We are lucky to have today’s Germany. When Chancellor Merkel arrived in London last week, she came as the accomplished leader of Europe’s most successful liberal democracy. Germany’s economic strength is taken for granted; more subtly, we also take for granted that this is an essentially good country. It is not going to assuage any demons by behaving aggressively to its neighbours or blaming foreigners for any of its problems. It is quietly and determinedly going to attempt to anchor Europe in the same successful combination of liberal democracy, social solidarity and productive capitalism that it enjoys – and it has the economic and moral wherewithal to do just that.

This very new country – after all German reunification was completed just 25 years ago – could be so different. It could have a poisonous political movement aiming to restore Napoleonic glories riding high in the polls – see the Front National in France. It could be captured by venal, vested-interest groups locking the economy in permanent stagnation like Italy. It could be in thrall to a know-nothing political right whose objective is to run the country in the interests of its top 1% like the US’s Republicans. It could be led by a self-regarding nationalist such as Russia’s Mr Putin. It could live in a cultural time-warp like today’s Britain, hankering to restore the lost certainties of the 1950s.

Germany is none of those things. If it were, Europe would be fundamentally and worryingly unstable. Rather, this is a firmly liberal democratic country looking forward in the 21st century because its relationship to history, as director of the British Museum Neil MacGregor argues in his revelatory and illuminating book Germany, compels it never to look back. Germany can only face its otherwise unintelligible historical crimes, genocide and futile millions of war dead with a resolve to never again make the same mistakes. Its capital city, Berlin, forces its citizens every day to confront the fact that it exterminated six million Jews in its striking Holocaust memorial; no other world capital so uncompromisingly has built monuments at its heart to force it constantly to confront past disasters.

What does it mean to be us is a question every country asks, searching its history to reproduce whatever success it might have once enjoyed. MacGregor’s argument is that because Germany cannot take comfort or define itself by imagined past glories, it is free of imprisoning and destructive myths. It has become, of necessity, a force for good, too little recognised in Britain in part because we still define ourselves as a victor over Germany when it was evil. Angela Merkel chose to spend some hours of her time in London visiting the Germany exhibition at the British Museum, an exhibition MacGregor has curated alongside his book. MacGregor believes Britain does not understand today’s Germany, the complexities that delivered it or why it thinks as it does. Merkel agrees. The point of her British trip was not to devise ways of helping Cameron win his EU referendum in 2017, about which she was stubbornly reticent. It was very publicly to endorse MacGregor’s view of today’s Germany before his exhibition closes later this month – and perhaps trigger a different debate.

MacGregor organises the exhibition so that the first big quote you see is Goethe and Schiller’s 1796 declaration: “Germany? Where is it?/ I do not know where to find such a country.” There are eight different maps of ever-mutating German territory since 1500. Thus the home of Immanuel Kant, its greatest philosopher, is Kalingrad (then Königsberg) which is now in Russia; the city that most influenced its greatest poet (Goethe), Strasbourg, is now in France. From 1500 to 1806, “German-ness” expressed itself through the loose association of principalities, cities, dukedoms and minor states that was the shifting boundaries of the Holy Roman Empire until its defeat by Napoleon. Then came the nation state that was first imperial and then Hitler’s Germany. Postwar division followed defeat, then reunification.

For Germany, the nation state has been an aberrant, destructive interlude between the Holy Roman Empire and now the European Union – a 21st-century variant of the Holy Roman Empire, but with a single currency, market and trading rules. For Germany, it is the only way to conceive of the future, and create a peaceful and productive Europe. Senior German officials talk privately in these terms, categories that bewilder the British still locked in fundamentally traditional political categories. For its neighbours, one downside of Germany’s recent past – 1920s hyperinflation – is its quasi-religious attachment to sound money and budgetary rectitude. But the greater German attachment, trumping everything, is to think and build forward recognising today’s realities.

Thus the Greek political crisis – and the possible confrontation between Germany and the anti-austerity Greek left if it wins the elections – may have a happier outcome than the British consensus could ever imagine. Syriza has the 30 super-rich Greek families that pay no tax and run Greece as a payola for their own interests in its sights as much as it is targeting Greece’s suffocating external debt burden and excess of austerity. It is also keenly aware that abandoning the euro for the drachma and detaching itself from the EU exposes Greece to both huge inflation and the tender mercies of Turkey.

The potential deal with Germany is clear. The left will forge a proper liberal Greek democracy with the 30 families paying tax, secure the forgiveness of much of its external debt but stay in the euro: the price will be that it continues with tough constraints on public spending.

As France is shaken to its core by recent events, Germany will want to see the atrocities as the acts of a murderous cult fuelled by marginalisation rather than join in any putative clash of civilisations. It knows better than any other European country where that leads: why it will successfully handle its own backlash against Islam, Pegida. Equally, if there is a British referendum on EU membership, Germany will offer whatever British government the deal necessary to keep Britain in.

Its mission is to try to hold Europe together, keeping at bay the temptations of Islamophobia, nativism, political extremism and protectionism. It may not succeed. But imagine if it did not try or if Germany itself gave in to the same temptations. It would love Britain to recall that at different times it has fought alongside Germans, to drop its fixation with two world wars and now make common cause to build a great future. Europe would be so much stronger if we dared.