“You could not pay me enough to be 24 again,” a free-clinic gynecologist says with a weary sigh while examining the nether regions of Hannah Horvath, the talkative, deeply neurotic central character of HBO’s startlingly original new series, “Girls.”

“Well, they’re not paying me at all,” Hannah says, bitterly.

Hannah’s another 24-year-old adrift on the sea of self-discovery and only vaguely aware that there is no promised shore. She’s writing a memoir but four chapters in has realized she still has yet to live the other nine essays she’ll need to make a book. “I want to be the voice of my generation,” she tells her parents. “Or a voice of a generation.” She works as an unpaid intern at a publisher.

The very first scene in “Girls,” which premieres Sunday night, shows Hannah — played by the show’s creator-writer-director-star Lena Dunham — wolfing down a fancy plate of pasta at a Manhattan restaurant with her visiting mother and father. Her mother tells her that they’re no longer willing to pay her rent and expenses, including her cellphone. They’re cutting her off. “No. More. Money,” her mother says, while her doting father (Peter Scolari) nervously backpedals, agreeing with Hannah that it’s a net savings to keep her on the family phone plan. But even he admits, “It may be time for one final push.”

There are only a thousand or so demographic studies, surveys, parenting books, angsty memoirs and trend articles claiming to support this — most of it written in a way that ensures that anyone older than 35 will roll their eyes and leave righteously cranky comments at the bottom of the article. Whether we realize it or not, America is experiencing a spasm of cross-generational disconnect at a level not experienced since perhaps the 1960s.

Dunham, 26, is the Oberlin-educated daughter of two artists, raised in private-school privilege in Manhattan. She has followed the surest impulse of any budding storyteller by writing and filming what she knows. Her first feature film, 2009’s “Tiny Furniture,” was a bleak story of a young self-absorbed woman who returns to her artist mother’s downtown apartment after college graduation and awakens to the idea that she has no prospects.

The film was a haunting exercise in personal and sexual letdown — just the kind of thing HBO loves. Dunham’s real mother and sister played her character’s mother and sister in the film. Critics and film-festival denizens praised “Tiny Furniture’s” honesty, earning Dunham comparisons to the younger versions of Norah Ephron and Woody Allen.

But acclaim for “Tiny Furniture” wasn’t universal. Dunham’s invented, semi-autobiographical world may not resonate with the 24-year-olds who live among us and work two jobs while paying off student loans, or who go off to fight wars, or who finish nursing school while raising a baby, or who simply don’t have the sort of parents who can float the rent for a year or two while they explore their career options in the big city. Executive produced by Judd Apatow, “Girls” has already tantalized the New York cognoscenti, which may have less and less appeal the farther you get away from Brooklyn and Lower Manhattan. Still, Dunham has created a superior work of fictionalized anthropology.