Contemplating Bjork's always fascinating but increasingly wayward recording career, and the po-faced blandness of the MIF's publicity blurb ("A multimedia project encompassing music, apps, internet, installations and live shows" it joylessly declares) I arrive at the Museum of Science and Industry fully expecting an evening of caterwauling and pipe-banging. This is of course, no bad thing, especially not here in Quietus Land, but I did wonder how such a thing would go over with the audience in attendance.

Given this relatively rare live appearance in the UK, coupled with the £45 ticket price, there are a lot of late 30's / early 40's fans of Bjork's early-90s pop output, presumably hoping to hear at least a few of the hits in exchange for this substantial raid on the baby-sitting fund.

As soon as you enter the hall, though, every indication is that a joyous singalong through 'It's Oh So Quiet' is what you ain't gonna get. The stage is in the centre of the room, with the audience surrounding, and there is a distinct lack of anything resembling conventional instrumentation on display. There is, however, a massive Tesla coil, a huge set of pendula that would easily pass muster as a deadly obstacle in a dystopian video game and yes, some highly bangable-looking pipes and slabs of bronze.

This layout means the only way for the performers to reach the stage is through the audience, and due to a bit of fortuitously timed bar-visiting, I find myself briefly held up by the security staff right next the door from which they are to spill forth. And spill forth they do, a 25-strong gaggle of golden-cloaked female singers, Bjork in the centre of the huddle sporting a bizarre over-sized curly red wig. In something of a nod to the planned educational, child-oriented forthcoming phase of the Biophilia project, the overall visual impression is a cross between Grimm's fairy tales and the world's weirdest girl band.

Opening song 'Thunderbolt' is pretty bracing, with the Tesla coil wired up to some grimy bass emitting device providing the core instrumental backing to the choir's icy incantations of "great miracles". The purpose-built instruments don't appear to be passing through any kind of PA; the sounds emit from the contraptions themselves, lending the experience a three dimensional quality rarely heard outside of classical music. But the comparison ends there; this is electronic music reduced to its most basic single component, the sound of electricity arcing through the air. It's a bold opener, that visibly splits the audience into admirers and sceptics.

Bjork hardly speaks between songs during the show, deferring that role to a pre-recorded David Attenborough. "When I was a kid, my rock star was David Attenborough," she explained during a recent Rolling Stone interview, also discussing a childhood love of science and mathematics, which is another strand that runs through Biophilia, alongside its more overt biological themes.

In its own slightly oblique fashion, Biophilia is a joyful trumpet blast for rationalism. Like Richard Dawkins extolling the sheer majesty of reality-as-it-is as superior to any imaginable religious myth, the show's primary message appears to be "Look at nature... isn't it mind-blowing?"

This could of course, be horribly trite in lesser hands, but in the simple act of describing nature as it is in such reverent and awestruck style, Biophilia achieves, for this scribe at least, something of unnerving and profound beauty.

Second song 'Moon' is a fine case in point. Bjork and her gang of glittering pixies deliver exactly the kind of shivery lullaby such a title demands, but all the chiming spookiness is not in the service of any hackneyed lunar symbolism. It is, as is often the case with Bjork's lyrics, all about the artful single entendre; the song sounds like a metaphor for something, but it is in fact simply about how awesome looking at the moon is. Of course, you have to somewhat meet these ideas half-way, and if you've not got an innate sense of wonder of your own, this is possibly not the gig for you.

On the other hand, if you are willing to be taken along for the ride, this is a show so rich with such everyman shivers of pleasure, it's difficult to discuss without veering into spoiler territory. There are already setlists and blow-by-blow accounts all over the web, if that's what you're after. Suffice to say, this trick of borrowing the surface appearance of myth and magic and discarding the content is the modus operandi of the evening. Like a great stage magician, there is the sense of a knowing wink: sure, it's all just voices and funny looking machines, just as we know the lady isn't really getting sawn in half. The point is that the spectacle in itself is more than enough, if you only know how to look at it.

As the evening proceeds, and the listener adjusts to the experience – and make no mistake, this is not your grandaddy's "gig", by any stretch – it becomes apparent that for all its art-house trappings, this is actually pop music, but pop music with all constraint and convention gleefully cast aside. There are soaring melodies, big choruses, choreographed dance steps, and even the occasional re-worked crowd pleasing oldie thrown in. What distinguishes it from most long-serving stars' gigs – and Bjork is clearly aware of and happy to play around with her pop-star status, incongruously shimmying like a Girl Aloud during the more upbeat moments – is that the show takes the audience's intelligence as a given, assumes their open-mindedness, and exalts in the idea that being smart can be fun.

So, that's Bjork 2011, then. Geekiness as sexiness, experimental music you can whistle, and still one of the great idiosyncratic pop vocalists of the modern age. An international treasure still.