This edition: May 27, 1999; First edition: September 19, 1997.

Equidistant Letter Sequences in Tolstoy's "War and Peace"

In [WRR2], Witztum, Rips and Rosenberg found a surprising correlation between famous rabbis and their dates of birth and death, as they appear as equidistant letter sequences in the Book of Genesis. We make a smaller or equal number of mistakes, and find the same phenomenon in Tolstoy's eternal creation "War and Peace".
Dror Bar-Natan
Institute of Mathematics
The Hebrew University
Giv'at-Ram, Jerusalem 91904
Brendan McKay
Department of Computer Science
Australian National University
Canberra, ACT, 0200

1. Introduction
    1.1. Acknowledgement
2. Their choices, our choices
    2.1. Modifications to specific appellations
    2.2. Modifications to the list of personalities
    2.3. Modifications to the list of dates
    2.4. Our list of appellations
3. The Results
4. Bibliography

1. Introduction

Our inspiration comes from reading the paper [WRR2] by Witztum, Rips and Rosenberg (WRR). The outline of the story in [WRR2] is as follows:

The purpose of this note is to show that WRR-Havlin still had some choice in applying their "rigid" procedures - enough choice to generate comparable significance levels in War and Peace. We do this by purposefully constructing our own list of appellations, staying within the WRR-stated rules or breaking them by about as much as they did. If one can find a list of appellations that works well on War and Peace (and pretty badly on Genesis), the only remaining reason to believe WRR-Havlin is personal trust in the cleanliness of the procedures they used to determine the list of appellations (and the other aspects of their experiment). While many beliefs are founded on trust bestowed on a very small group of prophets or apostles, such beliefs are often false, contradictory or absurd, and are definitely outside what one would normally call "science".

1.1. Acknowledgement

We wish to thank Maya Bar-Hillel, Menachem Cohen, Alec Gindis, Gil Kalai, Elchanan Reiner, Shlomo Sternberg, and the others who helped, for their suggestions and support.

2. Their choices, our choices

In [WRR2], WRR write:

The list of appellations for each personality was provided by Professor S.Z. Havlin, of the Department of Bibliography and Librarianship at Bar Ilan University, on the basis of a computer search of the "Responsa" database at that university.
Contrary to what is suggested by the above quote, many of the appellations WRR use do not even appear in the Bar-Ilan Responsa database [Re]. Thus in addition to the Responsa database [Re] we will also refer to the Margalioth Encyclopedia [Marg], used by WRR to select the rabbis, and to the highly-regarded Encyclopedia Hebraica [Heb] used by WRR in several of their other investigations. We (like WRR) also use other sources as needed.

2.1. Modifications to specific appellations

  1. The word hmlaj (the angel) is a noun (sometimes used as an adjective), and is not really an appellation. Since it is a common noun, the word hmlaj by itself, does not uniquely identify Rabbi II-3 (the third Rabbi in WRR's second list of personalities), Rabbi Avraham HaMalach. It is inconsistent to use this as an appellation for Rabbi Avraham, while at the same time not to use hcsyd (the Hasid, the pious) for Rabbi I-11 (the eleventh Rabbi in WRR's first list), Rabbi Yehuda HaHasid (the word hcsyd at least always refers to a human...). We also note that when we turned to an independent expert to form a completely a-priori list of appellations for the Rabbis in question (see details in [MBBK]), he used the combination rby abrho hmlaj, but not the adjective hmlaj on its own. Thus we remove the appellation hmlaj.

  2. Rabbi II-6, Rabbi Eliezer Ashkenazi, is sometime called after his book titled "miwy h'". Thus we inserted the widely used appellations miwy h' and bil miwy h'.

  3. We add the acronyms hmhrc"a and mhrc"a (Rabbi II-10, Rabbi Haim Abulafia). The last acronym appears very often in the Bar-Ilan Responsa Database [Re], it is used in [Az], and its omission in [WRR2] is especially questionable. In [Hav], Prof. Havlin explains the omission of hmhrc"a and mhrc"a by asserting that they are also used in relation with other Rabbis. But in other places, Havlin does use appellations that refer to more than one Rabbi. A good example is hrab"d, which appears in Havlin's lists both as an appellation of Rabbi I-1, Rabbi Avraham, The Ra'avad of Posquieres, and for Rabbi II-1, Rabbi Avraham, Av-Beit-Din of Narbonne. We allow ourselves a similar leeway.

    Rabbi Haim Abulafia and 6 of Nisan
    The convergence of hmhrc"a and his date of death, v nys`, in War and Peace.

  4. In [Hav], Prof. Havlin described the methodology he employed in producing the list of appellations. In his report he acknowledged a few omissions he made in the original list. One of those omissions is the appellation hrb cby"b for Rabbi II-11, Rabbi Haim Benvenist(e). Thus we have added hrb cby"b to our list, with and without the definite article h. We have also added the widely used hrb hcby"b.

