People have a problem when it comes to putting numbers to things. In physics, the standard way of breaking up a problem involves spectral analysis. To break up turbulence, a set of waves, at a given scale, interact with other waves. The trouble you’ll run into is the fact that because the problem is non-linear, you’ll find that all of the scales interact with other scales. I’m speaking in the language of fluid dynamics here. What you’ll end up doing is applying the fudge factor in order to redistribute energies, varying from scale-to-scale. Now, with your fudge factor, you’ll have a variety of non-physical situations, like an unstable equation or something. This is something that is observable..and what you’re observing is complex behavior.
Now, that’s complex behavior, as it applies to fluid dynamics, but what about complex behavior as it applies to something that has absolutely nothing to do with fluid dynamics? I ask this because, as an employer, and I’m looking for a candidate to fill a particular position, I have to wonder if the “best” candidate for that position should be someone who has a complex behavior about himself, as in, how that individual approaches a problem that calls a complex means of solving or addressing such a problem–or, should I hire someone who’ll just stare at a computer screen all day until that “Aha!” moment occurs? The thing that I’ve learned over the years is that most people want the easy way out [of a situation]. The irony is that most people also want to have some sort of a legacy left behind about them when they die. Unfortunately, that’s not an easy task to get accomplished.
Complex behavior as it applies to employment would be advantageous to an individual that doesn’t necessarily focus entirely on one particular subject. An ideal candidate for a position that I would offer would be an individual that, even as a hobby, takes time to devote his or herself to engaging in subject matters (plural) outside of the realm of pure math and science, such as philosophy, history and literature. Despite the fact that the aforementioned aren’t all that much relative to any of the positions that I might offer, however, they are inclusively advantageous, and will produce a more qualified candidate seeing how the subject matters open up that individual’s means of being creative and a more agile candidate for a position [at HL]. As an example, knowing that the world changes will put you at an advantage. Studying history will do that for you.
Individuals, mostly whom are scared, have this “need” to prove something is right, but in order to do that you have to discover something original. Understand that very few people are adept at doing so. At your advantage, incorporating not only the study of complex behavior in your observations but also incorporating a complex behavior in your approach to discovering something “new” is knowing complex behavior helps to alleviate some of the pain associated with the grunt work of [scientific] research–and also how such behavior is contributing towards your research. Whatever it is you discover that’s “new”, in itself, isn’t complex nor is it some kind of a secret; and even if it is, it doesn’t matter, since you’ll quickly learn that there isn’t just one secret–rather, there are thousands of secrets out there and it’s not hard to find a niche [market] in which you’ll be able to discover something “new”….or useful.
If you’re going to be a risk-taker, be an intelligent risk-taker that digs for gold. However, it would be wise to dig for gold somewhere that someone else hasn’t dug before. For those of you reading this who are mathematicians, if you’re curious about developing techniques with many degrees of freedom or several interdependencies, then you have no other option but to develop new math. This is difficult for some physicists inasmuch as their “strong points” are largely in, for one, linear algebra, seeing how manipulating mathematical techniques are, needless to say, in the corner of the mathematician. But, this is room for collaboration between the two professions. Also, you need to bear in mind how simplicity and complexity can combine in effort of allowing the math to be sustained at an equilibrium. Increasing the degrees of freedom will vastly simplify the problem to rest at an equilibrium. Keep in mind, that a lot of what we’re accustomed to assume is vastly complex despite how easy the assumption turns out to be. I mean, just look at circles as an example. People are quick to think that because it’s easy to describe a circle, that naturally, the universe is also circular, but you’re applying the description of something that’s easy to make out (i.e., a circle is round) to something that is complex and void of determinism (the universe).
Oftentimes, comprehension of complexities can lead to solutions or help researchers devise ways of developing those solutions. Yet, solutions are known for specific cases. Numerical solutions, as an example, are accompanied by a lot of work that just so happens to be a part of the problem in the first place. Again, solutions are known for specific cases, but for the general case? Let’s say, I’m working with equations that are non-linear (Scenario A and Scenario B). Since both scenarios are non-linear, I can have a solution for Scenario A, but when you mix the two scenarios together, the solution for Scenario B results in a complex behavior that is completely different than when the two scenarios are mixed together. You cannot break up equations that are non-linear.
When it comes to complexity or trying to have an understanding of how the universe “works”, you will likely burn out–and then you die. There is no end game. Once you come to terms and reason that there is no reward for getting the top of the mountain, other than you get the chance to climb to the top of another mountain, things will start to look different.