However distant the goal, however bitter many Turks may feel about the disdain in which their country has been held since it first applied 40 years ago, that dream has endured.
Membership could transform the economy of this still impoverished nation. The process of qualifying for membership has already changed much in the country and will change more before it's over.
Even if the diplomatic waters can be smoothed for negotiations to begin on Monday, it will be at least 10 years before the 70 million-strong, predominantly Muslim nation becomes one of us: a fully-fledged member of the EU.
Like the accession of any new member, the arrival of Turkey on Europe's doorstep is all about economics, trade, social reform, democracy, criminal justice, media freedom - everything that constitutes a modern state.
Many of these factors are already in Turkey's favour: it is in many ways far better prepared for membership than the former Warsaw Pact countries. It was on our side of the Iron Curtain for all those years. It is a key member of Nato.
It has had a customs union with the EU since 1996: trade in goods has already been liberalised, and more than half of Turkey's trade is already with the EU. It has already adopted many EU rules, such as those regarding intellectual property and competition. There is no wholesale privatisation that must be undertaken. The democratic system is looking increasingly stable and mature. The death sentence has been abolished.
But uniquely in the case of Turkey, membership is not just about the nuts and bolts of belonging to the EU. It is also a profoundly moral issue, for both sides. Whether we admire or despise the EU we don't often think about it in moral terms. But with Turkey, the moral questions cannot be dodged.
One week ago, a group of scholars in Istanbul braved the eggs and rotten tomatoes of protesters to attend an extraordinary conference. They were there to discuss the murder of 1.5 million Armenians in the dying years of the Ottoman empire.
Raising this subject has been taboo in Turkey ever since. It is as if Germany had risen again after the Second World War with no public admission, ever, of how the Nazis murdered six million Jews, and as if they had lived and prospered in denial for the best part of a century. But despite hitches, threats, two cancellations by judges and all-round hysteria, Turkey last Saturday finally got round to discussing "the first genocide of the 20th century".
Orhan Pamuk, the celebrated Turkish novelist, told a Swiss newspaper earlier this year: "Almost no one dares speak about these things but me." To his country's lasting shame, he is to go on trial in December for mentioning what Turkey did to the Armenians and the Kurds. But now at least he is not quite so alone.
The conference was the work of the EU. "This is a fight of 'can we discuss this thing, or can we not discuss this thing?'" a member of the organising committee said at the start of the conference. Well, the discussion finally went ahead. It was the EU's - and Turkey's - finest hour for some time.
The question posed at last week's conference was: "Is this country forged out of the Ottoman empire's ashes less than a century ago mature enough to admit the ugly stains in its history and move forward?"
If it's not, the EU's door will undoubtedly be slammed on it. But if it can find those inner resources, the dream of Ataturk may finally be realised.
Turkey, whose inhabitants down the centuries were masters of empires as far-flung as the Mogul empire in India, the Safavids in Iran and the Mamelukes if Egypt, can become a modern secular state to compare with any in the West. For Europe the moral dimension is even greater - intimidatingly large for many. How big is Europe, in its heart and soul? Is it a cosy, well-heeled, Christian, white man's club, devoted, through things like the Common Agricultural Policy, to keeping happy those who are already fat; keeping the Old Continent looking picture-postcard perfect, while accepting with ever worse grace a fraction of the huddled masses battering at the door? If that's what Europe is, it is obviously doomed, as all the latest demographics make clear. It's on the way out, as obviously and miserably as was the South Africa of apartheid.
Or does it have the courage and the wit to avoid that fate? Most of Turkey will never be European the way Vienna, Paris and Prague are European. But Seville, Palermo and Venice are also European cities; and in all of them, Christian and Islamic strands are interwoven just as in Istanbul.
The identities of Europe and Islam are the products of more than a millennium of bitter conflict. But Britain and France were enemies for centuries as well: the European project is all about banishing war and the threat of war.
Never before has a huge Islamic nation asked for Europe's recognition the way Turkey has been asking these past decades. Turkey is the peaceful bridge to Islam of which the West is in desperate need.
Sticking points in Turkey's progress towards full EU membership
Austria wants Turkey to negotiate "privileged partnership" instead of full EU membership as advocated by the rest of the EU. Turkey has warned it will not accept "second class" status.
The Balkan state has become a bargaining chip in negotiations. Austria wants talks on Croatian accession to begin immediately, but issue is linked to co-operation with the war crimes tribunal.
Austria isolated in opposing entry of a Muslim nation to the "Christian" EU after France switched position to ally itself with UK and Germany, which favour embracing Turkey.Reuse content