Enemy is a puzzle that, if viewed literally, makes little sense. It demands a second viewing. Sad-sack history teacher Adam (Jake Gyllenhaal) lectures about totalitarianism and how dictators seek to crush individual expression in order to establish control. In doing so, he sets the stage for the ensuing doppelganger story by explaining that philosopher Georg Hegel stated all great events in history happen twice. This initial bit of monologue—along with the opening quote, “Chaos is order yet undeciphered”—provides our first clues to unlocking this labyrinthine film.

Away from the classroom, Adam dwells in a mostly barren apartment and has perfunctory sex with his briefly-visiting girlfriend, Mary (Mélanie Laurent). When a co-worker offers him an unsolicited movie recommendation, Adam rents it and spots a carbon copy of himself playing a bellhop. Through a bit of online sleuthing, he’s able to track down information about Anthony Claire (also Gyllenhaal), the actor in question. He poses as his double at a talent agency, where the fooled security guard mentions he hasn’t seen Anthony in six months and gives Adam a mysterious package. Even Anthony’s not-so-coincidentally six-month pregnant wife, Helen (Sarah Gadon), mistakes Adam for her husband when he calls their home. Eventually the doppelgangers agree to meet at an out-of-town motel room, but not before Helen tracks Adam down at his college and has a strange exchange with him on a park bench, departing the encounter oddly saddened. When Adam and Anthony meet, it’s confirmed that they are indeed identical, even down to the same scar on their chests, a scar that eliminates the possibility of their being twins separated at birth.

And then there are the spiders. The arachnids’ bizarrely repeated presence, often in dreamlike scenarios or otherwise implied by imagery, are the most crucial symbol to Enemy, especially given its shocking ending. The film opens with Gyllenhaal (at this point we don’t know which character) attending a slightly tamer Eyes Wide Shut-like sex show, where somber white men watch women masturbate. Anthony (as we learn later) also watches through his fingers as a tarantula is presented on a silver platter. A woman’s foot in a high-heeled shoe lowers toward the spider as if to crush it. Later, a surrealist scene of a mammoth spider lumbering over the skyscrapers of Toronto comes on the heels of Adam visiting his overbearing mother (Isabella Rossellini). Ultimately, the film ends with Adam, having assumed the role of Anthony, fingering the key to the sex club and telling Helen he’s going out that night, only to discover her transformed into a enormous spider that fills the whole bedroom as it recoils in fear. Adam simply offers a resigned nod.

So what the hell? A flurry of theories surfaced trying to untangle this web, some even involving the thought that the spiders were body-snatching oppressors taking over the world. Instead, Villeneuve has confirmed in interviews that Enemy is actually a story of one man’s subconscious. Repeated viewings make it clear that Adam and Anthony are the same person. Whether the car crash involving Mary actually occurred is open to discussion (the scar on the chest providing some support to that theory). What’s clear is that Gyllenhaal’s mind has split. A known philanderer (early on, Helen asks Anthony “are you seeing her again?”), Gyllenhaal’s actually singular character was forced to give up his unsuccessful acting career and take on a gig teaching history. Monogamy is oppressive to him. He resents his pregnant wife and overbearing mother, and in his mind he views them as dictators he must rebel against. Symbolically, they are spiders trapping him in a web of commitment. There’s evidence of this in a torn-in-half photo at Adam’s apartment, which is seen in full at Anthony’s, his wife Helen restored to the image. His mother also blurs the line between the two characters by insisting Adam likes blueberries and that he should give up the dream of being a third-rate actor. But debate rages about how much takes place in the character’s mind (is his sex with Mary real, remembered or imagined?), and how much is simply a story told out of chronological order.

In many ways, Enemy is Donnie Darko for grown-ups. The split takes place within Gyllenhaal’s character’s mind, prompted by the oppression of routine and requiring no elaborate parallel worlds. Director Denis Villeneuve (with whom Gyllenhaal also worked on the concurrently-released Prisoners) has given us the kind of film that comes along so rarely, stoking impassioned discussion while offering no easy answers. Spider web imagery pops up at important points, including a web-like intersection of cable car wires and a spider-web pattern of broken glass after the car crash. Nicolas Bolduc’s cinematography uses deep shadows and an unnerving yellow tint to give the whole film an ominous hue. And the Hitchcockian score heightens the sense of suspense and dread.

Regardless of what conclusions you draw from Enemy, this is a film that demands contemplation. Unlike similarly perplexing movies like Memento, Enemy doesn’t rely on a clever gimmick so much as it steeps itself in the distortions and symbolism of the subconscious. Unlike Fight Club, there’s no big twist moment explaining that Anthony and Adam are, in fact, one. As a result, Enemy is the type of film you just can’t shake. Regardless of whether all great historical events happen twice, Enemy insists that all great films should be watched more than once.