Torah puzzle

Sons of Haman

(part 2)

New claims

by Alex Rotenberg

In our previous report ("Sons of Haman", part 1) we have found that the names of the sons of Haman along with the title "Sons of Haman" (BNYHMN) group around a central expression

on the thirteenth of Adar (is) Purim YGB)DRPWRYM

which seems to be a kind of an "informational axis". Here we study the measure of closeness to this "axis" of basic data taken from the Book of Esther.

1. The Book of Esther indicates explicitly the place of the death of the ten sons of Haman immediately before (ch.9, v.6) and after (ch.9, v.11) the list of the names: "in Shushan" [ B$W$N ], "the capital" [ HBYRH ].

2. The date of the event is also explicitly stated (ch. 9, v.1): in the twelfth month that is the month Adar, on the thirteenth day of the same. As before we use 4 forms of the date:

the thirteenth of Adar YG)DR
on the thirteenth of Adar BYG)DR
the thirteenth of Adar YGB)DR
on the thirteenth of Adar BYGB)DR

3. The word "Purim" is the general heading of the whole subject; besides, it is indicated in the "axis" itself. In the Book of Esther we find it in three forms:

Purim (ch.9, v.26) PWRYM
the Purim (ch.9, v.28) HPWRYM
the Purim (ch.9, v.29) HPRYM

For all this data the values of c(w,w') with the "axis" are

in Shushan B$W$N 0.080
the capital HBYRH 0.080

the thirteenth of Adar YG)DR 0.016 Group 1
on the thirteenth of Adar BYG)DR 0.008

the thirteenth of Adar YGB)DR 0.648 Group 2
on the thirteenth of Adar BYGB)DR 0.523

Purim PWRYM 0.072 Group 3
the Purim HPWRYM 0.032

the Purim HPRYM 0.848

To avoid the problem of dependence between two expressions in each group we decided to delete the "best" member from each group and to preserve only the "worst" one (the delicate dependence problem needs special discussion). Here is the whole picture for the axis "on the thirteenth of Adar (is) Purim".

the Purim HPRYM 0.848
Purim PWRYM 0.072
Sons of Haman BNYHMN 0.040
Parshandata PR$NDT) ---
Dalfon DLPWN 0.040
Aspata )SPT) 0.512
Porata PWRT) 0.808
Adalya )DLY) 0.376
Aridata )RYDT) 0.064
Parmashta PRM$T) 0.088
Arisay )RYSY 0.064
Ariday )RYDY 0.024
Vayzata WYZT) 0.792
in Shushan B$W$N 0.080
the capital HBYRH 0.080
the thirteenth of Adar YG)DR 0.016
the thirteenth of Adar YGB)DR 0.648
P1 = 0.000 25, P2 = 0.000 47

As in our previous paper the enlarging of the population sharpens the results:

D=2 D=4 D=6
P1 0.000 25 0.000 25 0.000 25
P2 0.000 47 0.000 065 0.000 047

Note 1. Let L be the number of letters of the word/expression. In [WRR94] only the case of L > 4 is considered. In this case the last three letters are perturbed with (x,y,z) where -3 < x,y,z < 3. In the case of L = 4 , we perturb the last two letters with (x,y) where -6 < x,y < 6.

Note 2. We also computed c(w,w') for the list of the sons of Haman with each expression "in Shushan" [ B$W$N ] and "the capital" [ HBYRH ]:

in Shushan the capital
Sons of Haman 0.296 0.528
Parshandata --- ---
Dalfon 0.104 0.056
Aspata 0.864 0.160
Porata 0.440 0.096
Adalya 0.184 0.344
Aridata 0.800 0.592
Parmashta 0.056 0.232
Arisay 0.104 0.184
Ariday 0.416 0.264
Vayzata 0.768 0.312
P1 = 0.032, P2 = 0.056

Note 3. It is worth mentioning that the property of the expression "on the thirteenth of Adar (is) Purim" to be an "informational axis" remains when instead of the text of the Book of Genesis, the whole text of Torah is taken. By the way, in this case ELS's for Parshandata appear and our table becomes complete. Here are the results of computing c(w,w') for the whole Torah text:

the Purim HPRYM 0.792
Purim PWRYM 0.160
Sons of Haman BNYHMN 0.008
Parshandata PR$NDT) 0.223
Dalfon DLPWN 0.480
Aspata )SPT) 0.632
Porata PWRT) 0.832
Adalya )DLY) 0.408
Aridata )RYDT) 0.032
Parmashta PRM$T) 0.088
Arisay )RYSY 0.056
Ariday )RYDY 0.024
Vayzata WYZT) 0.776
in Shushan B$W$N 0.176
the capital HBYRH 0.242
the thirteenth of Adar YG)DR 0.008
the thirteenth of Adar YGB)DR 0.177
P1 = 0.002 6, P2 = 0.000 7

[R1] A.Rotenberg. Sons of Haman, part 1 (available online).
[WRR94] D.Wiztum, E.Rips and Y.Rosenberg. Equidistant Letter Sequences in the Book of Genesis, Statistical Science, 1994, Vol.9, No.3, pp.429-438.

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