### Sons of Haman

#### 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:

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.