Biblical Hebrew Forum

["Yitzhak Sapir" <yitzhaksapir AT gmail.com>]

Dear Peter and Karl,

I very much recommend not relating to much to any assumed statistics.
The power curve is interesting but significant also is the fact that it does
not model the observed statistics properly, so much that Peter suggests
there are problems with the medial Vav and Resh.  I could tentatively
consider the exceptional nature of the medial vav (namely, there are
often connections between medial vav roots and roots with equivalent
medial and final root letters) but the Resh is very problematic and I think
it is a big warning sign if the Resh cannot be explained.  Yes, there may
be many more roots that contain a Resh, even twice as any set of roots
with any other observed letter, but that is no reason to ignore the Resh.
It must be remembered that the power curve, especially the version
described by Peter, is a theory and this theory has to be substantiated
as well.  Our base of roots is not a live language base of roots but is
already a selected sample of roots from a wide statistical population in
that the language of the Bible is only a sample from the complete
linguistic variety that existed in the years during which the Bible was
written.  Peter's theory would have to hold true not just for a population
but also for such a sample from a population, and it would also have
to be shown true for other languages, namely Semitic languages.

Karl made the following statement: "If consonantal phonemes were
randomly distributed, then if two were sharing the same grapheme,
then the expectation is that the grapheme would show up as a
written homonym twice as often as those graphemes not shared by
two phonemes."  In general, my analysis of the data both confirms
and shows a certain weakness in this statement.  Specifically,
because roots are randomly distributed, the various graphemes
appear randomly in these roots.  There's a mean and standard
deviation to these appearances, but some graphemes appear
more and some less.   However, the observed relationship from
the statistics is that the more roots there are with a particular root
letter, there will be that much many more homonyms with that
particular root letter.  Roughly, the number of homonym roots
with a particular letter in the alphabet in their roots is proportional
to the total number of roots with that particular letter in their roots.
Comparatively, there are quite a significant number of roots with
*either* Shin or Sin and if most or even half of the total number of
roots that are all but equivalent except for the Shin/Sin different
are taken to be non-homonyms, the total number of homonyms
for either Shin/Sin would end up being significantly less than what
is observed in the proportional relationship described above.  While
this is not exactly what Karl claimed, it does have strong implications
that suggest that Karl's assumed "lack" or "relative absence" of
homonyms for Shin and Sin is a wrong assumption.

The linear/proportional relationship is observed, and since a linear
relationship is the simplest relationship that can be considered it is
probably best to stick with it.  Also a linear relationship is mainly
transparent to sound laws which involve mergers or letters that act
as graphemes that represent more than one phoneme because
these would both give an almost linear behavior.  (The deviation
from linearity has to do with sudden new homonyms that didn't
exist because of new matches, as well as homonyms that existed
in both letters -- say Shin and Sin -- that now join to form an overly
loaded homonym root).  Perhaps these two effects cancel each
other out anyway, but in general they seem to suggest a pretty
linear relationship, since these matches can be expected to be
rare.  That a linear relationship is transparent to these effects is
important in itself and another reason to prefer it to more complex
relationships such as a power relationship.  I think that if one truly
wanted to investigate the nature of the observed relationship one
would do the calculus to identify the relationship that is governed
by sound laws such as the above including the above mentioned
deviations.  That is, the equation of the sound law unification of
phonemes lays the framework for computing through calculus the
relationship that is to be expected of a language in which this
was a governing principle.  So that would be where I'd start, but
until then, I'd stick with the linear relationship which seems to
fit the observed data quite well, and because of its simple nature
does not also require complex explanations or substantiations.

Yitzhak Sapir