the List of Famous Rabbis Failed in War and Peace
In our paper, "Equidistant Letter Sequences (ELSs)
in the Book of Genesis", published in
Statistical Science (Vol. 9 No. 3, Aug. '94), we showed
that expressions have been intentionally
encoded in the form of ELSs in the book of Genesis. We
accomplished this by measuring the
tendency of the names of famous Rabbinic personalities to
converge with their dates of birth and/or
death (day and month). This analysis revealed such a
strong tendency that the probability of it
having occurred by chance is extremely small. According
to one measure of probability the chances
are only four in a million.
On the other hand, an article appeared on the Internet
on September 20, 1997, under the title
"Equidistant Letter Sequences in Tolstoy's War and
Peace," in which Dr. Dror Bar-Natan and Dr.
Brendan McKay claim to have found "the same
phenomenon" described in our paper in the novel
War and Peace.
Obviously the authors do not mean that there really
are expressions encoded in the form of
ELSs in War and Peace. Their real claim is that there are
no such intentionally encoded expressions
Dr. Dror Bar-Natan and Dr. Brendan McKay are in
essence claiming that the results of our
research were obtained through manipulation - that is, by
taking advantage of the latitude they claim
exists in the rules we used, or by deviating from the
rules altogether. Their claim is based on an
experiment they carried out, the results of which they
posted on the Internet, in which they were
able to produce a false "success" in War and
Peace through admitted manipulation within the rules
mentioned above, or by breaking them "to the same
extent" that we supposedly did.
In our response we show that:
1. The "success" in War and Peace was
produced entirely by breaking the rules, so that the
are completely without significance. (They, too, admit
that without rules one can produce whatever
result one wishes).
2. They did not succeed in demonstrating a single
instance in which we broke the rules while
carrying out the original research.
Paradoxically, their failure to produce an artificial
success within the framework of the
established rules is strong evidence against their claim
that within those rules there is still enough
freedom to produce a comparable level of significance in
War and Peace.
Furthermore, we shall see that the very points they
raise serve to substantiate the integrity of
our research, in particular by demonstrating that the
lists of names and dates were compiled
objectively and a priori.
In our paper, mentioned above, we showed that expressions
have been intentionally encoded
in the form of ELSs in the book of Genesis. We did this
by measuring the tendency of the names of
famous rabbinic personalities to converge with their
dates of birth and/or death (day and month).
This analysis revealed so strong a tendency that the
probability of it having occurred by chance is
very minute. One measure indicates a probability of only
four in a million.
The list of names and dates was prepared in advance,
following an objective procedure. The names and
appellations of the rabbis were determined by an expert
in bibliography, Professor
Shelomoh Zalman Havlin, who was head of the Department of
Information Studies, Bibliography
and Librarianship at Bar Ilan University at the time the
list was prepared.
[A detailed report on the principles and rules he used
can be found appended here in
Document 1 (which we will henceforth refer to simply as
"the Report"). A chronology of the steps
and stages which preceded the publication of the paper in
Statistical Science is presented in
Document 2: "Bar Hillel and Bar Natan Ask - Witztum
and Rips Respond".]
In the intervening years many more experiments have
been carried out which point to the
existence of intentionally encoded expressions in ELSs in
the book of Genesis (a number of which
will be presented in my new book, currently being
prepared for publication). Among them is an
important work by an American researcher whose expertise
is in deciphering codes for the U.S.
Defence Department. All of these researches were carried
out using objectively compiled, a priori
lists of expressions (lists which, incidentally, did not
require the services of an expert consultant).
Yet in the article "Equidistant Letter Sequences in
Tolstoy's War and Peace" the authors, Dr.
Dror Bar-Natan and Dr. Brendan McKay (who will henceforth
be referred to as: BNMK) make two
central assertions concerning our paper:
They criticize the rules established by Prof. Havlin.
They write that "Havlin
acknowledges making many mistakes in preparing the list
and says that if he were to do it again, he
would have done it differently."
