This image has become near-universal in the couple of days since it was taken. Around the world it has been taken as an emblem of everything Trump’s critics dislike about him: stubborn, deaf to others’ concerns, isolating the United States from its allies. It’s certainly a great picture, but, like one of those trick-of-the-eye pictures showing an old or young woman, it can be seen two contradictor ways.

The tweet I’ve embedded above, from Trump’s own ambassador to the United Nations, shows the other perspective. Sure, the President looks stubborn and unyielding in the face of insistent demands from other Western nations – but that is not a bad thing for many of his supporters. Put simply, if you voted for a President to dig his heels in, disrupt the established order, and start saying “no” to allies whom you believe the US has indulged militarily and economically for too long, then the image shows your chosen candidate fulfilling his promise.

It’s easier to see the way in which an image might have such contradictory effects among different audiences by transposing it to British politics. Consider the impact in the UK that a similar picture of Theresa May might have – refusing the hectoring of the EU Commission, for example, or crossing her arms to Trump rather than holding his hand. In each circumstance, there would be some outraged howls but also some satisfied domestic audiences. Indeed, I suspect Downing Street would quite like to have such a picture at their disposal, an illustration of the words “bloody difficult woman”.

Trump’s awkwardness towards others internationally might well be an admirable quality among his base, but it remains a troubling quality from the perspective of one of his country’s closest historic allies. The difficulty for the UK, NATO and the like isn’t just a question of an “America First” president. If everyone knew that they’d just have to cough up more for defence, offer better trade terms, and suck up a steady stream of egotistical proclamations from the White House, then it might be more bearable – disruptive and expensive, but understandable and navigable. But Trump is not just consistently awkward, he’s simultaneously awkward and inconsistent.

He tears up agreements shortly after approving them (often literally). He switches tack on supposedly fundamental issues apparently at a whim. He appears to be incapable of accepting even slight differences with the leaders of broadly like-minded nations, but is keen to negotiate personally with hostile tyrants. He threatens nuclear warfare in a way that makes even seasoned Cold Warriors flinch. He changes his top team almost as fast as he switches positions.

Aha, say some Trump-watchers, that’s his mad dog strategy. That certainly seemed to be Boris Johnson’s analysis in the leaked recording of his remarks last week:

“I am increasingly admiring of Donald Trump,” Johnson said. “I have become more and more convinced that there is method in his madness.”

“Imagine Trump doing Brexit,” Johnson said. “He’d go in bloody hard… There’d be all sorts of breakdowns, all sorts of chaos. Everyone would think he’d gone mad. But actually you might get somewhere…”

It’s certainly the case that the President’s approach keeps those he deals with on the hop, to put it mildly. It has in some ways broken ground that previous, more incrementalist, administrations never thought of reaching. A mad dog strategy is unnerving and risky, but it can bring benefits if combined with skill and luck.

The danger, of course, is that it can be hard to tell if someone is being deliberately erratic for effect, or is just genuinely erratic. Assuming the former can be a very dangerous mistake to make if the reality is the latter, so it becomes sensible to assume the worst. With every outburst, more and more of America’s allies are left wondering if they are dealing with a mad dog strategy or simply with a mad dog. Regardless of the truth of the matter, once it seems safer to work on the basis of the latter – to carry a stick, rather than extend a friendly hand – then that is very bad news for the Western alliance.