Google (GOOG) Chairman Eric Schmidt’s April 13 tweetwas bold, ambitious, and a bit inexplicable. “For every person online, there are two that are not,” wrote the co-author of the book The New Digital Age. “By the end of the decade, everyone on Earth will be connected.”

Commenters were flummoxed by Schmidt’s prediction. There are many parts of the world without reliable telecommunications infrastructure. How do you wire parts of Africa—or the Indonesian archipelago?

In my conversations with Astro Teller, Google X’s excellently named director of moonshots, for this week’scover story on Google X, I asked whether extending broadband Internet access throughout the world would be a problem deserving of attention from the top-secret lab. Teller gave nothing away, but it was clear from his answer that there’s plenty of passion for that particular goal inside his organization. “Having everyone connected is literally in the same category as making clean water available,” he said. “That sounds like a radical statement but I don’t think that it is. There is now a ton of evidence that connectivity drives freedom, democracy, economic development, health, and those things then turn into lower mortality and all of the things that we are trying to get at here.” Extending connectivity, he added, “is the most direct way, probably on an order of magnitude, to address the world’s biggest problems.”

Researchers who have examined the challenge of spreading Internet access throughout the world usually focus on one of three general solutions. There’s satellite access, which tends to be slow, expensive, and doesn’t function well in high-density urban areas. There’s ground-based wireless broadband, the most conventional solution, but in some parts of the world the towers where you would mount broadband transmitters would be quickly scavenged and sold as scrap metal.

And then there’s the unlikeliest but perhaps most promising approach: sending balloons mounted with broadband antennas into the stratosphere, where they can rain connectivity down from only 20 kilometers away. The Europeans tried this a decade ago. Lockheed Martin (LMT) and SoftBank in Japan have experimented with it more recently, with varying levels of success. No one has tried to push balloon-based broadband transmitters into wide production, though. Google X representatives declined to comment on this particular approach, but it fits well with the lab’s philosophy of moonshot thinking and its orientation toward practical yet science-fiction-sounding solutions.

David Grace, a senior research fellow at the University of York, spearheaded the European project, part of a multi-country initiative backed by the European Commission. He said that he has indeed heard Google is working on such a project. “They are highly innovative and very obviously have the financial resources and are always keen to take risks,” he said. “It does need the Googles of the world to push this forward.”

Per Lindstrand, the Swedish balloonist, is probably the world’s top authority on this topic. He says free-flying high-altitude balloons are impractical because of high winds; release a balloon on the equator and in a few weeks it will end up at the North or South Pole. But solar-powered balloons packed with a fuel cell and an onboard motor can remain stationary for up to five years and are “perfectly feasible.” Lindstrand has been urging companies to more aggressively pursue balloon-based wireless networks but says that no one has stepped up yet. “Everybody keeps telling me, ‘Show me an airship and I will buy it.’ No one wants to risk the money. The key is to find somebody who is brave enough. I believe the stratospheric airship is a viable project, but it needs to be created by a small elite team with past airship experience and not by a conventional bloated aerospace contractor. If Google is really on the scene, they would be the perfect sponsor.”