I keep thinking of the physics of gas...we have the statistical motion of individual gas molecules on "one level" and the fact that the gas (in whatever container it finds itself in whether that be a canister or a planetary atmosphere) has a temperature and pressure at "another level". Temperature and pressure are not properties of the gas molecules but the gas (always in some sort of container) as a whole does. The molecules motion are so lost in a complex dance that prediction of the motion of individual molecules is virtually impossible, maybe even, for quantum reasons, impossible on principle. But the whole collection of gas molecules' temperature and pressure will follow along easily measured and predicted courses that simple algebraic equations can model.
So here there is an important concept of a system, a whole, which is a localized (contained) group of parts in mutual interaction such that properties of the whole cannot be explained by virtue of the properties of its parts. Furthermore the randomness of the parts gives way to order in the whole. This appears to me to be yet another way in which randomness is intrinsically tied into predictability, order into disorder. It doesn't make rational sense, but it does drive the intuition that many support of the idea of the whole being more than the sum of its parts in many, many systems.
So what is this interesting inter-relationship between what is predictable and what is predictably un-predictable?