It never ceases to amaze me what young children see! If only everyone carried this ability with them into adulthood...
From what my mother has told me, I used to get fixated to a corner of the room as well. When she asked me what I was looking at, a spirit appeared of my grandpa, who was dead before even my parents met and said "you have nothing to fear, I am here to see my beautiful and gifted grandson." He then disappeared from her sight. According to my father, her description of the spirit was exactly how his father looked in life!
There was also other strange paranormal things that surrounded me. My mother walked into my room one night while I was asleep, I think I was maybe around 9, and saw the spirit of a lady sitting on the edge of my bed caressing my tired body and running her hands through my hair. The spirit was dressed in a robe, kind of like what a wizard would wear. It looked kind of like ones seen around Norrath in Everquest, for those familiar with the game. She had long, brown hair as well. She is the spirit guide I have come to know as Magathia, who is a part of my "group of close friends" so to say and is the spokesperson and advisor of state for my empire in my home plane. I did not find out about this enounter with my mother until very recently and I have known of this spirit for years now.
Something else I find interesting is the fact that my parents would always find me out of my crib as well. To this day, nobody has an explanation for how I would manage to get out of the crib. I feel there is something of the paranormal involved with that as well. Something else I find interesting is that I had so much control over my movment as a newborn. My mother said that everytime the nurses in the hospital would lay me in the crib one way, everytime they returned, I was faced another way. They said I would be found laying on my stomach, the opposite way from which I was laid in there, everything. Yet another unsolved mystery. I feel this has something to do with the paranormal as well.