They speak on behalf of majorities who see themselves menaced by the loss of their political power and the rapid diminution of their economic prosperity. They feel cheated by the demographic revolution that is underway around the world — one that threatens to make them minorities in their own countries. Mr. Trump’s crude directness and his unrivaled skill in manipulating the news media so strongly resemble the political style of the former Italian prime minister Silvio Berlusconi that I sometimes wonder whether Mr. Berlusconi is secretly coaching him from the sidelines.

Bernie Sanders should be familiar to Europeans as well. Most of the young Europeans I know view capitalism as a rigged and unfair system; to them, real socialism — and not just German-style, neo-liberal “social democracy” — is hardly a dirty word. They see themselves as the biggest losers of the status quo, and often dream out loud of revolution (though, thankfully, of a nonviolent kind). For them the war between generations is the new version of their parents’ (and grandparents’, and great-grandparents’) class war.

In countries like Greece, Spain and Portugal, almost half of the young people are unemployed, despite the university degrees they may have earned. They judge globalization as an unmitigated disaster and loathe the idea of free trade. And while Mr. Sanders is no Jean Jaurès or Leon Trotsky — I find him about as exciting as a cucumber sandwich — for many of the new radicals in America and Europe, his lack of charisma is one more sign of his integrity and authenticity.

Not even Mr. Obama’s sharp turn to foreign policy realism perplexes me. He says he has thrown out the “Washington playbook,” and that has surprised and frightened America’s allies in Europe. Mr. Obama’s infamous policy dictum, “Don’t do stupid” things, has been the sole organizing principle of Europeans’ foreign policy for years now. He’s simply making explicit something that we’ve known a long time — that America is becoming more cautious in its foreign policy, more European. Americans are no longer from Mars, and Europeans are no longer from Venus. Perhaps we are all on Saturn together, trying to keep the dirty rabble from sullying our beautiful rings.

If anyone is failing to “get” America these days, it’s Americans themselves. They don’t see that their country is rapidly becoming “normal,” unable to rely on infinite, widely shared economic growth and splendid geopolitical isolation. “It has been our fate as a nation not to have ideologies, but to be one,” the American historian Richard Hofstadter once said.