Tag: initial conditions

oCoC: Initial conditions … … … do you like skiing?

On the complexity of change

I do. Like skiing. So, please bear with me for a minute. This is one of those strange texts where things are only revealed at the end.

First, we are going on a skiing hill. And because we are talking about initial conditions and the sensitivity complex (adaptive) systems have to them, this is a very special hill. For this thought experiment, the hill has been designed by a mathematician. The slope of the hill is homogeneous. The hill has moguls. These are of perfectly identical smooth shape, and they are spaced evenly, both horizontally and vertically. Let’s take the comfortable chair lift and go up. Not to worry, you can come; you won’t need to ski, a ski will do all the work. All we have to do is make predictions, observe, take notes, and then compare our observation notes with our predictions. This way we will know a little more about the nature of complex systems. We are on top of the hill. Take one ski, please. You can also use a snowboard, if you prefer. Place it flat on top of the slope, mark its position, and let it go downhill. We are observing its path, the trajectory of this process. We know exactly how it went down the slope. And we mark its exit position at the bottom of the hill. Just memorize it. Meanwhile, I will go back down and fetch the ski. I am sure you noticed that the one initial condition, to which we are paying particular attention in our thought experiment, is the entry position, where we let the ski go. The end state of this complex dynamic system is the ski’s exit position at the bottom of the hill. Alright, I am back up; let’s do this again. Find the first entry position. Move the ski or snowboard just slightly to the left or right, whichever way you are inclined. Mark the second entry position. Now is the time for predictions! The entry position is minutely different. What trajectory will we observe? Identical to the first one, because minute differences don’t matter because they are just noise in the system? Parallel, because the slope is homogeneous and the moguls are identically formed and evenly spaced, and all we changed a tiny wee bit is the starting position? Or just different in so many parts? How about the exit point? Is it going to be exactly the same distance between exit points 1 and 2 as there now is between the two entry points? Or are the two distances going to be different? Unless you really are on this skiing hill, you will have to believe me: The trajectories are different, and the distance between the two exit points is not the same as between the two entry points. We can let the ski go down time and again. The probability of both the trajectory and end state being different to any one of the earlier ski runs is significantly higher than the probability of trajectory and exit points – the end state – being the same.

Why is this so? Because complex systems have a high sensitivity to initial conditions. To show in our thought experiment that the sensitivity is high we only introduced a minute change to the initial condition, the entry position, and we assumed that nothing else changed. The weather and snow conditions remained the same, the force of letting the ski go is always the same, the ski did not carve into any mogul, … And still, trajectory and end state are different, and sometimes wildly different.

In Chaos Theory, this has also been called the Butterfly Effect. (When talking I am often prone to go off on an – interesting – tangent. Here I won’t do it and you will have to wait for a later post. Or you can look it up in Wikipedia.) It is a good example of how important initial conditions are, because the system is highly sensitive to them, even when many other variables – also of a larger magnitude – interact and change in the process. There is one main reason why this is so: These variables – the initial conditions – are the first ones to impact the process, even if only slightly. When we observe a complex dynamic system, a complex process, we can split it into time segments, iterations. And in one way or another, the variables of the initial conditions impact each iteration. Or as they say: Constant dripping wears away the stone.

Are initial conditions equally important when we want to understand complex social processes, such as work in a team, leading and managing a project, or an intimate relationship or marriage? I think we all know what the answer is, simply from experience: Yes, they are. Once we encounter a complex problem, we are well advised to look for and at the initial conditions of the underlying process(es). How we can figure out what the initial conditions were and how they influenced how events unfolded, we will have to leave for after the introduction of the characteristics of complex adaptive systems. What is important to take away from this brief excursion is that all complex systems are sensitive to their initial conditions. And (not only) because of this sensitivity to initial conditions, complex systems cannot easily be reversed to a prior state. No one steps in the same river twice. Complex adaptive systems have what we can call a history. This is strongly connected to the characteristic of nonlinearity. And that is the beginning of another post.

oCoC: Complex and adaptive

On the complexity of change

Let’s forget about changing anything. Just for a little while. Let’s just think about complexity. Something complex. A complex process. Got it? Why is this process complex? What makes it complex?

