The most frightening prospect that Mr. Lenton has found is the vulnerability of the Indian monsoon. More than a billion people depend on this weather pattern each year for the rain it brings to crops. The monsoon, though, is being affected by two conflicting forces: the buildup of carbon dioxide in the atmosphere is adding energy to the monsoons, making them more powerful. On the other hand, soot from fires and coal plants acts to blocks the sun’s energy, weakening the monsoons.

This opposition creates potential instability and the possibility that the atmospheric dynamics that bring the monsoons could change suddenly. Mr. Lenton’s analysis shows this could occur in a remarkably short time. The monsoons could be here one year, then gone the next year.

Other possible tipping points are the melting of the North Pole’s sea ice, Greenland’s glaciers and the Antarctic ice sheets, and the destruction of the Amazon rain forest and Canada’s boreal forests.

We know that the dynamical-systems idea worked for Mr. Scheffer’s ponds because he achieved real-world results. But why should we believe that the principle explains things like El Niño and the Indian monsoon? The acid test will be whether the real world behaves the way Mr. Lenton says it will. If the Indian monsoon disappears, we’ll know he is right.

What then? The real worst-case scenario would have one such event triggering others, until you have a cascade of weather flips from one end of the planet to another. It wouldn’t be quite as dramatic as Hollywood might want to depict, perhaps, but it would be dramatic enough to rewrite the predictions for sea level and temperature rises that are part of the current consensus. This worst case is highly speculative, but sudden shifts in climate patterns may already be happening.

The policy makers aren’t likely to be discussing dynamical-systems theory anytime soon. Fortunately, scientists like Mr. Scheffer and Mr. Lenton are trying to work out the details of how closely nature hews to these mathematics, what a true tipping point would look like and what we might do if and when we face one.

We need a tipping point in climate politics, where all of a sudden we start paying attention.