I guess I got you wrong when you talked about "union". Yes, we have to try to
minimize something e.g. the number of sound changes required to go from the
presumed protolanguage to the daughter languages subject possibly to some
constraints.

etherman23 wrote:

--- In Nostratica@yahoogroups.com, "H.M. Hubey" <hubeyh@...> wrote:

> Then at worst you'd have two roots for every word, and there would
> be no patterns in the sound changes from the protolanguage to the
> daughter languages. If the change is a Markov process you'd expect
> to find patterns. And therein lies the answer. Ultimately
> the answer is in probability theory.

I don't think so. For every occurrance of X in language A that
corresponds to a Y in language B you'd have a phoneme Z (which is
chosen to be similar to both X and Y) in Proto-AB. In this way you'd
have completely consistent diachronic changes. I suppose probability
theory combined with typology is the ultimate answer. 



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-- 
Mark Hubey
hubeyh@...
http://www.csam.montclair.edu/~hubey