Two men fight over an American flag in Cleveland's Public Square on July 19, 2016. (Photo by Michael Robinson Chavez/The Washington Post)

CLEVELAND — Pat Mahoney, 25, is a communist. Matt Meister, 41, is an anarcho-syndicalist. They're both members of the Industrial Workers of the World, and local activists, and they and a gaggle of like-minded folks who wanted to spread their revolutionary beliefs in Public Square on Thursday afternoon. It didn't quite go as planned, to the extent that they had a plan at all.

The capitalists kept accosting them, and the police kept separating the two groups, and so the communism-vs.-capitalism debate became a migratory and improvisational march, randomly snaking through downtown, going in big circles, with occasional pauses for an exchange of views, which is to say, shouting matches.

Also along for the ride: an unbelievable number of police officers and state troopers. The cops were so numerous they had reserve forces, auxiliary lines, many on bikes, with the law enforcement choreographed with the aid of police helicopters hovering high overhead and keep an eye on the "event zone" around the Republican National Convention.

Ensuring that the great debate between communism and capitalism would be fully documented were scores of photographers and random people holding up cellphones and taking videos.

"We wanted a soapbox," Meister said in the shade of a tree at Willard Park after the hubbub was over.

"We got a little bit of that and we were forced into a march," Mahoney said.

The two leftists said they'd had some decent exchanges with the capitalists but couldn't maintain the conversation because of the tactics of the police, who wanted them to keep moving, and because the news media kept pushing, trying to get The Shot.

Many of the capitalists were from a group called Turning Point, and they wore shirts saying "Socialism sucks." That was also one of their chants as they chased the communists.

"Communism has led to the deaths of over 100 million people," said Timon Prax, 19, a student at Cleveland State and one of the people waving pro-capitalist signs. Nick Cocca, 21, of Youngstown, who carried a sign saying Taxation Is Theft, said, "We're just here to make sure that capitalism and the free market and the Constitution are represented."

From Public Square the two groups meandered to the Veterans Memorial Park, then a block east to 6th Street.

"Look around you! Inequality's rising to levels not seen since the 1920s!" Mahoney, carrying a red flag and leading the way for the communists, shouted at his pursuers.

But the capitalists shot back: How can you be against capitalism if you have a smartphone?

"I can contact my loving mother whenever I want. It's innovation!" Prax told a reporter.

The stream of protesters, cops and journalists reversed course to the veterans park again, then once again went east, this time to 9th Street, hanging a left and winding up at the Free stamp. That's the Claes Oldenburg outdoor sculpture — a giant, red rubber stamp that would spell that word if you could only find a giant ink pad and a giant piece of paper.

Suddenly it was all over. The communists found shade, and re-hydrated, and ate food from the Food Not Bombs tent. A few Trump supporters milled around, but the arguments were over. The police were still not far away, but the tension had eased. It was awfully hot. At some point, no matter how strongly you feel about something, you hit a wall.

The radicals’ migratory protest was just one of the protests Thursday. The biggest was a more traditional rally, called Stand Together Against Trump, in which hundreds of protesters marched under a blazing sun across the Hope Memorial Bridge and to the edge of the Quicken Loans Arena.

Among the crowd were several Republicans. "I'm here to show that it's okay to vote with your conscience," said Chuck Tyson, a self-described patriot from San Diego, in reference to Ted Cruz's Wednesday night speech. "People need to listen at a time like this."

But the protest hit barriers. Much of Cleveland's downtown area around the arena has been ringed with high security fences. The protesters’ chants echoed on empty streets.

Later in the day, as the GOP prepared to raise the curtain on its convention's closing night, a group of Bikers Against Trump sashayed into a communist protest in Public Square. As one side bellowed "U-S-A, U-S-A," the other screamed for revolution. When voiced hoarsened, the leather-clad bikers turned on their heel. "This is boring," jeered one. And with that his group was gone.