forecasting the weather is an attempt to get fairly precise information on the state of the atmosphere in the near future. Forecasting (climate) … involves an attempt to identify the atmosphere’s most probable states on far longer time scales. — Why weather != climate: the engine behind climate models
That quote is from an article on Ars Technica, a site that has a great track record covering technical topics such as computers and science in depth. In some cases (like this one), the article probably won’t make anything clearer than mud unless you’ve got the right background.
The article is based upon some of the core ideas in Chaos Theory. Most books on Chaos Theory talk about the Butterfly Effect. In 1961, Edward Lorenz was using a computer to simulate the weather. He decided to re-start a simulation in the middle. In the original simulation, the value at that point was 0.506127. When he re-started the simulation, he just entered 0.506. The new result was completely different than the first. This has been summarized in many ways (see Butterfly Effects – Variations on a Meme) including “Does the flap of a butterfly’s wings in Africa cause a hurricane in the Atlantic?”
The butterfly effect (and Chaos Theory in general) focuses on dynamic (don’t stay the same) systems that are very sensitive to how things start. If you put a ball on the peak of the St. Louis Arch, you really have no way of knowing exactly when it will roll off or which way it will roll or where it will end up. Chaos Theory and common sense say the same thing: there is no way to know exactly what will happen.
Both Chaos Theory and common sense also say that we’re almost certain that that ball is coming down. With a little Chaos Theory and a calculator, we can figure out that it will probably start moving within a very short period of time (perhaps there’s a 99.9% chance that the ball will begin to roll off the peak in under a minute) and where it will probably end up (say 80% of the time it will land between 150 and 300 feet away from the center of the base of the arch).
If you kept putting balls covered with wet paint on top of the St. Lewis Arch, over time you would end up with a lot of dots on the grass and those dots would have a pattern. Eventually, there would be a ring covered with paint. Moving inward and outward from that ring, you would see more and more grass breaking through the paint until you just found a splotch of paint here and there.
At the level of someone asking where will the next ball fall, there’s no way to know. If you ask me to guess what weather we’ll have a week from now, I can guess we’ll have a high in the ’80s or ’80s. Then again, this is Colorado, so there’s a small chance it might be 40 degrees and hailing. You just never know where that ball will land.
On the other hand, if somebody is watching you put ball after ball on top of the arch and they’re interested in what things are going to look like, they can come up with some pretty good answers. First, eventually, someone in charge is going to find out what’s going on and call the park cops on you. Second, there will eventually be a solid elliptical ring of paint around the St. Lewis Arch that fades to grass in both directions if you don’t change what you’re doing.