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In August, New York City mayoral candidate Zohran Mamdani hosted a citywide scavenger hunt, inviting voters to scour the boroughs in search of historic political sites. (Grand prize: a bag of chips.) Clues for it were written by veteran puzzle maker Natan Last, who has long endorsed the idea that puzzles at their best blend politics, community and a nerdy good time.

If you missed the hunt, Last’s book, “Across the Universe,” delivers similar pleasures. Though its subtitle — “The Past, Present, and Future of the Crossword Puzzle” — suggests a history tome, Last approaches the subject essayistically. Crosswords, for him, are arguments on behalf of things: of what qualifies as “common knowledge,” of what role puzzles should play in informing a citizenry, of how wordplay and slang snake into the mainstream. “The crossword is a uniquely capacious artifact ready to absorb and recast any group’s predilections and passions into puzzle form,” he writes.

That may seem like making too much out of an everyday diversion. But as Last points out, crosswords have long been a miniature version of America’s larger culture wars. Crosswords’ popularity exploded in the 1920s in various newspapers; Ernie Bushmiller, cartoonist of “Nancy” fame, exploited the “crossword craze” in a strip called “Cross Word Cal.” But killjoys swiftly arrived to dismiss it as paleolithic brain rot. The New York Times, now the best-known purveyor of crosswords, thought the puzzle beneath it, and didn’t offer one until 1941. (“The last adult in the newsroom,” Last smirks.)

The New York Times’ crossword is synonymous with its current editor, Will Shortz, who gave the puzzle a refresh in the 1990s, jettisoning academic jargon and obscurities in favor of layered puns and pop-culture references. Last recalls working as Shortz’s intern in 2009 and loving the experience. But Last is also the point of the spear among constructors who insist there’s plenty of room for improvement: tokenized ethnic terms, lack of gender parity among constructors, double standards (“erotica” is acceptable, but “gay erotica” isn’t?), a narrow view of what readers know or will accept. “The bar is on the floor,” USA Today crossword editor Erik Agard tells Last.

Last’s public statements on this subject, he writes, are often met with eye rolls: “Oh, so now the crossword puzzle needs to be woke?” But that high dudgeon, he notes, is “as good a proof as any that it’s not just a puzzle.” Not for the solvers he speaks to, who use their puzzle routines as calming influences or mementos of relationships. Not for constructors like India-born Mangesh Ghogre, who came to the U.S. on a specialized visa to make puzzles and who cleverly works Indian themes into his grids. And certainly not for institutions like the New York Times, which has made games a profit center in a news industry that’s often hemorrhaging cash.

Last’s range and intelligence help sell the importance of the crossword, then and now. Still, its lack of a direct throughline can be frustrating. Like a particularly manic solver, he attacks the subject in an across-and-down fashion, here contemplating the impact of AI on the game, there considering what role crossword-style wordplay had on Modernist writers like T.S. Eliot and Gertrude Stein, now contemplating the 1920s crossword craze, now skipping to its 2020s COVID-prompted renaissance. It’s all relevant, and Last is a bright and witty guide through all of it. He demands a certain comfort level with disorientation, though.

Still, that’s kind of the point: For him, puzzles should motivate solvers to be more than half-thinking box fillers. Instead, we should be comfortable learning new ideas through the puzzle. Mamdani’s scavenger hunt didn’t play a big role in his eventual election to the mayorship in October; it probably didn’t even play a small one. But it spoke to the concepts of play, surprise and diversity that the crossword at its best represents for Last. Maybe you don’t have immediate recall on the word “Haudenosaunee” (the Native name for the Iroquois Confederacy), but what’s so bad about a crossword puzzle introducing you to it? Like every other section of the paper, the crossword can bring the news. It can evoke — and shape — a culture.

