Against this insurgency, even President Andrew Johnson, an opponent of Reconstruction, continued the state of war for a year after Appomattox. When Johnson tried to end the war in the summer of 1866, Congress seized control of his war powers; from 1867 to 1870, generals in the South regulated state officials and oversaw voter registration, ensuring that freedmen could claim the franchise they had lobbied for. With the guidance of military overseers, new biracial governments transformed the Constitution itself, passing the 13th, 14th and 15th Amendments.

The military occupation created pockets of stability and moments of order. Excluded from politics before the war, black men won more than 1,500 offices during Reconstruction. By 1880, 20 percent of black families owned farms.

But the occupation that helped support these gains could not be sustained. Anxious politicians reduced the Army’s size even as they assigned it more tasks. After Grant used the military to put down the Ku Klux Klan in the Carolinas in 1871, Congress and the public lost the will to pay the human and financial costs of Reconstruction.

Once white Southern Democrats overthrew Reconstruction between the 1870s and 1890s, they utilized the Appomattox myth to erase the connection between the popular, neatly concluded Civil War and the continuing battles of Reconstruction. By the 20th century, history textbooks and popular films like “The Birth of a Nation” made the Civil War an honorable conflict among white Americans, and Reconstruction a corrupt racial tyranny of black over white (a judgment since overturned by historians like W. E. B. DuBois and Eric Foner).

Beyond the problem of historical accuracy, separating the war and the military from Reconstruction contributes to an enduring American amnesia about the Army’s role in remaking postwar societies. Many of the nation’s wars have followed the trajectory established at Appomattox: Cheers at the end of fighting are replaced by bafflement at the enduring conflict as the military struggles to fill the defeated government’s role, even as the American public moves on. After defeating Spain in the Spanish-American War, the Army undertook bloody campaigns to suppress rebellions and exert control over the Philippines, Cuba and Puerto Rico. After World War II, a state of war endured into the 1950s in the occupation of Japan and Germany. And in the recent wars in Afghanistan and Iraq, the United States military’s work had barely begun when the fighting stopped — and the work continues, in the hands of American-backed locals, today.

While it is tempting to blame the George W. Bush administration for these recent wars without end, the problem lies deep within Americans’ understanding of what wars are. We wish that wars, like sports, had carefully organized rules that would steer them to a satisfying end. But wars are often political efforts to remake international or domestic orders. They create problems of governance that battles alone cannot resolve.