Over the past decade scientists thought they had figured out how to protect humanity from the worst dangers of climate change. Keeping planetary warming below two degrees Celsius (3.6 degrees Fahrenheit) would, it was thought, avoid such perils as catastrophic sea-level rise and searing droughts. Staying below two degrees C would require limiting the level of heat-trapping carbon dioxide in the atmosphere to 450 parts per million (ppm), up from today's 395 ppm and the preindustrial era's 280 ppm.