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Donald Trump's rhetoric has clearly had an impact on Kim Jong Un

Mr Trump's insults have had an impact on North Korea's leader, who was moved to condemn the President in a rare on-camera address.

Kim Jong Un described Donal Trump as "deranged"
Image: Kim Jong Un described Donald Trump as 'deranged'
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Donald Trump and Kim Jong Un are locked in a head-scratching, escalating war of words.

It has taken us on a bizarre journey of insults - from "Rocket Man" to the revival of the arcane "dotard".

Mr Kim's unexpected caricature sent the world scrambling for its dictionaries and left diplomatic pulses racing.

The US President has been unwilling to take the latest public abuse lying down, labelling the dictator "a madman who doesn't mind starving or killing his people" and threatening to test him "like never before".

We're always told that in politics, words matter. Both leaders seem to be locked in a rhetorical joust with no obvious end.

Mr Trump has clearly got into the head of the North Korean despot.

His withering condemnation of Mr Trump as "mentally deranged", in a very rare on-camera address, arguably proved that.

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Image: Donald Trump has called Kim Jong Un 'a madman'

While looking strong is vital to his survival, Mr Kim has been characterised as a cartoon villain.

He is determined to keep his regime in place and trading threats is a natural consequence of that dynamic.

The question is: where does this public back and forth take us?

The US defence secretary, James Mattis, still insists America is focused on diplomacy and that the State Department will continue to lead on sanctions.

He has long said that conflict with Pyongyang would lead to a catastrophe, "the likes of which the word has never seen for decades".

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New sanction order 'targets' North Korea

Behind the scenes, however, they are re-calibrating their military options.

The problem remains as follows: how could they get the US military in and out, faster than Pyongyang could launch a counter strike on South Korea?

Crucially, and of course worryingly, no one knows what sort of comment could set the North Korean leader on a military path.

More significant than any invective, meanwhile, is Pyongyang's threat to test a hydrogen bomb in the Pacific.

An intercontinental ballistic missile test may be more likely, but the hint from Kim Jong Un has left Japanese officials deeply concerned that it would destabilise the region and ultimately the world.

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The frontline against North Korea

Privately, Pentagon sources suggest they might not even be able to detect it before it happens.

Mr Trump says dialogue is still possible - we mustn't lose sight of that.

The White House says it's pursuing "peaceful pressure" to rein in the rogue state's nuclear programme, clamping down on those who do business with it.

They are important steps and will cause additional damage to North Korea's economy.

They may not be enough alone to force the regime to capitulate and neither side seems willing to sit down at the table together yet.

But tougher sanctions are something to work with.

Tougher talk, though, hasn't stopped Pyongyang from marching on with its nuclear programme.