If you are going on holiday to Europe this summer, brace yourself for a nasty surprise. Compared to last year, the Continent has become almost 15 per cent more expensive, because of the rise in the euro against the pound.

At the euro's weakest, the mental arithmetic you had to do to convert prices into sterling was to divide by five and multiply by three. The euro will not have to rise too much further before the conversion will be to divide by four and multiply by three. The fall of the pound is a mere ripple, however, an eddy in the financial markets stirred up by the great tidal pull of the dollar as it sinks against the euro.

Forget all the talk about tensions at summit meetings and arguments over the reconstruction of Iraq: this is America's real revenge for opposition to the war. It has taken the dollar and dropped it on Europe's foot. Or, to be more accurate, on the fingers with which Europe is clinging to the precipice of economic growth.

The fuss about boycotts and blacklists is already fading. Don Evans, the US commerce secretary, is even said to have been spotted in a Hermes tie. But the dollar's plunge against the euro will shut more factories in France and Germany than any campaign of sanctions was ever likely to.

The value of the dollar is not, of course, decided by President Bush. But the American denials of responsibility are disingenuous. In part the dollar's fall has been a consequence of the US Federal Reserve's strategy of showing it is determined to fight deflation, which has held down US interest rates, making American assets relatively unattractive to foreign investors.

But the other prime cause is solely the administration's responsibility: the change in the way it talks about the dollar. The "strong dollar policy" instituted in the early years of the Clinton administration has always been a refutation of the sneer that American governments cannot handle philosophical sophistication. In a feat that would delight Jacques Derrida, the policy is a signifier without any signified attached: having a strong dollar policy means saying you have a strong dollar policy, without committing to any further action to make the dollar strong.

Nevertheless, currency dealers have taken the policy very seriously. Administration rhetoric on the dollar regularly moves markets, and if treasury secretaries fail to adhere to the prescribed form of words, then the dollar falls.

Last month, John Snow, the present incumbent, insisted that the strong dollar policy was still in place. But he made it clear that "strength", as he saw it, had nothing to do with the dollar's value.

A strong dollar, he said, was one that people trust because, for example, it is difficult to counterfeit. The only surprise is that he did not say a strong dollar was one that would survive being put through the wash.

The effect was to drop the dollar like a lift with a broken cable. It fell to its lowest level against the euro since the single currency was launched in January 1999, which is where it remains today.

For the eurozone countries, and especially for Germany, this looks like a catastrophe in the making. Growth has been running at a meagre rate of about 1 per cent per year for the past couple of years, but without the help of the euro's weakness, it would have been even worse.

The European Central Bank is cutting interest rates, but it looks like too little, too late. The eurozone is on the brink of recession already: if the euro rises much further, the result is likely to be deflation in Germany, and a steep downturn in the rest of the Continent. At the Evian summit at the beginning of this month, George Bush tried to soothe European fears, assuring his fellow leaders that he would not use "the monetary weapon".

Generous souls have suggested that John Snow's comments might have been merely careless: a result of the former railroad boss's impatience with the subtlety of the policy he inherited. But they were hardly a slip of the tongue: he repeated his points several times. More realistically, the decision to let the dollar go looks like another example of US unilateralism in action.

As John Connolly, Richard Nixon's treasury secretary, put it when devaluing the dollar by coming off the gold standard in August 1971: "The dollar may be our currency, but it is your problem." And if the escape route from deflation for the US entails trampling over France and Germany, that will not keep Bush awake past his famously early bedtime.

Another Connolly story probably captures the mood at the White House pretty well. Asked whether the Europeans would object to learning of the US devaluation by seeing it on television, he is said to have replied: "Fuck 'em."

Ed Crooks is the economics editor of the Financial Times. Patrick Hosking returns next week