During his recent trip to Georgia and Ukraine, vice-president Joe Biden assured them the United States would not recognise any spheres of influence. Countries can “choose their own partnerships and their own alliances”. In short, Nato membership is still open.

That position has a certain nobility. It is, however, wildly unrealistic.

In the first place, spheres of influence exist, even if some choose to not recognise them. The power of a state is like gravity: it has its greatest influence on those objects closest to it. As a saying popular in this hemisphere goes: “Poor Mexico: so far from God, so close to the United States.”

The most dangerous crisis of the cold war, the Soviet placement of nuclear missiles in Cuba, was settled on the basis of mutual acknowledgement of spheres of influence. Moscow agreed to remove its missiles from Cuba after the US provided assurances that it would remove similar missiles from Turkey. Even though Turkey was a member of Nato, the US in effect recognised that, at least for this purpose, it was within a Soviet sphere of influence.

If Georgia or Ukraine has a confrontation with Russia, there is not much the US can do. There are certain realities of geography that present military technology simply cannot overcome. They border Russia, and the US is far away.

American promises would be as valuable as the French assurances to Poland before the second world war. It is not well known, but France had pledged to launch an attack on Germany within 15 days of any German attack on Poland. Unfortunately for the Poles, the French promise was not serious. When Germany invaded, France declared war – and did nothing.

Placed in a similar circumstance, that is what the US would do – nothing. The US would do nothing because there is nothing it can do. Geography cannot be changed. In addition, American forces are now fully engaged. In order to increase troop numbers in Afghanistan, the US will have to reduce them in Iraq. Apparently, 200,000 American troops are now all that can be deployed in combat theatres at any one time.

For all the talk about the lone superpower, that number needs to be kept in mind. In Vietnam, the US deployed 500,000 in theatre at the peak, with a smaller population, and was not responding to an attack on its territory.

Today the US can deploy far fewer troops. Something has changed in American society. With defence spending increasing to fight wars in Afghanistan and Iraq, George Bush did not even propose a way to pay for the war, either through raising taxes or by cutting other expenditures. No war bonds were issued. The country just quietly accumulated debt.

A political judgment was made: the American people were told to go shopping. The war would not touch the general public. Only an honoured few would bear the burden.

The US did not take war seriously, but was not alone in underestimating the costs and complications of war. After 9/11, Nato invoked Article 5 to show its solidarity with the United States. Nato forces took increasing responsibility in Afghanistan. Thinking the war had been won, they focused on postwar reconstruction.

But as the fighting has intensified and their casualties have mounted, public support for the Afghanistan mission has sagged. “No one will say this publicly, but the true fact is that we are all talking about our exit strategy from Afghanistan,” a senior European diplomat revealed during last April’s Nato summit. “We are getting out. It may take a couple of years, but we are all looking to get out.”

When the cold war ended, the US concluded that its power was overwhelming. The appearance of relatively easy victories in the first Gulf war and in the Balkans reinforced that conviction.

But those triumphs now seem the exception, rather than the rule. Americans thought all their enemies in the future would crumble the way enemies in the 1990s did. They were wrong.

And yet the US continues to make promises. And people will believe in them. And if they get in trouble, they will wonder why the US does not help them.

It is time to be honest – with Americans, and those that depend on their promises.