“Anything that is polysyllabic and Latinate doesn’t sound threatening enough,” said Michael Ghil, a mathematician at the University of California, Los Angeles, who studies theoretical climate dynamics. “‘Tipping points’ does.”
The idea that there had been major shifts in the Earth’s climate was by then well established. Scientists had found geological evidence that supported the Snowball Earth hypothesis. They’d seen hints that patterns in deep ocean currents had once looked very different. And six thousand years ago, they’d discovered, the Sahara Desert was a lush Eden. Only later did it reach a tipping point that transformed it into a sea of sand; today, hippopotamus bones lie buried beneath its dunes, a reminder of that bygone era. The history of Earth’s climate is full of such rapid, massive transitions.
But what’s the right math to describe those changes? Scientists who study tipping points readily admit that the term can be somewhat vague. Sometimes it’s used loosely to describe any large, sudden change that arises from small perturbations. Other times it’s used in a more specific and technical way, to signify an irreversible bifurcation that has a rigorous mathematical definition.
Moreover, the global climate is a much more complicated system than Peter Lake. The oceans and atmosphere are massive and, importantly, open, shaped by far-reaching forces that act on timescales ranging from hours to eons. The forcing of the system toward a bifurcation — caused by, say, a gradual buildup of carbon dioxide in the atmosphere — is defined by myriad subtle and interconnected variables. These “dimensions,” as mathematicians call them, can affect one another in complicated feedback loops. Where do you even start?
“With the climate, a load of people basically argue, ‘Oh, because it’s high-dimensional, you won’t get this simple, low-order bifurcation or tipping behavior,’” Lenton said. “They thought it couldn’t be that simple when you got into all the messy complexity.”
But physicists studying bifurcations had found that near or at the point of transition, the behavior of a complex system can simplify as it passes from one state to another. “Sometimes a high-dimensional system can tip,” said Lenton, “and when it gets near tipping, it starts to behave like a much lower-dimensional system.” The lesson, he added, echoes the one learned at Peter Lake: to “simplify without oversimplifying.”
Still, while bifurcations offer a helpful way to understand many past climatic changes, looking into the future presents new challenges. At Peter Lake, ecologists had the luxury of observation. Pay close enough attention to the water, and it’s possible to see attractors come and go, and to study their dynamics. Early warning signals become clear, in part, because the progression from a murky lake to a clear one is predictable under certain forcing conditions. But often, climate scientists can’t directly observe multiple states of the Earth. While they may have clues about where the climate is heading, they must also make many assumptions. This includes assumptions about the relationships between variables, about what a new equilibrium state might look like after a tipping point is reached, and about the nature of that tipping point — whether it’s caused by slowly adding more carbon dioxide to the atmosphere, by a sudden change in the pace of carbon dioxide production, or by random, short-term perturbations.
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