French actress Marie Rivière had a specially close relationship with director Eric Rohmer. After seeing his work for the first time in the early 1970s, Rivière expressed her admiration in a letter, which led to a succession of parts and culminated with her appearing as heroine Delphine in Rohmer’s 1986 The Green Ray (Le rayon vert): the part was in some way centred on the experiences of the actress, who was allowed to develop the story through almost total improvisation.

Filmgoers will either find Denis Villeneuve's latest art-house thriller to be a tantalising head trip or so much celluloid posturing, but there's no denying its contribution to the rise and rise of leading man, Jake Gyllenhaal. Racing up the outside track as a potential Oscar nominee for Nightcrawler even as he is making a (splendid) Broadway debut in the Nick Payne play Constellations, Gyllenhaal here gets to impress twice over and for a simple reason: Javier Gullon's script casts the hirsute star in two different, teasingly complementary parts. 

Thoughts of Jeremy Irons's career-best work in Dead Ringers come to mind, or the sort of conceit one might expect from David Lynch, whose shimmering reality-vs-illusion landscape comes to mind here. And while the surface narrative is apparent enough, its larger meanings remain up for grabs, and one can only begin to imagine the PhD students who are going to be probing every frame for its fullest meaning for some years to come. 

For now, let me just say that I admired Enemy more than I warmed to it, and that there are numerous other movies whose deeper resonances seem to me more immediately worth mining (Lynch's Mulholland Drive to name but one). But whether you tune out to this movie or (as some are said to have been) are freaked out by it, there's no denying the absolute command of Gyllenhaal, who over time has learned to put his puppyish appeal to one side in favour of a more forceful, declarative style of performance that should serve him in good stead as he gets older and less obviously "cute". Think of this as part of Gyllenhaal's thespian insurance plan for an ever more varied screen future. 

Roughly half the film casts Gyllenhaal as Adam Bell (pictured above with Isabella Rossellini, who plays his mother), a faintly nerdy college professor who seems to spend his time when not lecturing having sex with his girlfriend (Melanie Laurent), and who can blame him for that? At least, that much is true until Adam rents a film one evening in which he happens to espy a bit-part actor, Daniel aka Anthony, who looks uncannily like himself, bodily scar and all. As purposeful – almost ominously so – as Adam is indrawn, Anthony responds to Adam's obsessional interest in him by commandeering significant (for which, read sexual) aspects of his doppelganger's life, the stakes escalating as the subconscious and the supernatural begin to take hold as well.

What follows tells perhaps the battle of a battered psyche or suggests a veiled political parable about societal misrule as it is allowed to infiltrate even the most ordinary lives. Or maybe the film is just about giving its leading actor the opportunity to push in two separate if ever-intersecting directions. Some won't care whereas others will be rapt. You could do worse than ponder Enemy's Cronenbergian affinities (yes, him too) and allow respect for Gyllenhaal to override the more self-conscious meanderings of what looks set to be this new year's murkiest film.

Watch the trailer for Enemy overleaf

It’s Turing versus Hawking, Cumberbatch v Redmayne, computer science v astrophysics, tragedy v the triumph of love. Ever since The Imitation Game and The Theory of  Everything appeared at the Toronto Film Festival last year, the head to head has been inevitable, leading all the way to the Oscars.

Directed by Alejandro González Iñárritu,Birdman is the story of a fading star’s search for professional rehabilitation and personal redemption that perches adroitly between dark humour and darker despair and injects a familiar story of mid-life crisis with fresh vitality and emotion thanks to vivid flights of an intensely cinematic fancy.

Michael Keaton, a leading man in light comedies before rising to the big leagues by playing Batman in the Tim Burton original and first sequel, has been cast for maximum meta-value as Riggan Thomson, an actor who found fame by playing Birdman, the superhero of an eponymous film franchise. Riggan is now seeking to resurrect both his career and artistic credibility by writing, directing, and starring in a stage version of Raymond Carver’s What We Talk About When We Talk About Love on Broadway.

As well as putting everything on the line creatively, Riggan has to manage personal and professional complications arising from clashes with his co-star, an intense, Sean Penn-like Method devoté played by Edward Norton (giving rise to a hilarious Fight Club nod in another meta-joke), an unwise affair with the show’s needy ingénue (Andrea Riseborough), and the appearance of his estranged, semi-rehabbed daughter (Emma Stone pictured, below right, like Keaton giving a career-best performance). The backstage saga is imbued with understanding of and affection for actors and their combination of wild egomania and profound insecurity.

But primarily Riggan has to battle himself, or the aspect personified by his filmic alter ego, who periodically turns up to suggest he’s going to make a fool of himself with all this highbrow stuff and should return to the safety of the mainstream. And Birdman also represents the self-absorbed, insensitive, career-driven side of Riggan that has undermined his marriage and his relationship with his daughter. Ironically, it is this persona that is dragging him down, preventing him from breaking free from old self-destructive patterns and soaring to new heights.

Even more than the Birdman, another entity hovers over the film – the spirit of Robert Altman. Like Altman (who directed Short Cuts, constructed from inter-leaved Carver short stories), Iñárritu has a fondness for creating films with multi-stranded narratives. And remember the epic, masterful tracking shot that kicked off The Player, Altman’s dark satire of Hollywood? All of Iñárritu’s dark satire of Hollywood looks like one epic, masterful tracking shot as the camera swoops and glides backstage, onstage, and outside the theatre to Times Square and the surrounding streets.

Birdman also evokes Bernard Rose’s lesser-known but wonderful Ivansxtc, in which a Hollywood player in extremis reconsiders his priorities to the strains of Wagner, as Riggan does to the strains of Mahler, when not engaged in conflicts accompanied by a driving solo jazz drummer (you wait years for a film with a solo jazz drum score and then two – this and Whiplash – come along at once).

A moving, exhilarating ride into the depths of the soul and up through the empyrean of the imagination

However – and I say this with trepidation, given the excoriating attack on critics Riggan delivers to Lindsay Duncan’s pinch-faced bluestocking of a New York Times reviewer, a creature so friendless and misanthropic she is always pictured scribbling alone at a bar – the ending is problematic, at least for anyone with a low tolerance for magical realism. There are elements of magic realism right from the start (for example, Riggan’s ability to move objects telekinetically), but it’s entirely possible his superhuman powers exist solely in his mind. But then in the final scene we are asked, I feel, to accept their objective reality, though I know others who think Riggan’s final action is only figuratively rather than literally true.

As well, Iñárritu lets several important plot dynamics just drop. I’m not saying they need to be tied up with a neat bow, but we shouldn’t feel he’s forgotten about the characters and it made me wonder if he likes multi-stranded narratives because he doesn’t really do wrapping up subplots. But for most of the time, Birdman is a moving, exhilarating ride into the depths of the soul and up through the empyrean of the imagination.

Overleaf: watch the trailer for Birdman