The three-body problem: chaos at innovation

First of all, let me wish you a happy and interesting 2016. As I warned you, I might write some more about the Physics of Innovation. The idea behind this series is to relate well-known physics theorems or phenomena with innovation activities, in order to use them as inspiration or means for reflection.

Let me start this second post with a question: Would you say that innovation is a random or a deterministic process? I will elaborate some more on this, because I believe that the correct answer would be a third one, innovation is a chaotic process.

What is a chaotic system? A simple definition would be “a dynamical system highly sensitive to initial conditions”. This means that “small differences in initial conditions yield widely diverging outcome, rendering long-term prediction impossible in general” (source: Chaos theory – Wikipedia). The system can be governed by simple and well known laws, behaving in a deterministic way, that is, with no random behaviour. However, it is so sensitive to initial conditions that sometimes it looks as if it was actually random because just the precision error of the measurement of the initial conditions could produce very different results.

I thought about the theme for this post while reading a very good science fiction novel (if you like SF with actual science into it). It is called “The three-body problem” by Chinese author Cixin Liu; I truly recommend it. I will not go into the novel, but suffice it to say that this classic physics problem is central to the argument. The three-body problem can be defined as the study of the motion and position of three isolated bodies according to the laws of classic mechanics. This apparently simple problem, which follows well known rules, has been nagging scientists for centuries. Henri Poincaré established many years ago that there is no analytical solution for it, although some restricted three body problem solutions have been found in some specific conditions. I cannot describe this in further detail in this post, but there is ample literature available if you are interested. However, let me just highlight that just a small difference in the initial position and speed of the bodies or in their relative mass can yield very different results, that is, chaotic behavior. You can find some online simulators that will allow you to play with initial conditions and see chaos into play (for instance,

Chaotic behaviour means unpredictability, but it does not mean lack of order. For instance, take the weather, a typical chaotic system. As it was established in the famous Butterfly effect, we do not know when a tornado will hit the coast of America, or if it will rain next week in Madrid, but we do know that some behaviours are more probable than others, that changes are more or less gradual, and that weather variables will not exceed some boundaries (150ºC for instance). We cannot predict weather in the mid or long term, but we can observe climate following some general rules. I can also mention the existence of “attractors”, which are areas in the system space that seem to be more probable, that exert an attraction to system states around them; if we look at the system from “a distance” we may see some patterns developing around an attractor (the title picture of this post shows a Lorenz attractor). For the sake of example (allow me the license), you can think of a ball rolling around the wall of a funnel; you don’t know its precise trajectory or when it will reach the bottom, but you know that most of the times, it will.

Business management needs to be ready to accept chaotic behaviour in terms of innovation, albeit the difficulty to do so. If you pretend innovation to be a linear deterministic process, most of the times you will be very off the mark. For instance, thinking that investing in innovation half of what are investing will yield half the results, or other linear simplifications like this one, will bring many surprises, because you may find the yield to be double, equal or even zero, and you cannot predict it! With this is mind some reader may think to invest zero in innovation to see if something pops into existence, and it actually may, but we would moving more into the realms of quantum mechanics, which is even more complex and out of the scope of this post (although I am already thinking about a new one related to the Uncertainty principle).

However, as I said before, there is order in chaos, and different studies of chaotic behaviour in business and organisations have shown that although you cannot predict how the system will behave, if you take enough distance to look at the whole picture instead of trying to micromanage the innovation process, or if you include some level of autonomy in the organisation, the system will iterate and adapt towards a better operation. The sooner the organisation realises that innovation is an unpredictable process, the better it can take advantage of the underlying order within its chaotic behaviour. Take some distance, allow innovation to run freely without too much control but within clear boundaries and objectives and you will see results. But most of all, do not expect each innovation endeavour to land exactly where you want it to (assigning it a target ROI, for instance), because you will most probably either kill it or completely miss the point.

Allow some chaos in your innovation practice, you will see it pays off… most of the times!



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