  5. The appellations bnbnwt and bnbnwty are both used for Rabbi II-11, Rabbi Haim Benvenist(e). WRR chose bnbnwt, we choose bnbnwty. Incidentally, bnbnwty appears in Responsa more than bnbnwt, as a surname of this rabbi in a ratio of between 2:1 to 3:1. The appellation bnbnwty also appears in the heading of this rabbi's entries in [Vin, Hala, Halp, St, Ei], and in other places.

  6. The last name of Rabbi II-12, Rabbi Haim Capusi, can be spelled either kpvsy or kapvsy. In Responsa, they appear in an 8:3 ratio, which indicates quite clearly that both spellings are valid. See also the title of this rabbi's entry in [Ei]. WRR state explicitly in [WRR2] that in such cases they use both spellings. But in their list they took only the first form. For our list, we make the opposite mistake and take only the second form.

  7. There is no doubt that the two forms bil ns and bil hns are most often associated with Rabbi Meir, whose grave is near Tiberias, rather than with Rabbi II-12, Rabbi Haim Capusi. The vast majority of references to bil hns in Responsa refer to Rabbi Meir and not to Rabbi Haim Capusi. In particular, in the Responsa of the Chatam Sofer, (Part 6, Likutim, Article 27), we find that the formula "for the soul of bil hns" (without the proper name Rabbi Meir!) was used for contributing charity for the soul of rabbi Meir Baal Hanes, and not for the soul of Rabbi Haim Capusi. We note that on several occasions Havlin ruled out an appellation for a certain personality because it was more closely associated with some other personality (see [Hav]). Hence we remove the appellations bil ns and bil hns.

  8. Rabbi II-15 is Rabbi Yehuda Hasid Segal. WRR omitted the appellation yhvdh sg"l, his full name. For example it can be found in [Be, pp. 141, 143-144]. Notice that in the similar case of Rabbi II-23, HaMaharil, who was also called Yaacov Segal WRR did use the full name yiqb sg"l. Following that precedent we add yhvdh sg"l to our list. We also use the appellation hr"y csyd, a parallel of the appellations hr"y imd` and hr"y imdy` used by [WRR2] for Rabbi II-24, the Yaabez. This appellation can be found in this rabbi's entry in [FR]. There are no appearances of these two appellations (for this rabbi) in the Responsa database, but then according to Prof. Havlin's this rabbi is one of the rabbis who are expected to appear only rarely in the Responsa. See [Hav].

  9. The last name of Rabbi II-16, Rabbi Yehudah Ayash, can be written as iyaw or iayaw. The independent expert mentioned above used for the a-priori experiment the forms iyyaw and iayyaw, but for our "experiment" here we follow the "grammatical" dictum that Wiztum has set in the case of Oppenheim, i.e. that we must not use a "double yud" in transliterating foreign names, so we write iyaw and iayaw. The ratio of appearances of iyyaw vs. iayyaw in the Responsa is about 800:1. However from the example of the name Caro for Rabbi I-19, we can see that WRR thought that, according to their "mater-lectionis" rule, both the forms (i.e. with and without aleph) should be included even when the ratio between them in the Responsa in 2000:0 (that seems to be the ratio between the last names qarv and qrv in the Responsa). Therefore, we add the appellation iayaw for Rabbi II-16, Rabbi Yehudah Ayash.

  10. We add the appellation hr"y erany to Rabbi II-19, The Maharit, along with the variations r"y erny, hr"y erny, and r"y erany. This puts the Maharit in a similar status with the Yaabez (see below).

    The Maharit and 14 of Tamuz The convergence of erany
    and his date of death,
    y"d tmvz, in War and Peace.

    Rabbi Yaakov Beirav and 30 of Nisan
    The convergence of hryb"r and his date of death, l bnys`, in War and Peace.

  11. The last name of Rabbi II-22, Rabbi Israel Yaakov Hagiz, can be spelled either cgyz (as in [Heb] and as in the biographical section of [Re]) or cagyz (as in [Marg]). But WRR use only cagyz, contrary to their explicit convention that where a is used as a "mater lectionis", they take both forms. Thus they fail to use the appellations mhr"y cgyz and r"y cgyz (both appear in Responsa). We allow ourselves to make the opposite mistake, taking the appellations mhr"y cgyz and r"y cgyz and omitting cagyz. We note that even though the WRR computations are restricted to appellations totaling 5-8 letters, we can tell which `short' appellations (such as cgyz, imd`, or mvl`) they consider as valid either by checking whether they have used longer appellations that contain the shorter ones as substrings or by reading their "blue preprint" [WRR1], in which the short forms are also listed.

