They were branded China's "Patriot Games", but here, 24 hours before the dousing of the Olympic flame that cut such a trail of anger and protest, another name, another verdict is required.
They have not been the Patriot Games; they have been the Saviour Games, the Olympics of reinvented glory and grandeur and heroes and heroines and an irresistible sense that they can still provide for a jaded world something that makes the heart beat a little faster and the spirits rise.
They have explained, day after day, that there is so much more to sport than that part of it that has been annexed by the money-gorged battalions of big professional team sport.
This other sport of Beijing has largely been about crazy ambition and years of dedication, and men and women who stand on the Olympic podium drained of everything but the pure elation of achieving something to which they have devoted the best years of their lives.
Of course the big winners – Usain Bolt, Michael Phelps and, relatively speaking, Britain's £12,000-a-year swimming star Rebecca Adlington – have enriched themselves enormously over the last few weeks. But on most flights home over the next few days the greatest currency will still be in dreams.
If sometimes the smog has made the mountains disappear and challenged the athletes, if the indefatigable charm of thousands upon thousands of young volunteers has not always hidden the intransigence and regimentation that still plainly shape a lot of their lives, there is no question that the overall effect of the 29th Olympics has been as brilliant as the sprinting of Bolt, the man who has mesmerised the world.
Whatever else they have done, or intended to do, the Chinese, with their vast undisclosed resources and open-ended budgets, have said that the Olympics matter to a high degree. Whether in their eyes it is mostly because of the propaganda, and distraction from such matters as human rights, the resulting focus has been on the power of sport and the salvation of the movement which started off 112 years ago with the intention of galvanising the youth of the world. Nor can it be said that such matters as Tibet have been lost from sight beneath the spikes of the athletes.
No doubt the last few weeks here will be the subject of intense analysis within and beyond the shores of China.
In the here and now, though, with the flame still burning for a few more hours and all the memories, and all the joy and the pain, stored in the hearts of all the winners and the losers and all those who have seen them push to their limits, it is possible to assert that these are arguably the greatest Olympics of all.
Certainly for someone in his ninth Olympics, starting in Montreal in 1976, it is possible to make a more emphatic statement. Nowhere, not Montreal, Moscow, Los Angeles, Seoul, Barcelona, Atlanta, Sydney nor Athens, gave quite the same sense transmitted here of an Olympics so secure on its stage and so confident that it had a product that had not been exhausted by cheating on the field and relentless commercialisation off it.
Damaged, no doubt, and compromised, yes, so many times, but over the last two weeks the old fear that these might be the last Olympics before terminal decline has not so much eased as flown off into the haze.
This is easier to say if you have been close to the extraordinary surge of British pride that has come with a success unrivalled since Edwardian days and built, surely, on the fact that the nation's athletes have finally been given the aid and support – from Lottery funds – that have long been a reality in front-rank sports nations.
That Britain may now be enjoying membership of such company is a heady idea, but for the moment it is an aspect of a wider success.
The 29th Olympics have undoubtedly sent a message of hope and recharged ambition to every corner of the world where some form of sport is played. They have done it through the lifeblood of every great sports event. They have done it with those moments that when you experience them you know right away you will have them always.
For Bolt to provide something so indelible, as he did in the first of two world-record-smashing runs, over 100 metres last weekend, he had, for this witness, to match or excel every unforgettable invasion of the senses in the past 32 years of Olympic history. He had to remind us that at every Olympics, however far below the level of staging that has been seen here, there is always a moment to hold against a tide of exploitation and cheating that so often has undermined the idea that what happens in a great city of the world every four years is really worth the trouble.
In Montreal there was the terrible sadness of hundreds of weeping young athletes returning home to Africa because of a political boycott. They filed into the airport as the opening ceremony played out in the stadium, and if the poignancy of that sight is imperishable so, too, was the later glory of the running of Cuba's Alberto Juantorena and the exquisite work of the teenage Romanian gymnast Nadia Comaneci.
In Moscow and Los Angeles there was more boycotting, first by the West and then by the Eastern block, but Sebastian Coe defied Maggie Thatcher in Moscow and dwindling form and illness in Los Angeles and his gold medals in the 1500 metres were so impressively won that Juan Antonio Samaranch, the president of the International Olympic Committee, tried to bend the rules and have him, despite his failure to qualify, run again in Seoul in 1988.
But whatever Coe – on whom the huge responsibility of following Beijing now falls as he leads the organisation of the London Olympics – might have achieved in South Korea he would, like everyone else, have been operating in the long dark shadow of Ben Johnson. Yet before the unprecedented shame that came to Johnson when he was stripped of his 100m gold medal after a positive drug test the Jamaican-born Canadian had produced no less sensational an impact than did Bolt here in the "Bird's Nest" stadium.
The moment when Bolt conjured his magic was, in an eerie way, so reminiscent of what promised to be Johnson's undying legacy to the history of his sport. There was the same stunned silence when Bolt crossed the line, his opponents destroyed and his celebrations before the finish line endangering an otherwise certain world record, and the same instant swivelling of heads to see the flashing announcement of the time. Bolt, like Johnson, had indeed lowered the record. Johnson ran 9.79sec in 1988, Bolton, 9.69 in 2008.
What, then, is the difference of one-tenth of a second spread over 20 years? It is the difference between night and day, life and death, and here the celebration of what Bolt achieved and how he carried these Olympics on to another dimension – one beyond even the serial acquisition of gold medals by the great swimmer Phelps – is still fraught by the fear that in the coming months and years the promise of a new era of athletics, freed from the curse of drug abuse, will be shattered by some evidence that he is not as clean an athlete as the world of athletics wants so desperately to believe.
That it is so is now fundamental to the health of Bolt's sport ... and also to a large degree the unique status so many are anxious to bestow on these Olympics that close in the beautifully designed stadium tomorrow night.
Bolt didn't make these Games, the Chinese did that, but he did carry them to the stars, and any subsequent crash would be so devastating that many here who believe so fervently in the Olympics and their most riveting event can scarcely bear to speak of their concern.
In the meantime, they can talk more freely of their pride in the ferocity of the competition here and, if they happen to be British, of how their sportsmen and women chose with such perfect timing to assert that London, in four years' time, must be a place fit for heroes and heroines.
For the Chinese, such a boast is enshrined at the top of the medals table which they have won, as expected, under the force of a commitment the world of sport has never seen before.
Some may worry about the manufacture of such epic sports success. They may say that the spirit of the Olympics is about the dreams of individual young men and women and not the best hopes of the makers of propaganda and they are right. But then remaking the world was not in the remit of the Saviour Olympics.
It was enough, surely, that they provided sport, everybody's sport, with the most fabulous stage it has ever known. The result, after all the perilous years and the dangerous places, is that the Olympics have never in living memory been so filled with life.