[The following is a guest post by Jim Unger (J. Marshall Unger), who wrote it in response to my invitation to him to draw up a Stammbaum to show the relationships of the world's scripts.]
The rationale for tree structures in language history is that languages never completely converge. When speakers of two languages come into contact, there are always clues in the resulting language(s) that reveal the identity of the input languages: apart from the effects of contact, languages diverge over time.
In the case of writing, one must first of all distinguish graphic methods per se from writing systems. The adaptation of existing graphic methods that originated in one time and place to a different time, place, and, usually, language, does not, in my opinion, show the spread of a writing system, just the diffusion of a technology. It only makes sense to speak of a writing system with respect to a particular language at a particular time and place. This is a corollary of the fact that every practical and learnable writing system co-extensive with the potential output of a natural language necessarily utilizes a certain amount of phonography with respect to that language (unless the system is contrived expressly for cryptographic purposes). Logography arises because of sound changes that obscure the motivations for some previously phonographic inscriptions, the purposeful suppression of certain phonographic information for the sake of brevity, or, as in the case of Chinese, historical accidents that militated against the adoption of an abjad, abugida, or alphabet.
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