My silly little cat keeps staring at the ceiling fan?

Your cat can be in what vets call Zen Mode. When a cat is in this state, it just means that they are relaxing and meditating in their own way. My cat use to do the same thing, I took him to the vet and he told me that cats can see what the human eye can not. Your cat's eye can spot even a dust particle that we can not even see. There must be something like a little insect or dust particle that is calling your cat’s attention. Sometimes cats tend to have a fascination for a certain object and look at the object to find ways to reach it. Your cat is probably thinking of a way to reach the ceiling fan to play with it, especially if it saw light or the fan moving. Cats are very curious and I would not worry about him. As my vet said, they tend to get bored and move on.