Writing for Writing's Sake

I often think that I write because I must write. In some ways the process of expressing thoughts, emotions, ideas and conflicts through the written word is a means of really hearing my own internal cogitations, and the arguments I might have had with people (if only I had thought fast enough to answer as I wished) and dealing with them in a reasoned way. It is both a safety valve and a means of clearing up the sometimes murky mixture of thoughts, opinions and questions floating around inside. Once a fear is written down,  it loses its fearfulness, once an argument is placed in the context of a conversation between two characters, their viewpoints are easier to understand. This of course is a selfish motivation for writing and entirely for the benefit of the author. It is also a reason to remain unpublished.
To take the leap out into the public arena, there must be a motivation beyond self, a sense of connection and shared experience. The purpose for publishing a piece of writing is beyond writing for self's sake or even writing's sake, it is all about others.