  12. In the case of Rabbi II-24, the Yaabez, we do not use appellations based on the spelling imd` for two reasons. They appear less often, and we wish to follow the precedent set by WRR when they did not use the form mvl` with Rabbi II-23, the Maharil. (The appellations yiqb mvl`, mhr"y mvl`, etc., appear often in Responsa, more often than forms with imd`, and were omitted in [WRR2]. See also [WRR1]).

    We note that there may be a case for removing the name imdy` altogether, for it is just the name of a town were the Yaabez was briefly a Rabbi, and not his last name. The Yaabez himself wrote in [Ya],

    ...hervd yiqb ywral mkvnh yib"u s"e la nqra mivlo yiqb imdy`
    (kawr iwh mk"t adris i"g hagrt kmv whrgyl htvib wr"y bpy
    hbryvt) ydvi waynny mbny imdy` la nvld bh vla mxph lravt' aj
    mbqw evbt' vtvilt' kmaz vmqdo bhyvty rvbu tct mwah, kkh ith
    any wvqd il tqnt'...
    In free translation to English, this reads:
    ... The busy Yaakov Israel known as Yaabez good omen was never called Yaakov Emdyn (imdy`) (as has done the honourable in the address on this letter as is the deplorable habit in the tongues of the people). It is known I am not from the people of Emdyn, was not born there, do not expect to see it, but am looking after its welfare and benefit as in the former times when I was under it's load, [and] so also am I now diligent for it's remedy. ...
    Little did his plea help, and the Yaabez has several common appellations which are variants of the word imdy`. We keep them in our list. However, we can learn from this example that WRR didn't mind using names that were not used (or were even rejected) by their bearers. This lesson will become relevant in the case of Rabbi Shlomo Chelma below.

  13. WRR are inconsistent about the use of the definite article, h. For example, they use hr"y imd` and hr"y imdy` for Rabbi II-24, but omit r"y imd` and r"y imdy`. (The latter two forms appear in Responsa more often than the former two!) We fix this mistake in our list.

  14. The last name of Rabbi II-25, Rabbi Yitshak HaLevi Horowitz, is spelled hvrvbyu at the title of his entries in [Marg], [Heb], and in [Halp]. We thus replace hvrvvyu by hvrvbyu.

  15. The Krochmal Story: We suspected that the spelling qrvkml for the last name of Rabbi II-26, Rabbi Menachem Mendel Krochmal, author of the responsa book xmc xdq and of the biblical commentary py xdyq, was not the original spelling. So we started searching. The word qrvkml does not appear in the Bar-Ilan Responsa database [Re]. The only variation of qrvkml that does appear there is qrakmal, which appears only twice. But in both appearances it is the Yiddish word for starch, and not a Jewish surname. In [Marg], qrvkml is in the header of Rabbi Menachem Mendel's entry, but no explanation for the origin of the name is given. In [Heb] Menachem Mendel doesn't even have an entry, though the index mentions him twice. Looking inside the text, we found the spelling qrvkml, but no further clues as for the original spelling. His books are signed mnco mindl and mnco mindyl, and no qrvkml is mentioned in them in any form. An eulogy for him [Shm] mentions only his first name(s), mnco mindyl, and the titles of his books. So where did "qrvkml" come from? [Az] was of no help. In the 19th century bibliography [B-Y] one of Krochmal's books is listed under qrakmil. In a 19th century biography [Du] of David Oppenheim, Krochmal is mentioned in passing, and his name is given as qrakmal. We are almost certain we also saw qrvkmal and qrvkmil, but after a long day in the Israeli National Library in Giv'at-Ram, the stairs leading to the photocopy machines seem very steep and the pencil becomes really heavy, so we don't have references for these two forms. The 19th century Rabbi Nahman Krochmal spells his own name qracmal, while in modern sources his name is spelled both as qrvkml and qrvkmal. All of that taken together indicates clearly that Krochmal was not spelled "qrvkml" in the 19th century, but it doesn't help us find how Krochmal was spelled when Rabbi Menachem Mendel lived, in the first part of the 17th century.

    At this point we got the advice of two wise men. One suggested that we look at [Hei], a book on the Jewish laws in the state of Moravia, where Rabbi Menachem Mendel was the state's Rabbi. From the other wise man we learned to check the citations in the footnotes. One footnote, on page 111 of [Hei], he checked himself. It lead to an article [Marx], that contains a letter written by the son of a nephew of Rabbi Menachem Mendel in the late 17th century, only a few dozen years after Rabbi Menachem Mendel died in 1661. In that letter Rabbi Menachem Mendel's surname is given as qracmal. The following day (and a continent away), we checked the footnote on page 102. It lead us to two articles, [Hor] and [Ka], devoted to our Rabbi and his descendents. Both articles use the spelling qrakmal extensively and not just in passing, and the latter one even explains where the name comes from! It relates the name qrakmal to a certain Dayan, Rabbi Jonah Krochmals in the city of Cracow, where Rabbi Menachem Mendel was born. A transcript of the tombstone of Rabbi Jonah Krochmals is given in [Zu, page 180] and Krochmals is spelled qrakmalw there. Thus there is no doubt that the original spelling of the name Krochmal is qrakmal and thus it is fully justified to remove the appellation qrvkml from the list, an to put qrakmal instead.

