Last year, a friend of mine sat down with his nine-year-old son to watch Stanley Kubrick's 2001: A Space Odyssey. Joined by his younger son, aged five, they were having a week of movie nights in their living room - The Thing From Another World, 1951's classic of claustrophobic sci-fi, had already proved a household hit. Kubrick's monumental 1968 film was up next because the kid had heard something about it somewhere, and was curious.

All the same, I figured the selection was something of a gamble. The Thing From Another World is, essentially, a quick 80 minutes about a violent alien vegetable wreaking bloody havoc at an isolated arctic base. 2001, on the other hand, clocking in at 143-minutes, of which less than 40 feature any dialogue, is a meditative, metaphysical attempt at creating a provocative new myth of mankind's origins, wrapped around questions about our relationship with technology, in which the most human character is a mad, prissy computer - a plot itself constructed as a Trojan horse for the movie's real mission: introducing an abstract new anti-narrative language into mainstream cinema, at once minimal and overwhelming in its sensory assault. Wishing him luck, I asked him to let me know how the screening went.

That evening, a message arrived. "2001 going surprisingly well so far. Nine-year-old asks: 'Did they actually film this in space?'"

Stanley Kubrick never got to see 2001. The actual year, I mean. He died in March 1999, one week after completing his final movie, Eyes Wide Shut. But 46 years after 2001: A Space Odyssey first arrived to stun, bore, challenge, infuriate, obsess, unsettle and inspire moviegoers, he would surely have relished that the 20th century technology and techniques he pushed beyond their limits to make its space-stations and shuttles dance their spinning, waltzing ballets were still holding up, fit-for-purpose enough to transport 21st-century boys today.

The illusion that this film is taking the audience into the stars is one of the most basic effects the director hoped to achieve. Its influence on the blockbusting wave of Hollywood sci-fi that exploded a decade later with Close Encounters Of The Third Kind and Star Wars is incalculable. Like almost all Kubrick's films, however, 2001 was received badly by the critical establishment on initial release: "it's a monumentally unimaginative movie," the New Yorker's opinion-maker Pauline Kael concluded in her spectacularly catty review. But Kubrick perhaps cared less about that reaction to his film than this one, from Alexei Leonov, the Soviet cosmonaut who, in March 1965, had exited the capsule of the Voskhod 2 to become the first man to walk in space: "Now I feel I've been in space twice."

Watching 2001 at home is one thing. But this month, you have the opportunity to go on the odyssey as it was intended, as the film is rereleased in cinemas as part of the BFI's sci-fi season, Days Of Fear And Wonder.

"You need to see it on the big screen" has long been the mantra of the film snob, but there are movies that really do demand the full, immersive cinema setting. 2001's opening, as the first notes of Richard Strauss' Also Sprach Zarathustra sound out, has been endlessly parodied. But to feel that music slam into you and all the strangers in the dark as the sun rises on a remastered 70mm print is still to feel goosebumps rise, a spine-tingling, experience that simply can't be replicated at home, no matter how wide your wide-screen.

True, we can't recapture today the context that helped blow audiences' minds when the film was first released. The excitement stirred up this month by the Rosetta satellite's landmark mission to land a probe on a comet is only a dim echo of the clamour in the air when 2001 appeared. The space race was at its most intense, the Cold War was at its most deeply-frozen, and, as we closed in toward touching the moon, new horizons for mankind seemed to be opening daily, alongside new ways for us to wipe ourselves out. Simultaneously, the counterculture was busy being born, and the smoke that wreathed cinema auditoriums wasn't just tobacco.

But 2001 remains a different entity when it surrounds you and you surrender to it. And surround you it does. With 2001, Kubrick set out to create a new kind of film, and, from the first, he signals you are about to see something different, more akin to music. In fact, from before the first, because this is a film that actually begins before it begins. The curtains part, but the screen stays blank. A dense, discordant, disconcerting slab of music commences, and for almost three minutes, the towering blackness and the uncanny music's rise and fall- the piece is Atmospherès, composed in 1961 by Hungarian avant gardist Györy Ligeti - are all there is.

Like astronauts cast into the void, we have nothing to hang on to. Eventually, the overture fades, the moon, the earth and the sun come into alignment, Zarathustra sprachs, and we are cast down among the hungry apes for The Dawn Of Man. It will be another three million years (or approximately 24 minutes of screen time) before the first line of dialogue is uttered.

When it first appeared, baffled audience members sat up all night trying to figure out 2001's plot. Co-authored with the great science-fiction seer Arthur C Clarke, however, the story is simple enough. A few millennia ago, alien intelligences had a look at Earth, and, for their own reasons, decided to help us evolve. Via a towering, jet-black monolith, they jump-start intelligence in an ape, so he suddenly, unaccountably, realises the bones lying around him might be used as tools, and weapons. For the next three million years, nothing much really happens, except we beat each other's brains out and eat. Eventually, though, we evolve enough to get to the moon, where we discover another ancient, enigmatic black monolith buried, waiting for us, which provides the divine spark that points us toward our next rendezvous: a mission to Jupiter, for a transformative date with destiny.

What continues to perplex us about 2001, and draw us to it, however, is not really its plot. When it comes to extraterrestrial life, Kubrick and Clarke could have gone either way: "Two possibilities exist," Clarke said, "Either we are alone in the Universe or we are not. Both are equally terrifying."

Rather than a story about aliens, 2001 is about humankind's relationship to the universe, and its real power lies in the cinematic approach Kubrick applied to this theme. "Stanley was determined to create a work of art which would arouse emotions of wonder, awe - even, if appropriate, terror," Clarke said. "I don't like to talk about 2001 much," Kubrick told writer Jerome Agel in 1970. "It's essentially a nonverbal experience. It attempts to communicate more to the subconscious and to the feelings than it does to the intellect."

It's in the way it communicates, and what it communicates, that 2001 still stands apart. For this rerelease, the BFI has made a stunning new trailer, featuring laudatory quotes from Alfonso Cuarón and Christopher Nolan, the directors of Gravity and Interstellar, the two most recent blockbusters to have drawn comparisons with Kubrick's film.

Those films are unimaginable without 2001, but very different in intention. Gravity, for all its technical genius, boils down to a don't-give-up self-help parable; Interstellar suggests love is all you need. Both seem products of the social media/ reality TV age that teaches us we are all special snowflakes. Their fundamental message is: it's all about you.

This is not the sentiment of 2001. In that famous, transcendent match-cut that equates a bone tossed into the air by a savage ape with a spaceship in the heavens, Kubrick wipes out the entire intervening history of human civilisation as not mattering much. If there is a message, it is: surely, one day, we might do better than this.

Whether that is pessimism or hope is left up to you. This is why the film is often described as cold and unemotional. But 2001 is alive with emotion: in its sheer music and vision; in the most moving death scene of 1960s cinema (albeit the death of a computer); in the constant, dark, sardonic humour that pulses throughout - consider the long moment depicting a high-ranking scientist chewing over the implications of a sign that reads ZERO GRAVITY TOILET.

Kubrick's masterpiece is itself like one of those monumental monoliths. It is jet-black, awesome, entirely mysterious, and, if you get close and touch it, it leaves you changed. The day after my friend watched it with his sons, I asked what the five-year-old had made of it. During the scene where the monolith first appears to the apes, he had offered this critique: "That ginormous domino is going to fall on the monkeys." Almost half a century since it first appeared, no one has summed it up better.

2001: A Space Odyssey is re-released in selected cinemas on Friday