By Roland Watson

In this series, I'm going to examine something that is known as chaos theory. I actually already introduced it, in the Behavior and Chaos article, in the human nature series.

Chaos theory is a field of mathematics. It describes the processes that underlie the transformation, or change, of physical systems in the universe.

That sounds pretty abstract, and I have to admit that I am not an expert at the mathematics that are involved. But, I have spent a lot of time thinking about the concepts - the ideas - of chaos theory. I believe they apply to much more than physical systems.

The reason I am talking about this at all is that the patterns of chaos that we see in the world are one of the fundamental elements of existence. The mathematics have in fact proven this universality.

In this article, I'm going to lay out some of the basic ideas. Then, in the balance of the series, I will consider how they apply to social change - how we can purposefully transform our society to achieve our underlying collective goals. I will also look at how the theory applies to individuals, in other words, what it means for your efforts to transform yourself.

Types of change

In the universe, nothing is constant - with a very few exceptions, such as the speed of light. Everything changes. This condition is itself a constant.

But, there are two different types of change. The first is continuous, and this is change within a system, to a part or parts of a system. Such change is equivalent to development. A simple example of this is a child growing into an adult.

The second type of change is discontinuous, and this involves the transformation of a system as a whole. This type of change, which is also called global system change, is distinct from development. It constitutes evolution. Again, an obvious example here is actual evolution, where a particular form of life undergoes a degree of change sufficient to establish a new, distinct species.

Initial conditions

One thing both types of change rely on is something called initial conditions. This idea is in fact easy to grasp. As I also noted in the human nature talk, where you are able to get to in life is heavily dependent on where you begin.

One of the foundations of chaos theory is an idea called sensitive dependence on initial conditions. This means that even a small difference in where something starts can lead to a huge difference in where it ends up.

But, this is not the only characteristic. Chaotic systems are non-linear, or dynamic. They cycle from an ordered state, to one of disorder, and then back to order.

Your might recall the introductory article where I examined the wide prevalence of repeating cyclical patterns in the universe. Chaos theory explains, at a mathematical level, why cycles are so prevalent, and how they actually work.

The role of energy

The other foundation - or fundamental - in a chaotic system is energy. Energy must be added to the system, otherwise it will stay the way it is, in an inertial state - an equilibrium. But, if enough energy is added, it will heat up and transform - it will become chaotic.

It's also worth noting that energy can be added two ways, either gradually, or through a stochastic, or unexpected, shock. An example of the first is slowly heating a pot of water until it boils. A stochastic example would be an asteroid striking the earth, such as the one that triggered huge changes in the life on our planet 65 million years ago.


I mentioned equilibrium. A system is in equilibrium if it has established a measure of stability. The system either is at rest, or it is following a periodic cycle - like the earth rotating, and day following night. But, if energy is applied to the system, it is forced to adapt. If possible, it absorbs the additional energy without altering its underlying structure. Or, if it is unable to do this, it creates a more complex form of order to accommodate it.

In the science of chaos, it has been shown that developments in order often occur via what are called bifurcations, or splits.

The rise of chaos

If the energy addition is sufficiently great, the system can no longer absorb it in an orderly fashion. A threshold is passed, and turbulence - chaos - ensues. In other words, the pressure builds until the system literally breaks. This threshold in turn is known as the tipping point.

Surprisingly, though, it has also been shown that chaos is not truly chaotic, meaning not truly random. Patterns are embedded in the turbulence, and these may eventually surface, giving rise to a completely new type of organization. To repeat: Order leads to disorder, and then back to order. Hence, we get a cycle. The change from the old system of order to the new one is a phase transition.

For the earlier example of water, it undergoes a phase transition from ice to liquid, and then another when it changes to a gas - to water vapor. Also, these embedded patterns are referred to as strange attractors. They are so-named because it is considered odd that there would be any underlying order in a state of chaos.

The universe contains an incredibly wide array of distinct systems, and these in turn have a vast range of stability. Some system equilibria are much stronger than others.

For a weak equilibrium, a small amount of energy - a slight trigger - can lead to turbulence and disruption. For a strong one, great energy, in the form of one major trigger, or many distinct minor ones, is required to initiate a change. Smaller disturbances may push such a system out of alignment, but not all the way into chaos. Without additional disruption, one would expect it to return to its equilibrium.

Unpredictability and other unknowns

Another factor is that developments in system complexity occur sporadically and unpredictably. For an increase in energy sufficient to lead to a complete system change, one action must follow another, action after action, faster and faster, until a threshold is reached, turbulence ensues, and the phase transition is accomplished.

There are many unknowns associated with chaos, the first of which is the amount of energy required to initiate the phase transition, the beginning of turbulence.

Secondly, chaos itself is - of course - unpredictable. Once turbulence starts, you cannot know where it will go next, or, how long it will last. Because of this, it cannot be controlled.

As far as we are concerned, for people - for human systems, it can only be experienced. Indeed, chaos is the opposite of control, hence it involves risk. You cannot predict what the consequences of it will be.

Even more, while the theory has shown that new forms of order are embedded in the turbulence - this non-randomness would seem to imply a measure of control - the problem is that there may be a number of possible outcomes once the energy addition is dissipated.

In other words, the underlying order serves only as a guide. As with water that ceases to boil when you stop heating it, the outcome could be a reversion to the prior state of affairs.

What I am driving at here is that the onset of chaos does not ensure evolution. Rather, the chaos could be so great that the system that is subject to it fails to adapt, and dies, so again there is no evolution. Instead, there is extermination and extinction.

Be prepared

At a personal and social level, the main consequence of all of this is that with chaos, you need to be alert and ready. It may be uncontrollable and unpredictable, but its negative consequences can be limited if you are prepared to confront them the instant they arise. Where possible, you should of course seek to prevent them.

Further, as the energy subsides and the turbulence dies down, you need to be ready to direct and shape the next form of order.

Finally, regarding the energy that is needed to instigate chaos, if you want to accomplish a change where a phase transition is required - what I mean by this is that you may actually want some chaos in your life - you can only keep pushing until the requirement, whatever it might be, is met. But, if you can plan and even orchestrate this, it may be possible to accelerate the onset of turbulence, perhaps greatly.

In conclusion, I hope this article hasn't been too difficult. The subject is technical. I needed to introduce a number of different, but related, ideas. In the balance of this series I will present examples so you can see the ideas in action - meaning, in reality. I hope this will illustrate how important they actually are to you.

© Roland Watson 2013