    We also note that once it is clear that qrakmal is an acceptable spelling for Krochmal, the usage of this spelling is mandatory according to the WRR rules, which state explicitly that Yiddish names are spelled as in the original Yiddish. Recall that qrakmal is a the Yiddish word for starch, and from [Ka] we learn that the first people to be called by the family name Krochmal were called so because they traded in starch.

    However, in his "refutation" of a draft version of this article, Witztum argued against the use of the appellation qrakmal. We completely disagreed with his argument, but were amused to note that Witztum himself gives a reference for a source that uses the form qrvkmal. If, as Witztum indicates, qrvkmal is a valid form, then it must have been used along with qrvkml, by Witztum's own "mater-lectionis" rule. Thus we may feel free to use either qrakmal or qrvkmal instead of qrvkml. This time we chose qrvkmal.

  16. The primary variant of the last name of Rabbi II-27, Rabbi Moshe Zacut, is zkvt, and not zkvta or zkvtv. See his own signatures in his book qvl hrm"z, see the Hebrew title of his biography [Ap], and see [Marg, Heb, Az, Ei, Halp, St, Hala]. Hence we remove the appellations zkvta, zkvtv, mwh zkvta, and mwh zkvtv.

    At the same time we note that WRR's use of variants like zkvta and zkvtv sets a precedent which we are allowed to follow elsewhere. Hence for Rabbi II-28, Rabbi Moshe Margalith, we add the variant mrglyvt of his last name. This variant appears in the titles of his entries in [Az, Vin, St, Ju, Fri], in the entry for his book in [B-Y] (p. 487) and also in the index of [Marg].

  17. The story of "Hon-Ashir" and "Yosher-Levav": Often great rabbis are called after their books. In section C of the chapter "Professional Judgment" in Prof. Havlin's report [Hav], it is explained that when we can find that a rabbi is called "the author of (the book) X" in a context where another of his works is discussed then we can regard it as an appellation of him. But, if we can find "the author of (the book) X" only in a context where the book X is discussed then we can regard it as nothing more than a shorthand way of referring to the content of the book itself (that is "the author of Such-and-Such says.." or "HaRav Such-and-Such says..", rather than saying "it is written in the book Such-and-Such.."). Now, ywr lbb is a name of one of several books published by Rabbi II-30, Rabbi Immanuel Hai Ricchi, and not the most important of them. To check whether it deserves to be regarded as this rabbi's appellation, we searched both the [Re] and [DBS] CD-ROMs. The second CD-ROM contains a collection of books on Cabala and Chassidic literature, the fields in which this rabbi is most likely to be cited. Yet, we found no appearance of "the author of (the book) ywr lbb" (or "the author of (the book) yvwr lbb") that is not in the context of discussing this book. On the other hand, we did find the following sentence: "the holy genius author of Mishnat Hasidim o.b.m. wanted to understand the secret of Tsimtsum. (see his book yvwr lbb)...". Within [DBS], see "Mavo Lechochmat HaKabala" part 1, gate 3, chapter 1. We see here that even when the book ywr lbb is being discussed this rabbi is called after his most important book Mishnat Hasidim. Therefore, according to the rule we mentioned above (from Havlin's report) we conclude that ywr lbb is not an appellation of this rabbi and we remove it. On the other hand we did find in the Responsa the following sentence (concerning the same rabbi): "the Rav Hon-Ashir in the book Aderet-Elyahu has said..". (See responsa "Peulat-Tsadik" part 3 section 184). Here we see that this rabbi is called after the book "Hon-Ashir", even when another of his books is being discussed. So we conclude (using the same rules in Havlin's report) that the name of the book hv` iwyr should be considered as an appellation of this rabbi, and we add it.

