WHEN Donald Trump, then America’s president-elect, said on December 11th that "I don’t know why we have to be bound by a one-China policy" he ripped aside one of the oldest sticking-plasters in the world of diplomacy. That he stuck it back on again two months later, telling Xi Jinping, China’s president, that he would honour the one-China policy "at President Xi’s request", does not alter the fact that an American leader had questioned a basic feature of Asian security. Nor does Mr Trump’s reversal solve problems with the one-China formula, on which peace between Taiwan and China has depended, that were evident well before his election. If they worsen, the two sides’ frozen conflict could heat up.

The one-China formula is not so much fraught with ambiguities as composed of them. China itself does not actually have a one-China policy. It has what it calls a one-China principle, which is that there is only one China, with its government in Beijing. It regards Taiwan as a renegade Chinese province and refuses diplomatic recognition to any country that recognises Taiwan as a state. Yet this rigid principle can be bent. In 2015 President Xi met the island’s then-president, Ma Ying-jeou, for what would have looked to innocent eyes very much like a bilateral summit of heads of state. And China looks the other way, albeit with some fulmination, when America sells arms to Taiwan—a traffic which, in 1982, America said it would phase out, but continues to this day.

America does not accept the one-China principle. Instead it has the one-China policy, which acknowledges that China has such a principle—not quite the same thing. America does not recognise Chinese sovereignty over Taiwan, nor does it recognise Taiwan as an independent state. It does plenty of trade with it, though. Small as it is, Taiwan is the ninth-largest buyer of American exports, outstripping Italy and India. America’s unofficial ties with the island are closer than many countries’ diplomatic links. The American Institute in Taiwan, a private not-for-profit institution with headquarters in Washington, DC, looks like an embassy and acts like one, too. The Taiwan Relations Act of 1979 commits America to helping Taiwan defend itself against invasion and embargoes, deeming any coercion of the island to be "of grave concern to the United States".

In Taiwan itself the one-China formula has an even stranger history. It is rooted in the fiction that the island’s first president, Chiang Kai-shek, who fled there in 1949 after losing a civil war to Mao Zedong’s communists, would one day recapture the whole of China. Hence Taiwan’s official name, the Republic of China. Thus the party that Chiang led, the Kuomintang (KMT), and the Chinese government can both subscribe to an agreement called the "1992 consensus", which says that there is only one China but recognises that the two sides disagree about what that means in practice, thus piling fudge upon ambiguity. Taiwan’s other major political party, the Democratic Progressive Party (DPP), rejects both the 1992 consensus and the one-China principle more generally. But its leader, Tsai Ing-wen, who succeeded the KMT’s Mr Ma as president last year, prefers not to do so openly.

In most areas of politics this surfeit of uncertainty would be worrying. Yet the agreement not to look too closely at the contradiction of "one China" has kept an uneasy peace across the Taiwan Strait. There have been political crises—most recently in the mid 2000s—and in 1996 China fired missiles towards the island while Chinese leaders scowled for the cameras. But by and large it has worked well enough for all three sides to want to maintain it.

Their reasons differ, just as their reading of the formula does. China believes that time is on its side. As the motherland becomes ever wealthier and more powerful, its leaders seem genuinely to hope that Taiwan’s people will want to rejoin it. Taiwan’s leaders think the opposite; that with time the island’s people will see themselves as having less and less in common with the mainland. Since the 1992 consensus, the proportion of people on the island who identify themselves simply as Taiwanese has more than tripled to almost 60%; the share of those who call themselves Chinese has plunged to just 3% (see chart). Among people between 20 and 30, 85% say they are Taiwanese. In America the attitude is a simpler ain’t-broke-don’t-fix-it one. The status quo enables the country to have diplomatic ties with China without breaking off links with Taiwan, and that is good enough.

But this equilibrium of incommensurable interests depends on certain conditions being right: that China continues to get richer, confirming its leaders’ optimism; that people on each side of the strait do not come to see each other as enemies; that Asia remains more or less stable, so the sides do not get caught up in other conflicts; and that, if the worst comes to the worst, America’s armed forces will step in to keep the peace.

All these conditions are now changing. China’s economy has been slowing. And Asia is no longer so stable. Mr Trump has threatened to impose tariffs on Chinese exports, risking a trade war. Chinese territorial claims over various islands are heightening tensions: America’s secretary of state, Rex Tillerson, told the Senate that America must be able to limit Chinese access to disputed islands in the South China Sea. Mr Trump confirmed to Shinzo Abe, Japan’s prime minister, that their two countries’ defence treaty covers the Senkaku islands, which China calls the Diaoyu.

