> If you throw a bag of a trillion^trillion^trillion particles into a purely self contained environment (i.e. the Universe), and let it stir for a while - whatever is going on - at least from a materialist perspective - is random.

This seems to lead to a meaningless/useless definition paradox. 'Randomness' comes to mean everything and nothing. This is one of the things that led me away from an interest in the materialist/physicalist position. Like you said elsewhere, it seems hard to swallow the idea that all that we can achieve in defining 'randomness' is a negative definition. Personally, I find it problematic that materialism has no positive definition of what 'randomness' is and does not seem capable of offering a meaningful/useful definition.