When faced with complexity, we tend to seek order and simplicity.  Most of us respond negatively to the uncertainty associated with complex systems and their apparent unpredictability.  Complex systems can be characterised as large networks operating using simple rules but without central control which results in self-organising behaviour and non-trivial emergent behaviour.  Emergent behaviour is the behaviour of the system that is not apparent or expected from the behaviour of its constituent parts [see ‘Emergent properties‘ on September 16th, 2015].

The philosopher, William Wimsatt observed that we tend to ignore phenomena whose complexity exceeds our predictive capability and our detection apparatus.  This is problematic because we try to over-simplify our descriptions of complex systems.  Occam’s razor is often mis-interpreted to mean that simple explanations are better ones, whereas in reality ‘everything should be made as simple as possible, but not simpler’, (which is often attributed to Einstein).  This implies that our explanation and any mathematical model of a complex system, such as the nervous system in the image, will need to be complex.  In mathematical terms, this will probably mean a non-linear dynamic model with a solution in the form of a phase portrait.  ‘Non-linear’ because the response of the system not proportional to the stimulus inducing the response; ‘dynamic’ because the system changes with time; and a ‘phase portrait’ because the system can exist in many states, some stable and some unstable, dependent on its prior history; so, for instance for a pendulum, its phase portrait is a plot of all of its possible positions and velocities.

If all this sounds too hard, then you see why people shy away from using complex models to describe a complex system even when it is obvious that the system is complex and extremely unlikely to be adequately described by a linear model, such as for the nervous system in the image.

In other words, if we can’t see it and its too hard to think about it, then we pretend it’s not happening!

The thumbnail shows an image of a fruit-fly’s nervous system taken by Albert Cardona from HHMI Janelia Research Campus.  The image won a Wellcome Image Award in 2015.

William C. Wimsatt, Randomness and perceived randomness in evolutionary biology, Synthese, 43(2):287-329, 1980.

For more on this topic see: ‘Is the world comprehensible?‘ on March 15th, 2017.