Punch-drunk Europe would do well to study the fate of US liberals. The more Donald Trump denigrates Nato, the greater outrage he provokes in Europe. Moral certainty feels good. But it can bring on intellectual blindness. Time and again, Mr Trump’s domestic critics have chosen righteous indignation over analytic clarity. Women could never vote for Mr Trump, Democrats reassured themselves. Then a majority of white women did. The US would never withdraw troops from Europe, says Brussels. Yet Mr Trump could do precisely that. Which side of the Atlantic would have the most to lose?

Mr Trump knows more than his critics give him credit for. He invents his own facts. But he instinctively grasps other people’s bottom lines. Mr Trump’s portrayal of Nato is profoundly error-ridden. It is also fundamentally correct. On the first, the US accounts for nothing like 70 per cent of Europe’s security budget. Its actual share, as the International Institute for Strategic Studies has set out, is a fraction of that. Five per cent of the US defence budget goes directly on Europe. Nor is Europe “delinquent” on its obligations. Since pledging four years ago to meet the 2 per cent of gross domestic product target within a decade, Europe’s Nato members have lifted spending $87bn in real terms, which is more than double what the US spends annually on European security. So much for Mr Trump’s relationship with the facts.

But quietly correcting Mr Trump — even shrieking it from the rooftops — will do nothing to change his mind. Technocracy cannot compete with diatribe. The most lethal demagogue is one who grasps an underlying reality. Mr Trump knows that Europe needs the US more than the US needs Europe. Every time Mr Trump meets a Nato partner, or listens to his advisers, he is told his actions are weakening US security. That is true. US power is magnified by alliances. Wrecking them reduces Washington’s global clout. But the bigger loser is Europe. Its survival depends on a US guarantee. A resurgent Russia poses deep threats to Europe’s eastern borders, its internal cohesion and ultimately its prosperity. With the US’s continued presence, Europe can rebuff Russian president Vladimir Putin’s probing. Without it, Europe would be dangerously exposed.