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?
Yup. You got it. It's the same principles that drive them to look at CBR. I am not a physicist. However, I share a language with them - the language of mathematics. I also shared a ton of coursework with 'em, 'cause I'm an *applied" maths type of guy. Alas, I graduated in 1991 - and so much has changed in the world of physics since then. I've tried to keep up, but so much has change since then! It's more than I can possibly devote the time to. I'd say my physics understanding is not much better than the average academic layperson. But, that's my understanding. From examining the CBR, they were able to observe the similitude across the visible universe and infer things like the big bang wasn't really a bang but a giant inflation. I think... Again, not a physicist.
It should also be noted that lots of people mistakenly believe Lorenz was the originator of chaos theory. He was not. That had been around for something like 100 years before his work with it began. My memory is a little fuzzy and I'm too lazy to Google, but I believe it was inferred from the 'three body problem.' (Which also has quite a bit to do with astronomy/astrophysics.)
It was Lorenz that made me interested in seeing where else we could apply the theory. Mass. DOT just happened to have free ('cause students like free) traffic data that they'd been collecting. And it's that simple twist of fate that got me started. Yup. That's the reason.
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?