Not so long ago, few Americans, very much including policy wonks and military officers, knew anything about Yemen. Government officials couldn’t even find it on a map, though it was right there, sprawling across the southern end of the Arabian Peninsula. Yet over the past year or so, a flood of reports were splashed across America's front pages, cautioning that Yemen was on the verge of being transformed into the next Afghanistan—a place where Al Qaeda could live, train, even thrive and plot with impunity. On Christmas day 2009, a Yemeni trained terrorist tried to detonate a U.S. passenger aircraft in Detroit. And now two packages have arrived from Yemen, addressed to synagogues in Chicago, but, according to official reports, rigged to blow up the planes transporting them. Within the space of a few hours, then, Yemen went from a desert strip many Americans had never heard of to the epicenter of the war between Al Qaeda and the West.

This should come as no surprise: Yemen is truly a mess, most of it governed in name only. Hence its appeal to Al Qaeda, which has always, and understandably, been drawn to the ungoverned spaces of Southwest Asia. Yemen’s petroleum supplies, the country's only real source of wealth, have nearly been depleted. It uses a sizable percentage of its water supply and decent agricultural land to grow the stimulant qat, on which an equally sizable percentage of the population appears to be perpetually stoned. Much of that population remains illiterate and resides in abject poverty. Yemen enjoys a never-ending rebellion of Houthi tribesmen in its mountainous northern regions. In much of the country, males tread about heavily and ostentatiously armed. Indeed, no one has ever really controlled the place, whether the Ottoman Turks who ostensibly ruled the country for several centuries, or the British who established a protectorate along the coast. It is here that Al Qaeda has found a welcome mat from those who may or may not share bin Laden’s commitment to global homicide, but who have proved perfectly willing to host him and his followers for the right price.

The government of Ali Abdullah Saleh, who has been president of a united Yemen since the early 1990s and of the North Yemen Arab Republic for more than a decade before that, has been cooperating with the United States against Al Qaeda in a sort of desultory, off again, on again way since 2001. Mirroring the support that the tribes lend Al Qaeda, his cooperation derives less from any commonality of interests than it does from the wads of American assistance it guarantees. Yemen subsists, as expert Andrew Terrill describes it, on a system of subsidies and bribes. The economy has no pulse. Its tribes don’t get along. It has no meaningful infrastructure. It exists in a state of perpetual war. It offers the perfect safehouse for Al Qaeda.

Despite or maybe because of this grim prognosis, the United States, concerned by Al Qaeda’s expanding presence, has increased its security and development assistance to Yemen. But this is like giving vitamins to a terminal cancer patient. Saleh faces the classic dilemma of leaders in the Islamic world who the United States cultivate as erstwhile partners in the struggle against Al Qaeda. He walks a fine and constantly shifting line, blunting American pressure when terrorists pop up in Yemen and staving off dissent at home when the United States looses fusillades in the Yemeni desert. In the meantime, Saleh can only pray that none of his subjects launches a catastrophic strike against the United States, prompting a direct and furious American intervention.

The dilemma, needless to say, hardly comes as news to Washington policymakers, or at least one can hope. We have, after all, been here before. Sudan, Somalia, Anbar, Afghanistan, Northwest Pakistan—Al Qaeda loves a vacuum. Yemen is simply the latest. But America doesn’t have the capacity to fill vacuums in every far-flung precinct. It can barely accomplish this end in Afghanistan, much less six Afghanistans. And, still, the engine behind America's strategy is precisely the assumption that, because Al Qaeda relies on ungoverned spaces to prepare for attacks, the United States must eradicate such spaces, preferably by assisting local governments, as in Yemen and Pakistan, but also via direct military action, as in Afghanistan.

What Al Qaeda's rise in Yemen shows is that this strategy amounts to nothing more than a game of whack-a-mole—when al Qaeda gets "whacked" in one place, it simply burrows on to the next. Today Yemen, tomorrow Somalia. The world, and particularly the Muslim world, consists largely of these ungoverned and, more to the point, ungovernable spaces. Most of them have been that way for centuries and may stay that way for just as long. There are simply too many for the United States—its reach limited, its resources depleted—to police, even by aerial drones, even by midnight commando raids. Alas, what one of those spaces presented us with this week offers a preview of something much worse to come.

Steven Metz is the author of Iraq and the Evolution of American Strategy.