Some character or other is constantly saying in the course of this family flick that they don’t have a clue as to what’s happening. And as “The Last Mimzy” unspools, you might very well sympathize with them. Even the title is a bit of a mystery. It obviously has to do with the famous nonsense poem by Lewis Carroll, and the script is in fact an adaptation (and modernization) of a 1943 short story by Lewis Padgett called “All Mimsy Were the Borogroves,” a line from “Jabberwocky.” There’s even a pointed “historical” allusion to “Alice in Wonderland” and its white rabbit in the picture. But even that part of the plot is never very satisfactorily explained, and it’s just one more way in which “The Last Mimzy” as a whole comes across as unfinished and more than a little chaotic.

The picture is structured as a story within a story, bookended by scenes in which some children, sitting in a flower-drenched field, are told a tale about one of their scientists, who helped save their world—and humanity—from destruction. The narrative proper then begins, focusing on a Seattle family: David and Jo Wilder (Timothy Hutton and Joely Richardson) and their two children, Noah (Chris O’Neil) and Emma (Rhiannon Leigh Wryn). Dad’s often off working late, and Noah’s having some trouble at school, but overall they seem a contented group. But things take a strange turn when the kids find an odd box on the beach near their summerhouse. It emits a curious sound, and opens like the puzzle from “Hellraiser” to release some weird artifacts—some spinning rocks that send out blue rays, what looks like a snail-shaped bubble of blown glass, a spangled shell, and a stuffed bunny, with which little Emma quickly becomes enchanted and calls Mimzy. Before long the objects are having a curious effect on the children. Noah becomes a scientific genius who can control the webbing activities of spiders and absently draws complicated designs that mirror the structure of the universe as seen in eastern spirituality. Emma can dematerialize her arm by inserting it in the spinning rocks’ rays and can levitate at will. And medical tests indicate that their brains are actually growing.

The powerful objects, however, also bring them government attention. When the shell apparently causes a massive electrical blackout in the area, Homeland Security steps in, led by hulking Nathaniel Boardman (Michael Clarke Duncan, who seems several sizes too large for his suits), and the family is taken into custody. The government scientists focus in on Mimzy, which turns out to be some sort of combination of organic material and artificial intelligence advanced far beyond anything known to man. It’s up to the kids to rescue the rabbit and, in a last act far too reminiscent of Spielberg’s flying bicycles, spirit it away to release it back to its world. They’re aided in this by Noah’s semi-nutty science teacher Larry White (Rainn Wilson) and his girlfriend, palm-reader Naomi Schwartz (Kathryn Hahn), who’s as fascinated with far-out philosophy and oriental mysteries as he is.

All the goings-on are eventually tied together; there is, as it turns out, an explanation of sorts for the box, its contents, and its effects on the children, though much of what happens remains fairly arbitrary because, in the end, when the artifacts achieve their purpose, it’s the result of pure accident. And the modernization of the narrative, with all the emphasis on alternate forms of spirituality and post-9/11 security concerns, muddies things up further. The result is a movie that’s cluttered and untidy, a New Age version of “E.T.” overstuffed with messages about expanding consciousness and saving the earth.

And “Mimzy” isn’t very well made, either. Long-time studio executive Robert Shaye, who directed (for the first time since the forgettable “Book of Love” in 1990), proves no great shakes with actors. O’Neil and Wryn, while personable enough, never seem like anything but likable amateurs, and Richardson, Hutton and Duncan don’t appear to best advantage, either. Wilson goes the goofy good-guy route in a departure from his “Office” character, but though he and Hahn make an energetic pair, they come across as all too aware that they’re in a kids’ movie, and play to the rafters. All of the cast, moreover, are undercut by Shaye’s lackadaisical style, as well as his clumsy, unattractive composition of individual scenes (for which cinematographer J. Michael Muro must also shoulder part of the blame). The effects, from the Orphange (supervised by Eric Durst and Alex Burdett), are mediocre. And Howard Shore’s score is disappointing, given the source—bland and conventional.

But it would have been difficult for any composer, however gifted, to be energized by watching rushes from this movie. “The Last Mimzy” struggles to be a heartwarming fable about the empowerment of children and the need to work together to solve humanity’s common problems. But in the end it comes across as more fuzzy-headed and inarticulate than the title’s stuffed bunny. It may reach for the stars, but remains resolutely earthbound.