Reik V. Donner

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.

The same orchestra sounds different when two different conductors stand at the podium. One swings the baton widely, and the whole hall hears his accents; the other barely nods, and only individual instruments respond.

Picture a web stretched across every corner of the Earth: each strand is a coincidence of temperature fluctuations at two points. In ordinary years, the web is neatly divided into regional clusters, but when El Niño arrives, the strands break and reweave, linking distant continents.

Picture a globe divided into cells: near the poles they shrink into narrow wedges, while at the equator they stretch into wide bands. If you connect random points on such a globe with lines, the compass arrows will lie: connections will point to where there are more cells, not where the flows actually go.

A fisherman pulls on his net and listens to it ring. Each strand quivers in its own way, but before a strong tug, all the strands begin to vibrate in unison. So it is with complex systems: before a sharp state jump, the individual parts suddenly start to oscillate in concert, and that synchrony betrays the coming jump.

Over the warm waters of the Indian and Pacific Oceans, a giant wave of moist air is born every month or two. It creeps eastward at a pedestrian pace, about five meters per second, dragging bands of downpours and droughts behind it. Meteorologists call it the Madden–Julian Oscillation MJO.