8. Complexity
Because systems tend to combine and become more structurally complex the concept of complexity is a central one in the study of self-organizing systems.
Definition
Complexity - a scientific definition is in the process of development. At the present there is no consensus on the exact meaning of this term. Its definition varies in different disciples.
A common meaning - something is complex when there are a great number of interacting elements with many interconnections.
Background
The common definition above is unsatisfactory because a large number of things with all their interconnections may still be a simple system. A glass of water contains a huge number of molecules. There are many internal interconnections yet the glass of water does not fit our concept of a complex system. What is missing is some coordinated activity; or a structure with many and varied parts. Those are the things we expect to be part of complex systems.
Discussion
Perhaps the concept of complexity is so hard to define because it is a subjective idea. We tend to think that those things that are complicated are complex. But complicated things can become simple with understanding. Is then their complexity lost? The ordinary driver looks under the hood of a modern automobile and is bewildered by the intricacies. The experienced mechanic says, Look! Its simple. He tweaks a gizmo and the stalled engine comes to life. What is complex seems to depend, to some extent, on what the observer brings to the observation.
Recognizing complexity
1. Internal complexity
There are different ways in which a system can be considered to be complex. The first of them, mentioned above, is when a great many in dependent parts within a system are interacting with each other in a great many different ways and many interactions are occurring simultaneously. This is internal complexity: arising from the organization and the interactions. Clocks may have internal complexity but they still produce a relatively simple action: the same repeated pattern of change.
2. Behavioral complexity
Regardless of a systems internal complexity, a system can be considered to be complex if its behavior is controlled by many variables or is unpredictable. Simple systems are predictable; they offer no surprises. If a system surprises us, acts in ways that are counterintuitive, we assume that complex functions are at work. Such a system has behavioral complexity. In mathematics, for example, the simple equation z > z2 + c describes what is most probably the most complex mathematical object ever invented: the Mandelbrot set. The behavior of the values generated by the equation in a complex plane as pictured on the computer screen are unbelievably varied and unexpectedly beautiful.
The computer is to the study of complexity what the microscope was to microbiology. It makes the study of the field possible.
3. Property complexity
Similar to behavioral complexity but important enough to warrant a separate designation is property complexity. Systems which exhibit a more diverse number of properties must contain a multitude of factors and interactions to produce them and deserve to be called complex. A maple leaf has the properties of color, special shape and photosynthesis.
4. Structural complexity
A system with many feedback loops is hard to understand because of all of the subtle and changing inputs and must therefore be considered to be complex. Such a system can be said to have structural complexity. The system is continuously modifying itself by changing the interactions among its variables. Consider the difference between a greenhouse and an ecosystem.
5. Informational content
This is the idea that complexity of a system is measured by the length of the shortest possible description of that system. In this view, if the most concise description of a system is lengthy the system is complex. If it is easily described it is simple. (For contrast consider the Mandelbrot set mentioned above; simple to describe in mathematical terms but wondrously complex.)
6. Hierarchical depth
The more levels a particular object contains, the more complex it is. The universe, containing all levels, is the most complex system we know. An atom used to be considered the most elementary (meaning simple) particle. We now know that its nucleus is a complex structure made up of different kinds of quarks and gluons seething with interactions in bewildering complexity. The number of nesting systems contained within a system relates to the idea of hierarchical depth.
7. Organic complexity
Biologists have suggested that the complexity of a living organism can be gauged by the number of different cell types in its organization. This is similar to the idea of internal complexity already mentioned but restricting it to living things. Clearly a worm is more complex that an amoeba and humans are more complex systems than either.
Discussion
If, in general, systems tend to increase in complexity, what might account for this? One hypothesis is that increased complexity expands the ability of a system to respond to a changing environment. This would enhance the systems survival and make for increase in complexity in the Darwinian sense. Some organisms, notably human beings, expand their response to that of attempted control over the environment. This concept would involve the notion that systems progress by becoming more advanced by greater control of their surroundings and their lives. The philosophical question of the relationship between increased complexity and freedom is an interesting subject but one which is beyond the scope of our discussion and will not be addressed here.
Conclusion
An individual system may exhibit many of the different kinds of complexity described above and may do so simultaneously. Researchers have begun to try to develop a science of complexity and move it away from the subjective frame of reference. This is an important task. In our increasingly technological world we are beginning to recognize our need to deal with complex systems. New concepts and methods are required. These may be forthcoming as the study of complex systems continues.
Many educational institutions have recognized the importance of the subject and have organized departments for the study of complex systems.