From Shakespeare to Hitchcock, mistaken identity makes for a powerful narrative.

A police officer who’s proud of his reputation for getting along with black officers, and for teaching cadets to avoid racial profiling, feels maligned to be cast as a racist white Boston cop.

Image Maureen Dowd Credit... Fred R. Conrad/The New York Times

A famous professor who studies identity and summers in Martha’s Vineyard feels maligned to be cast as a black burglar with backpack and crowbar.

Race, class and testosterone will always be a combustible brew. Our first African-American president will try to make the peace with Gates (who supported Hillary) and Crowley (whose father voted for Obama).

I tracked down Gates by phone at J.F.K. on Friday after he had talked to the president and agreed to go to the White House for a symbolic beer with the man he labeled “a rogue policeman.” Gates, coughing from a cold he picked up in China, said he wondered if perhaps “fate and history chose me for this event.” He was pleased with the thousands of empathetic e-mail notes he’s getting, material for a PBS documentary on racial profiling.

He says he’s ready for “marriage counseling” from the “Solomon” in the Oval, who wrote in his memoir that the police pulled him over “for no apparent reason.” “If Sgt. Crowley and the president and I meet, it’s clearly not going to be like Judge Joe Brown, OK? ‘You tell your side, you tell your side.’ We have to agree to disagree. But I would be surprised if somebody didn’t say, ‘I’m sorry you were arrested.’ ”

How can they ever reconcile their accounts? Crowley says he asked Gates to come outside and the professor replied, “Ya, I’ll speak with your mama outside.” Gates wryly suggests Crowley got the line from watching “Good Times” as a child.

“Does it sound logical that I would talk about the mother of a big white guy with a gun?” he asked. “I’m 5-7 and 150 pounds. I don’t walk on ice, much less (expletive) with some cop in my kitchen. I don’t want another hip replacement.”