“Hey, what are you guys doing this Saturday?” crew members of the US guided missile destroyer USS Lassen asked over the radio as it ploughed through the South China Sea last autumn. “We got pizza and wings. What are you guys eating?”

The questions were directed at the Chinese ship shadowing the Lassen as it moved into the 12 nautical miles of territorial waters claimed by Beijing off its newly constructed base on Subi Reef, a speck of land in the Spratly Islands. China has built a radar-

equipped weather station and stationed 200 troops there but its claim is disputed by several east Asian countries – and by the United States. The Lassen’s course was deliberately plotted to affirm the right to “freedom of navigation” in what Washington regards as an international maritime area through which any ship should be at liberty to sail.

After a short delay, the Chinese sailors responded to the questions from their US counterparts, talking about their home cities, their families and the ports they had visited. Then the two ships parted course.

The friendly conversation obscured a chilling fact: that these were crews of ships from two nations which, in some scenarios, are heading for an earth-shaking confrontation as they play out the “Thucydides Trap”, in which rising and status quo powers are bound to come into conflict along the lines of Athens and Sparta, as recorded by the ancient Greek historian. In this case, the protagonists are China and the US.

In 2012 Hillary Clinton, the then US secretary of state, said that America and China needed to “write a new answer to the age-old question of what happens when an established power and a rising power meet”. A year later, after a US-China summit aimed at producing understanding between the two powers, the national security adviser Tom Donilon said that the reformulation of the relationship was “rooted in the observation . . . that a rising power and an existing power are in some manner destined for conflict”.

According to Graham Allison, a professor of political science at Harvard, armed hostilities have been the outcome in 12 out of 16 past confrontations of this type in recorded history. These include the long confrontation between the established power of France and the rising challenge of Britain in the early 18th century, as well as the wars between Germany and Russia, France and Britain between 1914 and 1945.

The immediate theatre for the showdown is the huge expanse of the East and South China Seas. China’s increasingly expansionist drive to assert sovereignty there has led to confrontations over the past five years with Japan, Vietnam and the Philippines, which regard waters and islands claimed by Beijing as their own. Early this month, China said it had sent four warships with helicopters, one supply ship and special forces troops to carry out an exercise in the South China Sea.

The US is deeply involved because of its security treaties with Japan and the Philippines, its restored relations with Vietnam and its role as the main military power in east Asia since 1945 – the US 7th Fleet, based in Japan, has between 60 and 70 ships, 300 aircraft and 40,000 navy and marine corps personnel. The Americans also have nearly 30,000 troops permanently stationed in South Korea and an implicit undertaking to defend Taiwan if China were to threaten the island separated from the mainland since the Communist victory of 1949.

Admiral Harry B Harris, the US commander in the Pacific, has said that China “is clearly militarising the South China Sea . . . You’d have to believe in a flat Earth to think otherwise,” and he insisted this spring that his fleet will increase operations to assert freedom of navigation in the same sea. Summit talks between Presidents Barack Obama and Xi Jinping in late March and early April produced no agreement on the issue. A US aircraft carrier was subsequently refused entry to Hong Kong Harbour for a port visit on 15 April. The US then sent aircraft to fly by a disputed shoal off the Philippines where China appears to be on the verge of launching a new stage in its campaign of reclaiming reefs and islands that could act as a base in any open conflict.

Washington and Asian nations are also concerned about North Korea, whose nuclear policies have exposed Beijing’s inability to control its “little brother”. Although the Chinese government announced on 5 April that it was restricting some exports to its neighbour, it hesitates to cut off supplies of food and energy completely, for fear of causing instability across the border that might lead to reunification under the leadership of South Korea. All this makes the nations of the region look to the US as the guardian of their security, even as they seek to make the most of the economic relationship with China.

Other powers, including Australia, are concerned because of the importance they place on freedom of navigation, while China’s forceful defence of its fishing fleets has brought conflict this spring with Indonesia and possibly, in a murky episode at the end of March, also with Malaysia.

