When Peter Thiel ventures outside for a run, typically in the early-early morning, when the fog drifts low and slow into the San Francisco Bay, he's often drawn to what the poet Lawrence Ferlinghetti called "the end of land and land of beginning." That means the San Francisco waterfront—especially the one-and-a-half-mile stretch of pathway hugging the marshy shoreline from Crissy Field to the base of the Golden Gate Bridge. Aesthetically, the appeal is obvious—a postcard view of the bridge and the bay, the lapping tidal rhythm, that sort of thing—but for Thiel, a 43-year-old investor and entrepreneur whose knack for anticipating the next big thing has yielded him a $1.5 billion fortune and an iconic, even delphic status in Silicon Valley, there's a symbolic angle as well. This waterline is precisely where the Western frontier ended, where unlimited opportunity finally hit its limit. It's also where, if Thiel is betting correctly, the next—and most audacious—frontier begins.

Thiel spends a lot of time thinking about frontiers. "Way more than is healthy," he admits. Not just financial frontiers, though that's his day job: He cofounded PayPal, the online money-transfer service, and, most famously, was the angel investor whose half-million-dollar loan catapulted Facebook out of Harvard's dormitories and into the lives of its 750 million users. (In The Social Network, Thiel was portrayed as the crisp venture capitalist whose investment, and dark questioning, widen the rift between Facebook's cofounders.) He manages a hedge fund, Clarium Capital, and is a founding partner in a venture-capital firm called the Founders Fund, both of them housed in an airy brick building on the campuslike grounds of the Presidio, not far from Thiel's jogging path. Yet his frontier obsession extends much further than spreadsheets, further than even technology. Political frontiers, social frontiers, scientific frontiers: All these and more crowd Thiel's head as he navigates the shoreline.

"We're at this pretty important point in society," he says during a brisk walk toward the Golden Gate Bridge, "where we can either find a way to rediscover a frontier, or we're going to be forced to change in a way that's really tough." Thiel is a medium-size man with a compact and blocky frame, close-trimmed reddish-brown hair, and eyes the limpid-blue color of Windex; he has a small, nasal voice and tends to exert himself as he speaks, frequently circling back to amend or reconfigure or soften what he's saying. Discussing the concept of frontiers, however, animates him to an almost uninterruptible degree; concepts, more than anything else, seem to do that.

"One of the things that's endlessly dazzling and mesmerizing is this question about the future—what the world is going to be like in 20 years, and what can or should we do to make it better than the default track that it's on," he says, gesturing with his hands while maintaining a fixed stare on the pathway. "But it's a question you can never quite master. I played a lot of chess when I was growing up, and it's similar to some elements of chess, where you can see some moves but you can't see to the end of the game. Even a computer the size of the universe couldn't actually analyze it. There's, like, 10 to the 117th power possible games and something like 10 to the 80th atoms in the observable universe, so it's off by something like 37 orders of magnitude. And chess is something much simpler than reality—it's 32 pieces on an eight-by-eight board. Figuring out the complete future of a chess game is a problem more complicated than anything that can be solved in our universe, so figuring out this planet or just our society in the next 10 or 15 years is just not a solvable problem."

Despite the innovations of the past quarter century, some of which have made him very, very wealthy, Thiel is unimpressed by how far we've come—technologically, politically, socially, financially, the works. The last successful American car company, he likes to note, was Jeep, founded in 1941. "And our cars aren't moving any faster," he says. The space-age future, as giddily envisioned in the fifties and sixties, has yet to arrive. Perhaps on the micro level—as in microprocessors—but not in the macro realm of big, audacious, and outlandish ideas where Thiel prefers to operate. He gets less satisfaction out of conventional investments in "cloud music" (Spotify) and Hollywood films (Thank You for Smoking) than he does in pursuing big ideas, which is why Thiel—along with an all-star cast of venture capitalists, including former PayPal cohorts Ken Howery and Luke Nosek, and Sean Parker, the Napster cofounder and onetime Facebook president—established the Founders Fund. Among its quixotic but potentially highly profitable investments are SpaceX, a space-transport company, and Halcyon Molecular, which aspires to use DNA sequencing to extend human life. Privately, however, Thiel is the primary backer for an idea that takes big, audacious, and outlandish to a whole other level. Two hundred miles west of the Golden Gate Bridge, past that hazy-blue horizon where the Pacific meets the sky, is where Thiel foresees his boldest venture of all. Forget start-up companies. The next frontier is start-up countries.

Thiel (center) with his Founder's Fund partners Ken Howery (left) and Sean Parker.

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"Big ideas start as weird ideas." That's Patri Friedman, a former Google engineer, the grandson of the Nobel Prize-winning economist Milton Friedman, and, as of 2008, when Thiel seeded him with the same initial investment sum he'd given Mark Zuckerberg four years earlier, the world's most prominent micro-nation entrepreneur. Friedman, a short, kinetic 35-year-old with a wife and two children, maintains an energetic online presence that ranges from blogging about libertarian theory to tweeted dispatches such as "Explored BDSM in SF w/big group of friends tonight." Four years ago, a Clarium Capital employee came across a piece Friedman had written about an idea he called "seasteading." Friedman was soon pitching to Thiel, a staunch libertarian himself, the big, weird idea.