What a mess. There's a dead guy slouched on an beautiful neoclassical rooftop, bathed in electric blue light. There's a girl pulling a sword out of his body, and when I say "sword," I mean a wide-gauge, Cloud Strife-looking overgrown chef's knife.

The rooftop's ornamented like a circuit board. There's a torn gown discarded nearby and decorative chevrons on the ground, the walls, pretty much everything. And then there's this voice. This weird, raspy, disembodied voice. Oh wait, it's the sword. The sword's talking to me.

Like a great first line, Transistor's puzzling, stylish setup nails its in medias res tease right off the block. I'm hooked. I want to know why the sword can talk, why the girl can't, and why she's going to wind up pulling a weapon which, if you look closely, resembles the unsheathed insides of a USB stick out of this guy's body. It's neo-noir creepy. BioShock Rapture creepy. Her creepy.

Transistor is the sword's name. (All the best swords have names.) I don't know why it does what it does – absorbing the mental detritus of people found lying by the wayside, or enemies it defeats, then translating their personas into powers.

I'm still working my way through this new PlayStation 4 and PC role-playing opus by Supergiant, creator of the indie hit Bastion, so the payoff's still in the offing. But in science, transistors amplify and convert electric current. In the game, the sword amplifies and converts people into single-word special abilities, the names of which end in double parentheses.

Those double parentheses, in math, signify something called an empty set: a unique set that contains no elements, its size zero. Transistor's abilities all function effectively by themselves, but they can also nest within each other, letting you forge devastating, synergistic combos.

Oh, and the Empty Set, proper noun, is also the name of a place you'll visit in the game early on. Curiouser and curiouser.

Transistor. Image courtesy Supergiant Games

Transistor is littered with similar math references and novel bits of jargon-as-play. The sword's battle abilities are all computer language-related functions, for instance. So Crash(), your default attack, sends Transistor stabbing downward, while Turn() lets you execute planned moves or combo maneuvers. Get() yanks targets toward you while bolstering your distance attacks, while Ping() deploys rapid-fire projectiles in a straight line.

Now imagine rearranging those abilities, each one tactically potent and weaponized in its own right, like shifting variables around in a relational database or colors on a Rubik's Cube. That's where Transistor leaps from being a cool-sounding idea with a promising setup to something that's downright riveting to play.

You'll kit out your combat profile by tapping "access points" stationed around the city of Cloudscape, little terminals that rise from the ground Tron-like to let you tap Transistor's memory. Then you can map abilities like the ones mentioned above to buttons or keys.

But there's no pull-down character menu or ability-fiddling screen, the kind you expect in an RPG, when you're out and about. You have to commit, or at least commit to a play style, crafting a four-way stack of functions with active, upgrade and passive slot effects that complements your penchant to either smack enemies upside the head or pelt them from a distance.

My favorite part of the game at this point, the feature that pulls all the other pieces together, is Turn(). You can actually try to fumble your way through the action without it, since the game doesn't force turn-based play on you. But forget about it. Turn() is the meat and potatoes of Transistor's gameplay. It's where you build all those custom-tailored abilities into lethal attack formulae, dropping functions into sequential chains like words in a sentence – while the game kindly pauses for you.

Turn() even has an undo button. So you can get a glimpse of the future, in precise "this is what'll happen if you do that" terms, then back up a step or three if you want to try something else.

The downside – and this is probably part of why the undo function exists – is that Turn() sometimes feels fiddly, asking you to make and finesse exacting position-related choices using Transistor's very retro but sometimes confusing isometric perspective. In other words, there's a lot of fuss and undo (and fuss and undo, and repeat two or three more times) to Transistor's battles.

But it's also partly because the battles scale up fast, iterating from simple encounters with an enemy that executes this attack or that one, to puzzles where different robot attacks dovetail, threatening to overwhelm you almost instantly. So instead of simply squaring off against a laser-beaming robot, you might have to take out a robot spawning a force field that protects another robot doling out regeneration points to a third robot that currently beating the living crap out of you.

There's so much to think about between functions and Turn() that playing without an undo option would probably destroy me.

I'm hooked. I want to know what the Camerata (the Kafka-esque force pursuing you) are really after. I really want to know why they've dispatched robot-creatures to "process" the city (and its inhabitants) piece by piece like sci-fi dementors, converting it into a facade of ethereal symbol-scapes and abstruse, ghostly lattices with sinister, crimson windows.

But I'm most impressed at this point with Supergiant's roll-your-own battle system, scrupulously balanced and steeped in nerd argot. Hello, world.