JUDY WOODRUFF: But first: the dangers of domestic terrorism, extremism and efforts to counter its use of social media.

The attack in Charlottesville underscored just how real this is.

As Miles O'Brien explains, experts who study the psychological and technological underpinnings of extremism say neo-Nazis and Islamic terrorists are cut from the same bitter cloth.

It is this week's Leading Edge and a co-production with PBS' NOVA.

HUMERA KHAN, Muflehun: We want to make sure that people can openly talk.

MILES O'BRIEN: At the University of Illinois-Chicago, on this summer morning, a small group of determined people gathered in a classroom to figure out what they can do about terrorism.

HUMERA KHAN: My name is Humera Khan. And your name?

MILES O'BRIEN: Humera Khan was schooled as a nuclear engineer. She holds four degrees from MIT. But now she is doing something perhaps more complex, and most certainly less predictable, than splitting atoms.

In sessions she calls viral peace, she tries to find ways to battle extremism online using social media to counter the narrative.

HUMERA KHAN: The idea is teaching them how to recognize when they are being manipulated, and then teaching them the skill sets for how to respond, should they respond, when should they respond, and using social media to come up with their own campaigns.

MILES O'BRIEN: She thinks stories effectively told on social media can motivate people to turn away from violence.

Participants identify flash point issues and underlying causes of extremism. The problems are posted, sifted and prioritized. Then they work on their own campaign. The winner gets $1,000 to implement the idea.

But this is not just about Islamic terrorism. It's about all kinds of hate and extremism.

CHRISTIAN PICCIOLINI, Former White Supremacists: My name is Christian Picciolini. I'm the co-founder of Life After Hate.

MILES O'BRIEN: Christian Picciolini is a former white supremacist skinhead, who was the lead singer in a racist heavy metal rock band. He ran an organization focused on identifying white supremacists who might be convinced to walk away, de-radicalization.

CHRISTIAN PICCIOLINI: Big place for people who are involved in hate groups to leave.

I think it's tough for us as a country to hold a mirror up to ourselves, to address a problem that's inherent in our own population and our own citizens.

PROTESTERS: Jews will not replace us!

MILES O'BRIEN: The ugly scene in Charlottesville made it difficult to avoid that mirror.

PRESIDENT DONALD TRUMP: Charlottesville is a great place that has been very badly hurt.

MILES O'BRIEN: President Trump was reluctant to blame white supremacists and neo-Nazis for the violence, and offered support for their protest march to save a statue of Robert E. Lee.

PRESIDENT DONALD TRUMP: I think there's blame on both sides.

MILES O'BRIEN: Former Ku Klux Klan grand wizard David Duke said he was thrilled by what the president said.

CHRISTIAN PICCIOLINI: What's scary about Donald Trump and what's happening is not that he's creating racists. I don't believe that. I believe that these people existed. He's created a safe place for them to now vent.

MILES O'BRIEN: And he has retweeted messages from neo-Nazis, giving them a global audience.

J.M. Berger is a fellow with the International Center for Counter-Terrorism.

JM BERGER, Terrorism Analyst: If you are somebody who believes that white people are being subjected to genocide, and, you know, that desperate measures are required to preserve the existence of the white race, and you get Donald Trump to retweet your content, then, suddenly, you have an audience of millions of people that you didn't have before.

MILES O'BRIEN: Berger studies the links between extremism, terrorism and the Internet. He has carefully tracked the rise of online recruitment and propaganda created by Islamic terrorists.

JM BERGER: Social media has inherent advantages for extremists that mainstream movements don't have. And ISIS is only the first group to realize this. And we're going to see many others. I think we're in for a decade or more of significant instability that can be attributed to the interconnectedness of the world.

MILES O'BRIEN: Social media companies have had some success thwarting the online threat from ISIS, because the message is so extreme and so violent.

JM BERGER: It is easier for these companies to step on them.

White nationalists, while they are marginalized in our society, they are still very much embedded in our society. And they are currently enjoying a pretty good run of mainstreaming some of their beliefs. If they are not advocating for violence directly, it's a much harder problem.

CHRISTIAN PICCIOLINI: And until we can classify white extremists as terrorism, it won't have the same resources, it won't get the same priority, and won't get the same funding to fight it.

MILES O'BRIEN: The Trump administration has gone in the opposite direction, killing a $400,000 grant for Christian Picciolini's Life After Hate Group.

PROTESTERS: You will not replace us!

MILES O'BRIEN: It was part of a broader effort to cut federal funding for campaigns against domestic terrorism.

But should the Trump administration treat white extremism differently?

Not according to University of Maryland psychologist Arie Kruglanski.

ARIE KRUGLANSKI, University of Maryland: There's a universal process that prompts people to the extremes, prompts them to deviate from the mainstream and move to the fringe.

And the same process applies to neo-Nazis in Germany, Sri Lankan Tamil Tigers, Muslim extremism, or the militia, the far right in the United States.

MILES O'BRIEN: Kruglanski says extremist groups thrive during times of uncertainty, offering simple black-and-white answers in a world filled with many shades of gray.

Their messages, transmitted via Twitter, Facebook and the like, offer something they crave, certainty. The psychological term is cognitive closure.

ARIE KRUGLANSKI: At the psychological level, it's the very same dynamic that gives us ISIS, because ISIS also thrives on a very clear-cut ideology that promises the world and promises order and fame and structure, and that's what Trump promises as well.

MILES O'BRIEN: Terrorism expert J.M. Berger believes the Internet is hastening the polarization of our society, and he says there is no easy way to stop it.

JM BERGER: I don't think that there's a solution is going to come around soon. I think it's going to take quite a while, and I think that identity-based extremists are going to get the most benefit out of these technologies. And I think that we're going to see the things we have seen with ISIS with other groups.

MILES O'BRIEN: But the proliferation of the Internet and social media cuts in both directions. And that is what has brought these people together in Chicago.

CHRISTIAN PICCIOLINI: While there is a lot of misinformation and a lot of recruitment to extremism happening online, it also serves as a wonderful platform for counternarratives, for people to reach others with an alternate message to what the extremists are proposing, and also to link the facts, so people can do their own homework.

MILES O'BRIEN: Humera Khan strongly believes in promoting a counternarrative, stories that can motivate people to turn away from violence.

HUMERA KHAN: We are talking about a minuscule, less than a percentage, which means we have the numbers on our side, if we can actually mobilize them to actually do good, not just watch, but actually step up and say, OK, I have a role, and I will do it.

MILES O'BRIEN: Extremists have always been among us, and they have always been small in number, but, these days, everyone owns a global megaphone.

HUMERA KHAN: Because anyone can have a role in bringing others in to the community.

MILES O'BRIEN: In Chicago, I'm Miles O'Brien for the PBS NewsHour.