  18. The story of the appellation a"c hi"r of Rabbi II-30, Rabbi Immanuel Hai Ricchi, is particularly telling. First, we couldn't find it anywhere, and nobody we asked could tell us what it meant. When we inquired with Doron Witztum, he said Rabbi Ricchi used it as his signature in some of his books, and that it expands to "any cy, hxiyr imnval ryqy". After some more investigations we have found that in fact (as far as we could determine) it appears only once as a signature in a printed addendum, that survived only in 1 or 2 copies (that we know of), of Rabbi Ricchi's book "miwh cvwb". This signature is also mentioned in the bibliographical article [Shi] that describes one of these copies (the one in Zurich), and this article is also where the explanation "any cy, hxiyr imnval ryqy" comes from. We think the inclusion of this acronym is extremely wrong. First, it is a very rare signature; not an appellation. Indeed, it seems that nobody refers to Rabbi Ricchi by this name, for we could find no such references and we could hardly find anyone who even knows what it means! Second, it is in fact only a part of a signature. Anyone looking at the article [Shi] can see that the signature that actually appears there is achir rph! Third, it is not "pronounced" (nhgh), while WRR claim to use only pronounced appellations. Here we have to say that Wiztum's speculation that it should be pronounced "Ach-HaEr" is highly original, but not convincing at all. First, he gives no source for this suggestion. Second, as we said, the signature actually appears as achir rph. That is, the first part of it achir appears as one word, and not as 2 words - a"c hi"r - the way Wiztum writes it, and the way one would expect if it was intended to be pronounced "Ach-HaEr".

    More than that, one expert we consulted said that there is a possibility that even this single appearance is no more than a typo in the original addendum. The reason for this suggestion is that a different permutation of these letters, ahic"r rph, appears with its expansion, any hxiyr imnval cy ryqy (me the young, Immanuel Hai Ricchi), and an explanation of the rph part, several times in several of this rabbi's books. We note that in Hebrew the latter expansion makes much more sense than the former, since the former taken literally means "I'm alive, the young Immanuel Ricchi". Indeed, the acronym ahic"r is listed in the dictionary of acronyms [AY], while a"c hi"r is not. (By the way, since ahic"r rph is also a non-pronounced signature it may be considered wrong to include it as well, if one wishes to take WRR's commitment to pronounced appellations more seriously than they did.) Be that as it may, the reasons brought before are more than enough to show clearly that including a"c hi"r is extremely wrong. We remove it.

    On the other hand, we found two other signatures (or self-references) used by this rabbi, that unlike ahic"r rph and achi"r rph, are definitely pronounced, and therefore we add them. These are: hiwy"r - appears in [Ri1] page 4. It is a permuted acronym of hxiyr wwmy imnval ryqy yx"v, and also serves as a word-play on the name of the book "Hon-Ashir". avhb vr"i - appears in [Ri2] - part 2, page 53b. means "loving friend" and also is an acronym of "Ricchi Immanuel".

  19. The entries of Rabbi II-31, Rabbi Shalom Sharabi, in [Heb] and [Marg] and in the sources [Az], and [Re] never refer to him as wr wlvo, and we found at least 7 other rabbis that carry the name wr wlvo (and that are referred to by this name extensively). One of these rabbis, Rabbi Sar-Shalom Gaon, is a "Rishon". We note that in similar situations WRR have removed this kind of "shared" appellations; see [Hav]. We follow suit in this case. We should also add that even if this appellation was not a shared one there was another case for removing it. The appellation wr wlvo is not R. Shalom Shar'abi's given name, nor is it his last name. It is only a poetic epithet (meaning "Prince of Peace") which was conferred upon him by other scholars throughout the generations. We can see that WRR didn't always use this kind of epithets. For example they didn't use prw` dta for Rashi, hrb hmwbyr for R. Yosef Caro, and (h)r"o bmz"l and hrb hmvrh for Rambam. Thus we are allowed to follow suit and omit wr wlvo.

  20. The appellation mzrcy for Rabbi II-31 is related to him just like the name awknzy relates to Rabbi I-6, Rabbi Gershon Ashkenazi and to Rabbi II-6, Rabbi Eliezer Ashkenazi. In both those cases WRR did not use the appellation awknzy. Thus, it is inconsistent to use mzrcy, and we remove it.

  21. The appellations mhrw"w and hmhrw"w for Rabbi II-31 are only variants of the more well-known appellation hrw"w. In the Responsa and DBS CD-ROMs the variant hrw"w appears more often than mhrw"w and hmhrw"w. In Responsa the ratio for this rabbi is about 256:6. In the famous book "Ben-Ish-Hay" which was much influenced by Rabbi II-31 (and which appears in the DBS CD-ROM) he is mentioned 72 times as hrw"w but never as mhrw"w or hmhrw"w. See also the titles of this rabbi's entries in [Heb] and [Marg]. In Havlin's report section F, Havlin says that when there are two close variants of an appellation like mhrw"l vs. hrw"l, he used only the one more frequently used. For comparison the ratio between mhrw"l and hrw"l in the Responsa is only about 3:1. Therefore we can clearly see that by this rule it was wrong to include mhrw"w and hmhrw"w and accordingly we remove them. (It would have been right to include the appellation hrw"w, only that it is shorter than 5 letters, and hence automatically excluded by the rules of [WRR2]).

