September 17, 2015 5:32 AM EDT

War sends people fleeing in mortal terror, and when their flight takes them across the border of their country, what aid organizations offer, along with water and shelter, is a certain hopeful logic. Both the logic and the hope are revealed by the location of the shelter, clustered as near as safely possible to the country the refugees have just fled. Partly, the idea is to spare them a long journey home when the fighting finally ends. But the policy is also meant to spare the host country the burdens of absorbing thousands upon thousands of desperate, poor and unexpected newcomers.

Which only hints at the dilemmas facing Europe as the last, dim pools of hope drain from Syria, along with much of its population. None of the 28 nations that make up the European Union bears the obligations of hospitality that comes with proximity. Those have been borne for four years now by neighboring Turkey, Jordan and Lebanon. Yet in a gush of feeling, Europe, or at least its largest nation, essentially laid out the welcome mat earlier this month to the war’s 4 million refugees, as well as the millions still trapped inside Syria.

For those with the resources to reach Berlin, it’s a godsend. And for the E.U., it’s an existential crisis, the second this year.

Europe has no Statue of Liberty. It is chiefly a continent not of immigrants, where all citizens can trace their ancestry to somewhere abroad, but of discrete peoples. Redirecting those peoples’ troublesome pride, and the wars it long spawned, was the reason behind the E.U., first conceived decades ago to provide a unifying identity that erased borders and shared the wealth. The wealth part was tested over the summer by the economic collapse of Greece, a poorer member that sought succor from the richer nations of Europe’s north, with precarious results. Now a human torrent of Syrian and other migrants is testing the limits of identity and open borders.

The test is being conducted by Germany, the E.U.’s most powerful nation and the one that set off the migration tidal wave Aug. 24 by opening its doors to asylum seekers. The resulting surge set in motion deeply affecting events that by Sept. 12 brought 13,000 people to the Munich train station alone, overwhelming a nation that values order. Two days later, E.U. members rejected a proposal to compel each nation to accept a “fair share” of the migrants. The E.U. operates by consensus, and not all members are as accommodating as Germany, or as in need of cheap, young labor.

The most prominent dissenter is Hungary, which on Sept. 14 sealed a gap in its border with Serbia, a non-E.U. state that has been the corridor for migrants arriving from Greece. In protest, some Syrians caught in no-man’s-land began refusing food and water, evidence enough that in Europe–even as the bodies of 38 more drowned migrants were being collected from the waters between Turkey and Greece–the focus has shifted from the humanitarian realm to the political.

As it must. Once ensconced in Europe, the Syrians will absorb aid, housing and jobs–all the things they absorbed in Turkey, Jordan and Lebanon when they wandered away from the U.N. camps. Hungary and others complain that the human stream reaching Europe includes not just political refugees but economic migrants from poor nations that are not at war. It’s a good bet. Global polls show that 700 million people would like to leave their country, and the door to Europe does not open every day. But Syrians are themselves educated and entrepreneurial, building a shopping arcade in Jordan’s Za’atari refugee camp with a speed that dazzled U.N. officials.

It’s been a heady, even unreal few weeks. Germany’s expectation that it will take in up to 1 million migrants calls into question a basic assumption about Europe. Is its nativist culture, which in the past has resisted integrating immigrants (especially Muslims) somehow softening? Or are its leaders getting dangerously ahead of things, in what amounts to a summer romance?

“Dream of Europe,” the French statesman Valéry Giscard d’Estaing implored 13 years ago, making the case for an E.U. constitution. “Let us imagine a continent at peace, freed of its barriers and obstacles, where history and geography are finally reconciled.” That vote fell short. But the dream lives on. And not just for people born there.

This appears in the September 28, 2015 issue of TIME.

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