In the 1983 War Games movie, a computer made life and death decisions that could have resulted in World War III. As far as I know, technology wasn't able to pull off such feats at the time. However, in 1997, the Deep Blue supercomputer did manage to beat a world chess champion. In 2005, a Stanford self-driving car drove by itself for more than 130 kilometers in a desert. In 2007, the car of another team drove through regular traffic for more than 50 kilometers. In 2011, the Watson computer won a quiz against human opponents. If we assume that computer hardware is the limiting factor, then we can try to extrapolate into the future. Ray Kurzweil did just that, and according to him, we can expect human-level intelligence around 2029.
In this chapter, we will focus on the simpler problem of forecasting weather for the next day. We will assume that the weather today depends on yesterday's weather. Theoretically, if a butterfly flaps its wings at one location, this could trigger a...