Not all ghosts are frightening, and some may not even be human. I discovered this at 4 a.m. two years ago when I met the White Cat.

I typically visit my small bathroom, awash in the diffused light of a street lamp and sometimes the moon, several times between dusk and daybreak. Washing my hands there on a chilly November morning just before dawn, I noticed my cat Charlie coming through the doorway.

Well, I thought it was Charlie. I looked again. No, this was not Charlie. Charlie was tan and sleek. This cat was white, a bit larger, and had a rough coat. I glanced up at the window where moonlight was streaming in. It had to be a trompe d’oeil. I sat down, and the cat meandered around the tiny room. He had a drink out of Charlie’s paper cup of water in the corner. Then he came over and rubbed against my leg. I could feel the gentle, friendly brush of unfamiliar fur.

This is ridiculous, I thought, I’ll pet him and know for sure if it is Charlie transformed by moonlight. The white cat came back in front of me as I reached down and began to pet him. My hand fell through him as a knife slices through air. The cat’s form disassembled and crumbled, like Mr. Spock in a Transporter, and my hand landed on the bath rug below. I pulled back and as gently as it had fallen beneath my touch, the body of the white cat reassembled. He licked his shoulder, flicked his tail and quietly passed out the doorway into the hall.

For a dozen mornings—not every morning, but over the course of a month—I met the White Cat. Sometimes he would be sitting in the hall waiting for me. Other times, he would wander into the bedroom, think better of it, and return to the bathroom for a drink. Sometimes I would stand still in the doorway as he swam around my ankles in that way cats have of asking for food or affection. One morning I had had enough. I had told my friends about these encounters; they scoffed or rolled their eyes. I began watching ghost programs on television, and wondered whether I was a pawn in a deadly cat and mouse game (in which I was the mouse) or whether I was opening a portal to a world in which the living had no place.

In December, I made the decision to shun the White Cat. I walked into the bathroom, avoiding any glimpse of the floor. I learned to navigate without lowering my sight from the ceiling. I did this for a month, and did not see the White Cat. After Christmas, I began to look cautiously to the floor. He was not there. He was gone.

Charlie died the following spring, and several other flesh-and-blood cats took his place. But there was an emptiness in my heart where the White Cat had roamed. After a time, I began looking for him in earnest, studying the play of light on doorways and behind the stairs between midnight and the break of day. In fact, after many disappointing attempts, I saw him twice, ever so briefly, but the close connection I once felt was gone. One night, there were three white cats sitting in the hall; then I knew I had better not play this game and closed the door for good on the world of creatures dimly seen by moonlight.

Not all ghosts are frightening. And some are not human. But after we meet them once or twice, it is probably best to let them go.