Europe finally appears to be recovering from its worst crisis in seven decades. Even Greece, the most bloodied of the victims, is showing signs of economic life. At some point this summer, the most important European indicators returned to 2007 levels. On the surface, it's over.

That's not to say that all is well in the world's largest economy. Tens of millions of people are perpetually jobless. There are mountains of debt. It will be a decade before Spain and Ireland are back to full health, and Italy and Greece face larger challenges. Hungary is a political and economic catastrophe. Britain has starved its economy into years of trouble. Germany, the continent's economic engine, has just re-elected a government whose policies will continue exporting bankruptcy. The euro remains in place. The demographics of aging will make social policies extremely difficult.

But stop for a moment and consider what did not happen. Nobody starved. The social safety net, even where it was badly shredded in the Mediterranean, kept working. Crucially, not a single country elected an extremist – of the left or the right. While hateful anti-immigrant parties won third-place positions briefly in the Netherlands and Scandinavia, the violent neo-Nazi Golden Dawn won seats in Greece's political vacuum, and a fifth of French voters cast a ballot for a candidate devoted to racial hatred, these frightening tendencies were always overwhelmed by the far larger masses of people opposed to them. Voters flocked to parties of the moderate centre-right and centre-left. Extremists failed to seize the day. No country threatened any other country with violence or economic isolation – in fact, nobody even seriously considered leaving the European Union (which, at the height of the crisis, grew from 27 to 28 members).

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It is the first time a continent-wide economic catastrophe has not provoked a continent-wide political, military and humanitarian catastrophe. What kept Europe from falling? In large part, it was the decisions made the last time Europe was in such bad shape, during the awful years after the Second World War.

"How did the world emerge from the wreckage? What happens when millions are starving, or bent on bloody revenge? How are societies, or 'civilization,' put together again?" Those are the questions posed by Dutch-American writer Ian Buruma at the outset of his Year Zero: A History of 1945. Its title, borrowed from Roberto Rossellini's great film, is apt: This was the moment when the next 70 years of history were born. Post-colonial independence, the welfare state, public medicine, sexual equality, the United Nations and what became the EU, the creation of Israel and Pakistan: All sprang from the world's reactions to the shock of postwar reality.

The war was awful, but even worse for many was the postwar calamity – when the word "refugee" entered our vocabulary to describe the largest involuntary human displacement in history, and new institutions were created on the fly to deal with the unprecedented millions of once-dignified people now starving, homeless, begging, prostituting themselves, prone to bouts of vengeful murder and teetering on political extremism. Starvation, malnutrition and food rationing were all more serious in the postwar years than during the war. Our memories tend to compress tragedies, so we think of the postwar recovery as rapid and assured. But it was not: Foreign aid did not start flowing for many years, and for a time, it looked like Europe's future was squalor.

That led to new ideas. In 1944, British writer Cyril Connolly described an idea that would soon find a wide following: "a European Federation – not a nominal federation, but a Europe without passports – a cultural entity where everyone is free to go where they like … if Europe cannot exchange economic nationalism for international regionalism it will perish as the Greek City States perished, in a fizzle of mutual hate and distrust."

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That prescription, when it came to the crunch, did the trick. The continent-wide institutions are often comically bureaucratic, wasteful and democratically dubious, but they proved their worth in the post-2008 years by holding safety nets aloft, by keeping governments at the same table – and, importantly, by allowing citizens of wrecked economies to use their continent-wide citizenship rights and migrate freely to better ones (a million Spaniards, Italians and Greeks moved to Germany last year to fill its gaping labour shortages).

This may have been the peak moment of that postwar dream: The German-concocted economic solution will entail a more powerful, more political and more Berlin-focused EU, which could turn many countries against it. But at least it worked when it was needed most.