Where does randomness come from?

The Global Consciousness Project, sponsored by Princeton University, measures deviations from randomness from 65 randomness generators stationed around the globe. This random data is communicated to a central Princeton server specially protected from extraneous electromagnetic radiation.

The data is made freely available so that outside institutions can conduct independent analysis if they desire. (If you follow the link, you will note that quite a few have).

Their results appear to indicate that the introduction of structure (non-randomness) can be assosciated with human psychological patterns.

If you've heard of the noosphere, well, it's the existence of the noosphere that they're postulating. "Just as the biosphere is composed of all the organisms on earth and their interactions, the noosphere is composed of all the interacting minds on earth."

While my initial reaction to all this was "what a load of crock"; they do not appear to be pulling any statistical tricks with the math. And they are at least not searching for their desired results strategically, per se:
(from the FAQ)

How do you make the leap that the deviations from randomness are related to world events or consciousness? After all, when you find a deviation you can check the news and ALWAYS find some world event that is taking place, because world events happen every day. There are never days without world events anymore, so it seems that there is a possibility that this is just a coincidence.

The leap we make is only to ask the question. The answer seems to be yes, there are correlations. With regard to your concern that we can always find a special event to fit the data, we fully agree. However, we do our experimental work the other way around from what you have inferred. First we make a prediction that some identified event will have an effect, then we assess the data to see the actual outcome. Though some people suggest that we should do so, we never "find a deviation [and then] check the news", because you are right -- it will always be possible to find some event that we might imagine was the cause. The GCP methodology is prediction-based. Before the data are examined, a prediction is registered, with all necessary analysis specifications, and only then do we perform the analysis that allows us to quantify the correlation and assign it a probability against chance.

In spite of that, I still am not a believer in any of it, in no small part because there is not an assosciated analytic rationalization for the perceived correlation. I am not one to buy into any kind of corellatory data without an explanatory theory to go along with it. As it happens, they have given no reason why there should be a connection between the human consciousness and their generation of random data.

So, why do I bring it up? Well, it's interesting, it's on the news lately (because the same spike observed right before 911 was observed right before the Indian earthquake) and because it got me thinking, "Where does randomness come from?"

It's a mathematical fact that there is no mathematical way to generate random numbers. Math is strictly deterministic. It can certainly be used to analyze probabilistic behavior; it can tell you, for example, what the probability of an event Y occuring is given that at each opportunity n there is a chance x of Y occuring. But it cannot produce probabilistic results itself because the output of a mathematical algorithm will always be the same.

So, if the universe has truly random events, where does the randomness come from? It can't be from any mathematical rule--that would be impossible.

It could be that there actually is not any randomness in the universe, just very good pseudo-randomness. When you talk about pseudo-random, you are generally talking about an algorithm that gives you widely varying results from ordered input. For example, if F(x) is a pseudo-random function, you might have F(1.001)= 3.14, F(1.002)=-83, F(1.003)=10^99+2, etc. Still not random, since F(n) always gives you the same result for that particular n; but it can give you something that *seems* random.

Well, if that's the answer--the universe isn't really random--is true randomnes even possible? Can we step outside mere mathematical limitations to generate something that is beyond math?