This is a huge region that is vital for the world’s economic health. Its manufacturing and trade have acted as drivers of growth since the emergence of Japan and the four “Tigers” – Hong Kong, Singapore, South Korea and Taiwan – in the 1960s. With China having vaulted to second place among the world economies and Japan still in third place, east Asia as a whole accounts for a quarter of the world’s GDP.

The matters of sovereignty in dispute are trivial in themselves, involving strings of small, often uninhabited islands and reefs. The claims that China has been pressing are based on old maps or tales of allegiance dating back to a misty historical past. Yet this does not make them any less significant, with implications that play into concerns about confrontation involving not just China and the US, but the entire region. News in February that China appeared to have deployed two batteries of eight surface-to-air missile launchers on one of the disputed islands added a new edge to fears that the build-up of forces and the lack of a diplomatic solution could boil over into open conflict.

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Nationalism is on the rise in east Asia and national interests are becoming more deeply entren­ched. Amid a regional arms race, most countries are increasing their military spending. China’s military budget has been rising by 10 per cent a year as it builds up its “blue water” navy (capable of operating outside coastal waters in the wider Pacific), constructs a second aircraft carrier and develops its submarine and missile forces. Since 2000, it has added 41 new submarines to its navy and, at a big military parade in Beijing in September, the official commentary on the arms on show in Tiananmen Square boasted of missiles that the Chinese said could sink an aircraft carrier at the base the United States maintains on Guam, across the Pacific.

In Tokyo, Shinzo Abe’s government is pushing through changes to Japan’s pacifist postwar constitution to enable it to play a bigger military role in the region. Vietnam has acquired six submarines from Russia, which are due to be fully operational by 2017. Indonesia has ordered ten fighter jets from Russia, according to media reports in Jakarta. Military expenditure across the nations of south-east Asia (with the exception of Burma, Brunei, Cambodia and Laos) has risen rapidly from $14.4bn in 2004 and will reach an estimated $40bn this year, according to the Stockholm International Peace Research Institute.

The forceful way in which China has advanced its maritime claims under the banner of the “China Dream” of national rejuvenation championed by its no-nonsense leader, Xi Jinping, has provoked responses from its neighbours, for all that they value their commercial relationships with the world’s second-largest economy.

Vietnam has put its forces on the border with China on high alert. The Philippines has been stirred to take an unusually martial attitude in response to Chinese claims in the South China Sea, acquiring additional ships and filing a suit against Chinese expansion there with the United Nations arbitration tribunal at The Hague. China has refused to recognise the suit or the tribunal’s competence, and said this month that its position was backed by three regional states – Brunei, Cambodia and Laos – and by Russia. But the UN ruled itself competent to deal with the case at the end of last year and a verdict is expected by early June. A judgment in favour of Manila would test Beijing’s readiness to abide by international rules or whether, in the words of Daniel Russel, the US assistant secretary of state for east Asian and Pacific affairs, China is “prepared to be seen as an outlier that flouts international law”.

At the same time, historic animosities are being revived. Though each country is ruled by a communist party, China’s not very successful invasion of Vietnam in 1979 is not forgotten in its southern neighbour. Anti-Chinese riots broke out across Vietnam in 2014 after China deployed an oil exploration rig in waters claimed by both countries and after state TV broadcast video footage showing a Vietnamese fishing boat being rammed by a Chinese vessel and sinking.

The acute antagonism between China and Japan dates back to the humiliation of the Qing dynasty by the rising power in their war of 1894-95. It was then hugely increased by the ruthless occupation of much of the mainland by Japanese troops after they launched a full-scale war in 1937, epitomised by the Rape of Nanjing, in which up to 200,000 people died. The way in which some Japanese politicians honour their country’s dead at the Yasukuni Shrine in Tokyo, which memorialises over 1,000 convicted war criminals, is a cause of constant complaint by Beijing. The “Patriotic Education Campaign”, conducted in China since the 1990s, presents Japan as the main villain, one that plays a leading role in China’s narrative of its “Century of Humiliation” before the Communists won power in 1949.

