Is Super Mario Galaxy the greatest Mario game of all time? Edge gives its verdict on arguably the most important game of the year.

Super Mario Galaxy is impossible. Don’t get the wrong idea – it’s not a particularly difficult game, although it does have its moments. What we mean is, it obeys no rules, contradicts everything you know, and has no right to exist.

Mario Galaxy turns 3D into 2D, and 2D into 3D. It takes complex spatial ideas and makes them simple and instinctive; it takes the most basic, most familiar acts in gaming and makes them strange, finger-twisting and fresh. It resurrects the pure platform game in a universe where it’s hard to fall off things. It rewrites its own rules in almost every level, sometimes more than once. Super Mario Galaxy rejoices in turning the world upside down.

It really ought to feel more familiar than it does. Mario’s basic controls work almost exactly as they did in Super Mario 64: a supple range of clumsily exuberant acrobatics, distilled to the manipulation of one stick and two buttons. Exactly as last year’s New Super Mario Bros did for Mario’s 2D incarnation, it serves as a reminder of how his peerless controls have been widely imitated, but never successfully copied. The timing is slightly more forgiving, and the sense of inertia is mildly restrained (in normal gravitational conditions – which are rare enough). But the elastic, chaotic, joyfully expressive freedom is as it ever was.

So far, so reassuring. But after a clunky and cutscene-ridden intro has laid out a needless backstory for Super Mario Galaxy’s sheer nonsense, the game dumps you on its first little spherical planetoid. As you hare around, you run down its flank, and along its bottom; you plunge through a pipe and pop out on the other side. Left becomes right and down becomes up in the blink of an eye.

Confusion and disorientation slowly melt into surprise and delight; your brain baulks at the message from your eyes, but your fingers know, instinctively, that Mario will just go where you point him. It’s an identical feeling to steering Mario’s first steps in 3D over a decade ago; the hesitant thrill of understanding that what was absolute has become a matter of perspective. Only this time, that feeling never goes away.

Since a fourth dimension of space doesn’t exist, Nintendo has found it necessary to invent one. It has wrapped Mario 64’s bas-reliefs around spheres, cylinders and lozenges. There are planets with prongs, planets in the shape of a mushroom or of Yoshi’s head, planets made of interlocking beams, planets that double back on themselves, planets that are just globes of water you can swim through. The ground keeps shifting, your faith keeps being challenged, the sense of amused wonder at each rewiring of your brain never fades.

Incredibly, these mind-bending spatial concepts – so much more complex and elusive than anything seen in thirdperson gaming to date – are displayed by a camera that’s nothing short of perfect. Nintendo has stepped back from user control and let its own code and careful direction do the talking. There are larger, more traditionally designed flat planets too – a welcome change of pace, for the most part, though one ice world veers dangerously close to cliché – and here basic rotation of the camera is allowed. It speaks volumes that you will very rarely think to touch it.

Thanks to its host platform, Super Mario Galaxy has another perspective twist in store. Its use of the Remote is more subtle, but more pervasive, than the vigorous literalism of Twilight Princess. Shaking it for a spin attack, or to activate the star gates that send you soaring ecstatically between planets, gives you that now-familiar tactile buzz. But as a pointer, it does so much more.

It lets you reach into the screen, collecting and shooting the star bits that litter the universe, grabbing on to tractor beams, steering bubbles through mazes, twanging Mario and Toad out of catapults. It lets you play the game in two ways and two places at once, and breaks a hitherto unseen barrier between the player and the action. That you can both be Mario and help him is another of Galaxy’s initially strange dislocations, but it comes to feel so comfortable that losing this godlike power is like losing an arm.