First answers are simple: a process with more than one actor is more complex than a process with just one actor. But it is not just the participants. Many natural or industrial processes are complex, and they do not necessarily even have participants (humans) that act in them. So, there can also be many components. And if that were not enough, more often than not there are many variables. You remember these variables from math classes in school.

x + 7 = y

This is a nice linear equation – and thus not complex. For each x there is exactly one y, which can be calculated, if you know how do do this sort of thing.

Think about the complex process you have in mind. It does not just have one variable, one x, that changes or can be changed. Most processes in life, in society, in biology, in physics, in nature, … in most places where we care to look, have more than one variable. More than one (in)observable trait, characteristic, or feature that can change or that can be changed.

Now that’s OK, you say. We just have to look at a few more things. Right! Problems arise when there are very many, often too many, to always keep our eyes on, to look out for, to consider. And not only that. Each of these variables, each x, if you like, does not just have one dependent y. More than one variable can depend on each changing variable.

I am changing the period of time I use for exercise in the morning. I am changing time t. Time t influences my fitness level; I am increasing muscle mass and flexibility. Because of the increased muscle mass, my metabolism changes during the day. I feel better, I am more agile, I move more and quicker, burning more calories than on the days prior. And by increasing time t for exercise, I am reducing time r for reading … Twitter, my favorite book, a newspaper, or some emails. I am also reducing time c for cooking, so I will have to have my lunch prepared the evening before or will have to go to the cafeteria to buy something to eat.

You get the point.

A complex phenomenon does not just have many variables. Each of these variables potentially interacts – metaphorically speaking bounces off and changes – one or more other variables. Overstating just a little bit: each of the many variables changes all the time, in concert and against each other.

Did I say at the beginning: Let’s forget about change for a little while? Impossible. We quickly returned to the concept of change. Change is part of complexity and complexity is part of change. We cannot – and should not – consider one without the other. [Maybe just for a quick thought experiment, or if we are really tired in the evening.]

What are the consequences? Complex phenomena are in constant flux, change constantly. That’s why we often talk about complex dynamic systems. Variables interact with one another, components interact, actors (participants) interact. In these many continuous or iterative interactions, each variable, component, and actor are also prone to change. They co-adapt. Especially for social systems, we often use the label complex adaptive systems (CAS). And if we want to understand change better, be able to influence it a little bit, or just deal with it, it is useful to look at some of the characteristics of complex adaptive systems.

  • CAS are likely to be on a nonlinear trajectory, which means a change I put in does not necessarily result in a proportionate change to come out.
  • CAS are sensitive to initial conditions. The variables, however small they might be, that were there from the very beginning are most likely to have had a relatively large impact on the whole process, simply because they have been around for long enough.
  • CAS have attractor states – states they are more often and more likely in. They also have repeller states, states which they could reach theoretically but never or hardly ever reach.
  • CAS are likely to reach an equilibrium – like a standstill, change is very close to zero – if no new energy enters the system.

I am glad I got this out of the way. And maybe so are you. Remember that I said it is often useful to apply a theoretical lens to gain a better understanding of a problem? At some stage I had to introduce the lens. In subsequent posts, I will look at these characteristics of complex adaptive systems, one by one. And I will show for each one what role their understanding can play in solving personal problems, problems at work, in social interactions, or just around the house.

The neat thing with these CAS is that there has been a lot of research that tried to figure out how to get a better handle on the complexity. And I am as sure as one can be that what we learn about the ever-changing complexity will come in handy almost every day, when solving problems. Whether this is in your personal life, when making leadership decisions, or simply when you are trying to fix something that you believe needs fixing.

And to finish off, if you’d rather read the texts on the Complexity of Change in one possible order … a table of contents is emerging.

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