On the face of it, North Korea doesn’t have a huge amount of skin in the game in Syria. Yet Pyongyang’s condemnation of the US air strike as “an intolerable act of aggression against a sovereign state” is more than the usual bluster from this end of the “axis of evil”. The bombing of one of Bashar al-Assad’s airfields must have sent premonitions through the minds of Kim Jong-un and his generals: they could be next. The deployment of significant American naval assets to the South China Sea must also represent evidence to the North Korean leadership that Donald Trump wants to send a message to all of his nation’s enemies in the world: don’t mess with America.

The Obama strategy of “strategic patience” is over. Secretary of State Rex Tillerson explicitly said so a few weeks ago. Perhaps always a euphemism for a policy of bemused inaction, it certainly has not succeeded in curbing North Korea’s single-minded determination to acquire intercontinental ballistic missiles with nuclear warheads. One of the wackiest and poorest states on the planet it may be, but North Korea wishes to be feared like any superpower. Or rather the latest representative of the Kim dynasty and his cronies wish to insure themselves against the fate that befell Saddam Hussein, Muammar Gaddafi and others who failed to maintain an adequate arsenal of weapons of mass destruction. That is the deeply logical reasoning of Mr Kim; he is not mad, but he is ruthless and paranoid.

Having seen “beautiful babies” gassed to death in a Syrian village, Mr Trump will not have beautiful American kids incinerated by a nuke from North Korea that can cross the Pacific to San Francisco. President Obama himself warned his successor that Mr Kim could do just that by the end of Mr Trump’s first term in office. It is a galling and terrifying prospect. The President has said it is not going to happen. He is right to do so.

Does that mean he will bomb North Korea? The more the North Koreans believe he might, the more circumspect they ought to be. After all, if America can wipe out the leadership of the so-called Democratic People’s Republic of Korea at a stroke, then Mr Kim will think twice before he lobs another missile towards South Korea or Japan. He might stall his programme: it would be analogous to the successful “caging” of Saddam before the disastrous invasion of 2003. It also has distant echoes of the US-USSR stand-offs over Berlin in 1949, Cuba in 1962, Afghanistan in 1980 and indeed Korea itself during the war there half a century past. It means permanent instability in the region, but it is the inevitable outcome under conditions of mutually assured destruction, in this case between North Korea on one side and South Korea, Japan, the US and allies on the other.

North Korea says it is ready for war with the US

If in addition China has offered tacit support to the White House in an attempt to calm its troublesome neighbour, then America’s show of force will be still more effective. The assassination of Mr Kim’s half-brother at Kuala Lumpur airport earlier this year was further proof that China has little control over Pyongyang. Kim Jong-nam was a harmless playboy living under supervision and protection in the gambling paradise of Macau – but to Kim Jong-un and maybe China too he was a dynastic threat.

China still doesn’t want a unified Korea allied to America on its doorstep and fears the huge dislocation and flood of refugees a war or collapse of the DPRK would bring. However, the problem of Korea will have received intensive scrutiny at the Florida summit between Presidents Xi and Trump. Through such American brinkmanship and “backdoor” political pressure from China, Kim Jong-un can perhaps be persuaded that his best chance of survival is to wind his neck in a little.