Comment by consilient

> Even if you knew the position, type, and velocity of every molecule of the atmosphere at a given moment you would still need a model that explains how they interact over time in order to predict the future. So, I'm not sure that actually is a knowable unknown because that assumes there is a model that can be made in addition to the information. Maybe the weather is chaotic.

It is, but that doesn't mean you couldn't predict it with perfect information. A chaotic system is roughly speaking one that is

- sensitive to initial conditions, in the sense that the distance between nearby trajectories in phase space grows as e^{l*t} for time t and some positive number l

- mixing, meaning that given any two open sets in phase space X and Y there's at least one trajectory from a point in X to a point in Y.

and so if you have any error bounds at all on your measurement of the initial state (which of course you always do) then you can't predict where it ends up in the long term. But there are plenty of chaotic systems for which exact numerical computations are quite simple. The logistic map x_{n+1} = rx_{n}*(1-x_{n}) for instance, is chaotic for many values of r.