by Alex Rotenberg

The widely known paper [WRR94] claims that there exists statistical evidence for "unusual closeness" into the Book of Genesis between ELS's (equidistant letter sequences) for the names of famous rabbinical personalities and ELS's for their dates of birth and/or death.

Amazed by this claim, I decided to perform an experiment of my own. The way by which [WRR94] obtained their list of rabbinical appellations is complicated and depending on expert knowledge. In order to avoid such difficulties it is preferable to deal with preexisting lists of names of personalities with firmly known dates of birth and/or death.

In fact, there is a very well known explicit list of personalities all of whom happened to die on the same well known day. Namely, the Book of Esther tells us that on the 13-th of Adar, the very day that was planned by Haman as the day of extermination of all Jews of Persian empire, the Jews gained power over their haters and killed, amongst other enemies ten sons of Haman. The Book of Esthter stresses the list of ten sons of Haman by writing in a form of a column (Esther, ch.9, 6-10).

Here is the list of names:

Parshandata	PR$NDT)
Dalfon	DLPWN
Aspata	)SPT)
Porata	PWRT)
Adalya	)DLY)
Aridata	)RYDT)
Parmashta	PRM$T)
Arisay	)RYSY
Ariday	)RYDY
Vayzata	WYZT)

Following [WRR94] we consider the pairs

(name, date)

(1)	the thirteenth of Adar	YG)DR
(2)	the thirteenth of Adar	YGB)DR
(3)	on the thirteenth of Adar	BYG)DR

Adding the fourth one:

(4)

on the thirteenth of Adar

BYGB)DR

we computed the values c(w,w') and the P1 and P2-statistics as defined in [WRR94] for their pairs. The results are not especially interesting:

	(1)	(2)	(3)	(4)
Parshandata	---	---	---	---
Dalfon	0.336	0.440	0.416	0.432
Aspata	0.672	0.624	0.648	0.432
Porata	0.688	0.600	0.896	0.523
Adalya	0.032	0.264	0.696	0.750
Aridata	0.336	0.112	0.928	0.364
Parmashta	0.008	0.464	0.064	0.773
Arisay	0.328	0.416	0.952	0.250
Ariday	0.208	0.344	0.688	0.455
Vayzata	0.480	0.032	0.288	0.341
P1	0.56	0.56	0.87	1.00
P2	0.045	0.19	0.82	0.71

It should be the end of story, but the real story only starts here. Looking on the ELS's for the date I noticed that one of them had the extension with the same skip - Purim! So appeared the expression

on the thirteenth of Adar (is) Purim

YGB)DRPWRYM

with skip 2547.

I believe that many of the readers will share my feelings that some truly rare event happened (however a precise evaluation of its chances to appear meets with the difficulties of distinguishing between a priory and a posteriori probabilities; we will not pursue this topic here). This finding struck me very much and captured my imagination. In the course of history a lot of different events happened on each particular date, the same can be said about the thirteenth of Adar. It seemed that just this ELS for the date, with its extension Purim was specifically marked for its relation to Purim event.

What if we match the names of the sons of Haman with this specific expression?

The result turned out essentially better:

Parshandata	PR$NDT)	---
Dalfon	DLPWN	5 / 125
Aspata	)SPT)	64 / 125
Porata	PWRT)	101 / 125
Adalya	)DLY)	47 / 125
Aridata	)RYDT)	8 / 125
Parmashta	PRM$T)	11 / 125
Arisay	)RYSY	8 / 125
Ariday	)RYDY	3 / 125
Vayzata	WYZT)	99 / 125

The result for the name Parshandata is undefined since the word has no unperturbed ELS's.

We observe close proximity to the central expression of five sons of Haman (Dalfon, Aridata, Parmashta, Arisay, Ariday).

The values of statistics are

P1 = 0.02 ,

P2 = 0.013 .

The computation of c(w,w') is based on comparison of the ELS's with the population of (x,y,z)-perturbed letter sequences. When we enlarged the population the results strongly sharpened:

	D=1	D=2	D=4	D=6	D=8	D=10
Parshandata	---	---	---	---	---	---
Dalfon	0.0740	0.0400	0.0357	0.0368	0.0291	0.0255
Aspata	0.4444	0.5120	0.4718	0.5038	0.5037	0.5119
Porata	0.7777	0.8080	0.8381	0.8200	0.8128	0.8120
Adalya	0.3703	0.3760	0.3635	0.3472	0.3413	0.3458
Aridata	0.0740	0.0640	0.0370	0.0309	0.0346	0.0369
Parmashta	0.1481	0.0880	0.0699	0.0546	0.0539	0.0512
Arisay	0.0740	0.0640	0.0685	0.0646	0.0608	0.0593
Ariday	0.0740	0.0240	0.0068	0.0072	0.0054	0.0063
Vayzata	0.8148	0.7920	0.7558	0.7823	0.7852	0.7856
P1	0.02	0.02	0.02	0.02	0.02	0.02
P2	0.046	0.013	0.0035	0.0028	0.0020	0.0021
Size of popul.	27	125	729	2197	4913	9261

Note 1. The Book of Esther summarizes the list of the sons of Haman by saying in the next verse "ten sons of Haman" and thus it provides us with the title

Sons of Haman

BNYHMN

The idea of adjoining of a title to the list was already employed in the preprint [WRR95] in particular in the "Mishna" sample. If we accept this idea the results look as follows:

	D=1	D=2	D=4	D=6	D=8	D=10
Sons of Haman	0.0740	0.0400	0.0342	0.0400	0.0435	0.0415
Parshandata	---	---	---	---	---	---
Dalfon	0.0740	0.0400	0.0357	0.0368	0.0291	0.0255
Aspata	0.4444	0.5120	0.4718	0.5038	0.5037	0.5119
Porata	0.7777	0.8080	0.8381	0.8200	0.8128	0.8120
Adalya	0.3703	0.3760	0.3635	0.3472	0.3413	0.3458
Aridata	0.0740	0.0640	0.0370	0.0309	0.0346	0.0369
Parmashta	0.1481	0.0880	0.0699	0.0546	0.0539	0.0512
Arisay	0.0740	0.0640	0.0685	0.0646	0.0608	0.0593
Ariday	0.0740	0.0240	0.0068	0.0072	0.0054	0.0063
Vayzata	0.8148	0.7920	0.7558	0.7823	0.7852	0.7856
P1	0.0064	0.0064	0.0064	0.0064	0.0064	0.0064
P2	0.024	0.0045	0.0011	0.00094	0.00073	0.00072

As in [WRR94], we consider the statistics P1 and P2 as intermediate data. The experiment estimating the overall significance of this list is yet to be performed.

Note 2. The "corrected distance", defined in [WRR94] is useless for such a long word as YGB)DRPWRYM: the word has no perturbed ELS's. Thus we modify the [WRR94] algorithm as following: perturbation of ELS's is made as usual for all the words of the list, while for the central expression only its unperturbed ELS's are considered.

Note 3. The expression "on the thirteenth of Adar (is) Purim" turned out to be a real key to the Purim subject, related to a group of interesting findings.

[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.

[WRR95] D.Wiztum, E.Rips and Y.Rosenberg. Hidden Code in the Book of Genesis (in Hebrew), Preprint, 1995, Jerusalem.