There has perhaps never been a band to more perfectly expose the utterly redundant pursuit that is rock criticism than U2. They don’t need reviews in the way that most artists do: for the purposes of selling records. The cultural space that they occupy is singular: as they enter their fourth decade together, the players will always have been in U2 for longer than they haven’t. No one has been kicked out, no one has left, and no one has died. They defy easy genre categorisation and remain one of the world’s great live bands.

There is no reason for them to keep going together, other than because they can. No matter how many arbiters either quaintly opine, “What is this shit?” or meter out four and five star reviews like they were handing out fistfuls of Monopoly dollars, both are going to achieve the exact same end: nothing. Millions of people will buy U2’s new album regardless, and they will love it, unswayed by its relative artist’s merits. Likewise, people who hate U2 will continue to hate them, and a five star review in Rolling Stone will not change their mind. It will likely reinforce their disdain.

And yet U2 appear to crave critical acceptance, the one thing their frankly disproportionate influence cannot buy. As perennial outsiders (from Dublin, not quite punk and never quite cool) they want to be seen to be Important. Why else do they keep making records? They are hardly wanting in units shifted or tickets sold or accolades accrued. Rather, to be written about, and dissected and agonised and fought loudly over at the pub; that’s what everyone in a band wants (usually along with money, fame, power, drugs and women, though not in the case of U2, came certain of those). It’s why they’re in a band: to matter to people. U2 have always been refreshingly transparent about this and their desire for it in the biggest possible sense. They could very easily sleep soundly every night atop their giant piles of money and fritter away their lives on vastly more leisurely pursuits, like colonising their own South Pacific atoll, or farming fish, but they aren’t.

Their 12th studio outing, No Line On The Horizon manages to be more than the sum of its parts, which on first airing should not add up to anything remotely coherent, yet defiantly reveals its rewards on repeat listens. This album is obtuse and weird. A disjointed, strange jumble of disparate influences that at once sounds nothing like U2 while sounding exactly like U2. Evidently, it’s the kind of music they make when trying to please no one but themselves, surely the most legitimate of all reasons to keep releasing records.

The pretty well universal drubbing of 1997’s unjustly maligned Pop – a sometimes misguided but sonically adventurous, anxiety-riddled curveball -seems to have rung in their ears ever since, sending U2 on a retrograde cakewalk through their own back catalogue, rehashing the sonic trademarks for which they were beloved (and also reviled) in the – œ80s in an effort to win back the fans who were scared away by all the blips and pre-millennial angst. Those “return to form” albums ( All That You Can’t Leave Behind and How To Dismantle An Atomic Bomb ) might have been heavy on production gloss and anthemic sheen, but they were fundamentally lacking in anything approaching grit or determination or risk: their cores were anti-gravitational. And yet they were met with almost universal critical praise, something a little like ferociously applauding Roger Federer for doing away with an neophyte opponent; like you or I, say.

Which is perhaps why U2 feel safe now in flipping the switch back on to reconnect with their nineties triumvirate of experimentalism which began with 1991’s Achtung Baby. There was a nanosecond in time in the early to mid—œ90s when U2 were actually cool and most everyone agreed that they were; the time which coincidentally coincided with my introduction to them, and a time that Bono mainly, has spent the last decade neatly erasing from history. But it’s that looser U2 – mischievous, knowing, sexy, fun – that most often appears on No Line, alongside the unashamedly naïve, stadium-ready U2 that jostles occasionally, inevitably, to be heard above the din.

Opening with the title track, The Edge recycles the riff from The Fly while Larry Mullen crashes in with busy, up-in-the-mix percussion and Bono sings in an unrestrained, slightly unhinged register about a girl with whom he shares the same dream, who tells him that “time is irrelevant, it’s not linear” before sticking her tongue in his ear. A Kings of Leon-ish vocal inflection, whoa-ooh whoa-ooh, and the chorus brings in the first of many (too many) “Oh oh, Oh, Oh OH” refrains in the place of actual lyrics.

There are several times though, when this is preferable the many largely nonsensical Bono-golisms which pepper the album (“I got a submarine, you got gasoline”, “Napoleon is in high heels”, “My ego is a small child crossing an eight lane highway”, “Force quit and move to trash”). Magnificent then continues along with another mashing of the old and new U2, its slide guitar figure reminiscent of Even Better Than The Real Thing and a quicksilver bass-line sidling up to a 4/4 disco-rock beat, a template so familiar now it almost sounds like U2 taking the piss while deftly trumping their imitators; no one does unabashed uplift and triumph quite like them. “I was born to sing for you,” Bono croons, “I didn’t have a choice but to lift you up.”

Moment of Surrender is a down-tempo, gospel-tinged epic coming in at seven and a half minutes that was captured in one take. Pre-release hype had this song pegged as the band’s new One, which it is not. U2 have never recaptured the majesty of that tower of a song, but then again neither has anyone. U2 are now miles away from the anguished collisions that produced Achtung Baby, an album so laced with romantic desperation and recrimination. (Like how it’s hard to imagine a line like “This is where you gotta be/Love and community/Laughter is eternity if joy is real” – from the cheekily catchy Pump It Up Xerox, Get On Your Boots – fitting in anywhere on Pop.) A world-weary love note to abandon (“I folded to my knees”), the protagonist wanders a city through “the stations of the cross”, once spooked by his reflection in an ATM screen.

Unknown Caller is more waking dream imagery: a sunny opening riff augmented by birds chirping abruptly shifts to a minor key, as Bono drives to the scene of an accident, “then I sat there waiting for me. No signal on a mobile phone at three in the morning, a chorus of voices chant instructions, – œDon’t move. Or say a thing.’” A strange pair of songs reminiscent of the same techno-paranoia U2 explored on Zooropa.

