Most people have heard of that classic thought experiment where a butterfly flaps its wings somewhere in Japan and the minute air currents it generates roll across southern Europe ultimately causing a hurricane to form in the Atlantic. Basically unless you know every possible initial condition of a given system, it's impossible to predict, with any degree of accuracy, what the final outcome will be. It's possible to look a short distance into the future but the further ahead you look the more chaotic the system becomes. And in the real world, it's impossible to know every possible initial condition.
Weather is a classic example of a chaotic dynamical system.
Back in December a nor'easter headed up the east coast of the US dumping a ton of snow along the way. Our local weather people predicted, with a fair amount of confidence, that here on Long Island we would get between 3 and 6 inches of snow. The storm was far enough inland that it would only skirt the island. Well, somewhere out west maybe six months earlier, a butterfly flapped it's wings and the resulting shift in air currents blew the storm just a hair off the predicted track and we ended up with 2 1/2 feet of snow for which no one was prepared.
Today another nor'easter is heading up the coast. Right now it's following the exact same path as the last storm with the exact same results as it travels up the coast.
The predictions from the local weather people this time: anywhere from 2 inches to 2 feet by tomorrow night.
With any luck the butterflies were resting at the appropriate time last summer.