This piece discusses David Simon’s HBO miniseries “Show Me a Hero.” It references aesthetic details, but no significant plot developments, from the first five episodes. At the beginning of the third episode of “Show Me a Hero,” a new miniseries about housing desegregation in Yonkers, N.Y., from David Simon, William Zorzi, and Paul Haggis, Yonkers Mayor Nick Wasicsko (Oscar Isaac) takes his girlfriend, Nay Noe (Carla Quevedo), to look at a long-vacant and dilapidated house blessed with a remarkable view of the city. “This could be the best house in Yonkers,” Nick tells her. “I mean, a little time, a little money.”

He’s talking himself into the courage to call the real estate agent; though he has been poking around the house through the course of the series, Nick is only 28, and he has never owned a home. “Maybe it’s cheaper than we think,” he speculates. “Maybe it’s haunted. Maybe it’s on an Indian burial ground. Oh, s—, maybe it’s on Oscar Newman’s list of alternate housing sites for public housing.” But for all the other reasons Nick hasn’t bought the house, the real thing that has given him pause is the sense that he wasn’t yet accomplished enough to live in such a place. “I hadn’t done anything to deserve a home like this,” Nick tells Nay.

The question of the homes we deserve is at the heart of “Show Me a Hero,” which is based on Wasicsko’s real-life fight to implement a court order that Yonkers desegregate its public housing. He won the mayoralty by campaigning against the court decision but fought a desperate battle to comply with it once it became clear that the city had no real option other than to build townhouse-style public housing on sites across the city ordered by Judge Leonard Sand (Bob Balaban). Other reviews have justly praised the way “Show Me a Hero” builds high drama out of the minutiae of city council negotiations and noted the shortcuts the series takes in some storylines. But what stood out most to me was the way “Show Me a Hero,” a carefully composed show shot with great attention to detail, shows us what home means in almost every scene; its visuals make arguments as powerful as any line of dialogue.

One of the most audacious shots in “Show Me a Hero” comes early in the series, and it provides a stark illustration of the different ways people in Yonkers live. A helicopter takes off from Manhattan and flies up the Hudson toward Yonkers. From the air, we see houses set on large lots, separated from one another by swaths of green lawn: the American dream. But that idealistic geography gives way to a starker vision. The buildings get taller until they’re the high-rises that are instantly visible as American public housing. When there are lots, they’re paved in concrete and have buses or construction equipment huddled in corners. These are the basic conditions of life in Yonkers, the physical sorting of people seen from high in the air.

Mary Dorman (Catherine Keener), who joins the movement against the new public housing units, sums up the ugly core of anti-desegregation sentiment from the ground up early in the series. “These people,” she says, disgusted by the plan to bring West Yonkers residents into East Yonkers communities. “They don’t live the way we do. They don’t want what we want.” “Show Me a Hero” constantly proves her wrong, and not merely by portraying residents of the high-rise projects as industrious people who are committed to their families and to hard work.

Many of the scenes set in the project apartments of people such as nurse Norma O’Neal (LaTanya Richardson Jackson), furniture restorer Alma Febles (Ilfenesh Hadera) and Janet Rowan (Melanie Nicholls-King) take place in kitchens, and they almost all include shots of neat dish drying racks. The rooms may be cramped, but there’s a brightness and order to them: the light that shines through Mary’s white curtains in East Yonkers, the black and yellow design on the curtains in Alma’s apartment, and the flowered curtains in Norma’s bedroom is the same everywhere.

Their tastes in home decor betray a similar dignity, and at times, proof that occupants of these very different residences have reached the same stage of life. even if they aren’t proceeding from the same place. Brass clocks hang on the hallway wall in Mary’s handsome brick house, while family photographs tile the walls in Norma’s apartment. The white, promising walls in the apartment that young widow Doreen Henderson (Natalie Paul) moves into with her young son show the same potential as the larger, blank canvas of Nick’s dream house, which he and Nay eventually move into together. A beautiful butterfly even emerges from the chrysalis of graffiti outside the elevator in Doreen’s new building.

“Show Me a Hero” is sensitive to the emotional geography created by housing, too. Norma’s familiar building becomes unnerving to her when diabetes starts to eat away at her sight; the red nail polish she paints on her buzzer to make it easier to see gets rubbed away. Later, Norma isn’t surprised when the home health aide who is supposed to start working with her claims she got hopelessly lost trying to find Norma’s apartment.

In another storyline, Billie Rowan (Dominique Fishback) remarks to her boyfriend John (Jeff Lima) that he’s never been to visit her in the unit where she lives with Janet, her mother. The apartment may be housing, but it’s not quite a home. And Mary Dorman tells a reporter, “There are two black girls on my bowling teams. I haven’t been in their homes, but I’ve driven them home.” She’s trying to prove she’s not prejudiced, but teammates whose houses you won’t go inside aren’t really your friends.

By contrast, stubborn NAACP lawyer Michael Sussman (an excellent Jon Bernthal) bounds happily into a big, Tudor-style house for negotiations intended to break the deadlock around the housing plan, taking control of a foosball table with an air of puppyish enthusiasm. No character in “Show Me a Hero” needs to use words to explain the luxury of excess space an adult man can use to store a game, the security of not needing to worry who might come rushing through his door.

And when Bob Mayhawk (Clarke Peters) comes calling to Mary’s home, asking her to serve on a commission to help residents adjust to their new public housing units in new neighborhoods, the visit might have been a disaster. After all, he looks like the Yonkers residents Mary had deemed “these people,” insisting “They don’t live the way we do.” But Mayhawk takes exquisite care with the home Mary loves so much, wiping his shoes carefully on her doormat, brushing up the crumbs from the pie she offers him and depositing them back on the plate so they won’t sully her rug.

“Your houses are just houses,” city official Peter Smith (Terry Kinney) tells Oscar Newman (Peter Riegert), the consultant who designed the townhomes and fought every proposal that might prevent the new developments from being successfully integrated into the surrounding neighborhoods. “The people we put in them are going to matter even more.” While “Show Me a Hero” certainly acknowledges that there are some people who crave the stability of a well-appointed residence more than others, the miniseries is a forceful argument that you can’t be house-proud without a home. The designs Oscar sketches on graph paper with a confident hand and the blueprints Nick rolls out on his desk aren’t communities. But you have to break ground somewhere.