Here's a helpful answer from Shelby Steele, in an interview he did for the book Black and Right:
C & S: Your work, as a whole, has emphasized psychological aspects of race and race relations. As you look at race relations today, what frame of mind and general attitude do you think people should adopt as they think about race and racial politics?
Steele: Well, simply, I think people should try to put themselves in the place of the other. We often hear whites say "I can't imagine what it would be like to be black!", but I think that's just silly. We are not talking rocket science, here. We are talking about imagining if one was of a particular race--and knowing what we all know about how that race is generally perceived--what would it be like? It is a matter of empathy. Sometimes we resist that, but when we enter into that we learn things about others and ourselves we didn't understand before. Of course, what militates against this is that it is usually to my disadvantage. In this politics that we have, it is to my advantage not to know what life is like for you.