Google: master innovator of search, advertising, and ... health care?

Google has launched a mysterious new project called Calico. It's "a new company focused on health and well-being, in particular the challenge of aging and associated diseases," Google (GOOG) said in a short press release on Wednesday.

What will Calico do, exactly? That's unclear; Google didn't provide many more details on the new venture. One curious bit of news: Calico's CEO is Art Levinson, the chairman at none other than Google's chief rival Apple.

In a rare move, Apple (AAPL) CEO Tim Cook weighed in on his competitor's venture. "For too many of our friends and family, life has been cut short or the quality of their life is too often lacking," he said in Google's press release. He praised the selection of Levinson, who is also the chairman and former CEO of biotech giant Genentech, as well as a director of its parent company Hoffmann-La Roche.

With so few details available at launch, Google's long-term plans in the health sector remain unclear. Google CEO Larry Page elaborated just slightly more on his Google Plus page.

"OK ... so you're probably thinking wow! That's a lot different from what Google does today," Page wrote. "...But as we explained in our first letter to shareholders, there's tremendous potential for technology more generally to improve people's lives."

Related story: Walgreens shifts workers to private health exchanges

The Google CEO gave an interview to Time magazine that included a bit more information about his philosophy, but the end goal was still vague: "Maybe we should shoot for the things that are really, really important so ten or 20 years from now we have those things done."

On his Google Plus post about the Calico launch, Page warned that shareholders shouldn't "be surprised if we invest in projects that seem strange or speculative compared with our existing Internet businesses." He also noted investments like Calico "are very small by comparison to our core business."

He's made similar statements about side projects like Google Glass, but the Calico health-care venture is unique in that it will be a company separate from Google.

It's not the first time Page has waded into the health-care field. In May 2013, Page disclosed that he has vocal-cord paralysis and announced he will personally fund a "significant research program" through the Voice Health Institute. Page's announcement came after nearly a year of speculation about his shockingly raspy voice at public events.