Without neodymium, your ears would be sad. The magnetic fields generated by drivers made of this strange metal, a component of high-end speakers, create the crisp vibrations your brain interprets as your favorite Weezer album.

Without dysprosium, Prius owners would be sad. A little added dysprosium will shield neodymium magnets from distortion by heat, crucial for the setup that powers the motors in many hybrid and electric cars. Or consider lutetium. Without it there would be no PET scans. Without yttrium crystals, lasers would be less bright.

Chemists call them lanthanides; you know them as rare earth metals. But by any name, they behave in ways that other matter simply can't: They have piles of electrons, but unlike most elements they don't stash them tidily, filling up one orbital shell before moving up to the next. They prefer, instead, to toss some up to higher levels, orbitals that go unused by many metals, like dusty closet shelves onto which you have tippy-toed shoeboxes of old love letters. This makes them act … odd.

And it makes them essential for modern life. The US imports 10,000 tons of refined rare earth metals a year, and globally we consumed well over 100,000 metric tons in 2011. In the ground, rare earths are usually bound up with radioactive elements like uranium and thorium, which makes mining and refining them expensive. Plus, they are unevenly distributed throughout the planet's crust. (Hence the term rare, though hard to get would be more accurate.)

Global supplies of rare earths are more uneven still: China controls more than 95 percent of rare-earth-metal exports. That could change though, not least because China is about to run out. Current projections estimate China's domestic appetite for rare earth metals will top 130,000 metric tons as early as this year, a number exceeding China's current total rare-earth-metal exports. Even with existing stockpiles and untapped reserves within its borders, it will be difficult for China to continue to provide the world with an affordable supply of these indispensable elements.

Unfortunately, options for tapping new supplies are extremely limited. In the US, mining operations are finding it difficult to revive dormant mines profitably. In Australia, rare-earth-rich Mount Weld is mired in a political game of hot potato with Malaysia over whether the ore would be refined there and whether the radioactive result would be allowed back into Oz. No, the best possible source for the next batch of squirmy-electroned elements is Greenland.

Bigger than Mexico, farther north than Denmark (of which, technically, it is a possession), and with a population that would barely fill Yankee Stadium, Greenland is a weird place. Actually, it's a very sad place. Unemployment hovers near 10 percent, and population growth is nil, since young people commonly leave for (ahem) greener pastures and better opportunities in Iceland and Canada. The suicide rate is 10 times that of the US.

Eighty percent of Greenland is topped by a 1.5-mile-thick sheet of ice, but the exposed remainder is the size of California. Dig just below the surface and you'll find the Kvanefjeld deposits. Second only to China's Bayan Obo deposit, they contain uranium and rare-earth-metal resources—2 million metric tons by a conservative estimate, enough to furnish us for at least a decade with the key ingredients for electric-car motors, clean-energy-generating wind turbines, rechargeable batteries, and lightweight alloys. (Not to mention nuclear batteries that could keep unmanned aerial vehicles aloft for weeks at a time.) Unfortunately, excavation of the area ended in 1988 due to a ban on the mining of radioactive materials. No nukes, no rare earths. But in 2013, Denmark's national parliament repealed the ban, opening the door to development of Kvanefjeld and giving Greenland a chance at financial independence.

There, the industry could start operations fresh, with state-of-the-art techniques and an environmentally conscious mentality. Sure, no one would argue that mining in Greenland or anywhere else is good for the environment, but the Kingdom of Denmark, for better or worse Greenland's big brother, exhibits an environmental conscientiousness that would likely shape exploration of natural resources in Greenland. Denmark is pushing to end all domestic coal usage by next decade and plans to make Copenhagen carbon-neutral by 2025. Its stewardship philosophy has been successfully adopted by nearby Iceland, which is a pioneer in renewable geothermal energy.

GREENLAND COULD FURNISH THE WORLD WITH 2M METRIC TONS OF RARE EARTHS.

Environmental mitigation aside, the other potential upsides are hard to dismiss. A reduced dependency on a single source—China—for rare earth elements would increase competition and decrease prices. There might be a mental health advantage as well. Mining in Greenland would not alter the perpetual winter night—nothing can change the circadian extremes that life this far north entails—but it would provide diversity in employment, stem the exodus from the island nation, and offer a glint of hope for future generations.

There's another benefit to mining in Greenland: Techniques and experience garnered while plumbing this icy place could be applied to an even larger prize—the last Terran frontier, Antarctica. That continent is currently protected from mining and drilling by the Antarctic-Environmental Protocol. But that agreement may fail to be renewed in 2048. If that happens (and I expect it will), nations will turn to Antarctica in hopes of extracting rare earths, oil, and natural gas from the wedges of territory they have already staked out. (Seven nations have claims to segments of the continent, while several more, including the US and Russia, have reserved the right to stake one in the future.) The claims might well be worthwhile: In 2008, ice core studies confirmed the presence of rare earth metals. While handicapping a treaty three decades before its expiration is risky, the potential resources there (and the likely depletion of rare earths elsewhere by that point) could sway the opinions of those responsible for deciding the treaty's fate.

Exploiting Antarctica may seem far-fetched in 2015—it probably won't happen in our lifetime. And yes, getting through its 1.3-mile-thick ice sheet would be challenging to say the least, but consider the upsides: There are no native populations to displace, no salmon runs to despoil. It's the ultimate not-my-backyard. If Antarctica were to join Greenland in providing the world a supply of vital rare earth metals, it could be without the conflict all too often coincident with the pursuit of natural resources. In other words, something rare on this earth.

KEITH VERONESE (veronesepk@gmail.com) is the author of Rare: The High-Stakes Race to Satisfy Our Need for the Scarcest Metals on Earth, published in January by Prometheus Books.