“Whoever wants to know the hearts and minds of America,” Jacques Barzun wrote more than half a century ago, “had better learn baseball.” There are some misguided souls who feel that this is less true now than it used to be because of the Super Bowl’s ratings or because the NBA markets jerseys in China. Ask them if Ken Burns has ever made a nine-part series called “Basketball”; ask what museum display exhibits on the glory days of pro football?

The Museum of the City of New York’s new exhibit, “The Glory Days: New York Baseball, 1947–1957,” may make you nostalgic for a place and time you might never have known. For the 11 years covered in the exhibit, the New York Yankees, Giants, and Brooklyn Dodgers won 17 of 22 pennants and 9 of 11 World Series. To paraphrase Yogi Berra on Don Larsen’s perfect game in the 1956 World Series, nothing like that had ever happened in baseball history, and it hasn’t happened since. “The Glory Days” is an extraordinary collection of both mainstream and arcane memorabilia, as well as interactive exhibits such as a “virtual” Ebbets Field that takes visitors on a ghostly tour of the Brooklyn Dodgers home park. Things like the glove and silver bat that greet you as you enter could come from just about any era; the sight of their owner, Willie Mays, enjoying a Chesterfield cigarette in a magazine ad immediately cue you in that these are relics from a more innocent time. For that matter, a full-page ad featuring Jackie Robinson, his wife, Rachel (resplendent in white gloves, her arms filled with grocery bags), and Jackie Jr. plugging a brand of white bread (“It’s homogenized!”) seems no less alien than the sight of smiling athletes selling cigarettes.

The 1947–1957 era, beginning with the Yankees’ first postwar pennant and ending with the Dodgers’ and Giants’ move to California, seems in many ways a poor ancestor of the game we know today. Attendance dropped as returning GIs fled the inner city for the suburbs. Ballparks, particularly the Giants’ Polo Ground and Ebbets Field, decayed. Players’ salaries were a tiny fraction of those today; a memo from a Brooklyn Dodgers trip to Japan in 1956 shows not a single player, including Jackie Robinson, Pee Wee Reese, and Duke Snider, being paid for a season anywhere near what Alex Rodriguez is paid today for each game. Yet, it’s hard for modern fans to escape the notion that we missed something. Clear black-and-white photos take us back to a world of working-class heroes: 1954 National League Most Valuable Player Willie Mays playing stickball with children on the streets of Harlem, 1950 American League MVP Phil Rizzuto selling men’s hats in a department store, 1955 NL MVP Roy Campanella at his Harlem liquor store — these are ballplayers New Yorkers related to in a way we’ll never relate to any professional athletes.

Half the fun of walking through “The Glory Days” is listening to grandparents tell their grandchildren about what it was like; the other half is in observing the children’s reactions. For instance, one of the exhibits features World Series commentary delivered in the lilting Alabama drawl of Mel Allen (were all baseball announcers back then from the South or did they just sound that way?). A 12-year-old’s response: “It must have been great to watch a game without all of that other garbage” — network logos, ticker tape stats, plugs for upcoming events — “on the screen.”

More than any baseball exhibit I’ve ever seen, “The Glory Days” is about and for fans — their obsessions (private collections of baseball cards, board games, and scrapbooks), their agonies (in the stricken faces of Dodgers fans when Bobby Thompson’s 1951 “Shot Heard ‘Round the World” home run beat Brooklyn for the pennant), and their community of baseball.

For a modern fan, the most exhilarating photograph isn’t of Joe DiMaggio hitting a game-wining World Series home run or Willie Mays’s amazing catch in the 1954 series, or even of Jackie Robinson in 1947, the year he broke baseball’s color barrier. The eye-opener, which takes up an entire wall, is a street celebration of average men and women smiling, cheering, hugging, and otherwise reveling in the Brooklyn Dodgers’ first and last World Series victory in 1955. For someone observing the scene in 2007, there is a poignancy that the Dodgers fans could not possibly have anticipated: In less than three years’ time, their beloved team would be gone, and Ebbets Field a memory. Probably never again in their lives would they know a collective joy so unqualified, and, probably, neither will we.

Until December 31 (1220 Fifth Ave. at 103rd Street, 212-534-1672).