Insights into Deterministic Chaos

I was recently asked in an online ‘Art of Hosting’ group to comment on the difference between how the term chaos is used in the Cynefin Framework, in the Art of Hosting description of The Chaordic Path and in how scientists use it. My response is below. However, if you want to learn more about the Cynefin Framework first you can click here, and for the chaordic path you can click here.

I don’t want to speak for the chaordic path and the cynefin framework definitively. Whilst I am familiar with these processes, I am certainly no expert in these theories. If you want to be sure how they are using the term chaos then perhaps you need to ask their founders. That said, I am happy to give you my impression and to explain a bit more about chaos in the mathematical sense…

In a mathematical sense, chaos is quite specific (and it is technically called deterministic chaos). Deterministic chaos was discovered through the study of how dynamical systems change over time. Scientists use very simple iterated equations to generate and model chaos. Iterated just means repeated over and over. So you might have a simple equation that models population growth where you start with a particular population and then run the equation to see what the population will be in the next generation. This output becomes the new input and is put through the equation again to determine the following generation’s population and so on ad infinitum. Even though the equations used are often very simple and totally unambiguous, the results of these equations can be very unpredictable in the longer term and they can generate wild and seemingly erratic fluctuations – which is called deterministic chaos.

There are some consistent features of these kinds of chaotic systems.

  1. A system like this is very sensitive to the initial conditions – this is often called the butterfly effect (this means very sensitive to small changes in the state of the elements involved – one more person added to the population in one of these equations can cause the future population statistics to change dramatically)
  2. They can often generate seemingly random behaviour
  3. They sometimes have ‘strange attractors’, so that seemingly random behaviour to the observer can be shown to have some pattern to it if you map it in a certain way
  4. “even though prediction becomes impossible at the detailed level there are some higher level aspects of chaotic systems that are indeed predictable.” (Quoting Melanie Mitchell in her book Complexity a Guided Tour)

In the last point Melanie is talking about phenomena such as the period doubling route to chaos and Feigenbaum’s constant. As a system approaches a transition to deterministic chaos, it will often have a repeating pattern that contains a higher and higher number of values by doubling it’s period each time (the period doubling route to chaos). For example a dripping tap will drip with one drip first, then if you increase the flow a little it will go to two drips in a cycle, then 4, then 8 and then it will eventually become chaotic in how the drips come. This is the period doubling route to chaos (as the number of drips double each time) and it is seen frequently in systems capable of producing chaos.

This is all getting a bit technical, and it becomes difficult to build links back to the real world sometimes from the very abstract world of mathematical chaos. Real world chaotic systems include convection currents, the pattern of dripping taps, the pattern of the human heartbeat and chaos is also present in weather dynamics (which is why prediction is impossible in the longer term). In the real world each system we look at is networked with other systems. So it then becomes near impossible to be able to just literally transfer knowledge from the abstracted and simplified world of mathematical chaos to a real world situation. If you take the human heartbeat as an example, this is a dependable organ which whilst having slight variations in the beat to beat interval time which show a chaotic pattern on the micro scale, is still producing very dependable results. In this way you can see how there can be small elements of chaos blended into larger, quite dependable complex systems.

If you want to learn more I can highly recommend:

Scott Page’s online course called ‘Model Thinking’ where de deals with both complexity and chaos.

David Feldmans course ‘Introduction to Dynamical Systems and Chaos’ for a basic understanding of deterministic chaos in general.…

With respect to the chaordic path and the Cynefin Framework: I think they are using these terms in line with their colloquial meaning, simply meaning disordered.  This kind of disorder may well be deterministic chaos or it may not. If scientists bothered to look for the signatures of chaos (such as sensitivity to initial conditions) they may be able to prove if it is deterministic chaos or not. In a way that doesn’t really matter for the purposes of these processes/theories. Personally, I think it should be called randomness or disorganised rather than chaotic when used such theories to make sure people don’t believe it to mean deterministic chaos. However, the term chaos is commonly used in theories in it’s colloquial sense, this is just a part of how language has evolved. Whilst I feel it can be confusing and misleading sometimes, it is not actually ‘wrong’ to use it that way. The colloquial use was there before deterministic chaos was discovered I imagine. In some ways it is a small point at the end of the day, as I feel that both the Chaordic Path and Cynefin provide metaphors that are useful to people when working in complex situations.

I will just clarify one more thing. When David Snowdon (of Cynefin) speaks of systems being sensitive to small changes in his video, he is not necessarily only referring to the butterfly effect. The butterfly effect refers to changes in the state of individual elements in a system. There are also other sensitivities complex systems can have. Systems can be very sensitive to changes in the way that the elements are connected or the rules/constraints that govern how elements can operate in the system. Metaphorically, the butterfly effect might refer to changes that happen if one person is home sick from work one day and that sets a whole different chain of events in process in the organisation. The other sort of sensitivity I describe might refer to one small change in the rules governing how people can trade online leading to a whole other pattern emerging in the economy. In the first case the system hasn’t changed in nature and is still capable of the same spectrum of behaviour it was before. In the second case, the nature of the system has changed and it might now display new patterns of behaviour that it was not capable of before. The butterfly effect describes the first scenario, the second scenario is not a result of the butterfly effect as the fundamental nature of the system has changed, not only the initial conditions.

I will end by quoting Peter Senge from this video of him speaking:

“What is all this ‘systems perspective’ stuff? … although we are familiar with the some of the lingo and a lot of the ideas … I think none of us understands what it means. Underline none of us, myself included. It really is the awakening of something that I think is very deep and will ultimately have a transformative impact on all of our institutions over the next 2-3 generations”

I agree with him 100% and I think it is very important to understand this and realise that these theories (when taken out of their scientific and mathematical arena) provide metaphors in the real world that can help us develop ways of thinking that are useful when dealing with complex situations. But – we should be wary of taking them too literally.