On September 11, the nuclear-powered aircraft-carrier USS Enterprise was on routine patrol in the Indian Ocean when news began pouring in of the terrorist attacks upon New York and Washington DC.

The Enterprise is a vessel that defies the landlubber's imagination. It is more than 1,100ft long a nd its flight deck is 250ft across. It is as high as a 20-storey building. An entire village — no, a small town — lives within its powerful steel frame, but it is a garrison town that can move across the oceans at more than 30mph.

It has a crew of 3,200 to run the ship alone, plus the 2,400 pilots and aircrew who fly and service the 70 state-of-the-art aircraft that roar on and off the flight deck day and night.

But this super-dreadnought never travels alone. It is always accompanied, at the very least, by an Aegis-type cruiser, a large surface ship designed to shoot down incoming missiles; by a bevy of frigates and destroyers to protect it from enemy submarines; by a lurking hunter-killer submarine or two; and by some supply vessels and other specialised craft. Marine troops and their helicopters will be in the task force. In offensive and defensive terms, this is a behemoth.

It is difficult to estimate the exact costs of a carrier battle group, but it certainly goes into many billions of dollars. The ships, the aircraft, the logistical supplies and the personnel, together, probably equal a quarter or more of the defence budget of a medium-sized country.

What is more, no equivalent concentration of power to a US carrier task force exists in the world; the few UK, French and Indian carriers are minuscule by comparison, the Russian ones rusting away.

Leaving aside nuclear weapons, which are always problematic and perhaps destined to be forever inapplicable, this group of warships constitutes the strongest and most flexible core of military force today. A carrier force is virtually indestructible, and yet it has the capacity to deal out death and destructio n across most of our globe.

The US possesses 12 such carriers (another, the USS Ronald Reagan, is to join the fleet soon), each with the attendant group of complementary warships. There are also smaller carriers designed, not for open-ocean combat against all, but to take powerful Marine Corps battalions ashore.

This array of force is staggering. Were it ever assembled en masse the result would be the largest concentration of naval and aerial force the world would have seen.

But the US carrier battle groups are never assembled together, because they are carrying out a worldwide mission — the preservation and enhancement of US interests in a volatile, unpredictable world, and the support of America's many obligations abroad.

At the beginning of September last year, for example, three carrier groups were in the North Atlantic and Caribbean, one in the South Atlantic, one off the Persian Gulf, and two in western Pacific-east Asian waters. Another five were in home bases for maintenanc e and crew rotation; and one was being worked up for commissioning.

Given these facts, most shrewd punters would assume only a madman would attack a country with that much clout. On September 11, messianic, US-hating fundamentalists did just that, and truly staggered and hurt the Number One nation.

In the weeks that followed, strategic pundits everywhere (including this one) wrote of the vulnerability of the US to so-called "asymmetric" attacks; that is, blows by enemies who could not match American conventional forces but who could hurt by unorthodox ways. This is still true.

But the other side of the coin was that, stung by the indiscriminate terrorist blow, America sallied forth to deploy the vast forces at its disposal: forces, ironically, that had chiefly been designed for the cold war struggle against the Soviet Union but turned out to be just as suitable for the battle ahead.

The whereabouts of the US Navy's vessels, large and small, were available on the navy's own central website before September 11, partly for public relations reasons, partly to let families know where their loved ones were. Ironically, but unsurprisingly, the terrorist attacks led to a clampdown on such information.

Still, in the age of the communications revolution it is possible to learn — from, of all places, the Enterprise's own website — about the enhanced force that composed the battle group by mid-January. Accompanying the enormous flagship by that time were two cruisers, six destroyers and frigates, two attack submarines, two amphibious vessels with their troops, and supply-dock ships — in all, 15 vessels and 14,300 men (including 3,250 troops).

By then, this force had been joined by other fleet carriers, whose aircraft were pounding Afghan targets day and night, and by the helicopter-Marine carriers.

The global reach of these instruments of war is truly impressive. The second carrier to join the Enterprise was the USS Kitty Hawk, which was being overhauled in Yokosuka, Japan, last September. It covered 6,000 miles in just 12 days and then took up position as the "forward staging base" for hundreds of flights in support of the Marines and US Special Forces into Afghanistan.

