But even as the consensus among experts builds that coal and other fossil fuels must be sharply reduced and eventually removed from the energy matrix, there is no agreement on what sources of energy could feasibly take their place, and how to get from here to there.

As in the 1970s, environmental activists remain enthralled by the sun and the wind. But three decades’ worth of renewable energy dreams have yielded too little to entrust them with the job of replacing fossil fuels.

Today renewable energy supplies only about 6 percent of American demand. And most of that comes from water flowing through dams. Solar energy contributes next to nothing.

Averting climate change is likely to require much less eco-friendly sources of power. This includes natural gas, of course, which emits about half the carbon dioxide of coal. But over the long term it is likely to require much more investment in a big bugaboo of the environmental movement: nuclear power.

The arithmetic is merciless. To make it likely that the world’s temperature will rise no more than 2 degrees Celsius above the average of the preindustrial era — a target agreed to by the world’s governments in 2010 — humanity must spew no more than 900 billion more tons of carbon dioxide into the air from now through 2050 and only 75 billion tons after that, according to an authoritative new study in Britain.

The question is how to square that both with the energy that we need and the energy that we have.

The United States Energy Information Administration forecasts that global energy consumption will grow 56 percent between now and 2040. Almost 80 percent of that energy demand will be satisfied by fossil fuels. Under this assumption, carbon emissions would rise to 45 billion tons a year in 2040, from 32 billion in 2011, and the world would blow past its carbon ceiling in fewer than 25 years.

“We have trillions of tons of coal resources in the world,” Vic Svec, spokesman for Peabody Energy, told me. “You can expect the world to use them all.”