A useful way of understanding the class of problems that interest me, at least from a blogging perspective, is that I am interested in what this blog post has called "wicked problems", in contrast with "trivial problems," of the kind that their blog focuses upon.
Two major technical fields I know have areas that call themselves “complexity”—ours and dynamical systems. . . . [Another sense] reflects the way we use “complex” in ordinary speech: big, involved, hard-to-describe, requiring much effort even to comprehend. It included a cool notion that I think you may like called wicked problems . . . . This is different from our notion of a problem being wickedly hard—it has to do with framing the problem itself. . . .
The key is the notion of a wicked problem(WP). It is not that easy to define what they are, but here is the standard list of properties they have:
*The problem is not understood until after the formulation of a solution.
*Solutions to wicked problems are not right or wrong.
*Every wicked problem is essentially novel and unique.
*Every solution to a wicked problem is a “one shot operation.”
*Wicked problems have no given alternative solutions. . . .
In 1967 West Churchman introduced the concept of wicked problems in a journal article. . . . Horst Rittel and Melvin Webber formally described the concept of wicked problems later in 1973 where they contrasted WP’s from “trivial” problems such as those from mathematics, chess, or puzzle solving.
Put another way, I enjoy the unstructured fumbling around trying to figure out how to determine what is going on and how to make sense of it and problem defining part of the process from unstructured or contradictory data, as much as I do the colder and more purely rational process of solving a well defined, but possibly very difficult, problem. I like big, messy, unsolved "one shot" problems.
Three senses of the word "complexity"
Put another way, the post distinguishes between three kinds of complexity, the first of which is the wicked problem sense (called it "real-world based" complexity) described above.
Their blog focuses on complexity in a second sense of problems that are wickedly hard to solve (generally the address whether it is theoretically possible to solve a kind of problem in a reasonable amount of time defined in a technical way, which is used to evaluate computer algorhythms and cyptography strength) because they are resource intensive to solve:
When we say “complexity” we almost always are referring to the resources needed to compute and solve some problem. The resources measured can be: time, space, randomness, nondeterminism, rounds, quantum operations, or other resources. Indeed sometimes we mix these together to get measures that limit two or more resources.
They also mention a third sense of the term which they call behavior based complexity, which is also a more common sense of the word than theirs, as used by places like the Sante Fe Institute, and which they claim is based upon:
[T]he notion of “a complex system.” . . . When many say complexity theory, they usually are referring to the type of behavior of a system. This type of complexity theory is all about behavior, about prediction, about chaos, about the tremendous forking of paths (bifurcations) that can arise from even simple systems that evolve over time.
I would quibble with their definition here. "Chaos theory" generally refers to deterministic dynamical systems whose outcomes are hard to predict because they are highly sensitive to initial conditions (like the weather), even if you know the often simple equations that govern them exactly, causing their outcomes to seem quasi-random, and happens to be related for non-obvious reasons to fractals.
Complexity theory is a kindred but analytically distinct endeavor (closely aligned with what sociologists and business management professors mean when they talk about "complex organizations"), and while chaos theory typically involves simple underlying equations, complexity theory does not. Complexity theory involves notions like "emergence," the conditions that cause systems to be complex, and how to apply simply strategies to deal with complex systems.
Still, while I quibble with their definition, I know what they mean and I agree that it is distinct. Indeed, I think that complexity is a pretty poor term to define the study of how intrinsically difficult certain classes of problems are to solve computationally, in terms of the resources necessary to solve them. It is a very valid area of study, but "complexity" theory is a poor name for it, because the problems that are addressed are generally straightforward and well defined.