Far above the carriers, B-1 bombers flew all the way from the US mainland to drop every manner of hardware on al-Qaeda and the Taliban, and B-52s lumbered up from Diego Garcia to reduce hillsides to rubble.

American Special Forces were also flown to the area from Central Asia, and then backed by extraordinary logistical and stealth-technology support as they in turn functioned as "pinpointers" to aerial attacks through smart weapons. The military campaign is virtually over, apart from Taliban hunts in the distant hills; and the early ground forces, the air squadrons and warships such as the Kitty Hawk are returning to base, with hardly a casualty in sight.

What is more, those bases are not restricted to the continental US. American forces poured into the combat zone from Japan, the UK, the central Pacific, Germany, Italy, the Middle East and elsewhere; that is, they were summoned from the largest array of bases the world has seen since the British empire was at its height a century earlier.

What does this all mean?

It is easy to say that when Osama bin Laden assaulted the world's remaining superpower, he and his network and those who supported him got their just desserts and appropriate oblivion.

But that conclusion is almost beside the point. The larger lesson — and one stupefying to the Russian and Chinese military, worrying to the Indians, and disturbing to proponents of a common European defence policy — is that in military terms there is only one player on the field that counts.

For political and diplomatic reasons, the US invited the world to combine in the fight against bin Laden, just as so many other countries had been invited by Washington to oppose Saddam Hussein's aggression a decade earlier.

But who else in the coalition really counted in this amazingly one-sided Afghan spat? The "Brits" — one of President George W. Bush's genuinely favourite words — qualify for certain things: shared intelligence, the SAS going in first (probably) to the mountains, a dozen Tornado bombers, Prime Minister Tony Blair's supportive stance, the post-victory garrison role, all helped. Indeed, to the American public they are the only other significant ally, albeit in a smallish way.

Was there anyone else? As the campaign unfolded, the Japanese government rather desperately dispatched three destroyers to the Indian Ocean. This was a bold political deed given domestic anti-militarist constraints, but a contribution that in reality was mere tokenism. It had as much effect on the outcome as Brazil joining the allies late in the second world war.

To put it another way, while the battle between the US and international terrorism and rogue states may indeed be asymmetrical, perhaps a far greater asymmetry may be emerging: namely, the one between the US and the rest of the powers.

How is this to be explained? First, by money. For the past decade and well before that, the US has been spending more on its defence forces, absolutely and relatively, than any other nation in history. While the European powers chopped their post-cold war military spending, China held its in check, and Russia's defence budget collapsed in the 1990s, the US Congress duly obliged the Pentagon with annual budgets ranging from about $260bn in the middle of the decade to this year's $329bn.

Everyone knew that, with the Soviet Union's forces in a state of decrepitude, the US was in a class of its own. But it is simply staggering to learn that this single country — a democratic republic that claims to despise large government — now spends more each year on the military than the next nine largest national defence budgets combined (see note on this point).

Only a few Americans realise that fact, and many have denounced former president Bill Clinton for allegedly under-funding the US military. Had that really been the case — and there have been many comparisons to Baldwin and Chamberlain in the 1930s — then it is difficult to see how the US armed forces could have produced such an impressive and overwhelming display of power in recent months.

Still, just last week Washington insiders reported that Donald Rumsfeld, the defence secretary, plans to ask Congress for an increase of $48bn next year, a sum more than twice Italy's entire annual defence budget.

To put this another way, a couple of years ago the US was responsible for about 36 per cent of total world defence spending; its share is now probably closer to 40 per cent, if not more. Even Enterprise carrier groups are affordable on an annual budget of $350bn.

Nothing has ever existed like this disparity of power; nothing. I have returned to all of the comparative defence spending and military personnel statistics over the past 500 years that I compiled in The Rise and Fall of the Great Powers,and no other nation co mes close. The Pax Britannica was run on the cheap, Britain's army was much smaller than European armies, and even the Royal Navy was equal only to the next two navies — right now all the other navies in the world combined could not dent American maritime supremacy.

Charlemagne's empire was merely western European in its reach. The Roman empire stretched farther afield, but there was another great empire in Persia, and a larger one in China. There is, therefore, no comparison.

