move far away from our “new” objective N, while others point to still unexplored territories – and that the entire system has taken a shape that may be less “logical”, but is structurally more simple than those generated by forcing the system to follow a “linear” model.

The fact is that “complexity” (or “chaos”) isn’t inherently more complex than apparently “orderly” systems – and it can lead to simplicity. The problem is that we are not trained to understand how it works.

This looks more like the growth of a climbing tree than the structure of a machine or the manufacturing of an industrial product. Quite often the study of complexity leads to biological analogy.

It could be quite complicated to study the theoretical implications of this (pretty obvious) conclusion. But a simple, intuitive perception of this fact can help us to understand how to behave in a world dominated by turbulence and complexity, where “non linear” thinking is often the winner.


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