Complex or Complicated. What's the Difference?

Very often, the terms 'complicated' and 'complex' are used to convey the idea of sophistication or extreme difficulty. What is the difference? One dictionary states that complicated means consisting of (many) interconnected parts, difficult to analyze or understand, intricate. The same dictionary states that complex means made up of interrelated parts or units, involved, intricate. Essentially the same thing. The problem is with 'complex' not with 'complicated'. In reality, the issue is simple: what we lack is a good definition of 'complex'. If we accept the definition of complexity championed by Ontonix - we omit here the mathematical details - and namely the one which defines complexity as an attribute that reflects the capacity of a system to evolve, or its fitness, things change substantially. In order to be fit - take a biological system for example - it must possess the capability to generate novelty, to surprise, to devise new ways of behaviour. It must contain elements of uncertainty.

A great way to quantify the 'amount of uncertainty' is via entropy. Systems with low entropy are extremely organized and have a very limited potential in terms of surprise. They are essentially deterministic in their behaviour. Take a mechanical wrist watch. In some cases, up to 1000 parts compose the movement. However, these are, for all practical purposes, devices with one degree of freedom! Such a system functions in a very precise and repeatable fashion. It has very low entropy, and, therefore, according to our philosophy, very low complexity. Complicated but not complex. We can also say that a system with high complexity does not necessarily have to be complicated. A family has typically 3, 4 or 5 members but because the interactions between humans are highly unpredictable, or entropy-rich, the system is highly complex. Five components only, according to our dictionary, imply a system that is not complicated. So, complicated and complex are two entirely different things. The first reflects sophistication, while the latter is related to fitness in a broad sense. Wisdom starts by calling things with their right names (Chinese proverb).