A note on estimating chaotic systems

This is a short note unlike other posts but it is necessary: Recently I came across with some complex systems presentations in Youtube. Most of the scientists, especially complex system scientists, treat chaotic dynamical systems as mysterious objects. The models are beautiful (so you should be careful around them)  and they are not that difficult to deal with in real world. The typical example you would hear that a chaotic system is extremely sensitive to the uncertainty in the initial condition. That's true: If I give you the initial condition of a deterministic chaotic system with a machine epsilon uncertainty along with the exact dynamics, the trajectory you would predict will differ from the real one vastly after a while. This, then they say, can be counted as the evidence of undecidability in chaotic systems.