They add to this the critique of Prof. Menachem Cohen
of the Biblical Studies Department
of Bar Ilan University, concerning the "objectivity
and accuracy" of Prof. Havlin's list and
concerning the Report.
We will respond to this criticism in full in Part I.
There we will show that Prof. Havlin
proceeded according to proper professional guidelines, in
a manner which was objective and a
priori. We will also show that the assertions of Prof.
Cohen, as well as those of BNMK are
groundless in every detail, and that on the contrary, by
analyzing their assertions one can come to
appreciate the extent to which Prof. Havlin proceeded
without the slightest bias or impropriety.
To this section we append Document 3: Prof. Havlin's
letter of response to Prof. Cohen.
They claim further that we "still had some choice in
applying their rigid procedures -enough
choice to generate comparable significance levels in War
and Peace." That is to say, BNMK
claim that within the rules which were established before
the compilation of the first list, there is
enough latitude to produce through manipulation an
artificial "success" for another list in War
They try to substantiate this claim on the basis of a
list of names which they presented via
the Internet on the Sept. 20, '97, in their article:
"Equidistant Letter Sequences in Tolstoy's War and
It is clear that BNMK invested considerable effort in
the preparation of a list of names
which would succeed in War and Peace and fail in
Genesis. It was an effort which involved
searching for many sources, and a great amount of
computer time to make the calculations. This list
was prepared over the course of many months, and what
they published was not the first version of
the list. They try to justify their selections by a set
of 24 assertions (section 2.1 in their article) and
by the considerations mentioned in section 2.2 (ibid).
They claim to have prepared their list:
"by purposefully constructing our own list of
appellations, staying within the WRR-stated rules or
breaking them by about as much as they did."
As we will show in Part II, their claim to have
performed their manipulations within the
established rules is entirely without foundation. There
is no comparison whatsoever between what
they did and what we did. Their entire list of
modifications consists of nothing but flagrant and
unjustified deviations from the rules mentioned above.
Therefore their attempt to demonstrate the
latitude which supposedly exists within those rules is a
complete and total failure. On the contrary,
it is precisely the complete and total failure of their
efforts which demonstrates conclusively the
spuriousness of their assertion that within the rules
there remains: "enough choice to generate
comparable significance levels in War and Peace.
From our responses to their list of assertions it
emerges clearly that Prof. Havlin selected his
list of names and appellations in a manner which was a
priori and without bias.
We append to our response another
document, Document 4, which demonstrates that our
original research was performed in a manner which was a
priori and unbiased. The proofs are built
on the assertions of the critics themselves.
In this section we will deal with the criticisms leveled
against the rules used by Prof. Havlin.
BNMK write that in Prof. Havlin's report: "Havlin
acknowledges making many mistakes in
preparing the list and says that if he were to do it
again, he would have done it differently." A closer
look at the Report (Document 1) reveals quite a different
In the Report no such expression is to be found. What
we do find is that in the section where
Prof. Havlin explains his reasons for not including in
the second list certain appellations which
appear in the Bar Ilan Responsa database, he indicates a
number of appellations which were left out
inadvertently, or for which he could no longer recall the
reason they were omitted.
We tallied these omissions and found that in all only
10 of the omitted names should have
been on the list. That is to say, only ten of the omitted
names were between 5 and 8 letters long. Of
the ten, three do not appear as ELSs in Genesis at all.
We decided to investigate what would have happened if
the remaining seven names had
been included in the original list. Here are the results
(recall that in the original experiment the
statistics P1 and P2 served as the measures of
probability. This is how they were presented in the
"Blue Preprint" - the permutation experiment
was suggested at a later date):
Originally, the best result was: P2 = 0.00000000201
If we add to the list the seven names which were omitted,
we receive: P'2 =0.000000000101
In other words, the results improve by a factor of 20!
