What compares with the Coming of Barack Obama? March 1933 perhaps, when an America brought low by the worst slump of the modern era entered a New Year in the hope that the incoming president, a Democrat with an infectious optimism and an interventionist philosophy, could lift it out of the Great Depression.

Or maybe 1945, when the same Franklin Roosevelt was about to be sworn into office for a fourth time. By then FDR of course was physically exhausted, gaunt and hollow, with scant trace of the jauntiness of old. But even though he would not live to see it, victory was in the air. After five years of bloodshed, America and the world hoped that before the year was out, the most destructive conflict in human history might at last be over.

And then there was 1961, when an elegant and handsome young president – hatless and clad only in a light morning coat even though eight inches of fresh snow lay on the ground in Washington DC – proclaimed that the torch of leadership was passing to a new generation of Americans, a generation forged in war but not too old to dream.

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Had he lived, John Kennedy would be 91 today. Instead, he is frozen in that moment of dazzling, seemingly boundless promise. Not yet 44, he was the youngest man ever to become president, having promised his fellow citizens not just change but national renewal. Some of course believed he was too young. Others muttered darkly that he had stolen the election. Nonetheless, a country felt proud and exhilarated by what it had brought about. But even JFK did not unleash the hope inspired by Obama in these dark times.

Ever since Roosevelt's day, once the US had emerged as the richest and most militarily powerful nation on earth and had sealed the century as its own, an American president has always been the property not just of his own country, but to a certain extent of the whole world. But never, surely, quite like now.

Washington itself may be swamped by up to five million visitors for the festivities that reach their climax when Obama is sworn in on the western steps of the US Capitol building at noon on Tuesday 20 January. But they will be the merest fraction of a global audience that will run into billions.

And this audience is not simply drawn by the prospect of a spectacle to match the marriage of Charles and Diana, or the opening ceremony of the Olympics. This vast cross-section of humanity is yearning for a miracle. Neither Kennedy, nor even FDR, was burdened with quite the weight of expectation that presses on this president-elect. Recession, global warming, the travails of the Middle East, terrorism and great civilisational clashes – these crises and others, it is so tempting to believe, can be solved in the Age of Obama.

Never, to paraphrase Winston Churchill, have so many invested so much hope in a single individual. Except that the object of their fixation is not a proven titan like Churchill. Barack Obama's career on the national political stage began barely four years ago. He has run nothing of note, except an admittedly brilliantly conducted campaign for the White House.

Now he must run everything. He will be ultimately responsible for a federal budget of three trillion dollars. He will lead the mightiest military on earth. Most important of all, he will be in charge of his country's government, at a moment when Americans look more intensely to government for solutions than at any time since the Great Depression.

This huge outpouring of hope moreover ignores a paradox. In 1945, the US stood at the pinnacle of its power. The Red Army might have been about to conquer Berlin, but America was far and away the wealthiest country on earth. It could create, and to all intents and purposes impose, a new global financial system. Singlehanded, it could promote international economic recovery, as it did with the Marshall Plan in a Western Europe that might otherwise have fallen under Communist control.

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Six decades later, the biggest creditor nation on earth has turned into the world's biggest debtor. In a globalised age, the US is one economic power centre among several. The slump of 2008 may have started there, but the key to ending it is to be found in Beijing, Delhi and Brussels as well. Yet for now these inconvenient truths are forgotten in the euphoria over Obama. Can he do it? The deafening chant echoes back: Yes He Can.

This huge investment of hope is testament to America's enduring appeal. That the world looks to one country, to one man, for an answer proves that however much his country's reputation has been tarnished by George W Bush, the US remains the world's supplier of last resort of hope, the belief against the odds that the human condition can be improved. America's struggles, excesses, failures and triumphs are those of all of us.

By all these measures, the advent of Obama is an especially stirring moment. After eight years, each one of which felt longer than the one before, George W Bush, at home and abroad the most unpopular US leader of the modern era, will be gone. Once again, a generational torch is being passed on. The soon-to-be 44th president may be only 15 years younger than his predecessor, compared to the 27-year difference between Kennedy and Dwight Eisenhower in 1961, but to all intents and purposes he comes from a different generation.

Obama was born that same year, and technically he could be placed in the rearguard of the baby-boom cohort to which Bill Clinton and George W Bush belong. But his formative years were the late Seventies and Eighties, not the self-indulgent Sixties. Moreover, by dint of his parentage, and his upbringing in Hawaii and Indonesia, he has been able to look upon America from the outside as well as from the inside. That, too, helps explain the unmatched anticipation abroad. Finally, the rest of us believe, the US will have a leader who understands not just how his country sees itself – but how it is seen by the 95 per cent of human beings who are not American.

Obama's victory however means even more than that. If you believe in the perfectibility of America, this is your moment. If slavery was the country's original sin, the election of the first black president has expunged that sin, at least in part. The start of his journey to the White House was unforgettable enough. He announced his candidacy on a morning in February 2007 even more frigid than the day JFK was inaugurated, on the steps of the old State House in Springfield, Illinois, where Abraham Lincoln, arguably America's greatest president, started his own political journey.

Almost a century and a half after Lincoln issued the Emancipation Proclamation that freed black slaves in the midst of America's Civil War, an African-American, whose political journey had begun in the same state legislature, was declaring his ambition to follow Lincoln's steps to the summit of the political mountain. Not only that, too, he had a real chance of winning. And he did.

Thus the end of the journey will be even more memorable and extraordinary than its beginning. Fittingly, the inauguration takes place just 24 hours after the annual US federal holiday in honour of Martin Luther King, leader and martyr of the civil rights movement, a man venerated in every nation and who did so much to make Obama's achievement possible.

In August 1963, three months before Kennedy was cut down in Dallas, King told hundreds of thousands of people gathered in front of the Lincoln Memorial in Washington of his dream, of how black and white Americans one day would live side by side in harmony and equality. Just 17 days from now, not thousands but millions of people will gather at the other end of the Mall to hear Obama's inaugural address. Could there be a better moment to dream? Has this sour, jaded and pessimistic planet ever needed a pick-me-up more?

Dreams by their nature defy everyday logic. Surely 2009 cannot be worse than 2008 – except of course it can. Economic forecasts are uniformly dreadful. The US car industry remains on the brink of collapse. The interlocking crises of the Middle East, Iran, Pakistan and Afghanistan look, if anything, more intractable than they did 12 months ago. Quite possibly, the heroic efforts of Obama notwithstanding, we will be feeling even more gloomy in December 2009 than we do now – and next year of course, there will be no Obama inauguration to savour.

But at this dawn of 2009 he embodies the magic of America, its endless ability to reinvent itself. F Scott Fitzgerald famously declared there are no second acts in American lives. But in the life of the country itself, the do-overs are countless – and we are about to witness one for the ages. The Bush era of wilful ignorance, anti-intellectualism and zealotry is out. The English language is back. So is nuance, pragmatism, and a respect for non-partisan expertise.

What other country but the US could elect a man whose middle name, Hussein, is the same as that of the dictator against whom the country went to war in 2003? Obscure colonels may grab power in less fortunate parts of the world. But in what other democratic country could such an outsider have come from nowhere to claim the supreme prize? Barack Obama is but the latest proof that in America, everything is possible. And that is why the rest of us are so excited, even though we know that only in America do such things happen.