But this money has to come from somewhere, primarily from the country's own economic resources (in long wars, powers often borrow from abroad). Here again is an incomparable source of US strength, and one that has been increasing in the past few years.

During the 1960s, 1970s and 1980s, the US share of total world product steadily declined, so that by the late 1980s it may have possessed only about 22 per cent of global gross domestic product compared with a far higher share in the Truman and Eisenhower years.

Had this decline continued for another decade or two, America would have come troublingly close to "imperial overstretch". Moreover, the Soviet Union still seemed powerful, and some touted Japan as the coming "Number One".

Then three things happened. First, the Soviet empire collapsed, and its successor states imploded economically (Russia's GDP is less than that of The Netherlands). Second, Japanese growth stalled, its banks got into trouble, the strong yen faded, and the country entered a puzzling era of economic malaise. Third, US businessmen and some politicians reacted strongly to the debate about "decline" by taking action: cutting costs, making companies leaner and meaner, investing in newer technologies, promoting a communications revolution, trimming government deficits, all of which helped to produce significant year-on-year advances in productivity.

Thus, as the Russian and Japanese share of the world economic pie shrank, the US share steadily expanded; right now, it contains about 30 per cent of total world product, perhaps a little more.

This steady economic growth, along with the curbing of inflation in the 1990s, produced the delightful result that America's enormous defence expenditures could be pursued at a far lower relative cost to the country than the military spending of Ronald Reagan's years.

In 1985, for example, the Pentagon's budget equalled 6.5 per cent of gross domestic product and was seen by many as a cause of US budgetary and economic-growth problems. By 1998, defence spending's share of GDP was down to 3.2 per cent, and today it is not much greater. Being Number One at great cost is one thing; being the world's single superpower on the cheap is astonishing.

Reinforcing this disproportionate military and economic heft are further elements in the grand amalgam of US power in the world today. Indeed, a statistician could have a wild time compiling lists of the fields in which the US leads.

A full 45 per cent of all internet traffic takes place in this one country. About 75 per cent of the Nobel laureates in the sciences, economics and medicine in recent decades do their research and reside in America. A group of 12 to 15 US research universities have, through vast financing, moved into a new superleague of world universities that is leaving everyone else — the Sorbonne, Toyko, Munich, Oxford, Cambridge — in the dust, especially in the experimental sciences.

The top places among the rankings of the world's biggest banks and largest companies are now back, to a large degree, in US hands. And if one could reliably create indicators of cultural power — the English language, films and television, advertisements, youth culture, international student flows — the same lopsided picture would emerge.

What are the implications, for the world and for America itself?

First, it seems to me there is no point in the Europeans or Chinese wringing their hands about US predominance, and wishing it would go away. It is as if, among the various inhabitants of the apes and monkeys cage at the London Zoo, one creature had grown bigger and bigger — and bigger — until it became a 500lb gorilla. It couldn't help becoming that big, and in a certain way America today cannot help being what it is either.

It is interesting to consider the possible implications for world affairs of the existence of such a giant in our midst. For example, what does it mean for other countries, especially those with a great-power past such as Russia and France, or with great-power aspirations such as India and Iran?

Russian President Vladimir Putin's government is faced with the difficult choice of trying to close the enormous power gap, or admitting that would merely overstrain Russia's resources and divert the nation from the more sensible pursuit of domestic peace and prosperity.

French Europeanists need either to recognise that the chances of creating a true equal to American military, diplomatic and political weight in world affairs are an illusion, or they need to exploit the recent display of Europe's bystander role to make fresh efforts to unify the fractured continent.

Think, also, of the implications for China, perhaps the only country that — should its recent growth rates continue for the next 30 years and internal strife be avoided — might be a serious challenger to US predominance. More immediately, relish the message this mind-boggling display of American capacity to punish its opponents has sent to those nations who had hoped to change the local status quo — in the Korean peninsula, in the Taiwan Straits, the Middle East — in the not-too-distant future.

As the crew of the Kitty Hawk and other vessels of the US Navy take their shore leave, one hears the distant rustle of military plans and feasibility studies by general staffs across the globe being torn up and dropped into the dustbin of history.

