I've been trying to read some about Bell's theorem, and whilst I'm a bit confused it seems that it doesn't. What it is supposed to prove is that there can be no undiscovered local variables. If, however, your extra variables allow an event somewhere to have a causal effect somewhere else in less time than you could travel between the two at the speed of light, then such an undiscovered variable is not disproven. It has been suggested, for example, that information could be passed through higher dimensions in which two points are close to one another, despite being distantly separated in normal space.
That sounds like a cool place for free will to stem from in a deterministic universe. Like, our sentience comes from a higher dimension, man.
No they aren't. There are rules that determine which number gets generated next. Know those rules and you can predict the next number.
I remember having this discussion in college when we were using computer programs to simulate Brownian motion, which used a random number generator. We talked about if it was possible or not for a computer to generate random numbers, and the answer I came to was: "pretty much, but not really".
The professor talked about a hypothetical student who pointed an analog video camera closely at his lava lamp, converted the feed into a digital image, and then used values from the pixels in that image as the source or the stream of digits for his random number generator.
So we were looking at Brownian motion. It would be safe to call the outputs of an RNG like that to be "random numbers", even if technically they're not truly random in the strictest of senses.
I'm not saying this solves the problem of determinism. But if Brownian motion is a real thing, and it can be modeled with very simple computer programs that have random numbers generated, then that indicates that there is randomness in the universe despite the nitpick that a computer can't technically produce a random number.
The alternative is that the hidden variables that are causing Brownian motion are also controlling the computer programming behind random number generators, which isn't plausible.
If we don't know the rules behind the light output of the lava lamp (i.e. unpredictable), and we're confirming Brownian motion, then isn't that random enough to be considered real?