In a new six-part series entitled Age of Empire, the BBC's Jonathan Marcus sets out on a journey to examine America's place in the modern world.
"America has no empire to extend or utopia to establish. We wish for others only what we wish for ourselves - safety from violence, the rewards of liberty, and the hope for a better life."
So declared President George Bush in the traditional graduation address at the US Military academy at West Point in June 2002.
But despite his insistence that the US has no imperial ambitions, the word "empire" is increasingly used by academics and pundits alike when talking about America's role in the world.
We thought long and hard about the title for this series. Would Age of Empire prejudge the issue? Is America really in any sense an empire like Ancient Rome or Victorian Britain?
It is a question I put to virtually everyone I spoke to.
'Not quite right'
The answers differed dramatically.
The young British historian Niall Ferguson, for example, had no doubts.
"The United States," he said, "is an empire in every sense but one, and that one sense is that it doesn't recognise itself as such."
He called it "an empire in denial."
Strobe Talbott, former Deputy Secretary of State in the Clinton administration, found the notion of the US as an empire "grotesque, bizarre or laughable, depending upon what mood I'm in and who says it".
He said that, if anything, it was an anti-empire. "There is no interest among American people to set themselves up as an imperial power."
For others, like Michael Mandelbaum of the Johns Hopkins School for Advanced International Studies, America's current position is unique - there simply is not an adequate word to describe it.
As he put it: "Empire is not quite right but it seems to be closer than anything else we have in common usage, so we employ it."
Empire or not, there is a growing feeling around the world that America's unrivalled power is in some sense a problem.
It is something that Strobe Talbott recognises with regret.
"When our friends around the world get together behind our backs, they talk about the problem of American power, how to cope with it, manage it, even how to contain it.
"That is not the way we want others to think about us."
Globalisation meets 9/11
Today one of the buzz-words of international politics is globalisation.
It too is not an easy term to define; it encompasses the spread of market capitalism and the new communications technologies.
These seem to be shrinking the world and eliminating diversity.
Many trace a foreign policy shift to the events of 11 September 2001
Globalisation and US dominance are inextricably bound up.
The world of globalisation that was opened up by the collapse of the Soviet Union and the end of the Cold War seemed almost designed for the US, accelerating the emergence of American superpowerdom.
For Joseph Nye, dean of the Kennedy School of Government at Harvard University, US dominance has been a fact for years.
But it was the tragedy of 11 September which presented America's position in a stark new light.
Indeed, we began our series at Ground Zero in New York, the site of the Twin Towers of the World Trade Center.
Many people believe that it was from the rubble of the towers that a more assertive and ideological foreign policy emerged.
Afghanistan and Iraq were invaded. President Bush proclaimed a new doctrine of pre-emptive military action.
Military, economic, cultural
So how does the current position compare with the great empires of the past. Is America just the latest in a long line of dominant powers? Or is it really unique?
Fareed Zakaria of Newsweek International, fast becoming one of America's most interesting foreign policy pundits, insists that there has never been anything quite like America's dominance of the world.
There have been other great powers, like the British Empire, but none have towered over their rivals in the way the United States does.
US defence spending dwarfs any of its rivals.
American dominance is not just military; it is economic.
US popular culture has spread around the globe.
There is what Mr Zakaria terms "a comprehensive uni-polarity" that nobody has seen since Rome dominated the world.
The Romans with their language, currency and the spread of Roman citizenship perhaps foreshadowed an early form of globalisation.
Niall Ferguson believes it is the British Empire that offers one of the best parallels.
He argues that if you look at what the US has long tried to do - expand the global reach of free markets and ultimately representative government - it bears an uncanny resemblance to what he characterises as the project of Victorian Imperialism.
But there is another side to this whole debate. Joseph Nye of the Kennedy school of Government believes that all the talk of US dominance and influence obscures a much more fundamental reality.
He calls it "the paradox of American power", by which he means that for all its global might, the US is unable to get the outcomes it wants by acting alone.
He argues that in terms of issues like countering transnational terrorism, dealing with the spread of infectious diseases, global climate change, international financial stability, none can be managed by any one country.
The message for US policy-makers, he says, is simple.
"We are the strongest nation the world has seen for some two millennia and yet we can't get what we want by acting alone".
The Age of Empire series is broadcast on Mondays at 09:05GMT on BBC World Service Radio.