About the definition of complexity

The term 'complexity' does not have a unified definition yet. I used to think that a clear and widely accepted definition is necessary to do research on complexity, so the first objective of my research is to understand complexity and try to give it a general definition covering most fields. But after doing some literature review I found it not easy. This term has been used so widely, and even 'abused' [1],  in numerous fields. Complexity in one field can be defined totally different from it is in another. For example, in evolution, Kauffman viewed complexity as “the consequence of attempting to optimize systems with increasingly many conflicting constraints among the components” [2], whereas in computer science, complexity is often referred as the time or space used in computation [3]. The term 'complexity' itself is quite complex in the literature.

Why is this? It can be seen from the literature review that the definitions vary with the research target and scope. Each researcher lives in his/her own context, sees his/her own target, thinks about his/her own objectives. As a result, definitions are mostly limited to some specific problems, which cannot be applied to other areas. So others will then define their own complexity.

Do we need a unified definition? I would say no. Sometimes it is good we have various definitions for various fields and situations. Really general definitions will become those in dictionaries - 'the features of a problem or situation that are difficult to understand', which cannot provide much useful information to a specific problem or situation.

But we do need a definition for our own research scope in order to understand the problem and provide a basis for the research. So actually what we should do first is to clarify the research scope and target. 'Complexity in PD' is still big and need to be reduced.

1.Vicsek, T., Complexity: The bigger picture. Nature, 2002. 418(6894): p. 131-131.
2. Kauffman, S.A., The Origins of Order: Self Organization and Selection in Evolution1993: Oxford University Press.
3. Hartmanis, J. and A.M. Society, Computational Complexity Theory1989: American Mathematical Society.