“Thoughts & Prayers,” premiering Tuesday on HBO, is a documentary film about the $3-billion “active shooter preparedness industry,” that space where American failure meets American entrepreneurism. Though it approaches its subject with a certain formal neutrality, the title, a phrase now synonymous with political emptiness, does suggest a point of view. (Its subtitle is “How to Survive an Active Shooter in America.”)

That industry includes various forms of training involving teachers, students and first responders and products theoretically created to increase security — locks, alarms, robot dogs, bulletproof backpacks, bulletproof glass and bulletproof shelters that sit in the corner of a classroom. One company will put an image of your choice on a bulletproof wall hanging and sells a “skateboard [that] will outperform any other skateboard on the market, but it’s also a self defense shield.” “Every time there’s a tragedy, it economically benefits my family,” its founder admits. “We could be a $300-million company by the time this documentary airs.”

One company makes tourniquets “easy to apply in case of a mass casualty incident”; another specializes in latex bullet wounds for use in mass shooter drills: “the gunshot through and through to the neck … the multiple gunshot wound to the abdomen.” One senses in these endeavors a not insincere overreaction that substitutes for political action, shifting responsibility onto potential victims and accepting the problem as intractable. (Or as the Onion headline, published 38 times since 2014, has it, “No Way to Prevent This, Says Only Nation Where This Regularly Happens.”)

Directed by Zackary Canepari and Jessica Dimmock, it’s a sad black comedy, an Errol Morris sort of subject, shot in an Errol Morris sort of way — formal, neutral. The cinematography, by Jarred Alterman, is quite handsome and composed, amplifying the seriousness and eeriness, but also the banality and absurdity of the matter. Subjects face the camera head on, sometimes to speak, sometimes to sit silently for a portrait that might find them covered in fake blood and wounds from a role-playing exercise. The film gets a lot of mileage just settling on faces, tracking reactions, or lack of reaction. The camera is static, steady; action moves in and through the frame, sometimes in slow motion, like movie violence. This observational approach is regularly undercut, unfortunately, by a heavy-handed soundtrack that makes the film feel less trustworthy. It’s an aesthetic and rhetorical failure, but not a fatal one.

The documentary states that 95% of American school children practice lockdown drills.

(HBO)

More than 20 million adults have had active shooter training, learning how to keep doors shut or disarm a shooter, participating in multiplayer video simulations. In Provo, Utah, teachers learn to shoot. (“Breathe in through our nose, out through your mouth — let all that tension come out of you.”) But “Thoughts & Prayers” is most powerful when looking at or listening to the kids: 95% of American schools, we’re told, practice lockdown drills, which can begin as early as Pre-K (with “dinosaurs” substituted for gunmen, to, I don’t know, reduce trauma).

The film’s last act follows a massive reenactment at a Medford, Ore., high school, where a “mass casualty drill” was scheduled after a janitor turned himself into police before acting on homicidal thoughts. (They discovered many weapons in his home, and a written plan of attack.) Kids, made up as victims, litter the halls and gym field. Masked “shooters” go room to room. The police chief gives, as a sign on the podium reads, a “fake press conference.”

“This is the reality, this is where we are in this country, where we are in this valley,” says the school superintendent afterward. “But I do not want to lose the fact that it is still a sad thing that we have to do this. Still, you may wonder what good it will actually do, and hope not to find out.”

What passes for a gun debate is relegated to some warring soundbites from the floor of Congress, and the opinion of one trainer (named Thrasher) that guns aren’t the problem, but “family structures” and “the lack of tribalism.” But here’s Quinn, a high school freshman from Long Island, N.Y., as close as anyone here gets to addressing the issue. It’s worth giving her the last word.

“I don’t think that a lot of adults care about our opinions. We go through this every single day. We go through, like, being afraid of going to school because we might get shot, or we might lose a friend, or we might lose a teacher. And a lot of people care about their … rights, I guess, more about, ‘Oh well, I want to have the ability to own a gun, and so I don’t care if you get shot in your class.’ It’s just kind of disheartening. ‘Cause it’s like, oh, you care more about yourself than all of the students in America.”