With his stately drawl, Morgan Freeman has narrated nonfiction documentaries about penguins, slavery, the lemurs of Madagascar, ancient Egyptian pharaohs and the expansion of the universe. His is a voice of authority tempered by warmth and wisdom, capable of evoking felt human experience and the majesty of creation. In writer-director Luc Besson’s taut, fun Lucy, Freeman narrates several documentary sequences of soulful, unscientific horseshit about the human brain.

It’s not as if anyone will go all “Mythbusters” on Lucy as Neil deGrasse Tyson does on Gravity, but it’s fair to say that only people who actually use 10 percent of their brain capacity still believe that humans use only 10 percent of their brain capacity. But that’s the whole premise of Lucy, in which Besson classes up a pulp-superhero plot with half-understood evolutionary science and that old, smelly, percentage-based chestnut about brains.

None of that matters; it makes exactly as much sense as a radioactive spider bite or an overdose of gamma radiation. Besson’s film is about a woman who needs to find the meaning of life in a serious hurry. He opens Lucy with the image of a woman manipulated psychologically and physically by a man, who keeps grabbing her arm so she can’t walk away; he concludes with the image of a woman whom men literally can’t touch.

Scarlett Johansson carries the film effortlessly, bridging Besson’s narrative and logical ellipses by fully embracing his crowd-pleasing intentions and convincingly depicting Lucy’s psychological transformation. While Johansson is a high-status figure and a giant movie star, she lacks Maleficent-grade remoteness, alternating between accessible vulnerability and dispassionate violence without losing the audience’s empathy.

Probably because she uses only 10 percent of her brain’s capacity, Lucy, an American student living in Taiwan, fails to recognize her new boyfriend’s corn curl-shaped cowboy hat as an obvious creep signifier. Bullied into delivering a mysterious briefcase to a Taiwanese syndicate boss (Choi Min-sik), she’s knocked unconscious and wakes up with a bag of an experimental drug sewn into her abdominal cavity.

It’s a synthetic version of a human growth factor and, when the bag breaks open, the overdose stimulates Lucy’s brain into an evolutionary process that heightens her senses and gives her superhuman powers of cognition and memory. Besson tracks her cognition meter’s increase with title cards — at 20 percent brain capacity, she can shoot around corners; at 30 percent, she can see through walls. Ultimately, Lucy controls physics and matter with her mind. So that’s the mob’s plan: to sell a transhumanism-inducing drug to club kids, which futurist Ray Kurzweil probably never saw coming. Chased by police and the mob, Lucy travels halfway around the world in pursuit of the other drug mules.

However gaudy and baroque Besson’s films can become, the director has a core of sincerity that drives (and sometimes overpowers) his films. Lucy, with her enhanced neurology burning brightly and quickly, becomes aware that the drug will kill her in 24 hours. Amid the film’s crossfire of revenge confrontations, shootouts, and gravity-flouting car chases, Besson includes a surprisingly poignant moment in which Lucy, whose personality is evaporating in the heat of her transformation, makes a sad, final telephone call to her mother.

In a hurry to find the meaning of life before the drug burns her up, she turns to Freeman’s Professor Norman, a famous evolutionary biologist and stirring voice-over narrator. He tells her that the meaning of life may be to do what individual cells do: Pass on their genetic knowledge to a new generation. This Promethean task becomes Lucy’s quest and the film’s arc, which vectors toward an unexpectedly huge and cosmic finale — one perhaps best explained in the warm, sonorous tones with which the best life-affirming, science-y bullshit is conveyed.

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