Right now, renewable energy sources like solar and wind still provide just a small fraction of the world's electricity. But they're growing fast. Very fast. Three new pieces of evidence suggest that many policymakers may be drastically underestimating just how quickly wind and solar are expanding.

1) Solar is growing exponentially. Let's start with this chart from Gregor MacDonald, using data from BP's 2012 Statistical Review of World Energy, showing that global use of solar power has grown exponentially in the past few years. Watch that graph go parabolic:

Across the globe, 55 terawatt-hours of solar power had been installed by the end of 2011. That may not seem like much in itself — the United States by itself, after all, needed about one hundred times that much power in 2011. But solar has been growing at a stunning rate, as panels keep getting dramatically cheaper. If these exponential growth rates, MacDonald notes, solar could provide nearly 10 percent of the world's electricity by 2018.

2) Official agencies keep underestimating the growth rate of renewables. Perhaps MacDonald's predictions sound like a wild fantasy. After all, the International Energy Agency is forecasting that solar will catch on much more slowly — providing a mere 4.5 percent of the world's electricity by 2035. But here's the hitch: The IEA has almost always underestimated how quickly wind and solar can grow.

Want proof? Check out this new report from the Renewable Energy Policy Network for the 21st Century. Sure, that's not an unbiased source. But all the report does is compare past predictions about renewables by official government forecasters with reality. And the forecasters have consistently been too pessimistic. For instance, back in 2000, the IEA's World Energy Outlook predicted that non-hydro sources of renewable energy would make up 3 percent of global energy by the year 2020. The world reached that point in 2008, well ahead of schedule.

Obviously, trends could change. In the last decade, wind and solar have benefited a great deal from subsidies and other forms of government support from countries like Germany, China, and the United States. Thanks to the financial crisis and budget crunches around the world, those supports are now in danger of dwindling. But in the past, the solar and wind pessimists have very often proved wrong.

3) Using only current technology, renewables could technically provide the vast bulk of U.S. electricity by mid-century. Ah, critics will counter. Perhaps wind and solar are getting cheaper. But they're so intermittent! The wind isn't always blowing. The sun isn't always shining. How could we possibly depend on undependable sources like those for our electricity?

That's where a new report from the U.S. National Renewable Energy Laboratory comes in. The scientists at NREL took a look at what happened if the United States used only existing technology and tried to generate 80 percent of its electricity from renewables by mid-century. Technically, NREL found, it's feasible. The wind's usually blowing somewhere, and the sun provides a lot of energy during the daytime. Other sources can pick up the slack elsewhere, though power grid operators would need to do some serious juggling.

NREL even provides a neat animated map of where different power plants — from hydropower to photovoltaic solar panels to wind turbines to concentrated solar plants — would need to be built to make this a reality. Here's what things look like in 2050:

This map shows what, in theory, the U.S. electricity supply could look like in 2050. Blue dots are coal, gas, and nuclear plants — there are still plenty of them, particularly in the Northeast. But there's been a huge expansion of solar power (orange and yellow), wind (peach), hydropower (gray), geothermal (purple) and biomass (green). (There's more detail in the report on how the electric grid could possibly cope with these different sources.)

Now, this isn't a firm prediction of how the U.S. energy system will evolve — that will depend on all sorts of variables, including prices and energy policies. If shale gas remains dirt-cheap and keeps undercutting solar and wind, for instance, then it's quite possible that the above will never come to pass. But if the United States absolutely had to get most of its energy from renewable sources by 2050, this is how you could technically do it.