Whites tend to measure progress by comparing the present and the past -- and America has made giant strides since the Jim Crow era. Nonwhites, Eibach found, are likely to evaluate racial equality in comparison with an idealized future. These yardsticks create entirely different perceptions.

When Eibach asked each group to use the other's yardstick -- whites to focus on the future and nonwhites to think about the past -- the differences disappeared. Now, everyone agreed the country had come a long way -- and had a long way to go.

In a speech last week, Obama similarly argued that his former pastor had failed to acknowledge how America had changed for the better. But Wright's critics, Obama added, were also wrong -- because true equality is still remote.

The intriguing question prompted by Eibach's study is why whites and blacks are unconsciously drawn to different yardsticks. Eibach said one reason might be that racial equality means different things to whites and blacks: Whites see it as an ideal, blacks as a necessity. When people evaluate progress toward idealistic or optional goals -- saving for a vacation -- they tend to focus on progress made. But when people think of necessities -- paying the rent -- they focus on how much they are short.