If you’re going to be that pedantic, I’ll see your pedantry and raise you. Time travel is not only possible, but routine, just in the forward direction only. It’s only travel into the past which is probably impossible, and to be even more pedantic and abstract, impossible only in our observable spacetime geometry.
So is with the chaotic systems: we know for sure that approximating them is just a matter of boundary conditions: that is - the more you know about the starting points, the better you approximate the real world.
I mean, there might be a case where we will finally get to the point where we are just "good enough" at measuring the boundary conditions to predict weather for the next year, but it has got nothing to do with obtaining the knowledge about chaotic systems themselves.
