How neat it is when a film director admits to a childhood experience that seems to gesture towards their later career. Alfred Hitchcock was fond of explaining how, when he was once caught doing something naughty, his father took him down to the police station and asked to have the boy locked up. All those paranoid stories now make sense.

Shane Carruth, a neat, polite man in his early forties, doesn't intend to tell such an anecdote. But he does so anyway. Asked about his upbringing, he explains that his dad was an engineer who, after starting out repairing radios for the air force, found himself doing hush-hush work on satellites for a defence contractor.

“He wasn’t really allowed to talk about it,” Carruth says. “But we slowly got a sense of what he was doing. Little pieces of information came through. I remember driving through woods with my parents and we saw these huge white structures. The way my mom and dad were talking I knew it had something to do with his work. I later learned they were to do with microwave radiation.”

The scene could be plucked straight from either of Carruth's extraordinary first two features: Primer and Upstream Colour. The first of those films, released in 2004, told the unimaginably complex story – seek out the online flowchart explaining the various intersecting timelines – of two men who build a plausible time machine. The beautiful, obtuse Upstream Colour, one of this year's very best films, has to do with a woman who becomes infected with an organism that strips away all the everyday comforts in her life. (If you can manage a better synopsis then you're a better man than me.) Both films are deeply unsettling, fuelled by paranoia and hard to disentangle on first viewing.

Does he enjoy confusing the viewer?

“Hmm? Well, I know I don’t start from there,” he says. “I am led by my own aesthetic sensibilities. I don’t want everything to be handed to me in one sitting. I want to have a conversation after seeing the film. This level of obfuscation is what I enjoy as an audience member. It is wonderful to read somebody writing about my films who has thought about it and worked it all out. That is satisfying.”

At the same time, he must be frustrated by people drawing lunatic conclusions from the spooky, icy narrative laid out in Upstream Colour. There is so much to ponder. Kris, the protagonist, finds herself in psychic contact with a group of pigs on a distant facility. There’s something here about drug dealing. Characters read Henry David Thoreau’s Walden to one another. Heaven knows what people make of it in the madder corners of the internet.

“I certainly wouldn’t blame anybody,” he says. “But there is something happening now where people read a book or watch a film and then want to turn round to their friend and sum it up in a sentence. There’s a rush to assess. People have said it’s about the pharmaceutical industry, that it’s about memory, it’s about drug addiction. It’s about my attempt to get at all of these things.”

Shane Carruth came to his peculiar art via a suitably peculiar route. Raised in South Carolina, he studied mathematics in Austin and spent some time developing flight simulation software. In earlier interviews, he has made it clear that he is not one of those directors who was fertilised in film-buff mulch. He claims not to have heard of the French New Wave until he began making Primer.

It’s hard to avoid the suspicion that he background in maths has affected his disciplined, austere aesthetic. For all the oddness of his films, an underlying logic is always there to be discerned (after some hard study).

“No, I don’t quite see that,” he says good-naturedly. “The public opinion of math is that it is this cold cynical removal of beauty from things that are beautiful. I have always seen math as beautiful. It’s breaking beautiful things into a million pieces and seeing how they function. It’s seeing the microscopic and the larger beauty. It’s not just adding, subtracting, integrating and finding derivatives. I can’t see how that would work in terms of storytelling.”

At any rate, you couldn't argue that Primer and Upstream Colour are anything other than the work of an auteur. Like Steven Soderbergh, Carruth writes, edits, directs and produces his own films. Unlike Soderbergh, he also composes the music and appears in those movies. Heck, he even self-distributed Upstream Colour on its American release. Now these sound like the actions of a control freak.

“To be honest it starts with not having the resources,” he says. “But I do have to admit it is also about control. But when I started I didn’t have the money to hire a composer. I wouldn’t know how to go about it if I had. As I am preparing, I work out the music I want, the lenses and all that. Even if I could hire somebody I would drive them mad getting them to mimic what I did.”

He’s not wrong about working to low budgets. In the DVD commentary on Primer, Carruth points out that if you look carefully you can see him mouthing the word “cut” at the end of certain shots. That is how careful the director (also the star, of course) was being about not using more film than strictly necessary. Yet, despite being shot for around $7,000, the film has gone to become something of a modern classic. (Writing in December 2010, this writer named it as one of the 25 best of the decade.)

What was the starting point? Was he attempting a naturalistic take on the slippery notion of time travel?

“That wasn’t the starting point,” he says. “That was the sugar in the recipe. I wanted a story that deals with a normal relationship and inserts a new level of power into it. I knew it was about that before time travel came into it.”

Despite the acclaim, Carruth soon found that the industry didn’t speak the same language as he did. He was offered a dozen dull time-travel scripts. A personal project called A Topiary gradually ground to a halt. In the end, it took nearly a decade for Upstream Colour to follow Primer into cinemas. But he seems to have figured things out now. His next project will kick into action within months. Before then, he has to help us figure out the current intriguing head-stretcher.

“The films are hard to watch because you can only see your own mistakes,” he says. “Maybe in five years time I’ll watch Upstream Colour. I am really looking forward to seeing it then. It will be interesting to see what the film is.”

If he finds out be sure to let us know.