A little while ago I noticed that Mister Mittens was into some sleep at the top of my recliner so I snapped a shot. She's doing the "Sphinx Thing" and resting happily. She can't fall because parts of her cat brain are awake to her surroundings despite the narrow perch under her. She is not in a deep sleep and yet is virtually unconscious and oblivious to her surroundings until something out of the normal catches her ear. Her cat brain allows her to do several stages of sleep depending upon what she wants to do and the time of day.
These feline things are truly amazing.