This should make it perfectly clear that Prof. Havlin
did not omit these names in order to
improve the result. Nevertheless, BNMK may have intended
that it would be more proper to
evaluate the statistical significance (using the
permutation test) for Prof. Havlin's emended list. In
response to this challenge we performed the permutation
test with the addition of the seven names.
In an experiment in which we ran 100,000,000
permutations, and P4 came in eighteenth place, that
means that the probability is less than 1/5,500,000!
Now let us consider the criticisms of Prof. Menachem
Cohen. He raises two issues:
1. That "the principles according to which Prof.
Havlin chose the names and appellations are completely
arbitrary, and for every paragraph (in his report) one
could have proposed alternative principles, which would
not have been inferior, and in some instances would have
been superior to the principles presented."
2. That "the selection process itself is not
consistent, even in light of those very principles, and
is filled with contradictions."
Response to Criticism 1:
A. We recommend that the reader examine Prof. Havlin's
report (Document 1). By examining
the Report the reader will come to appreciate the
challenge which faces a bibliographer attempting
to compile such a list. He will discover what the
difficulties are, what factors he needs to take into
account, and what the reasonable solutions are. We also
recommend reading Prof. Havlin's letter
responding to Prof. Cohen's criticisms (Document 3). The
following discussion is based also on this
Prof. Cohen's criticism that the principles laid down
by Prof. Havlin are arbitrary is not true,
and we will see as we go on that Cohen's words are
themselves "filled with contradictions" (to use
his own language).
B. Nevertheless, it should be made clear at the outset
that the supposed "arbitrariness" of the
principles is, in fact, totally irrelevant:
B1. Let us suppose, for the sake of argument, that the
person compiling the list chose his rules
on a totally arbitrary basis. Or let us even suppose that
he operated without any guidelines at all,
writing the names and appellations according to his
personal store of knowledge, without any rules
whatsoever. From the standpoint of the experiment
performed, this would in no way impugn the
results, as long as the compiler had no prior knowledge
of which names or appellations would be
Therefore, Prof. Cohen's real criticism is not against
this or that arbitrary choice. Rather he
is accusing Prof. Havlin of "cooking up" the
rules to ensure that the names and appellations chosen
by means of them would lead to the success of the
experiment, based on the prior knowledge which
had been made available to him.
In fact, Prof. Havlin operated without any knowledge
of which names or appellations would
"succeed" in the experiment and which would
"fail." He was even lacking basic information
concerning the exact nature of the phenomenon under
investigation, and certainly about the
procedure for measuring the results. (In fact, to this
day Prof. Havlin does not know which names
"succeeded" and which "failed," with
the exception of those he learned about from this
Besides the absurdity of suspecting Prof. Havlin of
having conspired with the authors of the
paper, it will also become clear that the examples upon
which Prof. Cohen bases his accusation lead
to a conclusion directly opposite to the one he is trying
to draw. Not only do they not call into
question Prof. Havlin's integrity, they actually attest
B2. Prof. Cohen's criticism is particularly irrelevant
regarding the second list, because the
principles were established and employed in the
compilation of the first list. Even if one were to
suppose that they were chosen arbitrarily, nevertheless,
they were established long before the
reviewers requested of the researchers that they perform
a second experiment, for the sake of which
the second list was compiled. (See Document 2, Response 1
concerning the chronology of our
C. From all of the above it should be clear that Prof.
Cohen's criticism is irrelevant. We could stop right
here. But the truth is that besides being irrelevant, it
is also false.
C1. Prof. Cohen claims that "Havlin's decision to
choose only those appellations which are
pronounced has no scientific validity, beyond the
chooser's own whim."
This assertion is very strange. The very essence of a
name is that it is pronounced, as the
verse in Genesis (2:20) states: "And the man called
names, etc." A name is something that one
"calls." Among the acronyms and abbreviations
(which are used a great deal in Torah literature)
there are those which are pronounced, and those which are
simply a shorthand form of writing. (See
also the Report, "Professional Judgment" sec.
