Characteristics of non-linear systems

The idea of the non-linear seems strange and counter intuitive. That is because we inhabit a world where we make most judgements assuming that the world is fairly predictable. Our well-developed capacity to assume can make dealing with irregularities or the unpredictable problematic. For example, if we attempt to climb stairs with an uneven gap between treads we will stumble. It isn’t what we are expecting and, even if we can see that there is a difference, we ignore it.

Non-linear describes a dynamic system with feedback (iteration) in which input and output are not necessarily proportionate as the system iterates. For example, a stream flowing in the uplands or in a weather system will churn and this churning is feedback. A small disturbance can multiply until a vortex forms and carries far downstream where it may look like a random occurrence, but actually it’s not – most of the time. Ideally, let’s say with the example of compound interest, feedback can give predictable outcomes (see xxxx): if it starts from rest and all the feedback is fed back in, but if we change the starting assumptions so that we have a system already in motion (i.e. the starting conditions are not fixed) and we have feedback where it is not certain that all feedback will be exactly reintroduced then there is a different character to it.

Some of these characteristics of a dynamic system with feedback


We get patterns rather than end points. These patterns, as the system iterates, will vary slightly or more significantly and the result is a sense of where the action is but no way to determine it exactly. We get topographies, maps of the landscape of activity. Here is one. It shows the limits of the changes in normal times. It is often called the normal attractor.

However, we know – to the extent that it has entered popular culture – that there is something called a butterfly effect, a small variation can lead to disproportionate or even extreme results as it iterates through the system.

The existing pattern can be disrupted if the system goes turbulent, before settling down again – around a different attractor. Therefore, change can be one way, a tipping point can be reached and the fundamentals of the system reveal different results, quite unexpected ones.

These tipping points are often very sudden, which is due to runaway or undamped feedback or other cycles reinforcing the original cycle. Exponential relationships can give very little time for response. In our world this means that the cosy assumptions we make about change are very unsuited to real iterative systems, especially those with complex interactions.

However we perceive a world of order, there is a kind of resilience built in, a non-linear system is not chaotic (random) in the general sense but it is based on dynamic patterns which can be remarkably stable in the interplay between positive and negative feedback; never fully predictable, never something which we could think we could understand, predict and control – it’s not possible. It is a message, however, about participation and working by influence and with great sensitivity to the various cross currents and systems around us.

To get a sense of the difference in perspective, set a plank on a log and try and balance. You will never be still.