Draft                   BS"D
18 Sivan 5759

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The Nations Sample
By Doron Witztum


Abstract
The Structure of the article
Part I: Possible Presentations of the Chosen Topic
Appendix
Abstract:
        In 1995 I published (as a preprint, together with Professor Eliyahu Rips and Yoav Rosenberg) an article entitled: "Equidistant Letter Sequences in the Book of Genesis: II. The Relationship to the Text" [1]. This article dealt with convergences between expressions appearing as ELS's (Equidistant Letter Sequences) and expressions appearing in consecutive letters in Genesis. One of the samples discussed in the article was the Nations Sample (for a description of this sample in Hebrew see [2]). Measurements conducted on this sample indicated a particularly high level of statistical significance. In light of criticisms leveled against the composition of this sample and its measurement, in an article [3] by Dr. D. Bar Natan, Dr. B. McKay and Prof. S. Sternberg (henceforth, BMS), I am presenting here a description of the considerations and decisions that went into the construction of the sample. I will also present a new measurement of the significance. The criticisms of BMS are refuted in this article, and careful analysis of their data and suggestions leads to new results supporting our research hypothesis with high significance.

The structure of the article:
        BMS distinguished between two parts of the Nations Sample. The simpler part of the sample they label "regular," and the other part they call "irregular". In the present article I will focus on the part of the sample that they considered simpler - the "regular" part. I will deal with it in two parts:
Part I: "Possible Presentations of the chosen Topic" – This section will deal with the various ways of compiling the regular part of the sample for the chosen topic.
Part II: "The Range of Stories" – In this section I will discuss the range of possibilities in choosing a topic for such a sample.
(A discussion of the "irregular" part of the sample is the subject of a planned Part III.)

