"Are you monitoring the construction?" asked the middle-aged man on a bike accompanied by his dog.

"Ah, sì," I replied in my barely passable Italian.

"Bene," he answered. Good.

In front of us, a backhoe's guttural engine whined into action and empty dump trucks rattled along a dirt track. The shouts of men vied for attention with the metallic whirring of drills and saws ringing in the distance. Nineteen immense cranes spread across the landscape, with the foothills of Italy's Southern Alps in the background. More than 100 pieces of earthmoving equipment, 250 workers, and grids of scaffolding wrapped around what soon would be 34 new buildings.

We were standing in front of a massive 145-acre construction site for a "little America" rising in Vicenza, an architecturally renowned Italian city and UNESCO world heritage site near Venice. This was Dal Molin, the new military base the U.S. Army has been readying for the relocation of as many as 2,000 soldiers from Germany in 2013.

Since 1955, Vicenza has also been home to another major U.S. base, Camp Ederle. They're among the more than 1,000 bases the United States uses to ring the globe (with about 4,000 more in the 50 states and Washington, D.C.). This complex of military installations, unprecedented in history, has been a major, if little noticed, aspect of U.S. power since World War II.

During the Cold War, such bases became the foundation for a "forward strategy" meant to surround the Soviet Union and push U.S. military power as close to its borders as possible. These days, despite the absence of a superpower rival, the Pentagon has been intent on dotting the globe with scores of relatively small "lily pad" bases, while continuing to build and maintain some large bases like Dal Molin.

Americans rarely think about these bases, let alone how much of their tax money -- and debt -- is going to build and maintain them. For Dal Molin and related construction nearby, including a brigade headquarters, two sets of barracks, a natural-gas-powered energy plant, a hospital, two schools, a fitness center, dining facilities, and a mini-mall, taxpayers are likely to shell out at least half a billion dollars. (All the while, a majority of locals passionately and vocally oppose the new base.)

How much does the United States spend each year occupying the planet with its bases and troops? How much does it spend on its global presence? Forced by Congress to account for its spending overseas, the Pentagon has put that figure at $22.1 billion a year. It turns out that even a conservative estimate of the true costs of garrisoning the globe comes to an annual total of about $170 billion. In fact, it may be considerably higher. Since the onset of "the Global War on Terror" in 2001, the total cost for our garrisoning policies, for our presence abroad, has probably reached $1.8 trillion to $2.1 trillion.

How Much Do We Spend?

By law, the Pentagon must produce an annual "Overseas Cost Summary" (OCS) putting a price on the military's activities abroad, from bases to embassies and beyond. This means calculating all the costs of military construction, regular facility repairs, and maintenance, plus the costs of maintaining one million U.S. military and Defense Department personnel and their families abroad -- the pay checks, housing, schools, vehicles, equipment, and the transportation of personnel and materials overseas and back, and far, far more.

The latest OCS, for the 2012 fiscal year ending September 30th, documented $22.1 billion in spending, although, at Congress's direction, this doesn't include any of the more than $118 billion spent that year on the wars in Afghanistan and elsewhere around the globe.

While $22.1 billion is a considerable sum, representing about as much as the budgets for the Departments of Justice and Agriculture and about half the State Department's 2012 budget, it contrasts sharply with economist Anita Dancs's estimate of $250 billion. She included war spending in her total, but even without it, her figure comes to around $140 billion -- still $120 billion more than the Pentagon suggests.

Wanting to figure out the real costs of garrisoning the planet myself, for more than three years, as part of a global investigation of bases abroad, I've talked to budget experts, current and former Pentagon officials, and base budget officers. Many politely suggested that this was a fool's errand given the number of bases involved, the complexity of distinguishing overseas from domestic spending, the secrecy of Pentagon budgets, and the "frequently fictional" nature of Pentagon figures. (The Department of Defense remains the only federal agency unable to pass a financial audit.)

Ever the fool and armed only with the power of searchable PDFs, I nonetheless plunged into the bizarro world of Pentagon accounting, where ledgers are sometimes still handwritten and $1 billion can be a rounding error. I reviewed thousands of pages of budget documents, government and independent reports, and hundreds of line items for everything from shopping malls to military intelligence to postal subsidies.