Biblical Hebrew Forum

[Peter Kirk <peter AT qaya.org>]

On 17/01/2007 21:34, Yitzhak Sapir wrote:
> ...
>
> Having reconsidered, I think that a power curve is simply too weird.  I find
> a hard time explaining why the data would model a power curve.  While a
> curve does appear to be present in the data, and a power curve does
> model it well, a linear analysis can be more easily explained. ...

On the contrary, a power series is much more probable in a case like 
this. But my latest analysis suggests a simple square law rather than a 
2/3 power law, 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)

)      10    28
B      20    46
G       6    12
D      12    24
H      51    68
H.      0     0
W      29    35
Z       4    19
X      29    55
+       4    10
Y       8    13
K       8    17
L      36    67
M      18    40
N      26    41
S       6    18
(      26    56
P      19    35
C      10    33
Q      15    25
R      79   108
&       3    10
$      23    30
T       5    11
Total 449   801

I have added another chart to my spreadsheet based on this simple square 
law, and the fit seems fairly good if the data for resh are ignored.


> ... For example,
> my own explanation of the mergers of letters explained how linearity was
> maintained in such a process.  Also, if the (8,0) mappiq heh point is
> dropped (and the reasoning of its exceptionality have been noted), we still
> get 97% correlation. ...

But your best fit curve must pass through the origin, surely? Or would 
you expect some minimum number of verbs before there could be any 
duplicates at all?

--
Peter Kirk
E-mail:  peter AT qaya.org
Blog:    http://speakertruth.blogspot.com/
Website: http://www.qaya.org/