Jakob Runge

Picture a giant spiderweb stretched across thousands of points on Earth's surface. Each strand connects two places where air temperatures move in sync: if one node warms, so does the other. You can build this web from data for any given year, then compare how it looked across different years.

The puppet master pulls the strings, and the marionette dances. In forecasting the future from time series, the puppet masters are the few variables that truly control the system. The rest merely echo their movements, creating an illusion of complexity. The challenge is to find these puppet masters and watch only their fingers, not the whole stage.

In a tropical forest, the dry season gives way to the rainy season, and with the weather, the rules of life change: some animals go into hibernation, while others come out of hiding. Likewise, in complex systems, from climate to economics, the links between processes are not set in stone. They depend on a hidden "regime" that itself switches from time to time.