What makes something complex?
If someones mind can, in reasonable time, understand something considered complex, is it no longer complex?
If it's the brain changing in presence of a complex object, shouldn't the description of the complex object be a function of the observing mind, not the object?
Compare this with the question: what makes something heavy? If someone can eventually, in a small amount of time, lift it, is it no longer heavy?
Obviously some people can lift heavier things than others. The key word is heavier. There may not be an absolute property of heaviness, but there is certainly a relative one, which corresponds more or less to how hard it is to lift or move something. (Sheer size can make light things difficult to lift or move as well, of course.)
The same goes for complexity. The entire discipline of theoretical computer science could be said to be concerned with classifying, or reducing, the complexity of problems according to how much work it takes to solve examples of those problems (such as adding two n digit numbers, computing some digit of pi, and so forth). Whether a problem is "hard" depends on what resources the person or machine computing it has: just as a body-builder finds it easier to move a heavy weight than an average person, so a machine which has a lot of scratch-space available to it can more easily solve some problems than others. (Indeed, this is why most people tend to work out problems on paper, or these days with computers, rather than just relying on the organic memory that they have.)
Of course, sometimes a new way to solve a problem is found, and it reduces how much work a problem is; but the solution itself is sophisticated and not easy to understand without study. This is another way in which complexity can be measured: not by how hard it is to find a solution, but how complicated the procedure to find a solution is.
If you find a fast and simple solution to an old and complex problem, does the problem become less complex? Yes. But it's a qualified yes — depending on remembering the fast technique, which is akin to a body-builder maintaining their fitness once they have developed it (or perhaps a better analogue would be having built some simple machines, involving levers and pulleys, to lift the weight, and then either keeping that machinery in good shape or being able to re-build it). Finding the fast technique may not have been easy, but once done it reduces the significance of the problem as long as it is remembered. This could be described as the entire motivation for education.
I think that this is one of the problems of language, concepts like big, small, complex, simple...describe phenomena that cant be defined by themselves but by the comparison with other similar phenomenas. What makes something complex is us by bestowing the property of complexity upon that thing. If someones mind can in reasonable time, understand something considered complex, is it no longer complex for that mind. Is this thing still complex though? Well, if normally it takes more time for other minds to udnerstand this thing , this thing is still considered complex.
if it's the brain changing in presence of a complex object, shouldn't the description of the complex object be a function of the observing mind, not the object?
And yes, the description of the object should be a function of the mind, individually undesrtood. but as there are 7 billion minds if in average these minds find a thing difficult to work out, we categorize this thing as complex and this think gets to have the property of complexity.
Tremendous value in the answers provided, as complexity has both relative aspects (the question of degree) as well as semantic ones (Ludwig Wittgenstein has much to say on the topic of defining our terms!)
But there are inherent characteristics of complexity worth calling out. If we think of the interaction of many components or 'agents' that can't be adequately reduced to discrete cause-and-effect relationships, we have a complex system. My favorite example is a flock of birds. We can come up with rules that define how the birds move relative to one another, and computer algorithms can and have been written to simulate such complexity (see: "Boids" by Craig Reynolds 1986). But ultimately, the study of complexity mandates we accept the non-discrete interaction of variables, dealing with broader, non-linear factors and more generalized results. This leads us to 'emergent' or 'adaptive' outcomes that could not be predicted by a sum of the parts. In many ways, this thinking asks us to move away from (or embrace as inevitable in some domains) what science has come to appreciate as controlled, repeatable results.
Good examples of complexity in the world around us include the interaction of people in a society or culture, economic forces, and the weather. Another great example mentioned previously is psychology .. the study of how humans think and behave; clearly many levels of complexity at work there!
Coming from a computer science and engineering background, reductionist thinking is the obvious approach. But not all problems can be reduced to a simple formula. That's why complexity thinking can be a powerful alternative. It's a fundamentally different way of looking at things than archetypical philosophy or empirical science .. introduing a much more intuitive means of comprehending how things actually interact in the world.
See also books and papers by Scott Page (U.Mich); Murray Gell-Mann (1995); Santa Fe Institute. Related topics: fractals; chaos theory.
