New York - Since the birth of the Black Lives Matter movement three years ago, many white Americans have wrestled with how to respond. Some chose racist-tinged ridicule. Others, by word or deed, sought to show solidarity as blacks protested the deaths of fellow blacks in encounters with police. Still others, untouched personally, watched from a distance in silence.This past week, as graphic videos portrayed two more such deaths and five police officers were slain at a march in Dallas protesting the killings, whites have joined blacks in forceful calls for unity that cut across colour lines. Some see hope of a turning point from these tragedies, that this might be the eyes-wide-open moment that moves white America from apathy or remorse to action in pursuit of racial reconciliation."I definitely think there's a change in the atmosphere," said Johnetta Elzie, a black activist from St Louis who believes the events have galvanised more white people to confront issues that afflict blacks. "I hate the fact that it is this way, but with every police violence victim story that goes national, more and more people wake up."The Black Lives Matter movement began in 2013, inspired to a large degree by the killing the previous year of 17-year-old Trayvon Martin by a neighbourhood watch volunteer in Florida. It soon grew into both a national battle cry and phenomenon after a series of killings of blacks and other minorities by police.Over the course of the campaign, black activists have had mixed feelings about the response from whites - commending those who have supported the effort yet decrying what they perceive as disinterest or hostility from a majority of whites."Yes, White people are standing with us in response to these killings and we value that, but we need more Whites to tackle the systemic racism and discrimination that Blacks are subjected to," San Francisco activist Javarre Wilson said in an email response to questions."White people don't have to worry whether their child will be at the receiving end of a cop's baton or handgun. White people don't have to worry about whether they will be pulled over in their cars and aggressively harassed by racist cops."To be sure, whites, Latinos, Asians and others have joined black Americans in decrying the shooting deaths of Alton Sterling in Louisiana and Philando Castile in Minnesota, made all the more palpable because videos capturing the incidents were widely shared for all to see on social media and across the internet. The officers involved were placed on leave and investigations continue.Heart 'in a million pieces'"My heart is in a million pieces," Rachel Hockett, a white theatre director in Ithaca, New York, wrote in a Facebook post. "I can't even begin to imagine how it feels to be African-American in this country. But I certainly care, to my toes, and I know how I would feel if my son or daughter were gunned down in this way.""All #blacklivesmatter. Unconditionally," Nellie Fitzpatrick, director of Philadelphia's Office of LGBT Affairs, declared on her Facebook page.But words are not enough, in the view of many black activists. They argue that most whites have been too slow to speak out when injustices occur and that, once they do, such expressions rarely equate to meaningful change."It makes the killings worse to know that your disapproval of them has spared your reputations and not our lives," Michael Eric Dyson, a professor of sociology at Georgetown University, wrote in an op-ed in The New York Times after the deaths of Sterling and Castile. He addressed his piece to "white America"."You will never understand the helplessness we feel in watching these events unfold, violently, time and again, as shaky images tell a story more sobering than your eyes are willing to believe: that black life can mean so little," Dyson wrote. "You do not know that after we get angry with you, we get even angrier with ourselves, because we don't know how to make you stop, or how to make you care enough to stop those who pull the triggers."Matthew Shaw, a black law and public policy analyst at the American Bar Foundation, said too many white Americans lack empathy with blacks, and need to find ways to develop that."If you see someone being shot while sitting in a car with his family, and you don't have some empathy, you've got some work to do," he said in reference to Castile's death. "Work on your friends, your family, people in your neighbourhood."He urged whites to get active in campaigns to improve police practices and promote racial justice.Violence worst response"Violence is the worst response," he said. "Throwing your hands in the air and saying nothing can be done is a close second."Some whites have indeed taken steps to build support for the Black Lives Matter movement among their fellow whites, and they say they are making progress.Dara Silverman is the national co-ordinator of Showing Up for Racial Justice, a network launched a year and a half ago. She said it has grown from a dozen local groups to more than 150, expanding the base of whites committed to fighting racial inequality.The network encourages white activists to hold house parties and conduct door-to-door canvassing in an effort to attract more supporters. A statement issued after the deaths of Sterling and Castile also urged direct protest action."Join us in the streets," it said. "Now is the time for white people to be visible, courageous and relentless in our public opposition to racism and the state-sanctioned murder of Black people."Many white politicians, including top Democratic and Republican leaders, appealed for tolerance and unity in the aftermath of the deadly incidents. Hillary Clinton, in an interview with CNN, called on white people "to put ourselves in the shoes of those African-American families who fear every time their children go somewhere". House Speaker Paul Ryan implored Americans to "not lose sight of the values that unite us, our common humanity".'This is war'There were harsh comments as well. Joe Walsh, a former Illinois congressman, tweeted in response to the slayings of the officers in Dallas by a black Army veteran: "This is now war" and "Watch out black lives matter punks." The perpetrator, who was killed during an ensuing stand-off with authorities, told officials he was upset about the police killings of Sterling and Castile and wanted to exterminate whites. He said he acted alone and not in concert with any groups.Diana Bass, an author who specialises in American religion and culture, urged white people to speak out against racism - even if seen in those closest to them."With the exception of my mother and her father, I knew no adult who ever said anything good about any black person," she recalled of her childhood years in a Facebook post. "I disavow their beliefs. I utterly, completely reject their racism. They were wrong and used race to keep others down in order to try and protect their own fragile egos and privilege."The Reverend Russell Moore, a white evangelical who heads the Southern Baptist Convention's public policy agency, wrote an essay on his personal website that put the latest incidents into historical perspective - making references to slavery and to the era of segregation in which his denomination resisted black civil rights."African-Americans have lived with trauma from the very beginning, the initial trauma being the kidnapping and forced enslavement of an entire people with no standing whatsoever before the law," he wrote. "For the black community, these present situations often reverberate with a history of state-sanctioned violence, in a way that many white Americans - including white evangelicals - often don't understand."Moore's essay ended on a note of hope: "We can work for justice in the public arena as we learn to love one another in the personal arena, and vice versa."But there also were voices of despair."It's overwhelming to see what we are up against, to live in a world where too many people have their fingers on the triggers of guns aimed directly at black people," Peter Staley, a white HIV/Aids activist in New York City, wrote on his Facebook page."I don't know what to do anymore," he said. "I don't know how to believe change is possible when there is so much evidence to the contrary."