Root cause of Complexity

Human beings always describe, communicate and understand things using natural languages.

Natural language is a collection of words adhering to the semantics of the natural language.


On dwelling further we will realize that at the lowest level the brain processes these words to describe and understand artifacts.

Example


Let's look into the following figure which shows a system with at least 2 components along with the various possible interconnections and interrelationships.

Figure

We know that a system with a single component is not possible. We also know that every component will have a structure and behaviour.

Let's say on an average it takes us 10 words to describe the structure and behavior of a single component. Let's say that on an average it takes us 30 words to describe a possible interconnection or a relationship as there can be different types of relationship, multiplicities of a relationship, different role names at different ends of a relationship etc

So for a system with two components there are at least 3 possible interrelationships which are possible i.e. for a system with two components and 3 interrelationships we will need at least 10+10+30*3 = 110 words.

Now if I say my system is made up of 3 components the number of possible relationships could be 6 and we will need at least 10*3 + 30*6 = 210 words to describe it.

This makes it clear that the more the number of components within the system, the number of possible interrelationships will increase exponentially, and for every possible relationship the number of words needed to describe it will keep increasing further exponentially.


For a system made up of large number of structural components, one would need a large number of words to describe it. Probably this explains why the SRS document runs in to 400-500 pages.


Or

The number of words that one would need to describe a system increases exponentially with the number of components which are modeling the structural details of the system. The more the components the more the interrelationship and more are the number of words needed to describe.


 

Hence we can infer that the complexity of the system or a problem is exponentially dependent on the number of components modeling the structural details of the system.

Or

We can say more the number of components modeling the structural aspects of a problem or a system, the more complex or more difficult is the system or the problem.


 
Hemant Jha
Founder - VPlanSolutions
Researcher, Trainer

www.VPlanSolutions.co.in