Many Black parents give their children "the talk" to teach them how to stay safe when they encounter the police. Ashmore faces a different challenge with his sons, who are 6 and 8 years old -- explaining how wrong it is that their Black classmates do not live in a world as fair and safe as the one they live in.
"We have a lot of things that are given to us because of the color of our skin," Ashmore remembered telling his sons. "Mom and I try to make sure we don't use our advantages to hurt other people."
"If we do," he told them, "we're wrong."
Floyd's killing has filled Ashmore with sadness, anger and self-doubt.
He keeps thinking about the detached look on the police officer's face as he knelt on Floyd's neck.
"The eyes," he said. "It seemed so cold-blooded, lacking heart."
Ashmore said he can't fathom ever treating a Black person that way.
"I'm a nice person; I can't be racist." Ashmore has said those words to himself in the past, and he knows other white people say them too.
"But do I have parts that are buried somewhere in me that I've kept protected?" he's thought to himself.
"What are my blind spots" as a white man? "What am I tuning out?"
Ashmore has learned that he can be a good man and great father and aspire to make the world a better place, yet still benefit from a racist system that values his life more than that of the Black men, women and children captured in those wrenching scenes of mistreatment and death.
"This is serious surgery we're going through," Ashmore said of the self-examination among whites.
That inner conflict -- between thinking of yourself as a decent person and acknowledging the possibility that you might be contributing to racial injustice in some way -- has left Joakimides feeling disillusioned.
"It's hard to see yourself as part of the problem when you've spent your entire life trying not to be," said Joakimides, a chef in the Northern California village of Point Arena, situated in an area of windswept Pacific beaches and redwood forests about a three-hour drive north from San Francisco.
She was one of about two dozen sign-waving protesters, almost all of them white, who had gathered to demonstrate by the side of Highway 1 in the nearby town of Gualala.
They'd all come to show their solidarity with those around the country who were demanding an end to police brutality -- despite living in a remote corner where Black faces are few.
Wearing a mask to protect herself from COVID-19, Joakimides held back tears and stared solemnly at the ground.
She held a cardboard sign meant for anyone who's still not convinced they can help overcome racism: "Be an ally. Become the solution."
All she could say about Floyd's killing was, "I'm horrified."
"I thought we were making progress towards equality," she said. She let out a long sigh. "But things keep happening."
Even as a progressive who feels she's on the right side of history by supporting efforts to tackle climate change, sexual harassment and racist policing, Joakimides knows that she, too, has to be more honest with herself about what it means to be white in America.
"It's very easy to get used to the privilege of a safe life," said Joakimides, 57. "It's time to acknowledge my privilege -- and to use it to fight oppression."
Sexton, the salesman from Texas, said he's encouraged that so many white people in his community seem to feel as passionate about stopping police brutality as he does.
But he's also seen derogatory messages on Facebook about his efforts, including a post from a detractor who wrote "White lives matter" in response. Still, he's adamant that white conservatives like himself must look past the mockery and racist comments within their own ranks and do their part.
Like Ashmore, he understands that change starts not in the halls of government and in police departments, but at home.
Sexton speaks with pride about his 11-year-old son, Tyler, who stood next to him at the rally holding a sign he made by himself to express his outrage over the length of time the officer kept his knee on Floyd's neck.
It read: "It should not take 8 minutes, 46 seconds to see that Black Lives Matter."
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