Reflect also on the implications for international organisations, especially those involved in western defence and/or global peace and security. Tru e, some Nato armed forces played an ancillary role, and European states lent their airbases to the US, supplied intelligence, and rounded up suspected terrorists; but the organisation's other members may have to face the prospect of either being a hollow shell when the Americans don't play, or an appendage to Washington when they do.

Can one have a reasonably balanced United Nations Security Council when there now exists, in addition to the gap between its five permanent veto members and the non-permanent members, a tremendous and real gulf in the power and influence of one of the five and the other four?

Even before the present victories, the US played the game of using international organisations when it suited its own interests, and paralysing them when it disapproved. Yet probably nothing could be worse for global stability than the US steering a zig-zag course.

Think, then, of what might be the implications for the American democracy itself. It is, perhaps, si mply a historical irony that the republic whose first leader cautioned against entangling alliances and distractions abroad is now, a quarter way into its third century, the world's policeman.

After all, a political culture that dislikes interference by governments and cherishes its anti-colonial roots may not take kindly to being required to put its forces into Africa, central Asia, east Asia should dire crises arise, because nobody else can do the job, or to chase terrorists to the far corners of the globe, forever.

Americans, who like to be liked, may find it hard to bear learning that they are very much disliked and feared in many parts of the world because their country is so grand and powerful.

On the domestic front, may not its spectacular world position compromise other things that Americans care about? Eisenhower warned about the disproportionate influence of a military-industrial complex and Senator J. William Fulbright in the 1960s feared what he called "the arrogance of power"; those are apprehensions that still run deep in many American minds.

On the other hand, America's spectacular position in the world in military, economic, technological and cultural terms may be equalled by a wisdom in the executive and the Congress, and a judiciousness in the people for the decades to come. It might even produce a leadership that sometimes, only sometimes, is willing to give way in international quarrels, not because its own case is a bad one, but because it is important to show magnanimity and tolerance to those who lack US strength and privileges. That would be a rare act of statecraft.

Will this "unipolar moment", as it was once called, continue for centuries? Surely not.

"If Sparta and Rome perished," Rousseau said, "what state can hope to endure forever?"

It is a fair point. America's present standing very much rests upon a decade of impressive economic growth. But were that growth to dwindle, and budgetary and fiscal problems to multiply over the next quarter of a century, then the threat of overstretch would return. In that event, the main challenge facing the world community could be the possible collapse of US capacities and responsibilities, and the chaos that might ensue from such a scenario.

But from the flight deck of the USS Enterprise, that scenario seems a long way off for now.

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Paul Kennedy is professor of history at Yale University and director of international security studies. He has written and edited 15 books, including The Rise and Fall of the Great Powers, and Preparing for the Twenty-First Century.

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In a followup letter published in the 9/10 February FT Weekend, Senior Economist Peter Robinson of the Institute for Public Policy Research, London, questions Kennedy's mathematics on this point. Under the title Tricky arithmetic of military spending, Robinson writes:

In his analysis of the US/s pre-eminence as a world power, Paul Kennedy repeats a lot of misleading myths that threaten to distort the debate ...

To show that the US is in a class of its own, he claims that it now spends more on its military than the next nine countries combined. This result comes from counting up the defence budgets of other countries in dollar terms at current exchange rates. This has the consequence that if the value of the dollar were to decline by 10%, the relative military strength of the US would apparently decline by the same amount, which would be a silly thing to claim.

In 2000, China's gross domestic product was about half of the US when measured properly (in purchasing power terms). It spent about 5% of its GDP on defence versus 3% in the US. It is simple arithmetic then that China's defence budget was about 85% of the US's. Add in India's military spending and the US does not even reach a two-power standard in terms of its defence spending.

Now of course China and India's budgets are largely spent on huge strategically immobile land armies. US military superiority stems from its ability to intervene anywhere and from the unparalleled technological edge and the professionalism of its armed forces. But this just makes the point that spending comparisons are of limited value — especially when they are wrong.

We need a serious debate about the role of the US as the world's only superpower — but it would help if we first got some of the basic facts right and if Professor Kennedy learnt how to measure things properly.