... if the roots are actually randomly distributed. My(list repeated below)
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)
...
--
Peter Kirk
E-mail: peter AT qaya.org
Blog: http://speakertruth.blogspot.com/
Website: http://www.qaya.org/
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