What is complexity ?

WHAT IS COMPLEXITY?

 

Complexity, just like for example energy, is a natural property of every system. It is defined as a function of structure and  uncertainty.  Humans instinctively try to stay away from highly complex scenarios because of one fundamental reason – high complexity implies a capacity to deliver surprising behavior. Since complexity is a function of entropy, it is measured in bits. Complexity is an unusual function. It combines two "antagonistic" components which in Nature tend to oppose each other. Structure attempts to persist in the face of the erosive action of entropy. Our complexity metric blends them together.

‘Complex’ does not imply ‘complicated’. A highly complicated system may possess numerous components (e.g. a watch movement) and yet be unable to behave in an unexpected manner. Systems with very few components, on the other hand, may be extremely difficult to manage and without being complicated. This is why simply counting the number of parts in a system does not provide a serious measure of its complexity.

 

 

HOW IS COMPLEXITY MEASURED?

The complexity of a system can be measured using our QCM (Quantitative Complexity Management) engine OntoNet™. The two key components of our complexity metric are the so-called System (or Complexity) Map – which reflects how information flows within a system – and uncertainty, which measures the degree of disorganization in the system.

Our technology is model-free: we do not impose any analytical models on top of data in order to determine its structure. Models are always subjective; they require assumptions and introduce additional uncertainty into a problem. That is why do not use regression models, response surfaces, neural nets, cluster analysis or statistics. Our technology, which mimics the brain, is based on an innovative and proprietary approach which identifies structure and patterns within multi-dimensional data without using conventional math-based approaches. 

The process of complexity computation is as follows:

A rectangular array of data is provided, in which the columns represent particular variables while the rows correspond to samples.

OntoNet™ determines the existence of relationships - generalized correlations -  between all  variables.

A System Map, which illustrates by means of a graph the topology of these relationships, is constructed automatically by OntoNet™. The map is composed of:

• nodes, which correspond to the variables and which are aligned along the diagonal of the map. The order ot the nodes in the map is the same as that in the data array.
• links, indicated by means of connectors (see orange dots in map below). An example of a scatter plot, which corresponds to a relationship between two variables, is indicated in the figure below.

Complexity is computed as a function of the map's structure and of the nature of the relationships between the variables.

In the event a variable does not have any significant relationships with any of the other variables, it is indicated in the System Map by means of an empty node. Variables which possess the highest number of relationships - known also as degree - are known as hubs and are indicated by means of red discs. An example of System Map, which reflects the structure of the Dow Jones Index, is indicated below.

HOW IS ROBUSTNESS RELATED TO COMPLEXITY?

Complexity cannot grow indefinitely. The laws of physics ensure that every system can sustain its own specific maximum amount of complexity before it becomes unmanageable and before it loses integrity. This limit is known as critical complexity. In the proximity of this threshold systems become unstable. Close to critical complexity a corporation loses resilience, becomes fragile and vulnerable. Prediction of performance becomes unreliable and the business is unprepared to face extreme events (the so-called Black Swans).

Based on how close a business functions to its critical complexity therefore possible to issue a complexity rating. We may distinguish five categories of business complexity. Each level is assigned a number of stars ranging from one to five – a five star business being the healthiest in terms of resilience. Below we illustrate examples of different corporations, each having a different complexity, a corresponding critical complexity and the resulting resilience and complexity rating.

As may be noted, businesses which are more robust function closer to their lower complexity bound than to the corresponding critical complexity. See movie on complexity and robustness quantification.

In order to pinpoint the business parameters that impact complexity  the most (hence the resilience) it is sufficient to examine the Corporate Complexity Profile, which is illustrated below and which provides a breakdown of complexity in percentage terms:







Resilience and complexity ratings may be computed on-line, in our Rate-A-Business portal.

Read more about our technology (click image).




More details may be found in the book "A New Theory of Risk and Rating" (click image).