Late in the HBO miniseries "Show Me a Hero," which concludes this Sunday, several hundred public housing residents gather on folding chairs in a Yonkers gymnasium hoping for tickets out of the city's neglected high-rise projects. On offer are 70 new townhomes on the wealthier, whiter side of the city, under construction as part of a court-ordered desegregation plan several agonizing years in the making.

On stage at the front of the room spins a plastic tumbler with scraps of white paper inside. This is a true lottery, a bureaucratic necessity performed as public festivity. "Now I know there are a lot of anxious folks here, so let's just get started right away," says Peter Smith, the director of the city's housing authority, grasping the first white scrap. "Number One... is Delphina Page!"

One woman after the next leaps up, hooting with joy. The mothers wrap their children in bear hugs and dance in the aisles. Everyone applauds. This is the moment in the series, based on Lisa Belkin's book about an epic and true housing clash that occurred in the late 1980s, when the 200 units of housing at the center of the fight — over which Yonkers officials court contempt, jail time and municipal bankruptcy — cease to be a theoretical possibility or a political burden. Up to this moment, it's not even clear if the houses will ever be built, as pipe bombs and vandalism mar their construction.

At the lottery, as the houses are paired with families, they begin for the first time to take shape as homes. As places where specific people will raise their children and take out their trash and re-hang their family photos. Housing that symbolizes, to other characters, an economic threat, or a political accomplishment, or a social theory, now mean to someone a place to set up home.

As the lottery progresses, the mood in the gymnasium turns glum. The room starts to empty. The names still spinning in the tumbler outnumber the houses left. Their enormous value becomes even more clear in the grief of families who will not get them. By the end of the lottery, some of the show's recurring characters are winners. Others are not.

The scene dramatizes the hard-to-capture human side of every fair-housing fight. We talk about historic events like the Yonkers court case, or battles that precipitated the Fair Housing Act, with obscure statistics and impenetrable words. Sociologists track the snail's progress of desegregation with something called the "index of dissimilarity." HUD warns communities that they're obligated to "affirmatively further" fair housing. Another suburb boxes out the poor through "exclusionary zoning."

But these fights are all, always, about someone's home (or a home denied), and the deeply personal things that home entails: safety, security, opportunity, pride. Fair housing is an abstract concept. But there is nothing abstract about a blind woman who can't get a home health aid to visit her in the projects. HBO's drama has been widely celebrated by housing wonks because it illustrates that emotional reality as statistics and moral arguments often fail to.

The show, written by David Simon and William Zorzi, has aired with astounding timing. Ferguson and Baltimore have shown that deep racial inequality persists in America, and that it's still built into our housing patterns. In June, the Supreme Court upheld a crucial legal tool that has long been used to attack segregation. In July, HUD announced historic new rules strengthening the Fair Housing Act.

Now, in late August, here comes a sweeping television drama that captures why that Supreme Court decision matters, and how places like Baltimore and Ferguson were created, and what HUD means by integration. "Show Me a Hero" is the story we need in 2015 to interpret the significance of these other complex events.

To buy that, you have to recognize that Yonkers in the late 1980s and early 1990s is not so different from plenty of American communities today. In fact, Westchester County, New York, where Yonkers is located, is embroiled right now in its own years-long standoff over how and where to build court-ordered low-income housing.

St. Bernard Parish, on the edge of New Orleans, just last year settled a decade-long lawsuit over local laws that restricted rental housing and who could move into the community. This summer, many wealthy suburbs of Chicago shrugged off a state deadline to draft affordable housing plans.

Part of what's so powerful about the Yonkers story is that it has more in common with these recent episodes than with the desegregation fights of the 1950s and '60s. Opposition to the new black neighbors in the white part of town isn't, for the most part, violent. It's passive. It's a homeowner letting her poodles go on the public-housing lawn. It's coded: those people. In Yonkers, racism mostly lurks below the surface, among people waving American flags.

“You will never hear Jack O’Toole utter a racist phrase," Yonkers Mayor Nick Wasicsko (played by Oscar Isaac) says of one of the community activists fighting the housing, "because guys like that, they learn how not to say the bad words. ... No more 'n----,' nothing out of his mouth that will give it away. It’s all property value and life and liberty and people only living where they can afford.”

Opposition to HUD's new fair-housing rules sounded a lot like this, too: If the government moves poor families into the suburbs, property values will fall. And that just punishes people who worked hard for what they have. The government shouldn't meddle in a housing market that's already free and fair anyway.

There is a particularly infuriating scene in "Show Me a Hero" where Hank Spallone (another city councilman who takes a turn as mayor) drives through the projects with a photographer, collecting evidence to show at city council meetings of the mayhem that will reign on the nice side of town if 200 units of low-income housing are built there. The photographer snaps a drug deal and a craps game, and men idling on a couch on the street corner.

He puts his camera down as the car drives past students, lunch boxes in hand, walking home from school with their mothers, past a playground with children hanging from monkey bars, past a nurse returning home from her job. Silently, we watch the photographer edit out the humanity in the neighborhood. And what's left over feels, too, like how poor urban communities are often described in political fights today.

The show's closing credits remind us, one last time, that this story isn't so far removed from our own time, and that whatever parts of it made us comfortable can't be dismissed as distant history. The fair-housing case at the heart of "Show Me a Hero," stemming from a lawsuit filed by the NAACP in 1980, wasn't settled, completely, until 2007.

Correction: This post originally misspelled the name of Yonkers Mayor Nick Wasicsko.