Points and lines

I recall a defining moment of my life when I sat in my desk at school watching and listening as the teacher presented the basics of geometry. The idea of a line composed of infinite points consisting of nothing but a location intrigued and fascinated me. I contemplated for some time how this made intuitive sense and yet was incomprehensible until I looked up and realized the lesson had kept moving and left me behind. To this day I don't think I've ever caught up. In a meaningful way I'm still sitting in my desk trying to get my mind around these ideas.