"Those attempting to find a plot in it will be shot," declares Mark Twain with his opening words to The Adventures of Huckleberry Finn. Now the National Theater of the United States of America (NTUSA) throws down its own gauntlet, serving up a mutant piece of this same American pie in DUMBO with its latest collective theater piece: What’s That On My Head?

Just when you think you’ve caught the thread of Head— "Oh, it’s a distorted, sometimes linear take on American history"— its mercurial cast snips away all your preconceptions of where the play is headed next. Unlike the tidy narration of textbooks, one period of our history bleeds into another, and yet another, with an anarchic lack of respect to time, rhyme, or reason. From epoch to epoch, the only constant is the characters’ bi-polar tendencies to either loathe their lot or get swept up in Head’s ants-in-your-pants, song-and-dance numbers. In the process, NTUSA brilliantly caricatures varied periods of class struggle, all the while lambasting the entertainment industry, which is quite entertainingly portrayed as lulling the masses into complacency.

Audience members enter the spectacle on swivel chairs set on a rolling platform that cloaked cast members discreetly push through the play’s— count ’em— seven different sets in the 4,000 square foot venue at the Nest Arts Complex. Just like on a theme-park ride through a haunted mansion, the audience is literally transported from scene to scene, century to century. Stages are often set up on all sides, bombarding and immersing the audience in the social shenanigans at hand: actors sometimes even join audience members on the platform. No set or costume stays the same for long, and the NTUSA cast doesn’t miss a beat in negotiating the hair-trigger transitions.

The play concerns three characters from three different periods of history, who wind up on an afterlife game show, where they time-travel and then, on pain of even further death, have to guess what objects have been placed on their heads. An undead game-show host (Jonathan Jacobs), wearing corpse-white foundation and electric-shocked hair that makes Don King’s look as relaxed as Sade’s, conducts the three contestants through his Kafkaesque maze. A celebrity panel stocks the variety-show segments that include the ruffle-shirted, guitar-strummin’ Anderson Brothers (Ryan Bronz and Matt Kalman), a Girl Genius (Normandy Sherwood), and a Rhett Butler look-alike named Roy Canard, Jr. (Aimee McCormick). Many of the celebrities themselves meet their maker in the course of the play, but then step back on stage to join the jamboree. For added danger, a big Monster (Gina E. Cline) also stalks the stages and licks his chops for losers on the game show.

Gallows humor is the order of the day in NTUSA’s reenactments— from colonial penury, to temperance societies crashing western seraglios, to slavery in Georgia, to the Great Depression, to the Cuban Missile Crisis and beyond. Toward the end, Roy Canard, Jr. drives home the gist of the play in his lounge-singer’s remake of John Lennon’s "Jealous Guy": "I was dreaming of the past/And my heart was beating fast."

Head has all the fragmentation of a dream and the heart-stopping panic with which we may behold the future in view of past injustices. On that note, please also take advantage of the voter registration cards that NTUSA has up front at the bar.

What’s That On My Head? created and performed by the National Theater of the United States of America (NTUSA), January 8 to February 8, Thursday to Sunday, 8:00 pm, Nest Arts Complex, 88 Front Street, DUMBO, Brooklyn, $15. For reservations, call: 212/615-6607. For more info: www.ntusa.org.