It's really funny that something as simple is impossible to predict over longer times, because you would need perfect information. Yet climate science is 'settled'.

Take an undamped double pendulum and divide the space up into 2 sections. Suppose you can only check which section the pendulum is every N seconds. Every time you check, you record the value, and over time you build up a sequence of K numbers: 1,0,1,0,0,1,1,1,1,0,0,1,0,...

Suppose you know the exact initial state (dx/dt, x) of the pendulum.

What bounds on K and T are required such that the sequence of numbers is asymptotically indistinguishable from a purely random sequence?

So, because of a silly thought experiment, one might think there is very simple order to the apparent randomness. But, as Pauli would say, "it's not even wrong"...