One of the puzzling things about climate change is why there has been so much resistance to the scientific consensus about it. The science has been clear for decades, and even in the face of the global agreement just reached in Paris there still are too many people, especially in the US, who don’t acknowledge the problem. There are probably many reasons for this scepticism–but one might have to do with a way human beings think.

To us humans most phenomena appear linear–they seem to vary in a uniform way. For example, we perceive time and distance this way. But often reality is better described as non-linear. It is relatively easy to represent non-linear processes in terms of mathematical functions. But, unfortunately, it is usually difficult for us to make sense of these non-linear functions intuitively.

In a linear world an incremental change in one of two correlated variables will lead to a predictable change in the other variable. But sometimes this this linear relationship simply does not hold. For example, consider the autoignition point of paper–the temperature at which it starts to burn. As Ray Bradbury made famous, that temperature is roughly Fahrenheit 451. Below that level, slight changes in temperature are linear–the paper gets a little warmer. But with a slight change from 445 to 451 the behavior of the system changes dramatically: instead of just getting a little warmer, there are catastrophic consequences. The same increase in temperature from 300 to 306 has no real consequences.

In ecology, tipping points could be viewed as changes in a system that are not predicted by simple linear dynamics. Usually they are leading to a new state of the system and are viewed as negative.

Although not as well defined, the concept of tipping points is also used in Climate Change Science. In a recent review paper Tim Lenton from the University of Exeter in England summarizes attempts to model the effects of changes in “tipping elements” (processes which might have tipping points, where small changes have large effects) on the global climate. One such tipping element is the Gulf Stream, which sends warm water from Florida to the west coast of Northern Europe. The relative likelihood of a disruption in this process happening is considered low. But if it did happen the impact would be pretty large.

Lenton surveys mathematical modeling used to assess the risk of several tipping points on the climate along two axes: first how likely a tipping point might be reached (due to human activities), and second, the severity of the consequences. He is concerned that under climate change some low-probability events could tip, becoming high-impact, high-probability events. And in this category we find for example the irreversible Greenland ice-sheet meltdown and the West Antarctic ice-sheet collapse. Both events would lead to dramatic sea level rises, potentially at catastrophic rates. Some models predict that the melting of the Greenland ice-sheet would lead to a sea level 23 ft (7m) higher that current levels. A lot of land would be flooded then.

Lenton argues that the prospect of such high-impact events points to the need for early warning systems that would signal that a tipping point is being approached. Those systems would face the problem I identified at the beginning–they might indicate a danger that is not visible to our ordinary perception, which is sensitive to linear changes. But–can we afford not to put them into place?