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

> That is one of the great unsolved mysteries of historical
> linguistics. It requires much more careful mathematical analysis
> than the ones we are used to.

Despite having a degree in mathematics I suspect math might not be
the answer. If we treat two languages as sets then we can make a
proto-language from the union of these two sets and then create a one-
to-one mapping from the proto-language to the daughter language.
Typological arguments may be stronger if we assume languages of the
past were typologically similar to languages of today. We could then
find a range of how many phonemes is "typologically plausible." If
the proposed proto-langauge has significantly more phonemes then we
might confidently reject the reconstruction. So if the proto-language
requires 742 phonemes we can safely say they're not really related.
But then that runs into the problem of how many roots we should
expect to be reconstructable. We could drop down the number of roots
constructed which would drop down the number of phonemes required,
but then we may have too few roots for it to be reasonable. Some
mathematics would be necessary (probability and statistics primarily)
but the weight of typology would likely be greater.