  22. The last name of Rabbi II-32, Rabbi Shelomo Chelma, can be spelled either as clma or as cilma. This name appear at the header to his entry in [Heb], in his biography [Br], in the titles and prefaces of Chelma's books wv"t lb wlmh (Mossad HaRav Kook, 1972), mrkbt hmwnh il htvrh (Mossad HaRav Kook, 1975) and wvlc` irvj (il wv"i ah"i) (Machon Yerushalayim, 1988). This name also appears a few times in the Responsa database and in the 19th century bibliographical work [B-Y] (p. 373 entry 2295).

    Thus we wish to add the appellations clma, cilma, wlmh clma, and wlmh cilma. In practice we only add cilma and wlmh clma, for the other two appellations do not fit within 5-8 letters. We will add that it appears that this Rabbi didn't use these names himself, but was only called so by others, however as WRR's precedent with the name Emdin (that was mentioned above) shows, this needn't make any difference, and these names can be included.

    Rabbi Chelma and 21 of Tamuz
    The convergence of cilma and his date of death, k"a btmvz, in War and Peace.

2.2. Modifications to the list of personalities

We make the following additional changes to the list produced by WRR:

2.3. Modifications to the list of dates

The birth date of Rabbi II-30, Rabbi Immanuel Hai Ricchi, doesn't appear in Margalioth and was not included in the WRR list. We found in another source that he was born on the 15th of Tamuz [Vil]. We note that in the first list WRR has brought in the birth date of the Besht despite the fact that it does not appear in Margalioth. We follow that precedent in this case, and add to the list of dates for Rabbi Immanuel Hai Ricchi the date forms y"h tmvz, by"h tmvz, y"h btmvz, e"v tmvz, be"v tmvz and e"v btmvz, as dictated by the rules of [WRR2].

2.4. Our list of appellations

The resulting new list of appellations is given in the table below:

The old and new lists, a comparative table
# Original entry we remove we add new entry
1 hawkvl, hrab"d, hrab"y,
hrb ab"d, rby abrho
    hawkvl, hrab"d, hrab"y,
hrb ab"d, rby abrho
2 zri abrho, yxcqy, rby abrho     zri abrho, yxcqy, rby abrho
3 hmlaj, rby abrho hmlaj   rby abrho
4abrho sbi, xrvr hmr, rby
  --- completely removed ---
5 rby ahr`     rby ahr`
6 miwy hwo, miwy y/h/v/h   bil miwy h', miwy
bil miwy h', miwy h', miwy
hwo, miwy y/h/v/h
7 avpnhyo, rby dvd     avpnhyo, rby dvd
8dvd hngyd, rby dvd  --- completely removed ---
9 dvd nyev, rby dvd     dvd nyev, rby dvd
10 rby cyyo   hmhrc"a, mhrc"a hmhrc"a, mhrc"a, rby cyyo
11 bnbnwt, rby cyyo bnbnwt bnbnwty, hrb hcby"b,
hrb cby"b, rb
bnbnwty, hrb hcby"b, hrb
cby"b, rb cby"b, rby cyyo
12 bil hns, bil ns, kpvsy,
rby cyyo
bil hns, bil ns,
kapvsy kapvsy, rby cyyo
13 hmhrc"w, cyyo wbty, mhrc"w,
rby cyyo
    hmhrc"w, cyyo wbty, mhrc"w,
rby cyyo
14 cvt yayr     cvt yayr
15 rby yhvdh   hr"y csyd, yhvdh
hr"y csyd, yhvdh sg"l, rby
16 mhr"y iyaw, rby yhvdh   iayaw mhr"y iyaw, iayaw, rby yhvdh
17 rby yhvsf     rby yhvsf
18 mgny wlmh, rby yhvwi     mgny wlmh, rby yhvwi
19 hmhry"e, hmhrym"e, erany,
yvsf erny, mhry"e, mhrym"e,
merany, merny, rby yvsf
  hr"y erany, hr"y
erny, r"y erany,
r"y erny
hmhry"e, hmhrym"e, hr"y
erany, hr"y erny, erany,
yvsf erny, mhry"e, mhrym"e,
merany, merny, rby yvsf,
r"y erany, r"y erny
20pry mgdyo, rby yvsf, tavmyo  --- completely removed ---
21 hryb"r, yiqb byrb, mhr"y
byrb, rby yiqb
    hryb"r, yiqb byrb, mhr"y
byrb, rby yiqb
22 bil hlq"e, cagyz cagyz mhr"y cgyz, r"y
bil hlq"e, mhr"y cgyz, r"y
23 hmhry"l, yiqb hlvy, yiqb
sg"l, mhr"y hlvy, mhry"l,
mhr"y sg"l, mvly`, rby yiqb
    hmhry"l, yiqb hlvy, yiqb
sg"l, mhr"y hlvy, mhry"l,
mhr"y sg"l, mvly`, rby yiqb
24 hyib"u, hryib"u, hr"y imd`,
hr"y imdy`, imdy`
hr"y imd` r"y imdy` hyib"u, hryib"u, hr"y imdy`,
imdy`, r"y imdy`
25 hvrvvyu, yxcq hlvy, rby
hvrvvyu hvrvbyu hvrvbyu, yxcq hlvy, rby
26 xmc xdq, qrvkml, rby mnco,
rby mindl
qrvkml qrvkmal xmc xdq, qrvkmal, rby mnco,
rby mindl
27 hmhrm"z, hmzl"`, zkvta,
zkvtv, mhrm"z, mhr"o zkvt,
mwh zkvt, mwh zkvta, mwh
zkvtv, qvl hrm"z, rby mwh
zkvta, zkvtv,
mwh zkvta, mwh
  hmhrm"z, hmzl"`, mhrm"z,
mhr"o zkvt, mwh zkvt, qvl
hrm"z, rby mwh
28 mrglyt, pny mwh, rby mwh   mrglyvt mrglyvt, mrglyt, pny mwh,
rby mwh
29 rby izryh     rby izryh
30 a"c hi"r, ywr lbb a"c hi"r, ywr
avhb vr"i, hv`
iwyr, hiwy"r
avhb vr"i, hv` iwyr, hiwy"r
31 hmhrw"w, mhrw"w, mzrcy,
rby wlvo, wriby, wr wlvo
hmhrw"w, mhrw"w,
mzrcy, wr wlvo
  rby wlvo, wriby
32 rby wlmh   cilma, wlmh clma cilma, rby wlmh, wlmh clma
33--- new Rabbi ---  ayznweae, ayznwee, mhr"o
a"w, rby mayr

