Another headbutt, and Craig learns about the upstairs, and Amy in the sky and time, and the window adverts -- where, sometime but not yet, Amy will star the correct one and add a better address -- and then Craig gets a bit ahead of us: "That's a scanner! You used non-technological technology of Lammasteen!" The Doctor is like, "Chill, chill, chill."
But he shouldn't worry, because the upstairs -- this time a little girl -- is busy eating somebody else. Somebody named Sophie.
The Doctor radios to Amy -- whom Craig instantly remembers, and understands their language, entire new worlds in his head; really nothing so different than what the Doctor did to Amy last night -- and lets her in on what the cat said. "I know he's got a time engine in the flat upstairs. He's using innocent people to try and launch it. Whenever he does, they get burnt up, hence the stain..."
And then it all goes a bit mental. Craig gets stuck in another little loop, as the upstairs claims Sophie -- "People are dying up there! People are dying people are dying..." They snap out and run upstairs, figuring out that it's Sophie. Of course, Amy finally gets ahold of the plans, informing that there's no upstairs. There's never been an upstairs.
"The time engine isn't in the flat, the time engine is the flat! Someone's attempt to build a TARDIS..." Craig's not sure, and the Doctor explains about perception filters, most notably how they affect memory. What's there now? A sort of TARDIS-y kind of thing, with buttresses and spots you can put your hand on if you want to get all burnt up. Deadlocked inside with it, the Doctor and Craig are helpless to do anything but chat the Bad Guy up, with no small amount of charm.
"The ship has crashed. The crew are dead. A pilot is required." It's a hologram, a simple crash program, that's been bringing people up to see if they can run the engine -- never figuring out that humans can't do it, no matter how many people it burns out on attempt. The program figures out that the Doctor can help, after seventeen murders, and gets very excited. Essentially Wall*E is a serial killer and the Doctor is like the ultimate possible pilot. It begins to reel him in. "I'm way too much for this ship," he hisses at Craig. "My hand touches that panel, the planet doesn't blow up, the whole solar system does."
He swears to the program that it's wrong about this too, and then realizes that Craig is the only holdout. It didn't want Sophie, although now it does: What's the difference? Sophie isn't afraid of leaving anymore. And the Doctor, he's pretty much made out of leaving. Then there's Craig, who is turning into a sofa. The machine wants people who want to escape. The Doctor tells Craig that -- ...Gets a bit ropey here, but I don't mind. It's pretty much required by this story -- all he needs to do is touch the engine and, instead of thinking about the desire to leave, think about all the things he wants to stay for. All the ways he'd prefer stasis over change. Home over adventure. Sophie. "And I don't want to leave Sophie! I can't leave Sophie! I love Sophie!" Well, you know me. Sophie admits she's in love with him too, and it's all very sweet, and then actually in order to break the spell this damned show goes so far as to have everybody yelling, "Kiss the girl!"