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A Replication of
The Second Sample of Famous Rabbinical Personalities
By Doron Witztum



Abstract
Introduction
Part A: The Personalities of the Second List
  1. Collecting the Data for the "ben" (ןב) list
    1. Collecting the data
    2. The form of the appellation
    3. Spelling

  2. The "ben"-type sample
  3. The c(w,w') values, randomization and results for the "ben"-type sample
    1. Measuring the convergences
    2. The randomization test
    3. Results of the permutation test

  4. Collecting the data for the "ben Rabbi" (יבר ןב) list
  5. The "ben Rabbi"-type sample
  6. The c(w,w') values, randomization and results for the "ben Rabbi"-type sample
    1. Measuring the convergences
    2. The results of the permutation test

Part B: The Personalities of the First List
  1. The "ben"-type sample
  2. The c(w,w') values, randomization and results for the "ben"-type sample
  3. The "ben Rabbi"-type sample
  4. The c(w,w') values, randomization and results for the "ben Rabbi"-type sample
Acknowledgements
Bibliography and Notes


Abstract:
        The central experiment described in our paper Equidistant Letter Sequences in the Book of Genesis [1] was carried out using the second list of Rabbis. In order to replicate this experiment we have prepared two new lists of appellations for those same personalities, based on a suggestion made by one of our critics. Measurement of the convergences between the names and dates was carried out in the same manner as in [1]. Significance was measured and found to be high for one of the lists: p= 0.000042.
        In light of this measurement, two new lists of names were prepared for the personalities in the first list in [1], using the same method. Significance was measured, and for one of the lists it came to: p = 0.0344.

Introduction:
        Our paper, Equidistant Letter Sequences in the Book of Genesis [1], published in Statistical Science, dealt with the relationship between the names of famous rabbinical personalities and their dates of birth and death, appearing as Equidistant Letter Sequences (ELS's) in the book of Genesis. The primary experiment discussed in the paper, the permutation test, was performed on the second list of rabbis. The name/date convergences showed a high level of significance: p = 0.000016.
        Several critics [2] tried to explain away the experiment's successful results by suggesting that the list of names and appellations had been artificially optimized. According to the critics, the weak point in the experiment was the need to resort to the judgement of a bibliographical consultant. This left room for the investigators to conspire with consultant to compile an optimized list. We will not deal with this allegation here. In our opinion, we have already completely refuted this accusation elsewhere [3]. Nevertheless, a successful replication would clearly increase confidence in the original experiment.
        In the present work an experiment was conducted using a new list of appellations for the same personalities. The compilation of this list conformed entirely to the existing guidelines, and there was no need for further decision making on the part of a consultant.
        The second list [4] (which was prepared by an expert in rabbinical bibliography, Prof. S. Z. Havlin) included names and appellations of the following types:

  1. "Rabbi So-and-so".
  2. Surnames.
  3. Full names.
  4. Common designations.
  5. Designations of authors based on the titles of their works.

        Mathematician Prof. Alex Lubotsky, noted in a critical article [5] that there was another type of designation that could have been used – that is, the patronymic. Lubotsky [6] says that the patronymic is introduced by the word ןב – "son of," or with the abbreviation B "R, which "The New Dictionary" [7] expands to יבר ןב – "son of Rabbi." [we use the Michigan-Clairmont scheme for transliterating Hebrew letters].
According to Lubotsky's suggestion, if the father's name was ינולפ (So-and-so), the son should be referred to by the designation ןב ינולפ (son of So-and-so) or ינולפ יבר ןב (son of Rabbi So-and-so).
        I compiled two new lists of appellations for the personalities of the second list: one list comprised of names of the form ינולפ ןב , and another list with the form ינולפ יבר ןב . These lists were then used as the basis for evaluating name/date convergences following precisely the same procedure as in [1]. To round out the investigation I did another experiment: I compiled two more lists parallel to these for the personalities of the first list, and measured their convergences in the same way. The first part of this article will describe the experiment conducted for the personalities of the second list. The second part will describe the experiment for the personalities of the first list.

Part A: The Personalities of the Second List

I. Collecting the data for the "ben" ( ןב ) list:
  1. Collecting the data: To obtain the relevant data for the patronymics I used the Encyclopedia of Great Men in Israel [8], which was the source used as a basis for the compilation of the original lists [1]. I checked the entries of the personalities of the second list. If the name of the personality's father was given in the entry – I would take it.

  2. The form of the appellation:
    a) If the father had a single name, ינולפ , for example, we write:
    ינולפ ןב .
    b) If the father had a double name,ינומלא ינולפ (there were 3 such cases) we will use Havlin's rule, specified in paragraph 4 of his Report [9]. According to this rule (which was used in the composition of both original lists):
    • If the father's double name consists of two Hebrew first names, such as ןושמש השמ ("Moshe Shimshon"), we treat the double name as a single unit. Thus we write:
      ןושמש השמ ןב .
    • If, however, the second private name derives from another language, as in the name רעב בד ("Dov Ber"), for example, we take רעב ("Ber", which means "Dov" in Yiddish) as a nickname, and treat them as alternates, indicating the son both as בד ןב , as well as רעב ןב .

