  Indeed, the behaviour of a chaotic system will be intuitively random in other ways too. The sensitive dependence on initial conditions means that, no matter how accurate our finite discrimination of the initial state of a given chaotic system is, there will exist states indiscriminable from the initial state (and so consistent with our knowledge of the initial state), but which would diverge arbitrarily far from the actual evolution of the system. No matter, then, how well we know the initial condition (as long as we do not have infinite powers of discrimination), there is another state the system could be in for all we know that will evolve to a discriminably different future condition. Since this divergence happens relatively quickly, the system is unable to be predicted. (Anecdotally, at least, Lorenz’ model of the weather seems borne out by our inability to reliably predict future weather even a few days from now.) Insofar as randomness and lack of reliable prediction go hand in hand, we have another reason for thinking there is product randomness here  (§6.2).