(a)). Therefore there was really no choice to be made
here at all. After all, our subject was appellations of
Torah scholars. Abbreviations which are not
pronounced are not appellations.
The truth is that this complaint of Prof. Cohen
contradicts his own words in a previous
paragraph of his letter, in which he states that
"these appellations evolved for the most part
the framework of the written literature; most of them are
complete acronyms (like "Rambam"), or
partial acronyms (R"Y Caro), or the names of written
works (like "Beit Yosef"). In the course of
time some of them departed from the literary framework
and became pronounced names, which at
times even took the place of the original name."
In other words, Cohen also admits that there is a
category of names which are pronounced,
which have special status, to the point that they are
capable of displacing the original name. For
example, Rambam is such an appellation.
Clearly, then, this principle is not a convenient
invention of Prof. Havlin.
C2. Prof. Cohen cites as an example of one of Prof.
Havlin's "arbitrary principles" the fact that
when an appellation is associated with more than one
personality, Prof. Havlin identifies it only
with the personality who was most famous, or who belonged
to the period of the Rishonim (the
early sages). Cohen asks:
"Why is it not possible for two people to merit
being called by the same appellation if it is the one
which was conferred upon them by the people of their
generation and/or by succeeding generations?
Furthermore, Havlin does not apply the same principle
with regard to the original names of those
sages. It is possible to perform a matching of names with
birthdates even if four or five scholars
were called by the same name! Is there any fundamental
difference between the two categories?"
The answer is to be found in the words of Prof. Cohen
himself. In the first paragraph of his
criticism he distinguishes between a person's given name
and his appellations: "The soundest
principle is, in the natural course of the matter, to use
the name which was given to the man at birth.
It is difficult to argue with its validity." On the
other hand, regarding the various appellations,
"which sometimes came about and developed over the
course of hundreds of years and in different
locations," their status is less firm, and even
Therefore, a man's given name clearly belongs to him
even if someone else bore the same
name. We should not deprive him of it.
On the other hand, an appellation like
"Maharsha" is another matter. When can an
appellation such as this be said to belong to
such-and-such a personality? Is it sufficient that one of
his students referred to him in this way? Or should it
only be considered one of his appellations
when his entire congregation called him
"Maharsha"? Or perhaps only if everyone
referred to him
by this appellation? Should we treat this as his
appellation even if it was only used during his
lifetime? Or perhaps only if it was still in use three
From these questions it should be clear that it is
impossible to assign the appellation
"Maharsha" to anyone who was ever referred to
in this way. That would border on the absurd.
Prof. Havlin adopted the simplest solution: He reserved
the appellation for the most important and well
known sage with whom it is associated. The concept of
"most important" includes the accepted
distinction between the Rishonim (the "early"
sages) and the Acharonim (the "later" sages).
Report, "Professional Judgment" sec. (b)).
Any other solution (for example, criteria of
dissemination and duration) would have
necessarily been more complicated and artificial.
Bear in mind that Prof. Havlin established this rule
before the preparation of the first list. It
turns out that the only instance in which this principle
had to be applied in practice, in the first list,
was with regard to the acronym "HaRivash" for
R. Yisrael Baal Shem Tov. Havlin did not include this
appellation because it is too intimately associated with
one of the Rishonim, R. Yitzchak bar
It so happens that if Prof. Havlin had acted according
to Prof. Cohen's recommendation and
used the appellation "HaRivash" for R. Yisrael
Baal Shem Tov, the results would have improved:
The results for the first list were: P1 =
0.000000001334 and P2 = 0.00000000145
With the addition of "HaRivash" the results
were: P'1 = 0.000000000412 and P'2 = 0.00000000117
That is, the best result improved by a factor of 3.24!
