> What, then, are the complex multi-variable systems that have eluded
> prediction designated as? There must be a term for why we can't predict
> what the weather will be like in a year's time.
Well, weather is a chaotic system. It isn't random - it is deterministic. Weather, though, is aperiodic; it displays extreme sensitivity to initial conditions, so it seems impossible to predict. We don't have a chaotic model for weather that works, but chaos might provide the model, some day. E.g., there may be weather attractors that we just haven't discovered yet.
Chaos theory applies to physical phenomenon that may appear random but are in fact deterministic. We use chaos rather than classical mechanics because the systems are non-linear and aperiodic. The complexity and especially the number of variables really is orthogonal to the issue of non-linearity. I apologize if this seems like semantic quibbling but we are using words to describe things best represented by mathematics, so we want to be as specific as possible.
Matt
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