The invasion of Iraq succeeded in removing Saddam Hussein,

but at what expense for Iraq, the Middle East and U.S. policy?

When the Bourbon monarchy was restored in 1815, the French diplomat Talleyrand is reported to have said of the Bourbons: "They have learned nothing and forgotten nothing." Ten years after the start of the Iraq War, the question is whether anyone - Americans, Iraqis, Iranians, other Arab states - has learned anything from this terrible experience.

By the standards of modern warfare, America's losses were much lower than they were in other recent conflicts - more than 12 times as many American soldiers were killed in Vietnam. Yet the Iraq War has scarred America in many ways. It was, as many have pointed out, a war of "choice," a formulation rarely, if ever, used to describe America's previous wars.

In a certain way, Iraq was the first think-tank war. To be sure, in the early 1960s members of President John F. Kennedy's administration intellectualized war and debated the merits of strategies, including counterinsurgency. But there can be no comparison to the cerebral mud wrestling that played out in Washington over Iraq.

This partly reflected the existential threat that the terrorist attacks of Sept. 11, 2001 represented in so many people's minds. The United States, it was argued, needed to begin to think about war differently. Former U.S. diplomat George F. Kennan famously said that "democracy fights in anger." But the new strategic doctrine of "pre-emption," which many argued would define war-making in the 21st century, suggests that democracies also fight in dread.

Indeed, another reason for the war was America's internal divisions over what it represents as a nation - its purpose and meaning to the rest of the world. The war did not resolve such questions. On the contrary, in some ways, the United States emerged from Iraq even more divided than it was when it entered.

For Iraq, the complexities and contradictions of the war were more pronounced. No one can visit Iraq and talk to Iraqis without coming away with the sense that ridding the world of Saddam Hussein was an important - even noble - accomplishment. His tyranny rivaled the worst of the 20th century. Yet, in liberating Iraq, the United States failed to ask how the tyrant gained power in the first place, and what, therefore, the challenges in replacing him would be.

For some, sectarianism in Iraq appeared like a summer storm, which quickly passed once the "surge" of U.S. troops became American strategy in 2007. But even the colossal mistakes of "de-Baathification" (the dismissal of all Iraqi officials who had been members of Saddam's Baath Party) and the decommissioning of the Iraqi army - measures so foolish that nobody now admits to ordering them - cannot fully explain Iraq's continuing political crisis.

To believe that sectarian fighting started because of a foolish U.S. decision, and ended because of a subsequent wise one, is to ignore the role of sectarianism in a country that straddles the Sunni and Shia worlds and the Turkic and Arab worlds. These divisions, obscured by Saddam's totalitarianism, never went away.

Indeed, the Sunni-Shia divide exists in many parts of the Arab world. While Americans saw in Bahrain's protests in 2011 a people's democratic aspirations, no one in the region doubted that the real source of the troubles was a restive Shia majority (perhaps inspired by Iraq, or even, as Sunni Arabs claimed, Iran) trying to remove a Sunni monarchy.

Those who argue that the surge (and its close companion, new and improved "counterinsurgency") overcame Iraq's sectarian fault line suggest that Iraq's ongoing political problems are the result of Prime Minister Nouri al-Maliki's poor governance. If only he were more democratically minded, or would reach out to the Sunni community - perhaps offering another ministerial portfolio - suicide bombings of Shia religious festivals by Sunni extremist would end.

In fact, the Middle East - buffeted by the Iraq War, the Arab Spring, and the sectarian showdown in Syria - is unsure where to go next: liberal democracy and the rule of law, or Islamist rule? Yet, for the Sunni world, Iraq is the mistake that not only must not be repeated, but also must be reversed. Thus, Sunni Arabs and Shia Persians alike view Iraq as still up for grabs, a question rather than a country, a "great game" of the kind with which the world is very familiar.

The Saudis and other Sunni Arab states have shown little inclination to bring Iraq into the Arab fold, leaving it to find its own way in the world. These states contribute enormously - as they did in the 2010 national elections - to what they hope will be a Sunni restoration, when the Americans' great error is corrected and the Arab world is made whole.

Ten years after Saddam's removal, Iraq's future remains where it always has been: in the hands of Iraqis, who will have to rise to the occasion. No one can create a stable political order for them; with the Americans gone, meddlesome Arab neighbors and anxious Iranians can only lose by dooming Iraq to remain a tinderbox.

As for Americans, we need to learn from what happened in Iraq, lest our hubris doom us to similar ventures. And, when it comes to the vision that sent us there, that means that we must also forget.

Christopher R. Hill, former U.S, assistant Secretary of State for East Asia, is Dean of the Korbel School of International Studies at the University of Denver.