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 Remember how Wile E. Coyote, in his obsessive pursuit of the Road Runner, would fall off a cliff? The hapless predator ran straight out off the edge, stopped in midair as only an animated character could, looked beneath him in an eye-popping moment of truth, and plummeted straight down into a puff of dust. Splat! Four decades ago, a Massachusetts Institute of Technology computer model called World3 warned of such a possible course for human civilization in the 21st century. In Limits to Growth, a bitterly disputed 1972 book that explicated these findings, researchers argued that the global industrial system has so much inertia that it cannot readily correct course in response to signals of planetary stress. But unless economic growth skidded to a halt before reaching the edge, they warned, society was headed for overshoot-and a splat that could kill billions.

Don’t look now but we are running in midair, a new book asserts. In 2052: A Global Forecast for the Next Forty Years (Chelsea Green Publishing), Jorgen Randers of the BI Norwegian Business School in Oslo, and one of the original World3 modelers, argues that the second half of the 21st century will bring us near apocalypse in the form of severe global warming. Dennis Meadows, professor emeritus of systems policy at the University of New Hampshire who headed the original M.I.T. team and revisited World3 in 1994 and 2004, has an even darker view. The 1970s program had yielded a variety of scenarios, in some of which humanity manages to control production and population to live within planetary limits (described as Limits to Growth). Meadows contends that the model’s sustainable pathways are no longer within reach because humanity has failed to act accordingly.

Instead, the latest global data are tracking one of the most alarming scenarios, in which these variables increase steadily to reach a peak and then suddenly drop in a process called collapse. In fact, “I see collapse happening already,” he says. “Food per capita is going down, energy is becoming more scarce, groundwater is being depleted.” Most worrisome, Randers notes, greenhouse gases are being emitted twice as fast as oceans and forests can absorb them. Whereas in 1972 humans were using 85 percent of the regenerative capacity of the biosphere to support economic activities such as growing food, producing goods and assimilating pollutants, the figure is now at 150 percent-and growing.