Biblical Hebrew Forum

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

On 1/15/07, K Randolph <wrote:

> I did a spot check on the spreadsheet that Peter made, and I noticed
> that many of the homonyms he listed are not homonyms when using
> different lexicographic methods. But that should not significantly
> change the rankings, I don't think.
>
> In closing, my observation was that sin and shin together were found
> in homonyms no more frequently than other letters as a percentage of
> total uses. The statistical study by Peter bears that out. But I agree
> with Peter that that in itself does not prove that sin and shin were
> one phoneme in Biblical Hebrew, neither does it disprove it.

This is a restatement of your "observation" much differently than it was
before you investigated the numbers.  In any case, I am glad you approve
of his numbers because as far as I can see, his numbers assume your
"observation" is false.  To review, your "observation," stated a multitude
of different ways goes "the first problem I noticed is the lack of words
where sin and shin denote a difference in meaning" or "I was struck
by how seldom the sin and shin appeared in homonyms."  Peter assumed
all pairs of Shin/Sin are homonyms in his table.  This is stated flat out, and
is also borne out by the data itself: there are 31 pairs of words that Peter
lists for Shin/Sin, and there are 40 independent homonyms (homonyms of
only Shin or only Sin) in the separate Shin/Sin table.  Together they make
up 71, and this is indeed the value of homonyms Peter uses for the joint
Shin/Sin statistic.

In other words, your "observation" was that there are very rare cases where
Shin/Sin pairs of words are homonyms as opposed to the "synonyms."
Peter's data assumes that all Shin/Sin pairs are homonyms.  Furthermore,
Peter does not check your claim.  To check your claim one has to calculate
some 230 values for each possible pair of two letters (alef-bet, alef-gimel,
and so on) to determine how likely is it that the interchange of the two
letters will give us a homonym.  Then we check the Shin-Sin pair against
all other pairs.  Well, I'm not going to do that.

What about the statistics Peter gave us?  Well, the first question is, how
are they distributed?  Is this a normal distribution?  Is there any relation
between the percentage or the amount of homonyms and the number of
total roots?  There is a simple way to find out!  Graph it. For convenience,
there is a link to an online graphing utility and a list of these data at the
end of this mail.

When graphed, the data clearly show that there is a nice upwards curve.
Resh's data point appears way out there because there are so many
number of roots that have Resh in Peter's list.  The question is: why is
there such a nice curve?  why do the data for the letters cluster around
a curved line?  why doesn't it seem to matter if the letter is a letter that
did not merge from several hypothesized Proto-Semitic phonemes, and
if the letter merged from several (like Sade)?  In fact, why stop at Proto-
Semitic? There probably were many more such mergers (as well as splits
and other developments) prior to Proto-Semitic that we do not have
sufficient data to reconstruct.  So if the history of the roots is so complex
and random, why do they cluster around such a nice line (line in the more
loose sense that can include a curve)?  I think part of the answer lies in
the fact that when such a merger takes place, the number of homonyms
increases but so does the total number of roots.  That is, if two phonemes
X and Y merge to become Z, then the total number of roots with Z will be
that much higher as will the total number of homonym roots with Z.  It is
harder to explain a split this way, but a split is also a more complex
process.  Consider how the BGDKPT letters were probably phonemic in
their separate allophones, and yet it is very hard to find such examples
(with the reconstructed example ")alpe" vs ")alfe" being just that --
hypothesized).  Furthermore, the words are just as likely to be replaced
by other words or borrowed words independent of the phonemes.  This
leads to a process whereby mergers, splits, replacements and
developments don't drastically change the upwards "linear" nature of the
graph.  While the processes assumed here suggest an increasing linear
distribution, there are also interrelated factors, roots with multiple mergers
and others that might generate an increasing but not exactly linear
distribution.  This is how I explain the curve.

At first I thought the curve was exponential, but upon trying different
regression methods, it turned out that a power regression was much more
successful in modelling the data (with a 98% correlation coefficient).  I am
not particularly interested in the specific regression as I am in a curve that
accurately models the data.  This also was able to model the Resh whereby
the exponential curve did well for the data (not as well as 98%) without the
Resh and missed the Resh by a bit when the Resh datum was included.
Thus, the website linked below allows you to analyze a power regression
based on the data as well as plot the scatter graph of the data.  In both
power and exponential analysis, the Mappiq He datum has to be taken out
because an (x,0) datapoint cannot be handled.  The exceptional nature of
this data point has been noted by Peter already, so it's reasonable to
leave it out anyway.

So, what about your theory?  Well, as explained earlier, your theory actually
supposes that very few of the Shin/Sin pairs are homonyms!  So, if we, unlike
Peter, consider all Shin/Sin pairs to be synonyms, we will get that Shin/Sin
has only 40 homonyms (the separate counts for Shin and Sin taken together)
and not 71.  This is quite exceptional.  The datum when plotted clearly stands
out away from the curve, and the power regression coefficient drops to 94%.
The way it stands out away from the rest of the data suggests that no other
analysis will get much better results.  The rest of the data points suggest a
line or curve and this data point just skews that line considerably.

That is, if one assumes as do you that Sin and Shin never describe a 
difference
in meaning, one has trouble explaining that odd data point.  If one
assumes that
Sin and Shin always describe a difference in meaning, as Peter did, then, 
well,
isn't that reason to consider them unique phonemes?

In short, the data cannot bear your conclusions  out because it assumes your
"observations" are wrong.  If measured with your "observations" in mind, one
will get a low percentage that is still within the bounds of the other
percentages,
but it definitely does not fit the pattern that is described by the
rest of the data
when graphed.  This suggests that your "observation" as relating to the lack 
or
rare number of homonyms with Sin and Shin is wrong.  It does not contradict
an hypothesis that Sin and Shin were originally separate, merged in Hebrew
(as in Samaritan and probably Ugaritic) and later were re-identified
again since
the process of re-identification assumes the original roots were still
correctly
distributed after being identified again.  However, such an hypothesis cannot
tell us when the merge took place nor can such an hypothesis be supported
in any way on the basis of the number of homonyms.

Yitzhak Sapir

Power regression plotting website:
http://science.kennesaw.edu/~plaval/tools/regression.html

x-values:
178
253
135
194
299
176
104
291
109
118
159
312
241
271
140
280
248
179
219
481
114
336

y-values:
30
48
16
27
71
38
19
62
12
15
22
68
41
45
18
61
38
33
30
118
11
71