The current confrontation between China and Japan, which comes amid falling Japanese exports to the mainland and reviews of investment plans, followed Tokyo’s nationalisation in 2012 of eight uninhabited islands and outcrops in the sea that were previously under private ownership. That set off anti-Japan demonstrations in a dozen Chinese cities. Japanese shops and cars were smashed and Japanese flags torn up. Beijing then pushed its claim that the islands, known to the Japanese as the Senkakus and to the Chinese as the Diaoyus, were Chinese because imperial voyagers landed there in the 14th century. They lie south-west of Japan’s southernmost prefecture, Okinawa, east of China’s mainland and off the north-western coast of Taiwan, near strategic shipping lanes and rich fishing grounds, as well as possible oil and gas reserves. Japan insists it owns the islands and there is nothing to discuss, accusing Beijing of a “forceful, coercive attempt to change the status quo”.

Foreign ministry officials in Tokyo have noted an escalation of China’s maritime and aerial probing around the islands this year. “The situation in the East China Sea is getting worse,” an official told the Financial Times in January. An armed Chinese naval vessel sailed into waters around the islands for the first time last December, and an intelligence-gathering ship was seen in the area at the same time. The rare meetings between Abe and Xi have been awkward, and there has been no word of the installation of a promised hotline to deal with accidental clashes. Last year China commissioned four new gas platforms close to the median line with Japan in the East China Sea and sent research vessels on 22 missions there, according to the Japanese foreign ministry.

Moves by the Abe government to loosen constraints on Japan’s military imposed after defeat in 1945 arouse concern in China, where Communist Party newspapers warn of a “nightmare scenario” if the constitutional restrictions on military activity are relaxed. Beijing accuses Tokyo of going “against the tides of history”. In Japan, a survey by the Pew Research Centre found that China was the second-biggest cause of fear among the population, after terrorism. Abe has bolstered security ties with Vietnam and signed a security pact with the Philippines, following this up with a joint naval exercise. In response to Tokyo’s move, the Chinese foreign minister, Wang Yi, mused to reporters: “I wonder what Japan has to do with the South China Sea.” Last month, Prime Minister Abe joined the US to accuse China of militarising the South China Sea.

Besides jostling with China for regional influence, both by expanding investment in south-east Asia and by trying to build bridges with South Korea to counter Beijing’s charm offensive there, Japan feels a very direct interest in freedom of navigation, given the volume of its trade and energy supplies that transit through the South China Sea. It is in talks to transfer anti-submarine reconnaissance aircraft and radar technology to the Philippines. The Japanese are not alone in their concerns. In February, worried about its shipping routes, Australia announced a big increase in planned military spending, especially on the navy. Canberra is now weighing whether to send a warship on a freedom-of-navigation exercise similar to that of the USS Lassen.

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The regional dynamics are at their most complex when one heads south. China claims much of the South China Sea using a map dating from 1947, which laid out historical claims in the form of a nine-dash line defining its area of sovereignty. This conflicts with claims by Vietnam, the Philippines, Malaysia, Indonesia, Brunei and Taiwan. Even more so than waters off the Senkaku/Diaoyu Islands, this sea is a vital shipping lane for $5trn in trade annually: one-third of global maritime traffic, carrying oil and raw materials to Asia and Asian consumer goods to the world. It also contains rich fishing grounds and potential energy and mineral reserves beneath the seabed.

China’s intervention has greatly increased the stakes in what had been a set of competing claims among south-east Asian nations. As Singapore’s prime minister, Lee Hsien Loong, put it in March in a Wall Street Journal interview about Chinese expansionism, “When you are the biggest participant in the game, and you do the same as other countries, the consequences are on a different scale.” China has long-standing claims to the Paracel, Spratly and Pratas Islands as well as the Macclesfield Bank and Scarborough Shoal off the Philippines. More recently, it has conducted a programme of building up reefs in the sea, up to 800 kilometres from the mainland, to turn them into small islands. Seven have been finished or are near completion. China claims the rights to territorial waters stretching out 19 kilometres from the “Great Wall of Sand”, built on previously uninhabited reefs and now staffed with Chinese military personnel.