C3. Prof. Cohen cites another example of what he
considers an arbitrary rule, relating to what he
calls the "rules of Hebrew grammar" principle
(see the Report, "Professional Judgment" sec.
keeping with this principle, Prof. Havlin rejected using
the definite article before combinations of
words such as:
ףסוי תיבה , in which the article ה
specifies the expression ףסוי
תיב. Prof. Cohen
claims that "one cannot ignore with a wave of the
hand" a usage which exists, just because it
deviates from proper grammar. He insists that the matter
requires an "authoritative clarification",
and that "expert linguists would call into question
Havlin's decision in this matter."
In fact, Prof. Havlin did not ignore "with a wave
of the hand" any existing usage. In fact, he
sought the expert opinion of the linguist Yaakov
Auerbach, of blessed memory. He came down
firmly on the side of rejecting ungrammatical expressions
such as ףסוי
תיבה, particularly in light of
our intention to look for their appearance as ELSs in the
Torah. If ELSs of expressions do appear by
design in Genesis, they will certainly not be written
with grammatical errors! Therefore it is
preposterous to suggest that we look for mistaken usages.
Even Prof. Cohen acknowledges that there is room for
doubt whether an expression like
תיבה should be considered a mistake, as the
rules of proper grammar indicate, or whether one
should take common usage into consideration and stretch
the rules of grammar accordingly. If the
list Prof. Havlin presented to the researchers had
included doubtful expressions, which might
simply be mistakes (which according to the research
hypothesis there would be no point in looking
for in the Torah), could he have been said to have
fulfilled his assignment?
As a result of this criticism of Prof. Cohen we can
better appreciate not only of Prof.
Havlin's professional judgment, but also his reliability
- because out of all the expressions of the
תיבה pertaining to the first list, not one
appears as ELSs in Genesis. Therefore this
principle had no effect whatsoever on the results!
If Prof. Havlin had had any advanced information about
the appearance of these names in
equidistant letters he surely would have avoided
establishing such a principle. After all, why should
he open himself up to a situation where "expert
linguists would call into question" his decisions?
Response to Criticism 2:
In this criticism Prof. Cohen tries to demonstrate a
"lack of consistency" in the application
of Prof. Havlin's rules. Unfortunately, as will become
clear immediately, Cohen's criticisms
emanate from his lack of familiarity with the subject at
hand. He is an expert on the Biblical text,
not an expert in bibliography.
A. Prof. Cohen claims that the principle requiring
pronounced expressions is not consistently
applied and that not all unpronounced expressions were
rejected. As examples he cites the
ח"א, ז"מרהמ, ט"מירהמ.
Despite his assertion to the contrary, all of these
expressions are pronounced!
The proof he cites to support his contention is
particularly absurd. He says: "Undoubtedly if one
were to ask the average yeshiva student to explain these
acronyms he would not know what you
were talking about."
In fact, the "average yeshiva student" has
never even heard of the personalities Prof. Cohen
mentioned - not R Yosef of Trani, not R. Moshe Zacut, and
not R. Immanuel Hai Ricchi - therefore
it is indeed highly likely that he has never encountered
their acronyms. Does that prove that they are
not "pronounced" by those who are familiar with
B. Prof. Cohen also claims that the principle of
"rules of Hebrew grammar" is not applied
consistently, and that "the material is filled with
B1. He asks: "What is the difference between
ןידמע י"רה or ינארט
(in which the article specifies a combination of
words), which were included in the list,
תיבה which was not included?"
The answer is simple (and it is astounding that Prof.
Cohen could make such an obvious
י"רה is not ןידמע
י"ר with the definite article before it, it
is an acronym which stands
בקעי יבר ברה , just
is not ם"במר
with the definite article, but an acronym which
stands for ןומימ
ןב השמ יבר ברה
See for example the Even Shushan Dictionary, in the
section on acronyms, where he notes
stands for יספלא
קחצי יבר, whereas ף"ירה
is not ף"יר
with the definite article, but an
acronym for יספלא
קחצי יבר ברה. (By
the way, the abbreviation ינארט
mentioned by Cohen
does not appear on the list at all).
