Most commentators are assuming that George Bushs presidency will be assessed on the success of his Middle East strategy. But the judgement of history could be harsher on an entirely different front. The outcome remains very much in the balance, but it is possible that during these two terms, the US may be viewed as having "lost" Asia, just as the regions gross domestic product started to soar from 24 per cent of the world total in 2003 to an estimated 40 per cent by 2030.
It risks losing it, of course, to the proudly resurgent Middle Kingdom, to China. It is a sign of truly awesome power when a person, a corporation or a country can define the terms in which the rest of the world describes them. Thus the rest of Asia acknowledges what China's own new leaders describe as the country's "peaceful rise".
China has modelled this rise on that of the US in the past century: one rooted firmly in economic power.
The children of China's top cadres have been sent to leading American universities, most often to business schools, to reinforce Beijing's capacity to transform the country, step by step, into a dynamic China Inc.
China's stunning success at the Athens Olympics, its consumption of a quarter of the world's copper, aluminium, zinc and steel, its graduation of 325,000 software engineers a year - three times India's total - point to how far China has advanced down the track in this great project.
For the first half of the 20th century, China was crippled by fratricide and invasions. For most of the second half, it was a communist curiosity. The turn of the latest millennium, though, has seen the rebirth of the People's Republic as the centre of the new Asia, chiefly through exercising "soft power", boxing its full economic weight in a way that Japan has never achieved.
But China still needs to guard against prematurely over-reaching itself and sparking a regional reaction.
The continuing post-Cold War US presence in Asia remains widely accepted, including by China itself, as a steadying influence.
However, since the September 11 terrorist attacks, Washington has become inevitably distracted by the war on terrorism, which has its epicentre in the Middle East.
This savage yet unpredictable war has of course visited terrible damage in Bali, in the Philippines, in southern Thailand and elsewhere in South-east Asia, but has only lightly touched north Asia. Australia, rather than the US, has taken on the leading role in the Western alliance's involvement in combating terrorism in South-east Asia.
In solidarity with Washington, China has enlisted for the war - for Beijing has long been anxious about the capacity of its Muslim extremists to wreak havoc.
At the same time it has seized with both hands the opportunity to ease its way into an ever bigger role in the region.
Prime Minister Wen Jiabao has described China as "a friendly elephant" - one which backs the status quo instead of destabilising it as it mostly did under Mao. He says the country should "bring about lasting peace and stability in Asia through the establishment of a new international political and economic order that is fair and rational".
China won new, widespread respect during the Asian economic crisis of 1997-98, when thanks to massive accumulated US dollar reserves and sustained growth, it kept the yuan pegged to the US dollar and thus withstood the pressures that undermined most other regional currencies.
Since then, it has become the biggest or second-biggest trading partner of virtually every Asian country, with big deficits with most. In 2004, China bought 40 to 50 per cent of Asia's exports, accounting for all of Taiwan's and the Philippines' export growth and more than 50 per cent of each of Japan's, Malaysia's, South Korea's and Australia's.
Beijing is beginning to leverage off this massive business enmeshment into assertive cultural, diplomatic and strategic power, too.
Vice-Foreign Minister Wang Yi says that regional economic co-operation "will serve as a helpful trial for China's new concept of comprehensive, common and co-operative security". The Communist Party newspaper People's Daily goes further, saying: "The first 20 years of this century is an important period of strategic opportunity for China."
China is intent on obtaining international applause, which in turn feeds the nationalism that has replaced communism as the ruling party's driving force.
China's impressive performance at the Athens Games and its staging of the next Olympics in Beijing and the 2010 World Expo in Shanghai are valuable contributions to this mission. China Central TV International's slick English language satellite broadcasts, which began only four years ago, are already becoming as ubiquitous in the Asia-Pacific region as CNN and are rebroadcast by public TV networks in countries as distant as Samoa, as their major international news resource.
China's culture has a unique reach in the region, through the vast network of overseas Chinese, influential in virtually every capital and beyond. Eric Teo Chu Cheow, secretary of Singapore's Institute of International Affairs, says Chinese cuisine, calligraphy, cinema, art, acupuncture, herbal medicine and fashion fads "are all emerging in regional cultures" among young people, especially in South-east Asia.
In more formal terms, China's first big regional initiative was to form the Shanghai Co-operation Organisation, which also comprises Kazakhstan, Kyrgyzstan, Russia, Tajikistan and Uzbekistan. It is intended to meet two strategic aims for Beijing: to share the suppression of Muslim extremists blamed for problems in the vast north-western autonomous region of Xinjiang and to facilitate energy supplies, chiefly gas, from Central Asia.
The bigger-picture goal is slowly emerging. It is nothing less than to replace slowly and almost imperceptibly and with characteristic patience the Association of South-East Asian Nations as the main gatekeeper through which the East Asian region works together and is approached by outsiders.
The bombing of the Australian embassy in Jakarta in September reinforced a common business perception: China equals opportunity; South-east Asia equals problem.
China is already the economic hub of the region. It, together with an economically resilient Japan and South Korea, form the centre of gravity of successful East Asia today, rather than the disparate states of South-east Asia, despite the success of Thailand, Singapore and Malaysia. Beijing is making this process as palatable as possible. It is not only buying much of South-east Asia's exports, but also starting to invest heavily there. It is continuing to back regimes such as Burma's, regarded elsewhere as pariahs, and it is giving Asean's 10 members "early harvest" - easier access - to its markets, six years before the free-trade agreement between the two is set to start.
