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When someone is erratic, egotistical and eager for grand gestures, observers wonder if there is ever any sense or substance.
Mr Trump blunders onwards complete with his customary blizzard of lies, obfuscations and exaggerations - somehow, immune to scandals that would fell anyone else.
He continues to appeal to a solid core of supporters, and the US economy maintains its momentum.
What then to make of the superpower's relationship with North Korea, the future of denuclearisation and the Korean Peninsula as well as the broader picture in northeast Asia?
Narcissistic Mr Trump flourishes on being the centre of attention, and both American Independence Day, July 4, and his meeting with North Korean president Kim Jong-un last week provided him the chance to strut and preen.
Both occasions were more than cringe-worthy.
They displayed a figure who, given the opportunity, would embrace a dictatorial role and cult-like following.
The media, opposition politicians and proper process and conduct are pesky irritants. No wonder he waxes so effusively about Mr Kim and Russian leader Vladimir Putin.
Mr Trump greeted Mr Kim - a despot of the worst order - like a best mate. In echoes of prominent Europeans meeting Adolf Hitler in the 1930s, evil is ignored and the leader of a brutal, murderous regime praised. As Mr Trump put it, "I was really being tough and so was he. And we would go back and forth. And then we fell in love. No really. He wrote me beautiful letters."
This is the man who first threatened "fire and fury".
They then made up in an orgy of admiration, before falling out at the February Hanoi summit.
Mr Trump's trip to the demilitarised zone between the Koreas was dramatic - "a historic moment", as he put it. It was, indeed, quite some spectacle.
Sceptics, however, saw it as all show and no go.
All Mr Trump did was to legitimise Mr Kim and his power and prestige. Sure, the leaders agreed talks at diplomatic level could resume.
But so what. Mr Kim will never give up his protective nuclear weapons umbrella. Why should he discard the one powerful trump he holds?
Yet, there are pressures on both these apparent best friends forever.
Mr Kim needs economic development to buttress his rule and the international sanctions hurt an already impoverished land. Mr Kim and especially Mr Trump also have personal reputations that will be dented if the latest rapprochement proves to be another chimaera.
They are creating expectations and softening their domestic audiences for a possible, if unlikely, agreement at some stage.
Mr Trump's hints of some easing of some sanctions in exchange for some denuclearisation hardly matches the policy of "complete, verifiable and irreversible denuclearisation" that Washington has been so insistent on.
Nevertheless, that might be the only way forward. It is just possible, albeit remotely, that Mr Trump's spectacular making up with Mr Kim allows actual progress to be made.
Just do not expect Mr Kim to ever kowtow to the United States on its version of denuclearisation. If Mr Trump can stay out of matters and let the professionals do their job until another photo opportunity can be created, then just maybe the chill on the Korean Peninsula can thaw a little.
Just maybe Mr Trump's unconventional and crass conduct can occasionally break new ground.