For years now, world governments have been pledging to limit global average temperatures increases to 2°C (or less) over pre-industrial levels. That's been the big-picture climate goal. If we heat the planet up any further, the argument goes, then we risk extremely severe impacts that could prove irreversible. (To put this in context, the world has already warmed about 0.8°C since the Industrial Revolution, and the carbon-dioxide that's currently in the air has "locked in" another 0.6°C of warming—so a 2°C limit doesn't give us much wiggle room.)
But why 2°C? Where did this come from? Lou Grinzo has a smart piece tracing the history of the figure—it's actually been floating around since 1989—and it's worth emphasizing that not everyone agrees with it. At the Copenhagen summit, various African and small-island nations have been arguing that the consequences of even a 2°C rise could be too horrible to allow. Nations like Tuvalu, for instance, might get drowned out entirely, while widespread droughts could permanently cripple Africa. Those countries have been arguing that the world should aspire to no more than a 1.5°C rise. (Unfortunately, science can't decisively answer these questions—we know that the warmer we get, the deeper the impacts and greater the risks, but we can't identify a clear line below which everything will be okay.)
In any case, even 2°C is now looking difficult to attain. According to the Guardian, a recently leaked U.N. document reveals that if you tally up all the pledges various countries have made so far on cutting emissions, the world would be on pace for carbon concentrations in the air of around 550 parts per million, which the best evidence indicates would lead to a temperature rise of about 3°C. So there's still a massive gap between aspirations and reality here, and we'll have to see whether that can be bridged in the closing days of Copenhagen.
Follow Bradford Plumer on Twitter @bradplumer