Part I: Possible Presentations of the Chosen Topic
Introduction:
        In this introduction I will describe briefly how the Nations Sample was compiled. For the sake of clarity I will not address the criticisms of BMS at this point (I will do so in the chapters to come).
A.        In chapter 10 of Genesis there is a list of 70 names of descendants of Noah: the children of Shem, the children of Ham and the children of Japhet. Jewish tradition [4] treats these as the forebears of the 70 nations from which all mankind are descended. Later scholars also take this as a given, and this list of nations can be found in various Biblical encyclopedias under the heading "The Table of Nations" or "The Children of Noah" [5].
     I wanted to investigate whether the fact that Noah's 70 descendants developed into the 70 nations, is encoded in the Book of Genesis. Specifically, I wanted to see whether this can be demonstrated through convergences between the names of Noah's descendants and encoded expressions reflecting their eventual nationhood. It must be clear that the expressions indicate the names of nations. This can be achieved by first identifying the kinds of terms that indicate nationhood.
B.        One classical approach maintains that there are objective criteria by which nations can be distinguished from one another. This fundamental issue is discussed in the Encyclopedia Hebraica [6]:
        "Much thought has been given to the question: What are the indicators of nationhood, and how it is to be determined whether a particular individual belongs to one nation or another? There are two fundamental approaches to this subject. One approach looks for the answer to this question in objective criteria. According to this approach a nation is said to exist as an independent entity if it consists of a group of people who share a common language (הפש), are distinctive in their cultural forms and way of life, are concentrated in a certain territory, and frequently share a common religion as well. One extreme opinion holds that they must also be of common racial stock. According to this approach an individual's membership in a national group is determined by investigating these criteria."
We see that the Encyclopedia Hebraica recognizes three fundamental signs of nationhood:
1. Language (הפש) [7]. 2. Culture and way of life. 3. Territorial concentration (land).
These are frequently accompanied by a fourth indicator, religion, and according to an "extreme opinion," a fifth indicator, racial stock.
        In the Concise Oxford Dictionary [8], under the entry "nation," I found the following definition: "A distinct race or people having common descent, language, history, or political institutions."
        Other dictionaries and encyclopedias [9] give perhaps a few other indicators, but in any event there are altogether only a handful of them, and each of the sources emphasizes the ones it thinks are most essential.
C.        In traditional Jewish literature I found a discussion of this subject in the following excerpt from the Vilna Gaon [10] (for a comparison of this excerpt with quotes from the Vilna Gaon's other writings see chapter V):
        "It is well known that the nations mentioned in the Holy Scriptures were distinguished from one another by four characteristics:
  1. By their names. Each nation (םע) was called by the name of their first ancestor from whom they were descended, such as Cush ( שוכ ), Mitzraim ( םירצמ ), Put ( טופ ), Canaan ( ןענכ ), and the like from among the nations, and their descendants are all called Mitzrites and Edomites, after their first father, to this very day.
  2. By the names of their countries ( תונידמ ). Countries are also named after their founders. The Land of Mitzraim ( םירצמ ץרא ), for example, is called after its founder. So, too, the Land of Cush ( שוכ ץרא ) and the Land of Canaan ( ןענכ ץרא ), etc.
  3. By language ( ןושל ). The members of each nation have agreed upon a distinctive language, called the Mitzrite language (ירצמ ןושל), the Cushite language (שוכ ןושל) , etc.
  4. By script ( בתכ ). Each nation has a distinctive script."
        From this passage we can learn about four indicators of nationhood:
1. Name. 2. Land. 3. Language. 4. Script.
D.         The regular part of the Nations Sample:
        We must now look for four expressions that reflect the four indicators mentioned in C. In the regular part of the sample we will search for expressions of the form "prefix X," where X is one of the names from the "Table of Nations" and the "prefix" is a word in its appropriate Hebrew form, i.e., the construct case [semichut]. It is quite possible that each of these indicators can be expressed in more than one way. Therefore it must be decided ahead of time how the expressions will be selected.
        In view of our research hypothesis (that there is a hidden text encoded in the book of Genesis) it seems reasonable to assume that when Biblical themes are encoded preference will be given to the language used by the Scriptures themselves. For this reason my approach was to look for those combinations that are closer to the language of the Scriptures. How this was carried out in practice is described in Chapters III and IV. Here I will just list the expressions that were settled upon:
1. "X םע " 2. "X ץרא " 3. "X תפש " 4. "X בתכ "
For example: If X is the name רמג , the first name on the "Table of Nations" (found in the Appendix), we will receive for it the expressions: רמג םע, רמג ץרא, רמג תפש, and רמג בתכ . We will then measure convergences between the name רמג, as it appears in consecutive letters (that is, with a skip length of d = +1) and each of the four expressions as they appears as ELS's. In other words, we will investigate convergences for each of the word pairs: (רמג, רמג םע), (רמג, רמג ץרא), (רמג, רמג תפש) and (רמג, רמג בתכ). We will do this for every name X appearing on the "Table of Nations" [11]. The set of word pairs obtained in this way constitutes the regular part of the Nations Sample.
E.        Results of the regular part of the sample:
1. When we measure the significance of the sample using the original randomization test [1] we receive the following rankings:
Thus the overall significance using this method was r = 2 X r1 = 1.4 X 10-7.
2. In our article [2] we discussed samples similar the Nations Sample in addition to samples of a different type, for the sake of which a different randomization test (henceforth, RPWL = Randomization by Permutations of Words' Letters) was used. At a later date the RPWL test was applied to samples like the Nations Sample as well [12]. In their article, BMS criticized the use of the original test for the Nations Sample, claiming that the results obtained thereby were meaningless for a number of reasons particular to this instance [13].
Since these criticisms are not relevant to the RPWL test, it is preferable to use this test for measuring the significance. Here are the results:
Thus the overall significance using this method was r = 2 X r1 = 2.8 X 10-8.
For more details of the measurements see the Appendix.