Beijing, which began constructing “fishermen’s shelters” in the South China Sea in the 1990s, says its new bases are for humanitarian purposes, primarily to rescue those who get into trouble, but recent photographs show fighter aircraft deployed on the largest of the artificial islands in the Paracels, which are also claimed by Vietnam and Taiwan. Pentagon sources said evidence from satellite imaging in February showed Chinese HQ-9 surface-to-air missiles, with a range of 125 kilometres or more, on Woody Island in the Paracels; China has said it will not militarise the sea; and though it did not confirm the US report, which was backed up by Taipei, it said any country had the right to take defence measures on its territory. Beijing does not give out such information, but the defence department in Washington has estimated that the construction covers at least 800 hectares. Five of the sites, it said in a report on China’s military power, could be used for surveillance systems, harbours, an airfield and logistic support.

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China aims to establish “facts on the ground” or, in this case, at sea, projecting its regional power in a way that other nations may challenge but that they will not be able to turn back. This is in keeping with the higher profile in foreign affairs adopted by the Xi Jinping administration, which took over in Beijing in 2012-13. The time when China followed Deng Xiaoping’s advice to “hide your brilliance and bide your time” has passed. Xi, China’s most powerful hands-on leader since Mao Zedong, is pushing an agenda of centralised control and international expansion, undeterred by the slowing economy and multiple problems in the form of high debt, deflation, excess industrial capacity, the halting pace of much-needed structural reforms and an environment crisis.

A critical element of Xi’s “dream” is the projection of Chinese influence around the globe – or, as he put it in a speech in 2014, the need for China to pursue “great-power diplomacy with special Chinese characteristics”. This ranges through the grand scheme of the “One Belt, One Road” infrastructure programme through trade for south-east and central Asia and on to the underwriting of nuclear power stations in Britain. Beijing has launched the Asian Infrastructure Investment Bank as an alternative to the Asian Development Bank, winning wide backing (including from the UK) despite US opposition. China has become Vladimir Putin’s best source of support, with big, long-term contracts for Russian gas as well as finance for projects such as a 7,000-kilometre high-speed rail link from Moscow to Beijing.

Though China devotes a smaller proportion of GDP to its military budget than does the US (or the UK), modernisation of the 2.5 million-strong People’s Liberation Army (PLA) is a big part of Xi’s programme. In addition to sitting as general secretary of the Communist Party and state president, Xi chairs the Central Military Commission, which unveiled a streamlining of the PLA command structure this year and is fast developing China’s capabilities in submarines, missiles and cyber-warfare. This spring, he appeared in uniform as commander-in-chief of the armed forces.

In this calculus, the most immediate sphere for China’s power projection has been the one closest to its 14,500-kilometre coastline in the South and East China Seas. But the immediate effect has been to alarm other regional states, which are less than charmed by the thinking, expressed in 2010 by the then foreign minister, Yang Jiechi, that “China is a big country and other countries are small countries, and that’s just a fact”. This has led the smaller nations to seek shelter under the US strategic umbrella. Relations between the Philippines and China have become virtually frozen since a standoff in April-June 2012 that led to China seizing the Scarborough Shoal. Manila bolstered its small navy with purchases from the US and re-emphasised the defence treaty between the two countries, as well as submitting its suit to the UN tribunal.

The US defence secretary, Ashton Carter, has told his counterpart in Manila that Washington’s pledge to defend its ally is “ironclad”. Visiting Tokyo in June, President Benigno Aquino said he was reminded of how, in the late 1930s, “Germany was testing the waters and . . . nobody said stop.” A new defence pact in 2014 permitted deployment of US forces in the Philippines, and the Aquino administration has offered the US eight bases, two of them on an island near the South China Sea. In 2015 more than 100 US navy ships docked in the former US base at Subic Bay, and two nuclear-powered stealth submarines made visits in the first two weeks of this year.

The maritime quarrels spread to Indonesia at the end of March after eight Chinese fishermen were detained by a patrol vessel while trawling off the Natuna Islands, which lie across the southernmost section of the South China Sea claimed by China, over 2,500 kilometres from its southern coast. A Chinese coastguard vessel entered the area to recover the men’s ship. An Indonesian official in charge of maritime security said China’s action had created “a new ball game” that needed close attention from south-east Asian governments, and called Beijing’s claims to sovereignty in the area “fake”. The government in Jakarta then announced that it would deploy more troops to the islands, put in more patrol boats and strengthen its naval base there.

