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.