Biblical Hebrew Forum

["K Randolph" <kwrandolph AT gmail.com>]

Peter:

On 1/17/07, Peter Kirk <peter AT qaya.org> wrote:
> ... if the roots are actually randomly distributed. My
> reasoning is as follows (based on an argument I found at
> http://mathforum.org/library/drmath/view/62941.html): Suppose that there
> are N verbs with the first root letter A. There are thus (N^2)/2 (half N
> squared) pairs of such verbs. What is the probability that any such pair
> is identical? This depends a little on which the second and third root
> letters are, but as a rough approximation it is 1/23^2 (or 1/22^2 if we
> count sin and shin together), as there are 23 (or 22) possibilities in
> each position. And similarly for each of the other letter positions.
> Thus the mean number of pairs which match is ((N^2)/2) / (23^2), or
> (N^2) / 1058. While this formula needs slight adjustment for cases of
> three or more homonyms, it should give a ball park figure.
>
> In fact there seem to be about twice the number of homonyms expected by
> this calculation - except for medial vav and final he and resh, which
> may suggest that some special considerations apply here. Consider the
> following, for each letter (counting sin and shin separately) and adding
> across all three roots. This discrepancy is consistent with the effect
> of the non-randomness of distribution of the other root letters. (Second
> column: calculated estimate; third column: observed number)
(list repeated below)
> ...
> --
> Peter Kirk
> E-mail:  peter AT qaya.org
> Blog:    http://speakertruth.blogspot.com/
> Website: http://www.qaya.org/

Taking those column of numbers, I added a third column showing the
multiple for each letter, from the expected to the observed.


)      10    28    2.8
B      20    46    2.3
G       6    12    2
D      12    24    2
H      51    68    1.333
H.      0     0
W      29    35    1.207
Z       4    19    4.75
X      29    55    1.897
+       4    10    2.5
Y       8    13    1.625
K       8    17    2.125
L      36    67    1.861
M      18    40    2.222
N      26    41    1.577
S       6    18     3
(      26    56    2.154
P      19    35    1.842
C      10    33    3.3
Q      15    25    1.667
R      79   108    1.367
&       3    10    3.333
$      23    30    1.304
T       5    11    2.2
Total 449   801

#    26     40     1.538

Notice that the shin has the second lowest multiple. The sin and shin
together have a multiple still on the low side of the average of 1.784
(taken from the total row).

Even though I disagree with the lexicographic method, the results seem
to imply even stronger than defining by action that the sin and shin
together were originally one letter. (Defining according to action
gives an observed frequency closer to the predicted numbers than to
the "observed" frequency from your received list.)

To repeat my original observation, I noticed that sin and shin
together are observed to have a lower frequency of homonyms than
expected, especially lower than expected if they were originally two
phonemes. That, along with other clues, caused me to raise the
question, were they originally one phoneme with one letter to
represent that one phoneme?

Karl W. Randolph.