A US-Indonesia “action plan” envisages expanded military co-operation. Indonesia has protested against the way in which the “nine-dash line” appears to cover the Natuna Islands, and says it wants to hold regular naval exercises with the US near the archipelago in waters that the International Energy Agency says hold rich gas reserves. Indonesia and the US have also carried out joint maritime exercises involving surveillance and patrol aircraft.

At the same time, there was confusion about a reported incursion into Malaysian waters by 82 Chinese fishing boats; Malaysia’s national security minister appeared to confirm the reports, and said three ships from the Maritime Enforcement Agency had been sent to investigate. But then the defence minister, Hishammuddin Hussein, said there had been no trespass and “our waters are safe”. The People’s Republic of China has stepped up its investments in Malaysia over the past year and the government in Kuala Lumpur has been keen to maintain warm relations and ensure Chinese purchases of assets that it is selling off to reduce Malaysia’s debt burden.

Vietnam has reacted to China’s expansion by developing a dialogue with a former enemy: US naval ships pay frequent port calls. Carter and his Vietnamese counterpart, Phùng Quang Thanh, signed a “joint vision statement on defence relations” in June last year. The US is supplying Hanoi with coastguard patrol vessels. And Singapore signed an enhanced defence co-operation agreement with the US in December.

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As Xinhua News Agency warned that such developments could push the regional situation “to the brink of war”, the foreign ministry in Beijing questioned whether “military deployment and regional militarisation by the US [was] in line with the aspiration shared by countries in the region”. President Obama points to the region’s strategic importance, but some Chinese officials question what the US is doing there, given that it is not an Asian power. One answer is that, as Lee Kuan Yew of Singapore used to say, the region needs China economically but also needs the US strategically to maintain a balance.

The problem is that neither of the two leading powers has a properly thought-out policy towards the other. China and the US know they need a degree of co-operation but also want to hedge their bets to defend their own positions. There is a mutual lack of trust, complicated by the network of overlapping regional differences in a part of the world that lacks a strategic system to resolve disputes. The Obama administration’s declaration in 2011 of a “Pacific Pivot” to reorientate its foreign and strategic policy towards the Asia-Pacific naturally aroused China’s concern. As well as being hemmed in by the chain of islands running south from the Japan through Taiwan to the Philippines which hems in the Chinese navy, Beijing faces the prospect of the 12-nation Trans-Pacific Partnership (TPP), promoted by Washington to create a free-trade zone whose liberal economic rules would bar China. At least some regional leaders see the pact as essential to what Prime Minister Lee Hsien Loong calls “an overall substantive relationship” between the United States and Asia, because “without the interest in a broad range of mutual co-operation, America is just another country which has some claim or makes some assertion”.

Although the US “pivot” (since renamed a “rebalance”) has not been completely realised and the TPP deal is yet to be approved by national legislatures (among them the US Congress), the fear of containment – allied with the Xi administration’s desire to extend Chinese influence, including its alternative to the TPP – will prompt China to continue to press where it sees opportunities as it seeks to displace the US as the dominant power in east Asia. Washington’s policy towards the region has been hesitant but it seems to be adopting a tougher line. This was shown by the Lassen’s voyage and Obama’s meeting with leaders of the Asean grouping of nations in California in February to develop a cohesive response to China’s expansion in the South China Sea. The final statement from the consensus-seeking organisation of south-east Asian states was as cautious as usual, but it stated the importance of freedom of navigation, which Washington has made its central theme.

To date, the two big players and the associated states have managed to avoid hurtling into conflict, yet none has abandoned its position in the interests of a settlement. The ‘‘Thucydides Trap” may not be inevitable but it will continue to hang over a region of 14 countries that represents an area of critical importance for the prosperity and peace of the globe.

Jonathan Fenby is the author of “Will China Dominate the 21st Century?” (Polity Press) and “The Penguin History of Modern China”