I. Why םע ?
A1.
        BMS [14] proposed that the statement of the Vilna Gaon that "Every nation is called after their first father" should also be included in the experiment by looking for expressions of the form "X "םש ("name of X"). In other words, we should investigate whether or not the expression ןענכ םש (name of Canaan) converges with the name ןענכ (Canaan) in the text.

Response:
        This is simply a misreading of the words of the Vilna Gaon. The Gaon was addressing the question: "By what name is a nation called?" BMS are in effect proposing that we investigate the question itself! It is almost like the famous joke where one person says to another, "Please tell me - what is your name?" to which his companion responds by telling him literally the words, "What is your name."

A2.
       BMS further proposed investigating whether the name ןענכ in ELS form converges with the name ןענכ appearing in consecutive letters in the text.

Response
:
        I will try to illustrate the flaw in this proposal with the help of the following example: When we open up the dictionary [9] to the entry "לארשי" (Israel) we discover that this is a masculine personal name. In addition, however, we find the combinations "לארשי םע" (the nation of Israel), "לארשי ץרא" (the land of Israel), and "לארשי תנידמ" (the state of Israel). We also learn that the name "לארשי" alone can be used in place of all three of these combinations.
        When the name "לארשי" is used it can usually be deduced from context whether what is meant is the Jewish people, the land of Israel, the state of Israel, the patriarch Jacob or a child whose name happens to be "לארשי." On the other hand, when one considers the name "לארשי" in isolation, not in a context, how can one determine which of these possibilities is intended?
        What kind of message can be encoded by BMS's proposed tautologies? It gives us no new information, and it certainly does not indicate to us whether each of the descendants of Noah became a nation in his own right! The research hypothesis itself predicts that both of BMS's proposals should fail, and indeed (as BMS report) both of them do fail. Their assertion that these two proposals form "the most reasonable constructions suggested by the Vilna Gaon's explanation" is simply astonishing
B.         BMS further asserted [14] that we combined the prefix םע with a plural form of the name, as in the case of םידול (Ludim), and that such a combination is totally unjustified by the Vilna Gaon's first criterion.

Response:
  1. First of all, the reader should be informed [15] that despite the apparent "םי" suffix, םידול is actually the name of an individual, as are the names םימנע , etc. Therefore there is no difference between this name and the names רמג or ןוי .
  2. Even according to those commentaries who do say that םידול is a plural name, and not the name of an individual, nevertheless they agree that this is the name by which the nation was known. Therefore it is entirely legitimate to use the combination םידול םע [16].
C.        BMS [14] replaced the word םע with the word יוג , claiming that "the Torah uses the word יוג for nation, not םע . " They justify this claim by citing a passage from a commentary by the Vilna Gaon (Adereth Eliyahu on Isaiah 1:4).

Response:
        Both their assertion and evidence are incorrect.
1. The assertion that the Torah uses only the word יוג for nation is simply false. In the Encyclopedia Biblica (at the entry םע , v. 6, p. 235) we find a discussion of Scriptures usage of the term םע :
"The use of terms for a nation or people, in all their various shades of meaning, is the most frequent in the language of the Scriptures. The same connotations are indicated also by the words יוג and םואל . There are some (L. Rost, E. A. Speiser) who wish to distinguish between the Biblical uses of the terms םע and יוג in the following manner: יוג indicates the citizens of a certain kingdom or geographic region, whereas םע (according to Speiser) indicates common origin, and has overtones of a familial relationship, a shared destiny and a relationship with the national god."
        In other words, not only is the term םע , meaning nation or people, widespread throughout the Bible, but in this instance it is a more appropriate term than יוג because it emphasizes common origin.
        The reader should note, however, that this was not the basis for my decision to use םע rather than יוג (for a discussion of this decision see Ch. IV). In any event, it is quite clear that the assertion that the Torah uses only the word יוג for nation is simply incorrect.
2.        The evidence BMS cite does nothing to enhance their assertion. The relevant passage from the Vilna Gaon (Adereth Eliyahu on Isaiah 1:4) reads as follows:
     "The difference between יוג and םע is that םע is used to refer to a collection of many individuals, whether of the masses, whether possessed of a religion or not. יוג, on the other hand, only refers to those who properly adhere to custom. Even an individual who observes the customs received by the multitude is called a יוג . This is what the Sages mean when they say that [the Israelites in Egypt] 'became there a יוג – indicating that Israel behaved distinctively there'."

