As a similar but distinct theory, you might find Larry McEnerney‘s work interesting. Writing has two classes: a writing for thought and a writing for communication. Larry uses horizontal and vertical spatial metaphors here. Writing for thought still pre-dates cheap paper (and Socrates), but is mostly a private act. Writing for communication is a broad enough brush to span fiction and journalism. For his part, Larry teaches classes aimed at thesis writers who struggle to bridge the divide of using writing to think about a problem to conveying their answer in a paper.