To:  (mailing list discussing the Hebrew Bible)
Subject: Torah Codes

Regarding the probabilities of Torah Codes, there are several important
considerations that I have not seen anyone address:

(1) The probabilities of the sequences of the characters in any corpus of
literature cannot be evaluated as though the characters occur in random
distribution. The text of any literary composition is itself a code--that is,
the distribution of the characters is determined by the encoding of an
intelligent message, not by random chance. This distribution is determined by
language, subject matter, and author's vocabulary and style, to mention just
a few of the more important contributing factors.

(2) In a sufficiently large collection of randomly distributed characters,
the frequency distribution (or probability) of each character will be
essentially the same as that of all other characters. For the set of Hebrew
characters, the frequency distribution (or probability) of each character
will be approximately one in 23 (counting the space)--that is 0.0435. This
will also be true of any ordered interval of the characters--that is, the
frequency distribution (or probability) of the characters at ordered
intervals of one will be essentially the same as that of intervals of two, or
three, or four, etc.

     This is not true of the characters in a text of literature. The
frequency distribution (or probability) of each character is different, 
and the distribution at ordered intervals is different still, depending 
on where in the text one starts the ordering. For example, the probability 
of each character in the Book of Genesis (Westminster text of BHS) is as 

Char   Num. of          Probability
)            7629;  Prob= 0.0978
B           4330;  Prob= 0.0555
G            577;  Prob= 0.0074
D           1848;  Prob= 0.0237
H           6281;  Prob= 0.0805
W          8446;  Prob= 0.1082
Z             428;  Prob= 0.0055
X           1844;  Prob= 0.0236
+             308;  Prob= 0.0039
Y           9038;  Prob= 0.1158
C           2774;  Prob= 0.0355
L            5274;  Prob= 0.0676
M           6107;  Prob= 0.0783
N            3785;  Prob= 0.0485
S              446;  Prob= 0.0057
(              2823;  Prob= 0.0362
P             1203;  Prob= 0.0154
C             1091;  Prob= 0.0140
Q             1301;  Prob= 0.0167
R             4791;  Prob= 0.0614
$             3568;  Prob= 0.0457
T             4149;  Prob= 0.0532
Total =   78041; TotProb= 1.0000

(3) In the normal ordering of a text of literature, the probability 
of paired sequences of characters usually is not the product of their 
individual probabilities, as in a random distribution. Some pairs occur 
more frequently that expected by chance, and some occur rarely or never. 
For example, in English, Q is always followed by U and never by any 
other character, whereas U is found paired with other characters; TH, 
SH, and CH occur much more frequently than HT, HS, and HC. A similar 
(non-chance) distribution of paired sequences at ordered intervals can 
be expected, but with different probabilities. The same is true of 
triplets, quadruplets, etc.

(4) In a text of literature, the probability of a code like RESH-SHIN-YOD 
is the normal probability of the first character (RESH) times the 
probability of the first pair (RESH-SHIN) at the given interval, times the 
probability of the second pair (SHIN-YOD) at the given interval, and so 

(5) In a text of literature, the space (or equivalent) is a part of the
character set. I know that some ancient texts do not employ a word divider,
but nearly all the ancient Hebrew manuscripts and inscriptions I have seen 
do indeed have spaces or word dividers. This would make a significant 
difference in the search for codes.

(6) When one searches for a code at all intervals between one and 100, the
probability of finding the code is increased a hundred-fold.

(7) The codes for a rabbi's name and his date of death must be treated as 
two independent codes with independent probabilities. This is true because 
the codes do not occur in concatenated sequence, but rather in ill-defined
"nearness." Thus the problem is to compute the probability that two
independent codes can occur within the bounds of "nearness" at a given
interval. Unless the probability of the "nearness" can be defined, the 
actual probability of the problem cannot be determined. The use of 
"nearness" seems to admit a much greater probability that that of two 
concatenated codes. 

James D. Price
James D. Price, Ph.D.
Prof. of Hebrew and OT
Temple Baptist Seminary
Chattanooga, TN, 37404

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