If you're a mathematical theorist I want you to go ahead and skip this article. It's just going to make you mad, trust me. I'm going to bastardize and vastly over simplify a complex idea for my own purposes. If you don't want to deal with that then I suggest you turn back now!
Alright, with that out of the way I want to talk about chaos theory. While you may immediately think of dinosaurs and Jeff Goldblum it's actually a little bit more complex than that. Chaos theory itself is a branch of mathematics that deals with complex systems that are inherently unpredictable (but not random). For a system to be truly chaotic it has to meet three requirements, which I'm not going to go into (mostly because my understanding of the whole thing is tenuous at best). However, there is one characteristic of chaos theory that I do understand and is actually very, very relevant to thinking about how we live our lives.
A complex system is made up of many, many parts that are extremely interconnected. In chaos theory, a very minor alteration in one part of the system can have huge ramifications in another part of the system. Another way to think about this is as extreme sensitivity to initial conditions. Over enough time and space, two objects that started very near each other but at slightly different angles will end up at completely different end points (which I understand is more an example of exponential differentiation and not chaos -- but you get the idea).
One of the most complex systems I can think of is human life itself. Our relationships, habits, emotions, cognitions, work, physical environment, etc. are all deeply interconnected in ways where changes in one domain may (or may not) effect every other domain. It can be tempting to accept this apparent complexity as impossible to untangle but I prefer to think of it as a very optimistic way to think about personal development and growth. If you're facing challenges or a desire to improve in one area of your life it often makes sense to tackle it head on. You aren't happy with a relationship so you decide to do something that directly effects the relationship in question. Sometimes, though, that doesn't work as well as you'd like it to. Luckily, chaos theory and complexity can come into play and give you a different avenue to improving your situation. A small change in another area of your life, perhaps in your personal health or mental outlook, can have reverberations far more widespread -- perhaps even improving the relationship in question.
Here are two more examples from my own life to get you thinking about how this idea can be applied to your life. Something I seem to try to improve every couple of months is my diet. I'll go through phases where I eat very well but eventually end up sliding into bad habits. The obvious way to fix this problem is to focus specifically on the food I purchase and eat in my daily life. This works to a certain extent, but I always have more success when I expand my thinking and effort beyond food. If I start working out regularly I find myself unconsciously making better decisions about the food I eat. My ostensible goal is to "eat better" but the effort I place in achieving that goal is actually in "start working out." The connectedness between these two concepts allows changes in one area to have a greater effect in another area.
Another example involves times when I'm feeling frustration in my relationships. My first impulse is to do things that involve the other person -- have a conversation, write them an email telling them how I'm feeling, have an altercation, etc. However, I've discovered that when I am disciplined in my meditation practice my relationships throughout my life improve. Meditation is a distinctly private and individual effort but its effects reverberate far beyond the confines of my own body and mind. It effects how I interact with everybody on a daily basis.
Admittedly, this is not an earth shattering idea. Of course there are multiple paths to the same goal. I think it's easy to get stuck in a rut of failure where the initial effort to make a change fails and it seems like it's impossible to break out of the habit that's holding you back. In those cases, I encourage you to think about how everything in your life is connected like a giant web. Your efforts to directly change one node of the web may be thwarted, but you have an almost limitless array of more indirect approaches you can take. Harness a little chaos to bring more order to your own life.