We have shown our list of appellations (as it appeared in a draft version of this paper) to Professor Menachem Cohen, of the Department of Bible at Bar-Ilan University, Israel. In reference to our list and to the original WRR-Havlin list he wrote in [Co2]:

... I see no essential difference between the two lists for the purpose of using them for skip experiments in any text.
The present list is even more similar to the WRR-Havlin list than the one Cohen based his judgement upon.

3. The Results

The table below contains the permutation test ranks obtained by running our list against the same list of dates as in [WRR2] (with the addition of y"h tmvz, by"h tmvz, y"h btmvz, e"v tmvz, be"v tmvz and e"v btmvz for Rabbi II-30, Rabbi Immanuel Hai Ricchi, and k"z syv`, bk"z syv`, and k"z bsyv` for Rabbi Meir Eisenstadt), on an initial segment of War and Peace which is of the same length as Genesis, using the same four computation methods (P1-P4) used in [WRR2]. For comparison, we also include the scores obtained by running our list on Genesis and the scores reported by WRR in [WRR2] for their list on Genesis.

Permutation test ranks out of 108

P1 P2 P3 P4
our list on War and Peace 20,887 1,091 831 57
our list on Genesis 14,179,712 1,299,355 16,825,659 724,260
the WRR list on Genesis ([WRR2], rescaled) 45,300 500 57,000 400

Comparing the first and the last two rows, we see that our list does as well on War and Peace as the WRR list does on Genesis. Tolstoy would have enjoyed knowing that. Some of the numbers in the second row are "middle of the way" - smallish but not very small. They are "smallish" because our list is highly correlated with the original WRR list, on which it was based. The fact that they are not very small needs to be explained by WRR, not by us. Why is it that an equally valid list of appellations (our list) does so much worse than their list on Genesis?

Comments: The computations of the significance levels for our list was carried out using a program functionally equivalent to a program WRR gave us, els2.c. The significance levels for the WRR list were taken from [WRR2], except for a rescaling by a factor of 100 to account for the the fact that they used only 106 permutations in their computations. Using our own program, which is equivalent to a program WRR produced when their lists were already present and hence it is more susceptible to bias, we get somewhat better results for the WRR list on Genesis, but these results are still weaker than our results on War and Peace. Unfortunately, we were not able to obtain from WRR the exact programs they used to compute the results in [WRR2].

The text we used was given to us by WRR. It consists of the first 78,064 letters (the length of Genesis) of a Hebrew translation of Tolstoy's War and Peace.