And while Mr Trump and Mr Abe were meeting, North Korea conducted its first post-Trump missile test. A month before, North Korea’s leader, Kim Jong Un, had claimed his country would soon test its first intercontinental ballistic missile, which could hit the American mainland, though that was not what was tested. In response to Mr Kim’s threats America is fielding a missile-defence system in South Korea—to which China vociferously objects.

Taiwan might seem like the eye of the storm. Yet China still holds a threat of invasion, or blockade, over the island, and it sometimes shows signs of wanting to bring things towards a head. In 2013 Mr Xi sent a tremor across the strait when he told Vincent Siew, Taiwan’s vice-president, that their conflict "cannot be passed on from generation to generation". It sounded as if the president’s patience was starting to wear thin. On March 6th the head of the Taiwan Relations Office, a government department, said to the National People’s Congress (NPC), China’s rubber-stamp parliament, that "I have to emphasise that Taiwan’s independence...will lead nowhere. I hope the Taiwan government will think about this sentence carefully." All this is in the context of a military balance that has been shifted by a decade of double-digit increases in Chinese spending. Ten years ago Pentagon planners dismissed the idea of an invasion as "the million-man swim". You don’t hear such nonchalance much these days.

Strait and narrow

America might no longer be able to dispatch two aircraft-carrier groups to the Taiwan Strait to force China to back down, as it did in 1996. But if hostilities were to break out America would almost surely be drawn in. The Taiwan Relations Act does not fully oblige it to, but to refrain would be a mortal blow to its position and prestige as a superpower. There would also be economic considerations: Taiwan makes more than a fifth of the world’s semiconductors; a Chinese blockade could cripple the computer industry.

Against such a backdrop, the election of Ms Tsai of the independence-minded DPP was always likely to ratchet up tension. Soon after her inauguration last May the government in Beijing cut off communications between China’s Taiwan Affairs Office and Taiwan’s Mainland Affairs Council, increasing the chances of misunderstanding and miscalculation.

On November 25th China flew a pair of Xi’an H-6K bombers round the island, along with some escorts. Two weeks later another Xi’an bomber and three fighter jets again circled Taiwan. Then in January China’s aircraft-carrier, the Liaoning, sailed round the southern tip of Taiwan and into the Taiwan Strait. "It shows they mean business," says Andrew Yang, a former Taiwanese deputy defence minister.

Chinese pressure on Taiwan could increase further. The five-yearly Communist Party congress is due near the end of this year and Mr Xi may be tempted to burnish his hawkish credentials by holding several sabre-rattling military exercises in the run up. He could deplete Taiwan’s tally of 21 diplomatic partners. There have also been reports that China is considering amending its "anti-secession" law. At the moment it says that China would consider taking "non-peaceful methods to defend the nation’s sovereignty" only if Taiwan formally declared independence or if there is no hope of a peaceful resolution. On February 7th Yomiuri Shimbun, a Japanese newspaper, reported that China is thinking about amending this to say it could invade if Taiwan’s leader refuses to endorse the 1992 consensus—a refusal to which the DPP has so far stuck. During the NPC, a Chinese admiral, Yin Zhuo, said China should use the anti-secession law to make it clear to Taiwan that "independence means war."

Relations between China and Taiwan have been through fraught times before, though, without breaking down completely. And there are three reasons for thinking that, in the short term at least, things will not go horribly wrong this time.

Both Mr Xi and Ms Tsai have strong domestic reasons for setting aside their differences for a while. Mr Xi is consumed by the party congress, and though he may want to make himself appear tough with a few bellicose gestures he does not want a distracting crisis. As for Ms Tsai, she knows that her chances of re-election in 2020 depend on her handling of the economy, not on her handling of China. Taiwanese GDP growth and wages are flat. Her opinion-poll ratings are dismal. She is about to launch a politically risky reform of the bankrupt state-run pensions system. The last thing she wants is a fight with a superpower.

A second reason for guarded optimism is that Ms Tsai has taken the DPP further towards China’s position than ever before. At her inauguration she said that she recognised the "historical fact" of the 1992 negotiations, which is as near as she can get to accepting the consensus without actually doing so. In a speech in October she reassured the communist government that she "will, of course, not revert to the old path of confrontation". Ms Tsai is a trade lawyer, cautious, predictable and restrained—everything her risk-taking DPP predecessor, Chen Shui-bian, the president from 2000 to 2008, was not. China’s condescension towards her—the Taiwan Affairs Office called her inaugural address "an incomplete examination answer" as if she were a stupid schoolgirl—has been mild compared with the invective levelled against previous DPP leaders, whom they have called "insane", "evil" and "scum". That may mean Mr Xi wants to keep open the door for future negotiations.