B2. Prof. Cohen found another
"contradiction" in the application of the
" rules of Hebrew
"Why does Havlin not reject the many appellations
of scholars in which a ה
has been added to the
beginning (like: ם"במרה,
etc.)?" After all, he protests, the definite article
before a proper noun!
As we have already explained at length, ם"במרה
is not ם"במר
with the definite article before it.
which is a generic acronym for scholars whose first names
the letter מ
- for instance ריאמ
יבר ברה ונרומ- it
is sometimes necessary to add the definite
article when referring to a specific ם"רהמ.
is a generic acronym for rabbis with the name of ביל
ביל יבר ונרומ ברה.
Among the numerous "Maharal's" was the famous
Maharal of Prague, who is referred to with the definite
to distinguish him from
C. Prof. Cohen attacks what he calls "the
principle of using only one appellation" (see the
Report, "Professional Judgment" sec. (b)). He
attacked this principle already in his first criticism
(C2, see our response there).
C1. Here he adds that this principle can lead to
"internal contradictions in the process of
decision: How are we to act when the Acharon (the later
sage) is more famous than the Rishon (the
early sage)?" For example, if we were to ask the
average yeshiva student who the "Maharam" was,
he would undoubtedly reply "the Maharam of
Lublin" (an Acharon), and not the Maharam of
Rottenberg (a Rishon).
Here again Prof. Cohen is mistaken. There is no doubt
whatsoever that the Maharam of
Rottenberg is more important and better known than the
Maharam of Lublin. Once again his
reference to "the average yeshiva student" is
baseless. Prof. Cohen did not even bother to ask the
opinion of "the average yeshiva student" before
speaking in his name. (Besides which, as we have
already mentioned the "average yeshiva student"
certainly does not have the expertise to make
judgments such as these).
C2. Prof. Cohen expresses his astonishment at the
absence of Maharam Lublin from both lists.
From here he concludes: "I did not check the length
of his columns in the Encyclopedia of Great
Men in Israel, but the fact that he was omitted testifies
to the [un]suitability of this tool for
establishing the list."
Prof. Cohen is in error here on two accounts:
He did not bother to check, and he did not try to
understand. If he had he would have discovered
immediately that Moharam Lublin was omitted for the very
simple reason that his entry does not
list a date of birth or a date of death, whereas our
lists consisted only of those personalities for
whom a date of birth and/or death were supplied.
But Cohen makes a more fundamental error. The
encyclopedia was meant to serve as an objective
source from which to draw our list, nothing more than
that. This does not imply that the list
compiled on the basis of it includes every great scholar,
nor was this the purpose in using it. All that
was needed for the sake of the experiment was a list of
famous scholars, which was selected on the
basis of objective criterion (for example: "all
scholars whose entry is longer than three columns,
and for whom a date of birth or death (including day and
month) is indicated").
D. Next Prof. Cohen attacks the "principle of
selecting among similar variants of a scholar's
appellations" (the Report, "Professional
Judgment" sec. (f)):
D1. He asks: "Why should we reject one
appellation in favor of another, if they were both in
used by scholars?"
The answer to this question is related to the answer
to Criticism 1, sec. C2. There we
showed that even Prof. Cohen agrees that in comparison
with given names, the status of
appellations is less firm and even variable. Therefore,
if there exist several similar variants of an
appellation, it is sounder to use the most common and
accepted variant. Here also it must be
emphasized that this principle was established before the
first list was prepared.
When we read Prof. Cohen's criticism, it occurred to
us to investigate what would have
happened to the results of the first list if Prof. Havlin
had not established this rule: That is to say, if
he had included all related variants of the appellations,
as well. As it turns out, the results would
The results for the first list were: P1 =
0.000000001334 and P2 = 0.00000000145
With the addition of related variants the results are:
P'1 = 0.000000000262 and P'2 =
In other words, the best result would have improved by a
factor of more than 5!