We often hear people say that "higher complexity makes a system more robust and resilient". Is this true? Not quite. Like with many things in life, it's all relative. There is one fundamental point to clarify before we give an answer.
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:
In biology, the above can be combined into 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. In practice, critical complexity expresses how much uncertainty can the system withstand before breaking up. Complexity is measured based on a system's so-called state vector, which reflects the observable degrees of freedom of a system.This means that you can make a system more complex by adding more structure - this is in general a good thing to do. But you can also make a system more complex by making it more fuzzy, more uncertain. This is in general not a good thing to do.
Complexity is a function of two fundamental characteristics of a system:
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 for that particular system. Each system in the Universe has its own complexity bounds, in addition to its current value of complexity. 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.
Now, it is also true that higher complexity implies higher functionality. In fact, in our biosphere the process of evolution reflects this very eloquently. More capable organisms evolve from simple ones. More complex organisms are able to adapt better to a changing environment as they can perform more functions (e.g. manufacture clothes or shelters). So, from this point of view it IS better to be more complex because higher complexity implies more functionality. In such cases we are obviously speaking of adding new structure which, in turn, increases complexity. However, once you've defined the structure and then you increase complexity by merely adding entropy (chaos) to the system you are in fact making the situation worse, especially if you get close to your own critical complexity.