The US is continuing to buy massively from East Asia but increasingly via China, with Wal-Mart alone purchasing 1 per cent of China's gross domestic product. In return, Asian countries own more than $US1 trillion ($1.34 trillion) of US debt.
This Chinese rise has been sparked more by opportunism than by strong antipathy to a continuing American presence in the region. The South Koreans have objected to US plans to pull out a third of its 37,000 troops there. But while the government wants them to stay, Washington's resolution in removing them evokes the underlying sense of American withdrawal.
Beijing views America, the Japanese ally, as a restraining hand on Japan which China still, at heart, distrusts. And it sees America, which is Pyongyang's potential nemesis, as helping sustain pressure on maverick North Korea, which is more a nuisance than an ally to Beijing today, certainly compared with economically vibrant South Korea.
Nick Platt, the president emeritus of the Asia Society, a former US ambassador and executive secretary of the State Department, says: "The focus in the US is almost entirely on Iraq and the Middle East. The Chinese are perfectly happy to take advantage of whatever antipathies arise in the region vis-a-vis the US to set themselves up in the same sort of position as America. Within the region, people are saying yes there are challenges with China, but no we can't compete, and our economies are benefiting anyway from the peaceful rise."
The Congressional US-China Economic and Security Review Commission stated in late 2004: "While China has undertaken a diplomatic offensive in Asia to reassure its neighbours of its long-term peaceful intentions, buying time and space in the process to pursue its economic development and military strengthening, countries in the region appear to perceive the US as losing focus on Asia as it prosecutes the war on terrorism."
Leading US business analyst David Hale says: "It is too soon to speak of a new era of Chinese imperialism in the Third World, but China will certainly play a more influential role in the affairs of many developing countries. The US has been so obsessed with the issue of trade that it has not developed any long-term strategy for managing the consequences of China's new role . . . which will force everyone to rethink their assumptions about foreign policy, military policy and even monetary policy during the early decades of the 21st century."
Within Washington, the Bush administration began by describing China as a "strategic competitor" and offering to do "whatever it takes" to defend Taiwan. But after 9/11, and in the wake of massive corporate lobbying, that phase soon passed. Since then, an Iraq-obsessed White House has left the State Department's Asian professionals to run East Asian relations along predictable and professional lines. It is they who have helped foster Beijing's leadership of the six nations seeking to resolve the North Korean nuclear stand-off.
But this surge of Chinese pride has also led to tensions. When Japan won the soccer Asia Cup in Beijing last August 7, Chinese fans burned Japanese flags, shouted obscenities and sang patriotic songs outside the stadium. Japan is constantly reminded by Chinese leaders and academics of its cruel invasion of China in the 1930s.
A history war has blown up with South Korea over claims by Chinese scholars that the ancient north-east Asian kingdom of Koguryo whose name ultimately became Korea was really Chinese and not Korean at all. Some of China's neighbours are raising eyebrows about the "peaceful rise" in the context of more recent history, too.
Since Mao Zedong installed the communist dynasty in 1949, China has engaged in territorial conflict with India and Vietnam, and has sparred with a number of South-east Asian countries over the contested oil-rich Spratly Islands and with Japan over the Diaoyu Islands.
Beijing's difficulties with fractious parts of Greater China - Taiwan and Hong Kong - demonstrate the dangers of overconfidence and of attempting to run a fluid modern market economy with a static, centralised political structure.
Taiwan is viewed by Beijing as a particularly grievous thorn in its flesh, a reminder that its rise remains partial.
Paradoxically, Taiwan is by far the biggest investor in China the figure often used within Taiwan is $US 100 billion - supported by vital managerial and technical commitment.
It suits Beijing to have a nationalist target of easy resort to distract jobless workers or other potential troublemakers at home, as well as using Taiwan as a handy wedge to lever cracks in Western alliances.
Some of the same headaches are manifest over Hong Kong, where half a million middle-class marchers have started a tradition over the past two years of marking July 1 (the anniversary of the return of the city to Chinese sovereignty) with a demonstration for greater democracy.
Back home, the Communist Party's move to incorporate "capitalists" into the party ranks, and to install party representatives inside private companies, underlines the political conservatism of the regime, seeking to contain the most vibrant sector of society within the party.
Paul Monk, a leading Australian strategic analyst, says that one of the crucial tests for the sustainability of China's drive towards regional dominance will be its capacity to take further steps beyond its old imperial and communist ideological constraints "away from the haunted house of its past". He refers to the recent epic film, Emperor and the Assassin, in which Ying Zheng, who created a single China, is constantly reminded by automaton-like servants: "King , have you forgotten the command of your Qin ancestors, to unite all under heaven?"
Insofar as factional disagreements continue inside Beijing's leadership compound at Zhongnanhai, next to the Forbidden City, these are side-plays. There is unity on the essentials. China is ever more dependent on global supply chains, especially of energy. It is now a strong member of all the major international organisations. It is enmeshed in international trade as the key driver of new jobs, replacing the disintegrating state enterprises and inefficient farms.
Vitally for the region whose prosperity it is helping drive, China is risk averse. It craves stability. Its mission statement is: get rich and stay that way. And with the US buying as much as China can make and craving China's loans to feed its vast deficit, it is doing more than any other nation to help it get there.
Rowan Callick is Asia-Pacific editor of The Australian Financial Review