Brenton Thwaites plays Nic, who is being held in a secure facility and is separated from his friends, Jonah and Haley. At least he thinks that’s what has happened. (FOCUS Features)

Two of the major plot turns in “The Signal” — a good-looking sci-fi thriller with more fashion sense than brains — hinge on misdirection involving simple arithmetic and spelling. I won’t spoil the fun by elaborating further, but when each moment arrives, it’s cheapened by the implicit insult to the audience’s intelligence. The twists feel less like jolts of genuine surprise than like being had by a third-grader with a good knock-knock joke.

The movie starts straightforward enough, with M.I.T. students Nic (Brenton Thwaites) and Jonah (Beau Knapp) driving cross-country to drop off Nic’s girlfriend, Haley (Olivia Cooke), at school in California. It’s clear that these kids are all whip-smart and tech savvy, as they decide to use the drive as an excuse to track down an anonymous hacker who has been taunting them from afar — accessing traffic cameras and Haley’s laptop webcam to spy on the progress of their trip. Using the troll’s IP address and other identifying information, they pinpoint a location in a remote area of Nevada.

“You know this is stupid, right?” asks Haley, just before Nic and Jonah step out of the car and all hell breaks loose.

The next thing we know, a battered Nic is waking up in a secure underground facility outfitted with such antiquated technology as cassette recorders, and staffed by hazmat-suited scientists who experiment on cattle. Haley is in a coma, and Jonah has been locked away out of sight, able to communicate with Nic only through the air vents.

Or is this all in Nic’s head?

“Jonah was never here,” insists the facility’s sphinxlike chief scientist (Laurence Fishburne), a man given to speaking in cryptic riddles — “Do you have 10 toes?” — and answering Nic’s questions about what’s going on with evasions worthy of a Washington press secretary. “Due to circumstances surrounding your condition,” he says, “I’m afraid that our information is extremely limited.”

That last statement, at least, is an apt description of the film, which also parcels out expository details with extreme stinginess. I’ll say one thing: The general state of confusion fostered by the head-scratching plot is a surprisingly effective way of maintaining continued engagement with it — if by “engagement” you mean “This better lead somewhere.”

Oh, it does. It’s just a less than wholly satisfying destination, despite some fun detours. (Veteran character actress Lin Shay, in a nutty little cameo, is one such pleasure.)

Directed by William Eubank, who wrote the screenplay with his brother Carlyle Eubank and David Frigerio, “The Signal” has visual style to burn. And it takes good advantage of the current state of paranoia arising from our surveillance culture and the pervasive mistrust in government.

On paper, this sounds like a good formula. If handled well, it could really pay off. Unfortunately, the figures that the filmmakers plug in to their calculations — which involve elements cadged from sources as disparate as “E.T. the Extra-Terrestrial” and “The Matrix” — don’t add up to much.

½ PG-13. At area theaters. Contains some crude language and violence. 97 minutes.