One indication of how deeply rooted biases are: A rigorous study by economists found that even N.B.A. referees were more likely to call fouls on players of another race. Something similar happens in baseball, with researchers finding that umpires calling strikes are biased against black pitchers.

If even professional referees and umpires are biased, can there be any hope for you and me as we navigate our daily lives? Actually, there is.

The N.B.A. study caused a furor (the league denied the bias), and a few years later there was a follow-up by the same economists, and the bias had disappeared. It seems that when we humans realize our biases, we can adjust and act in ways that are more fair. As the study’s authors put it, “Awareness reduces racial bias.”

That’s why it’s so important for whites to engage in these uncomfortable discussions of race, because we are (unintentionally) so much a part of the problem. It’s not that we’re evil, but that we’re human. The challenge is to recognize that unconscious bias afflicts us all — but that we just may be able to overcome it if we face it.