In person, it can be a little hard to hear Larry Page. That’s because he has nerve damage in both vocal cords: one was paralyzed about 14 years ago, the other left with limited movement after a cold last summer. This rare condition doesn’t slow him down, though it has made his voice raspy and faint. You have to listen carefully. But it’s generally worth it.

Page, 40, is the co-founder and CEO of one of the most successful, ubiquitous and increasingly strange companies on the planet. Google is, of course, in the search business, and more important for its profitability, it is in the online-advertising business. But it’s also in the mobile-operating-system business, the Web-browser business, the free-e-mail business, the driverless-car business, the wearable-computing business, the online-map business, the renewable-energy business and the business of providing Internet access to remote areas via high-altitude balloons, among countless others. Google’s corporate strategy is one part mainstream services and one part risky long shots.

Page prefers to refer to Google’s more out-there ventures as moon shots. “I’m not proposing that we spend all of our money on those kinds of speculative things,” he says during a rare interview at the Googleplex, the company’s Mountain View, Calif., headquarters. “But we should be spending a commensurate amount with what normal types of companies spend on research and development and spend it on things that are a little more long term and a little more ambitious than people normally would. More like moon shots.” This is why Google, in Page’s words, is not a normal type of company.

(PHOTOS: Inside the Googleplex)

At the moment Google is working on an especially uncertain and distant shot. It is launching Calico, a new company that will focus on health and aging in particular. The independent firm will be run by Arthur Levinson, former CEO of biotech pioneer Genentech, who will also be an investor. Levinson, who began his career as a scientist and has a Ph.D. in biochemistry, plans to remain in his current roles as the chairman of the board of directors for both Genentech and Apple, a position he took over after its co-founder Steve Jobs died in 2011. In other words, the company behind YouTube and Google+ is gearing up to seriously attempt to extend the human life span.

Google isn’t exactly bursting with credibility in this arena. Its personal-medical-record service, Google Health, failed to catch on. But Calico, the company says, is different. It will be making longer-term bets than most health care companies do. “In some industries,” says Page, who spoke exclusively with Time about the new venture, “it takes 10 or 20 years to go from an idea to something being real. Health care is certainly one of those areas. We should shoot for the things that are really, really important, so 10 or 20 years from now we have those things done.”

It’s worth pointing out that there is no other company in Silicon Valley that could plausibly make such an announcement. Smaller outfits don’t have the money; larger ones don’t have the bones. Apple may have set the standard for surprise unveilings, but excepting a major new product every few years, these mostly qualify as short term. Google’s modus operandi, in comparison, is gonzo airdrops into deep “Wait, really?” territory. Last week Apple announced a new iPhone; what did you do this week, Google? Oh, we founded a company that might one day defeat death itself.

The unavoidable question this raises is why a company built on finding information and serving ads next to it is spending untold amounts on a project that flies in the face of the basic fact of the human condition, the existential certainty of aging and death. To which the unavoidable answer is another question: Who the hell else is going to do it?

(WATCH: Google and the Brief History of Immortality)

New Horizon

Google’s fondness for moon shots, and its ability to take them, can be attributed in large part to Page himself. When he was a Stanford computer-science grad student, his insight that the most relevant Web pages are those with the most links to them became the basis of a remarkably precise search engine, which he created with fellow student Sergey Brin. Google became a company in 1998 and a phenomenon shortly thereafter. Page served as its chief executive until 2001, when tech veteran Eric Schmidt was brought in from software giant Novell. Even then, the unconventional troika of Page, Brin and Schmidt raised eyebrows, but the power sharing led to Google’s monster growth years. In April 2011, Page reclaimed the CEO title, and Schmidt became executive chairman.

The effect of Page’s leadership at Google was immediately clear. In 2012 the company closed a massive $12.5 billion acquisition of troubled handset maker Motorola Mobility in a bid to begin manufacturing its own hardware. Page also reshaped Google’s management structure, creating the so-called L Team (L for Larry) of top managers. There were notable departures, including employee No. 20, Marissa Mayer, who left to run Yahoo. Most important, Page has shown that Google, long criticized as a one-trick pony dependent on serving ads, can grow its other businesses. Most of its $50 billion in revenue still comes from search-related ads. Analysts estimate that YouTube is a $4 billion business, and Android, its mobile operating system, is estimated to bring in an additional $6.8 billion from use on smartphones.

EXCLUSIVE: TIME Talks to Larry Page About Calico