Tilly in particular does this but all of my girls do. I know the spirit of my grandmother is around here sometimes (she lived with me until she passed away last year) and sometimes all three will stop whatever they are doing and stare into the hallway, and their tails will get all puffed up!! Sometimes it can be scarey . Tilly also stares at the walls and the ceiling. The other morning she was doing this and I kept telling her, "NOTHING IS THERE!!" so then I look up and what do I see? I big black spider crawling along the ceiling. I think she knew it was in my room and was looking to see where it would appear rather than AT it.. it freaked me out!! So we had a good spider killing session that morning. She is still staring at where she saw it last, but I think that's because I killed it and not her, so she keeps looking for more fun!