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Hi Shane,
I thought I'd come in on this one again but tackle the probability elements from a new direction.
In quantum mechanics, Heisenberg's uncertainty principle basically states that, at any particular time, you can't simultaneously measure to arbitrary precision all the properties of a particle (e.g. position and momentum). The greater the precision of one measurement (e.g. position), the less precise the other (e.g. momentum). Values become a matter of probability.
The significance of quantum theory is that it's description of nature is essentially probabilistic.
In classical mechanics, if we know the exact state of a system at any time, we can theoretically calculate its state at any other time. A classical description is deterministic. The difficulty to date has been reconciling the deterministic theory of general relativity with the probabilistic theory of quantum mechanics. To unify quantum mechanics with gravity some deterministic flavour may have to be used.
However, whether nature is deterministic or not, the underlying processes are usually so complex and chaotic that we have to resort to stochastic methods anyway. In practice, reduction of initial conditions, including approximation of measurements, can result in large deviations from expected behaviour over time (sensitive dependence in chaos theory). Example, it is impossible to predict Saturn's orbit in 100 million years with any accuracy. Unexpected influences over time can also cause havoc with predictions e.g. a large unknown body swoops past Saturn in 1000 years time.
The Universe today reflects the chaotic nature of the way energetic particles and matter were distributed after the Big Bang. It appears galaxies lie in a scaffold of randomly distributed filaments across the Universe. Any model of the origins of the Universe can at most build a similar universe from probabilistic considerations but not one that is exactly the same as ours.
In my mind, a world of mathematical approximations and probabilities fits in quite well with the notion of "unpredictable" thought. Our actions are not mathematically predictable because all the interrelating factors that influence our decisions are far too complex and not repeatable. For this reason, we have free will. For each new set of events, we make an approximated assessment and a probable forecast and then decide on a course of action.
Regards, Rob
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