In other words, the term םע is correct in any context. Only the term יוג is limited to specific contexts. Furthermore, יוג can sometimes refer to a single individual.
        It is worth noting that in two other places (Habakkuk 2:5 and I Chronicles 16:24) the Vilna Gaon writes exactly the opposite – that יוג indicates the masses. In any event, as mentioned above, I did not base my decisions upon such distinctions. I took from the Vilna Gaon only the four indicators of nationhood, not the terms by which they are designated.
        For anyone who still believes that the term יוג was no less appropriate a choice than the term םע there exists the simple option of calculating the significance of the sample twice:
a) Once using םע as the first term, and
b) once using יוג as the first term.
To account for this supposed freedom all one need do is multiply the best significance by a factor of 2


II. ןושל Versus הפש
        
In their article [14] BMS note that the Vilna Gaon, in the passage cited in the Introduction, used the term ןושל for "language," whereas when I compiled the sample I used the term הפש . BMS translate the term ןושל as "dialect" and the term הפש as "language." Their justification for this interpretation is the commentary of Rabbi Samson Raphael Hirsch [17] (on Genesis ch. 10). On the basis of this interpretation BMS claim that when the Vilna Gaon uses the term ןושל he means "dialect," whereas I used "language" as the indicator of nationhood.

Response:
  1. A dialect is not an indication of nationhood; language is (as I demonstrated in the introduction with the help of the Encyclopedia Hebraica and the Oxford Dictionary).
  2. It is interesting to note that according to the very source cited by BMS, the commentary of Rabbi S. R. Hirsch, the indicator of nationhood is הפש ("language") not ןושל ("dialect") [18] – precisely confirming my own word choice! It is strange that BMS neglected to point this out.
  3. Now let us deal with the words of the Vilna Gaon himself. The Hebrew language has many layers [19], beginning with the language of the Scriptures right up to the Hebrew used today. The Vilna Gaon was writing in the language of the rabbis ( םימכח ןושל ). The Sages have a general principle: "The language of the Torah is one thing and the language of the rabbis is another" [20]. The term ןושל is used by the rabbis as a synonym for the word הפש appearing in the Bible. This is particularly true regarding its usage in the context of the descendants of Noah, as can be seen from [21]. Thus the assertion of BMS that the Vilna Gaon meant specifically "dialect" when he used the word ןושל is without foundation.
Summary: It turns out that even according to the commentary cited by BMS the correct choice was
הפש . In the chapters to come it will be explained how this word choice was actually arrived at through a "mechanical" procedure (i.e., one involving no interpretation).
        For anyone who still believes that the term ןושל was no less appropriate a choice than the term הפש there exists the simple option of calculating the significance of the sample twice:
a) Once using תפש as the first term, and
b) once using ןושל as the first term.
To account for this supposed freedom all one need do is multiply the best significance by a factor of 2.

N.B.: According to Rabbi Hirsch, a single language may have several תונושל (dialects). Therefore if BMS considered use of the concept "dialect" to be so crucial, they should have used תונושל (dialects) rather than ןושל .