4. Bibliography

Abe Apelbaum aba applbvyo, biography of Rabbi Moshe Zacut titled mwh zkvt, Snunit, Lvov 1925.
Shmuel Ashkenazi, wmval awknzy, and Dov Yarden, db yrd`, a dictionary of Hebrew acronyms titled avxr rawy tbvt.
Azulai, Rabbi Haim Yosef David, Shem haGdolim haShalem, wo hgdvlyo hwlo, Jerusalem 1979.
Yitshak Isaac Ben-Yaakov, yxcq ayyzyq b`-yiqb, a bibliography of Hebrew books titled avxr hspryo, 1880.
Meir Benayahu, mayr bnyhv, "hcbrh hqdvwh" wl rby yhvdh csyd vilyth la"y, spvnvt 3-4 Jerusalem 1962.
Avraham Brik, abrho bryq, biography of Rabbi Shelomo Chelma titled r' wlmh cilma, bil "mrkbt hmwnh".
Menachem Cohen, A letter to Dror Bar-Natan dated September 2, 1997. Available at
Menachem Cohen, A letter to Dror Bar-Natan dated October 27, 1997. Available at
The Torah CD-ROM Library, version 7, D.B.S., Jerusalem.
Yaakov Kapel Duschinski, yiqb qapl dvwynsqya, Biography of Rabbi David Oppenheim titled tvldvt hgav` r' dvd avpnhyymir zx"l.
Nathan Zvi Friedman, nt` xby prydm`, avxr hrbnyo, A Treasury of Rabbis, Bnei Brak 1975.
Yehudah Eisenstein, yhvdh ayyznweyy`, anxyqlvpdyh avxr ywral, London 1924.
Aryeh Leib Frumkin aryh lyyb prvmqy` and Eliezer Rivlin alyizr rybly`, tvldvt ckmy yrvwlyo, Biographies of Jerusalem Sages, Jerusalem 1928.
David Halachmi, dvd hlcmy, ckmy ywral, The Sages of Israel, Tel Aviv 1980.
Rephael Halperin, rpal hlpry`, aels iu hcyyo, An Atlas of Genealogy (10 vols.), Tel Aviv.
Shlomo Z. Havlin, a brief dated October 30, 1996. English translation (by WRR) available at and at
Hebraica Encyclopedia, hanxyqlvpdyh hibryt.
Israel Heilperin, ywral hyylpry`, Regulations of the state of Moravia, tqnvt mdynt mihry`.
Shmuel Abba Horodezsky, wmval aba haradixqy, Biography of Rabbi Menachem Mendel Krochmal titled rby mnco mndl qrakmal, Hagoren, hgr`, 2 (1900) 32.
Encyclopedia Judaica.
David Kauffman, dvd qvypman`, Biography of Rabbi Menachem Mendel Krochmal and his family titled ldvd xmc, twvbt bil xmc xdq vqxvr tvldvt mwpctv, Hagoren, hgr`, 2 (1900) 38.
M. Margalioth, Encyclopedia of Great Man in Israel; a Bibliographical Dictionary of Jewish Sages and Scholars from the 9th to the End of the 18th Century, vols. 1-4, Joshua Chachik, Tel Aviv.
Alexander Marx, A seventeenth-century autobiography, Jewish Quarterly Review 8 (1917-8) 269.
Brendan D. McKay, Dror Bar-Natan, Maya Bar-Hillel, and Gil Kalai, The Bible Code: The Genesis of Equidistant Letter Sequences, Statistical Science, to appear.
The Bar-Ilan Responsa CD-ROM, version 6, Bar-Ilan University, Israel.
Immanuel Hai Ricchi, Hon Ashir, Warsaw 1881.
Immanuel Hai Ricchi, Aderet Eliyahu, Livorno, 1742.
Rabbi A. Shisha HaLevi, Rabbi Immanuel Hai Ricchi and his book dqdvqy inyvt-hv` iwyr, HaDarom, Jerusalem, 1972.
Shmarya Shmaril, wmryh wmiryl, an eulogy for Rabbi Menachem Mendel Krochmal titled qvners zkr ivlo, 1885.
Avraham Stern, abrho wer`, mlyxy aw, Jerusalem.
E. Vilenski, Biography of Rabbi Immanuel Chai Ricchi (Hebrew), Kiriat-Sefer 25 (1949) 311.
Y. Vinograd, ywiyhv vynvgrd, avxr hspr hibry, A Treasury of Hebrew Literature, Jerusalem 1995.
D. Witztum, E. Rips and Y. Rosenberg, Equidistant Letter Sequences in the Book of Genesis, "The Blue Preprint", an older version of [WRR2] (1987).
D. Witztum, E. Rips and Y. Rosenberg, Equidistant Letter Sequences in the Book of Genesis, Statistical Science 9-3 (1994) 429-438.
The Yaabez, The Yaabez Responsa, wv"t waylt yib"u, part B sub 24.
Yekhiel Matityahu Zunz, ycyal mttyhv xvnu, History of the rabbis of Cracow titled iyr hxdq.

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