What it really is, to sum it up, is a system that will appear to have a degree of randomness (not all randoms are equal) but actually aren't random. They can, through interpretation, be understood and predictions can be made
By extension isn't this just saying that randomness begins at the place where we lack the processing power to model a thing? Also, does chaos theory account for (or dispute) quantum mechanics, or is this more of a macro theory?
Well, first we have to tackle the idea of randomness. At some point, it becomes a philosophical debate and there's no way that it is falsifiable (currently) and so we can't really call it science anymore. In short, randomness is extremely difficult. There's pseudo-random, which is actually all you're probably familiar with. Then, there's true random.
With pseudo-random, you have things like the PRNG chips in old computers and randomness derived from statistical noise in your CPU with things like dev/random. They say dev/random is 'true' random, but that's a boldfaced lie. It just unpredictable because we don't know the initial starting state. You have dev/urandom which is pseudo-random.
So, there's lots of types of random - and they aren't all equal, much like all infinities aren't created equal. To put that in perspective, infinity + 1 is bigger than infinity and random with + 1 random bit is more random than random. (Don't try to think about it too much, 'cause it has driven people insane before - see Georg Cantor for example.)
Now, let's move on...
Bell's Theorem is well supported currently. Bell's Theorem applies to the world of quantum and has to do with random states. Currently, all supporting evidence means we have great confidence in there existing a true random.
This is outside the realm of chaos theory. A common misconception is that chaos theory is randomness. It's not. Chaos theory is a system that looks random until you can understand the initial starting state. So, because we can't know the exact initial starting state, we can't make long-term weather predictions with any degree of accuracy, to tie it to Lorenz's work.
And, to get back to your first statement, no. Randomness exists, or does not, without regard to our pesky human interpretations and observations. Throughout history, we've assumed many things were random - only to find out they were not. We ascribed those events to things like fate or to deities. As we've begun to understand the nature of the universe, fewer and fewer things turn out to be random at all. The more we learn, the greater we become at making predictions.
Make sense?
I don't pretend to comprehend (or understand the significance of) different degrees of infinity or randomness, but I think it makes sense conceptually. The chaos theory bit does makes sense though.
As we've begun to understand the nature of the universe, fewer and fewer things turn out to be random at all. The more we learn, the greater we become at making predictions.
Is this why physicists are so interested in cosmic background radiation? Are they trying to infer things about the initial state of the universe for the purpose of predicting the future of the cosmos?
Hmm... "Butterfly Effect."
I had the great honor to study under Dr. Lorenz, the man who coined the phrase and the application to chaos theory. I don't suppose anyone wants to talk about it? It's fascinating, really!
Chaos theory is mostly poorly understood by laypersons. What it really is, to sum it up, is a system that will appear to have a degree of randomness (not all randoms are equal) but actually aren't random. They can, through interpretation, be understood and predictions can be made - such as weather forecasts and traffic patterns. Traffic being my domain, so I admit my biases.
It boils down to knowing as much as you can about the initial starting state and the butterfly effect refers to small perturbations having a greater impact as the model (or reality) progresses. Something as simple as a rounding error can net wildly different results and make predictions less accurate.
It's fascinating stuff! Dr. Lorenz passed away about a decade ago. He wrote one of my letters of recommendation for the graduate program and it was an honor to work with him. He was brilliant, absolutely brilliant.
If you're ever bored, look into chaos theory and traffic modeling. I'm telling ya, it's fascinating!