Tag Archives: simplicity

Blind to complexity

fruit fly nervous system Albert Cardona HHMI Janelia Research Campus Welcome Image Awards 2015When 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.


Is the world incomprehensible?

For hundreds of years, philosophers and scientists have encouraged one another to keep their explanations of the natural world as simple as possible.  Ockham’s razor, attributed to the 14th century Franciscan friar, William of Ockham, is a well-established and much-cited philosophical principle that of two possible explanations, the simpler one is more likely to be correct.  More recently, Albert Einstein is supposed to have said: ‘everything should be made as simple as possible, but not simpler’.  I don’t think that William of Ockham and Albert Einstein were arguing that we should keep everything simple; but rather that we should not make scientific explanations more complicated than necessary.  However, do we have a strong preference for focusing on phenomena whose behaviour is sufficiently uncomplex that it can be explained by relatively simple theories and models?  In other words, to quote William Wimsatt, ‘we tend to ignore phenomena whose complexity exceeds the capability of our detection apparatus and explanatory models’.  Most of us find science hard; perhaps, this is not just about the language used by the cognoscenti to describe it [see my post on ‘Why is thermodynamics so hard?‘ on February 11th, 2015]; but, more about the complexity of the world around us.  To think about this level of complexity requires us to assemble and synchronize very large collections of neurons (100 million or more) in our brains, which is the very opposite of the repetitive formation of relatively small assemblies of neurons that Susan Greenfield has argued are associated with activities we find pleasurable [see my post entitled ‘Digital hive mind‘ on November 30th, 2016].  This might imply that thinking about complexity is not pleasurable for most us, or at least requires very significant effort, and that this explains the aesthetic appeal of simplicity.  However, as William Wimsatt has pointed out, ‘simplicity is not reflective of a metaphysical principle of nature’ but a constraint applied by us; and which, if we persist in its application, will render the world incomprehensible to us.


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

Susan Greenfield, A day in the life of the brain: the neuroscience of consciousness from dawn to dusk, Allen Lane, 2016.