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Michel opens on a TV studio where a show called Stephane TV is in progress. Stephane (Mexican heartthrob Gael Garcia Bernal) is “taping” a show about himself, but with cardboard box cameras and egg carton sets, and endless free-associative mumbo-jumbo. It soon becomes clear that we are in a dream unfolding inside Stephane’s head.

Or are we?

Stephane has come to Paris from Mexico to take a creative “graphic design” job at his mother’s request — only to find himself laying out cheesecake office calendars with a trio of oddball French co-workers. Stephane falls for his next-door neighbor, Stephanie (Charlotte Gainsbourg), but he’s too shy — and, we learn, mentally unbalanced — to make his feelings clear. Specifically, he can’t distinguish reality from his complex and fanciful dreams. But these are no Walter Mitty-type dreams; they’re Michel Gondry dreams. Weird, surreal stuff.

Gondry is a dreamer himself. He’s known for devising wild and kooky videos for Björk — stuffed bears running through cellophane forests and the like — and it’s hard to tell who’s more of a nutter: the Icelandic balladeer or the French director of Eternal Sunshine of the Spotless Mind and Human Nature.

Gondry himself is a bit of a quandary. He developed the “bullet time” film effect that was later used to great acclaim in the Matrix movies. He has directed straightforward fare like Dave Chappelle’s Block Party. Yet he excels at whimsical imagery involving toys and childlike art materials. He delights in slicing up time in his movies and videos for the White Stripes, Beck and the Chemical Brothers.

Like Eternal Sunshine, The Science of Sleep is a love story, of sorts. It also deals with the difficulty of communicating love, and the obstacles the mind puts in the way — such as bad memories, or in Stephane’s case, full-blown hallucinations involving oversized hands, an electric razor that attacks people and makes their beards grow, and cardboard car chases.

Stephane may, in fact, be experiencing a mental state known as hypnogogia. Coined by 19th-century French psychologist Alfred Maury, it describes the sufferer’s experience of vivid, tactile hallucinations while sleeping, or after waking up (technically, this version is known as hypnopompia). Effectively, the person can’t tell if they’re awake or asleep.

Poor Stephane can’t remember if he wrote a love note and slipped it under Stephanie’s door while asleep or if he only dreamed it. He says at one point he feels “schizometric.” A talented inventor, he has devised a machine that can travel back in forth in time — but only for a single second at a time. It induces weird time lags — the same phrase is uttered over and over again when set to the past, and when set to the future, Stephane uses it as an excuse to pounce on Stephanie with a kiss. The movie plays off the fluid broder between dreams and daily life.

According to Wikipedia (our compromised, though usually reliable, source), it’s not uncommon for 30-40 percent to experience a state similar to hypnogogia at least once in life — that sensation, perhaps, of waking up from a deep sleep, not knowing what time or even day it is… or whether you’re still dreaming. But the condition can be a sign of other problems, such as narcolepsy or temporal lobe epilepsy. It’s often accompanied by full-body paralysis: the person is aware that he or she is hallucinating, but cannot react to it, or even make a sound.

Says Wikipedia: “It is thought to happen when a person enters or leaves REM (rapid eye movement) sleep too quickly. During REM sleep the brain blocks the signals that allow the limbs to move to ensure that we do not act out our dreams. However, when experiencing hypnogogia or hypnopompia, the individual is still conscious of their surroundings, effectively dreaming while still awake. This fact enables lucid dreamers to enter the dream consciously directly from waking state (a Wake Induced Lucid Dream technique).”

Kevin Shields, the pioneer of shoegazing “dream pop” in the 1990s, says he has hypnogogia. The swoony guitar textures, blurred layers and time-warped echoes of his music are perhaps a side effect of this condition; one of his songs is titled (When You Wake) You’re Still In a Dream. He is said to employ an odd recording technique: he records all the musical instruments in a studio — echoes, effects and all — then strips away the instruments from the master track, leaving behind only the dreamy echoes and reverberations — shimmering “memories” of the song, in a sense. His band, My Bloody Valentine, last put out an album (the hugely influential “Loveless”) back in 1990. That’s possibly because, from 1993-1997, Shields was sidelined by hypnogogia. It drastically affected his recording pace. “That’s what happened between ’93 and ’97, until I joined Primal Scream,” Shields said in an interview. “Every night I would spend hours and hours in that state, tripping out basically — that was my main concern.

“I was actually wondering, am I purely insane, or what’s happening here? For some reason I can close my eyes and have three-dimensional experiences… It became so all-pervasive that the inner world and outer world were so equally three-dimensional that I realized I was bordering on mental illness, so I had to get out of it.”

Shields can control the hypnogogia (or hypnopompia) now. But his recorded output is still sluggish. Watching The Science of Sleep, you wonder what sort of drugs were behind the manic, wild visuals and bizarre surreal imagery. Could be that the only chemicals responsible were generated by the brain itself.