That was a good thing, that he had no idea who she was. The more that she was studying him, the more she wasn't sure that she wanted him to know. Not that Arcturus looked sketchy or anything, but his..eccentricities..reminded Ginny of exactly where she was.
And she wasn't sure if she wanted to make too good of friends with people in a mental place. Even if she were mental as well. People that she knew before were fine. But..the others might be questionable. There was a small part of Ginny that felt bad for thinking that, but it was what it was.
Although, with his offer that she was obviously meant to turn down, the not-so-small part of Ginny was perking up. It was a challenge of sorts, and the stubborn girl often had to prove herself just a little more than anyone else. Maybe that wasn't entirely true, but she had to prove herself to herself. It was that very nature of hers that caused the young woman to take the steps closer and crouch nearby. "I'd like mine a little more cooked, though. Please."