Denis Villeneuve’s collaboration with Jake Gyllenhaal has produced two films thus far: last year’s preposterously-plotted yet consistently engaging thriller, Prisoners, and now, Enemy. There aren’t a great many similarities between the two films; the former was literal and methodical while the latter is elliptical and abstract. Prisoners solidly held to genre conventions while Enemy takes its inspiration from David Lynch’s pop-surrealism. They don’t really even share an aesthetic, with the latest film adopting a jaundiced hue as opposed to Prisoners’ near-monochromatic palette of long shadows and dreary skies.

But despite these marked differences, I can’t help but feel that Villeneuve left a kind of clue to Enemy buried within the labyrinthine depths of Prisoners. The villain of that film abducted and brainwashed children, leaving them with a literally unsolvable maze that would grant them freedom if they could only escape it. This seems appropriate given how audiences have struggled to decode the tangled web that is Enemy, only to find themselves with an incomplete solution.

Enemy is presented as doppelgänger tale, adapted from José Saramago’s novel The Double. Morose history teacher Adam’s (Gyllehaal’s) repetitive existence of pontificating about dictators and fucking his girlfriend (Mélanie Laurent) is punctured by the eerie discovery that a wannabe actor, Anthony (also Gyllenhaal), shares his face and voice. Anthony isn’t the stark contrast to Adam you’re conditioned to expect in these stories, but he has a swagger and hardness that Adam does not. Things get weirder when these doubles meet as the film denigrates into a storm of sexuality, infidelity, confusion and immense arachnids, all consumed by a thick fog of anxiety.

The conclusion of Enemy – a jarringly wrong moment that triggers something primal and unfathomable – surely sends most viewers scrabbling to Google looking for an explanation. Plenty are forthcoming. Interviews with Gyllenhaal and Villeneuve support the supposition that Adam and Anthony are the same man – strongly hinted at in a conversation with Adam’s mother (Isabella Rossellini) – and posit the film as an exploration of the conflicting demands of male heterosexuality. Others suggest interpretations involving totalitarianism or even a twist on Invasion of the Body Snatchers.

None of these explanations are entirely satisfactory and, ultimately, I’m not convinced that an intellectual interrogation of Villeneuve’s motives (or that of his screenwriter, Javier Gullón) is likely to prove fruitful. The film is dotted with images that demand interpretation – clues – like the recurring spider imagery (including a naked woman with a spider’s head), Adam’s comments on repetition and dictatorship, shared scars, wedding bands, Vertigo posters … the list goes on. But trying to crudely combine these disparate elements into a key, an answer, seems futile. Like the maze in Prisoners, there’s no answer.

This isn’t to say that isn’t some coherency to be found within Enemy’s dense symbolism, of course, nor to say that the film is entirely incoherent. But to present the film as “solvable” is to do it a disservice, much as the “answers” to films like Mulholland Drive or Upstream Color (films with which Enemy shares much DNA) are never truly satisfactory. Perhaps this is a sci-fi allegory, or a rumination on modern marital infidelity, but it also works as its surface narrative – at least, up to a point. It can’t simply be reduced to one thing.

Enemy is one of the best films I’ve seen in 2014 not because of any pseudo-academic analysis to be battled out on internet forums. It should be applauded for driving its audience to seek answers, yes, but I’m not convinced it’s a fault of the film that the answers aren’t entirely satisfactory. This undecidability, to borrow some mathematical terminology, is entirely consistent with why the film works so well.

Enemy is a slow-motion anxiety attack, a dizzying elicitation of disassociation that channels that horrifying moment when things don’t make sense. When you looked at a loved one and see a stranger, or when your inner monologue starts to tear down every piece of scaffolding that makes you who are. When your mask slips, and your identity collapses into impenetrable oblivion. That moment that a depressive haze consumes you and pollutes your every thought. When something skitters into the deepest recesses of your mind and you’re flooded with ichor negativity that leaves you disconnected from reality, whatever that is. It’s fitting then, that these jagged puzzle pieces don’t fit together, because thoughts arising from dark pulses of anxiety never cohere into anything truly logical; only a razor-edged, tangled web.