  3. Spelling: For conventions in spelling I used the exact same rules as in [1].

II. The "ben"-type sample:
        The sample consists of pairs of expressions. In each pair one expression is the name of the personality, while the other is his date of birth or death. The dates were copied from [1]. Table A1 lists the data for the various names and forms of the date.


III. The c(w,w') values, randomization and results for the " ben"-type sample:
  1. Measuring the convergences: The convergences were measured exactly as described in [1]. 52 values of c(w,w') were obtained. The values of P1 and P2 were calculated and found to be:
    P1 = 5.19 X 10-6     P2=2.24 X 10-4
  2. The randomization test: This test, using random permutations, was carried out precisely as in [1], using the exact same statistical seed.

  3. Results of the permutation test:
The overall significance came to r = 2 X r1 = 4.20 X 10-5.

IV. Collecting the data for the "ben Rabbi" ( יבר ןב ) list:
        The data was obtained and the forms were determined exactly as described above in section I for the "ben" list, except that in this case, obviously, the form is "ben Rabbi So-and-so" rather than "ben So-and-so."

V. The "ben Rabbi"-type sample:
The sample consists of pairs of expressions. In each pair one expression is the name of the personality, while the other is his date of birth or death. The dates were copied from [1]. Table A2 lists the data for the various names and forms of the date.


VI. The c(w,w') values, randomization and results for the "ben Rabbi"-type sample:

  1. Measuring the convergences: All the measurements were made as above. 14 values of c(w,w') were obtained. The values of P1 and P2 were calculated and found to be:
    P1 = 8.02 X 10-1     P2= 8.80 X 10-1
  2. The results of the permutation test:

Part B: The Personalities of the First List

        The data was obtained and the forms determined in exactly the same manner as for the second list. Therefore we will present straight away the samples and their results.

I. The "ben"-type sample:
        The sample consists of pairs of expressions. In each pair one expression is the name of the personality, while the other is his date of birth or death. The dates were copied from [1]. Table B1 lists the data for the various names and forms of the date.

II. The c(w,w') values, randomization and results for the "ben"-type sample:
  1. Measuring the convergences: All the measurements were made as above. 77 values of c(w,w') were obtained. The values of P1 and P2 were calculated and found to be:
    P1 = 5.91 X 10-1     P2 = 6.30 X 10-1


  2. The results of the permutation test:


III. The "ben Rabbi"-type sample:
        The sample consists of pairs of expressions. In each pair one expression is the name of the personality, while the other is his date of birth or death. The dates were copied from [1]. Table B2 lists the data for the various names and forms of the date.


IV. The c(w,w') values, randomization and results for the "ben Rabbi"-type sample:
  1. Measuring the convergences: All the measurements were made as above. In this case only 5 non-zero values of c(w,w') exist. The values of P1 and P2 were calculated and found to be:
    P1 = 5.79 X 10-2     P2 =5.90 X 10-2


  2. The results of the permutation test:
    The overall significance came to r = 2 X r1 = 3.44 X 10-2.

Acknowledgements:
        I would like to thank Yoav Rosenberg and Yaakov Rosenberg for preparing the programs used in making these measurements.

Bibliography and Notes:
1. D. Witztum, E. Rips & Y. Rosenberg, Equidistant Letter Sequences in the Book of Genesis, Stat. Science, Vol 9 ('94), No 3, 429-438.

2. M. Bar Hillel, D. Bar Natan, B. McKay; One Can Skip in War and Peace Too, Galileo [Magazine], No. 25 ('98), pp. 52-57.

3. D. Witztum, The Additional Dimension: The Refutation of the Criticisms concerning the List of Famous Rabbis, [in Hebrew], March '98. The articles and documents included in this publication can be found (also in English) here . Abstract: D. Witztum, A Refutation Refuted, Galileo, No. 26 ('98), pp. 75-76.

4. The second list of names and appellations prepared by Prof. Havlin for use in the original experiment was published in full in a preprint of [1] in the winter of '88.

5. A. Lubotsky, Unraveling the Code [חנעפ תנפצ], Ha'aretz, Sept. 3 '97.

6. Prof. Lubotsky gave two examples of patronymics for the Vilna Gaon (number 5 on the first list), whose father's name was ןמלז המלש (" Shelomo Zalman"). The forms he chose were: ןמלז המלש ןב ןמלז המלש ר"ב .

7. A. Even Shushan, Hamilon Hachadash (The New Dictionary), Kiryat Sefer, Jerusalem, '89, "Acronyms and Abbreviations", p. 1624.

8. M. Margalioth (editor), Encyclopedia of Great Men in Israel, Joshua Chachik Publishing House, Tel Aviv, '61.

9. S. Z. Havlin, Statement of Opinion, October '96. This can be found on the Internet .

Attachments : Table A1, Table A2, Table B1, Table B2.