I’ll Go Crazy If I Don’t Go Crazy Tonight sounds initially the most throwaway track on the album, replete with Bono admirably falling short of his falsetto and singing “baby, baby, baby”, but proves itself a massive earworm once it skips along on a chiming George Harrison guitar figure which bursts out of nowhere. The narrator dispenses what sounds like parental advice to someone about to set off to climb a large, metaphorical mountain, fatalistically cautioning that “every beauty needs to go out with an idiot”, and more hopefully “listen for me, I’ll be shouting. We’ll shout out to the darkness, we’ll squeeze out sparks of light.”

The band ratchets up its cacophonous conclusion, one sure to go down a treat in stadiums around the world. The swaggering Get On Your Boots proves U2’s tested formula of a lead single not at all indicative of the album and is too derivative by half to be truly memorable. Stand Up Comedy is their most adventurous song of the last fifteen years by a vast distance; The New U2 Funk Soul Review Band, somehow Oasis by way of the Red Hot Chili Peppers, with a heavy, glam-inspired riff Edge might have picked up while making a guitar movie with Jack White and Jimmy Page. If that sounds like a recipe for ear bleeding, it somehow miraculously works through sheer force of will and persuasion with a hard to resist directive, “Come on ye people! Stand up for your love!” Who knew their humble post-punk beginnings would one day begat U2, psychedelic hippie edition, or moreover that it would sound like so much fun?

No Line On The Horizon likely sounds so mixed up thanks to its cut and paste gestation, recorded across four continents over 18 months. And forgetting for a moment what might have been had U2 not decided that they weren’t quite in need of a late career-saving record helmed by Rick Rubin just yet (one day, one day), its production team ultimately included three producers: Steve Lillywhite, who they have worked with going back to their debut Boy; and wonder duo Daniel Lanois and Brian Eno, who on this album actually joined the band, making U2 officially an in-studio six piece on seven songs out of twelve. So those quips about this U2 album being – œgreat and everything, but sadly it’s Brian Eno’s’ – as funny as they are – are moot.

A sore thumb track like FEZ-Being Born, with its deliberate opening allusions to Music For Airports, sounds so much like a Brian Eno song because it is a Brian Eno song. White As Snow is a gorgeous, elegiac country-tinged lullaby based on a traditional hymn O Come, O Come Emmanual. The ghost of Johnny Cash hovers while Bono renders a Cormac McCarthy pastoral landscape of “highways straight and wide” where “the road that refuses strangers”, across which two brothers travel, stopping to bathe in an icy river under the full moon.

U2’s – or more specifically, Bono’s (to accept here that there probably isn’t a band more defined by their frontman than U2 are) – statement of intent comes very late in the piece. A Dylan/Patti Smith (and so, Michael Stipe) inspired stream of consciousness, Breathe flies on manic energy as rapid-fire verses recount a near death experience (“If you want to stay a live a bit longer, there’s a few things I need you to know/ The doc says you’re fine, or dying. Please!”), the upshot of which “is running down the street like loose electricity” towards the glorious, life-affirming chorus firmly in the Big U2 tradition, where Bono’s raison d’être is laid bare: “Every day I have to find the courage to walk out into the street, with arms out/ Got a love you can’t defeat/ Won’t be drowned out/ There’s nothing you have that I need/ I can breathe now.”

It neatly captures the transcendental nature of the best of U2’s music: the persistent desire to escape yourself (“Sing your heart out”), even when yourself is Bono (“And I’ll sing my heart out”). It’s an infectious, joyful, shimmering kiss-off to the legions of haters, making Breathe the best thing U2 have done in fifteen years. A whole lifetime crammed sleight into five minutes.

And so U2 plough on like a minotaur, impervious to the whims of criticism, which first lifted them to very great heights and then watched with hand-rubbing glee as they plummeted back to Earth, not once in their career, but twice. Perhaps weary of ricocheting between these poles, Bono calls his critics (those “geniuses of compression”) out directly on the album’s downbeat spoken word closer, the narcotic Cedars of Lebanon: “Choose your enemies carefully because they will define you/ Keep them interesting because in some ways they will mind you. They’re not there at the beginning but when your story ends/Gonna last with you longer than your friends.”

And though this is passed off as the viewpoint of a psychically addled, synaptically exhausted war correspondent, it rings true as the sentiment of someone who is arguably the most divisive personality in all of rock and roll, who inspires either absolute devotion or flagrant derision. If all affectations are ultimately ridiculous, Bono’s wilful lack of an edit switch leaves him vulnerable, and makes him either a great artist or an insufferable gobshite, depending on which side of the fence you sit on. To me, someone who so openly wears their intentions on their sleeve can only be valuable.

No Line On The Horizon is rambunctious, unabashed, celebratory, straight pilfering, frustrating; nakedly, embarrassingly earnest, self deprecatingly knowing, quite often silly, triumphant and more than occasionally brilliant. A pastiche at once owing to everything that U2 has ever been and to everything that they might have wished they were. It is then, exactly like U2 themselves. Thematically they still grapple with the same universal tropes (love vs. hope, faith vs. death, freedom vs. responsibility), implying that not very many things get any clearer as you get older, but that only the desire to understand them is what makes investigating them over and over worthwhile.

It’s hard to imagine where they can go from here, but the fact that they undoubtedly will is what makes U2 so interesting. It is what makes them matter. Which at the heart of all things, is all that anyone wants.

U2’s No Line On The Horizon is out now through Universal Music.