The second irony is that the growing judgment fund — the accumulation of interest on a judgment the Sioux have refused to collect — has become a kind of monument to the unresolved nature of the dispute.

The larger it grows, the more visibly it marks the gap between the acknowledgment of wrong and the resolution of it.

The billion-dollar figure that attracts headlines is not a sign of progress toward resolution.

It is a sign of how long the resolution has been deferred.

The third irony is one of geography.

The faces of four American presidents — Washington, Jefferson, Theodore Roosevelt, Lincoln — are carved into the granite of the Black Hills, in the land that the Supreme Court found was taken from the Sioux in violation of the Fort Laramie Treaty.