It seems almost ghoulish to look for a silver lining in the dark cloud that blanketed the nation last week. But I think there was one. The killings by police in Minnesota and Louisiana, quickly followed by the killings of police in Dallas, knocked the lazy certainty out of almost everybody.

At least for a moment, antagonists on either side of polarizing issues could see beyond the epistemic horizon of their most comfortable talking points. Black Lives Matter activists thanked the police for their protection and sacrifice. Conservative Republicans, most notably House Speaker Paul Ryan and former Speaker Newt Gingrich, spoke movingly about race in America. Gun rights activists were dismayed that Philando Castile, the man shot by a police officer in Minnesota, had followed all of the rules — he had a gun permit, cooperated with the officer, etc. — and was still killed. Liberals who insist that rhetoric from their political opponents inspires violence were forced to consider whether rhetoric from their allies might have helped inspire the shooter in Dallas.

It was a welcome change. “National conversations” are usually efforts to bully everyone into accepting a single narrative when the reality is that, in this country of more than 300 million, many narratives can be in conflict and still be legitimate.

I don’t doubt that representatives of each tribe will eventually retreat back to their ideological bunkers, but before they do, let’s explore some blind spots, on both sides.

Former New York City Mayor Rudy Giuliani (who did not lose his lazy certainty) spent the weekend attacking the Black Lives Matter movement as “racist.” He wants people to focus on the fact that most black murder victims die at the hands of other blacks. That’s true, and tragic, and fairly irrelevant.

Conservatives, of all people, should understand that misdeeds committed by agents of the state are categorically different from the same acts committed by normal citizens. A father who slaps his son for no good reason, however wrong that may be, is very different from a cop who slaps a citizen for no good reason.

This country was created, in part, because the founders were outraged by arguably slight infractions — taxes on tea! — against their liberties and dignity. Is it really so unfathomable that African-American citizens should be outraged or distrustful of government when they have good reason to believe the state is murdering young black men?

It should be said that the data do not actually corroborate this belief — at least not as clearly as one might think. Harvard economist Roland Fryer found that when black suspects encounter the police, they are slightly less likely to get shot than white suspects. He called it “the most surprising result I have found in my entire career.” Fryer, by the way, is African-American.

But Fryer also found that blacks are disproportionately victims of bias when it comes to non-lethal use of force by police, such as use of pepper spray, manhandling and the like. Is it so unreasonable to assume that citizens who experience such bias would also believe that it extends into police shootings? Particularly when such tragedies receive so much attention in social media and the press?

In other words, if blacks experience being unfairly stopped, frisked and manhandled, is it really nuts for them to think the unfairness extends to shootings as well?

Liberals, meanwhile, have their own blinders when it comes to the police.

Although they have seemingly boundless faith in the power and nobility of government, many draw a line around cops, creating one of the strangest ironies of modern liberalism: Many of those most eager to support new laws and new regulations suddenly lose faith when it comes to the government employees charged with enforcing them. It’s particularly amazing given that law enforcement personnel typically receive far more training than your typical bureaucrat or legislator.

Another blind spot: Most of the problems with black homicide — by police or otherwise — take place in cities run by Democrats for generations, yet Republican racism is always to blame.

Just as conservatives need to recognize the ills of police abuse, liberals need to acknowledge that the first obligation of the state is to defend the safety and property of its citizens, and that nothing undermines the legitimacy of the law more than vilifying those sworn to uphold it.

I doubt the humility we’ve seen this week will last, but that it emerged at all is a source of hope.

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