## Monday, 29 July 2013

### Complexity? It's All Relative.

Complexity is a measure of the total amount of structured information (which is measured in bits) that is contained within a system and reflects many of its fundamental properties, such as:

• Potential -  the ability to evolve, survive
• Functionality - the set of distinct functions the system is able to perform
• Robustness - the ability to function correctly in the presence of endogenous/exogenous uncertainties

In biology, the above can be combined in one single property known as fitness.

Like any mathematically sound metric our complexity metric is bounded (metrics that can attain infinite values are generally not so useful). The upper bound, which is of great interest, is called critical complexity and tells us how far the system can go with its current structure.

Because of the existence of critical complexity, complexity itself is a relative measure. This means that all statements, such as, "this system is very complex, that one is not", are without value until you refer complexity to its corresponding bounds. Each system in the Universe has its own complexity bounds, in addition to its current value.  Because of this a small company can, in effect, be relatively more complex than a large one, precisely because it operates closer to its own complexity limit.  Let us see a hypothetical example.

Imagine two companies: one is very large, the other small. Suppose each one operates in a multi-storey building and that each one is hiring new employees. Imagine also that the small company has reached the limit in terms of office space while the larger company is constantly adding new floors. This is illustrated in the figure below.

In this hypothetical situation, the smaller company has reached its maximum capacity and adding new employees will only make things worse. It is critically complex and, with its current structure, it cannot grow - it has reached its physiological growth limit and can do two things:

• "Add more floors" (this is equivalent to increasing its critical complexity - one way to achieve this is via acquisitions or mergers)
• Restructure the business
If a growing business doesn't increase its own critical complexity at the appropriate rate it will reach a situation of "saturation". If you "add floors" at a rate that is not high enough, the business will become progressively less resilient and will ultimately reach a situation in which it will not be able to function properly, not to mention facing extreme events.

Complexity is a disease of our modern times (more or less like high cholesterol, which is often consequence of our lifestyles). Globalisation, technology, or uncertainty in the economy are making life complex and it is increasing the complexity of businesses themselves. An apparently healthy business may hide (but not for long!) very high complexity. Just like very high cholesterol levels are rarely a good omen, the same may be said of high complexity. This is why companies should run a complexity health-check on a regular basis.

So, the next time you hear someone say that something is complex, ask them about critical complexity. It's all relative!