Third, the military balance in the Taiwan Strait has not swung far enough for China’s high command to be confident of swift victory. If the country could sweep into Taiwan so fast the world did not have time to react (as when Russia invaded Crimea) other countries might conceivably treat an invasion as a fait accompli. But Taiwan is no Crimea. Only 10% of the population wants unification and less than 2% wants it as soon as possible. The island has a vibrant civil society capable of putting millions of protesters onto the streets against a Taiwanese government, let alone a Chinese occupying force.

The mainland has around 1,400 land-based missiles aimed at Taiwan, plus an unknown number of air- and sea-launched ones. Despite the presence of anti-missile defences—both American Patriot missiles and Taiwan’s own systems—the island’s air bases and many of its other defences might be quickly destroyed by all that firepower. But an invasion requires troops on the ground—ground which, in this case, lies the other side of 180km of open water. And Taiwan’s surviving forces could make that voyage very unpleasant. Mr Yang says that, for an invasion to succeed, China would need promptly to destroy 85% or more of Taiwan’s own missiles; if half of Taiwan’s missiles survived the first wave of attacks, China’s invasion force would be vulnerable.

Ex uno, plures

If the invasion could be slowed down, other countries would have time to react. At that point, any Chinese leader would have to decide whether to stop the invasion or risk a wider conflict. He would surely push on for fear of what might happen at home if he backed down. But he would just as surely prefer to avoid such a choice altogether. And that is where Taiwan’s real deterrence lies: it does not need to be able to turn back an invasion; it only needs to be able to buy enough time to force on China the choice between a coup at home and a regional war abroad.

Without the assurance of a quick victory, cleaving to the familiar ambiguities of "one China" will make the most sense to China’s leader. But those ambiguities will become ever more difficult to maintain. Mr Trump may yet return to his doubts about American support for the policy; it would hardly be the first time he has changed his mind. And popular attitudes across the strait are hardening. It is not just that islanders increasingly see themselves as Taiwanese; mainlanders, who used to regard the Taiwanese as brothers, have started taking a chillier attitude. They still see the islanders as part of the same culture, but they are now imposing loyalty tests, demanding (for example) a boycott of Taiwanese entertainers who last year did not condemn an international tribunal’s ruling against Chinese claims in the South China Sea. The Communist Youth League, long a training ground for ruling party officials, waged a social-media campaign against one well-known Taiwanese performer in China, Leon Dai, and got him blacklisted.

Chinese officials are encouraging suspicion. The number of Chinese tourists to Taiwan has fallen by more than a third in the past year, largely because bureaucrats have made it harder to travel. Chinese universities have also asked Shih Hsin University, in Taiwan, not to discuss "sensitive political subjects" (such as the one-China principle) with exchange students from the mainland. A senior KMT official fears the days of pro-Taiwan sentiment on the mainland may be over.

Political attitudes are hardening, too. Taiwan used to have a one-China party, the KMT, and a party that preferred independence, the DPP. But the KMT is in free fall after its defeat in last year’s election. The fastest rising force is the New Power Party, which has its roots in student demonstrations against close ties with China; it is at least as anti-one-China as the DPP. Mr Xi’s crackdown on dissent and civil society is leading the political system ever further from Taiwan’s vibrant democracy. The Beijing government’s interference in Hong Kong’s local politics is taken to show that "one country, two systems", a formula devised for Hong Kong and once offered to Taiwan, is a fraud.

In the face of these realities, both sides want the option of continuing to say that the one-China framework holds, and looking for fresh obfuscations to that end—new helpings of fudge to put on top of that served up in the 1992 consensus. In 2011 Wang Yi, now China’s foreign minister, then head of the Taiwan Affairs Office, said privately during a visit to Washington that China might consider replacing the 1992 formula, and there have been some signs that this could still be on the cards. Every two weeks Taiwanese officials meet to sift through new forms of words. A new formula might conceivably provide the basis of future talks.

The simple and natural solution is to admit there are two Chinas. But the communist government is not ready to do that. Instead, it is forcing the Taiwanese and Americans to deal with the fraying ambiguities of a one-China policy, as all three move slowly towards a new, more dangerous endgame.