III. The Range of Possibilities:

        The "regular" part of the sample consists of expressions of the form "prefix X," where X is one of the names from the "Table of Nations," and the "prefix" is a word in the construct case [semichut]. Given our research hypothesis, it seems reasonable to expect that when Biblical themes are encoded there will be a preference for expressing them in the language of the Scriptures themselves.
        In this chapter and the next we will explore ways of compiling a list of Scriptural prefixes to indicate the four categories of the Vilna Gaon:
1. The name of the nation. 2. Its land. 3. Its language. 4. Its script.
        We will begin by looking at the words used by the Gaon himself: םע , הנידמ , ץרא , ןושל , בתכ , יוג , המא .
A.         First we must examine whether these terms are indeed found in the Bible or not. We will locate each through use of the New Concordance of the Bible [22]. This concordance lists occurrences of each word according to meaning. The meaning is defined by a synonym or defining phrase.
        In this way I was able to identify the Scriptural synonyms for each term (for full details see the Appendix). Here is a list of the possibilities arranged by category:
1. יוג , םאל , המא , םע .
2. הנידמ , ץרא .
3. הפש , ןושל .
4. בתכ .
B.        The fact that a word occurs in the Bible does not guarantee that Scripture uses it in the construct case. We must again use the concordance to determine which of the terms in A. occur in the desired form (the New Concordance lists this form separately). It turns out that the following words occur in this form (i.e., singular construct case):
1. םע , יוג   2. ץרא   3. ןושל , הפש   4. בתכ  
Summary:
        There are two possibilities for representing category 1, one for category 2, two for category 3, and one for category 4. In all there are 1 X 2 X 1 X 2 = 4 possibilities. There is another possibility as well – to use all of them. Thus there are a total of 5 ways of compiling the regular part of the Nations Sample.
        Although in our original experiment on this sample we subjected this list to a further selection process, as described in the next section, for the sake of the reader's curiosity I will present here the results received when of all the terms are used (that is, םע as well as יוג , and הפש as well as ןושל ):
        Using the original randomization test, with 1,000,000,000 permutations, we receive:
r1 = 1.48 x 10-6,      r2 =3.70 x 10-6

Using the RPWL test, with 1,000,000,000 permutations, we receive:
r1 = 3.21 x 10-7, r2 = 1.37 x 10-7


IV. Decisions:

        In the previous chapter I listed five ways of compiling a list of Scriptural prefixes for the regular part of the Nations Sample. This is the number of ways we can conduct our experiment if we choose to ignore all other considerations, that is, if we do not try to distinguish between םע and יוג (in category 1) and between ןושל and הפש (in category 3).
        However, we must explore the possibility that there are differences in the usage of these synonyms in Scripture. Some of them might turn out to be more "appropriate" than others for use in a combination of the form "prefix X" (where X is the name of a nation). This question can be addressed with through interpretation, as we discussed in Chapter I regarding the terms םע and יוג , and in Chapter II regarding ןושל and הפש . Here, however, we will try to deal with it in a "mechanical" fashion to avoid the need for interpretation.

Decision by frequency:
        About a year after we first published our work on the Nations Sample
[1], Prof. Havlin's Report was published [23], in which he described the guidelines by which he compiled the list of famous rabbis. It turns out that in certain cases he distinguished between various alternatives based on their frequency in the database [24].
        Taking advantage of the fact that the New Concordance provides a list of all instances of construct case, we will check the frequency of the desired form (singular construct case) for each of the words in categories 1 and 3 (where there was more than one alternative). Then we can make a selection based on frequency.

1.
Word Singular, Construct Form Number of Occurrences
םע םע 63
םאל םאל 0
המא תמא 0
יוג [25] יוג 1

3.
Word Singular, Construct Form Number of Occurrences
ןושל ןושל 3
הפש תפש 5

Results: Using X to indicate one of the names on the Table of Nations, the expressions we will look for are:
1. X םע 2. X ץרא 3. X תפש 4. X בתכ
N.B.: In the case of םע and יוג the decision was clear. In the case of הפש , however, there is room to doubt whether we should base our selection upon a simple majority of usage, or should we only select the more frequently used term when there is an order of magnitude between them.

Decision by "precedent":
        This is the procedure I actually used in the original experiment.
        For each of categories 1 and 3 (the ones for which there are multiple possibilities) I selected the prefix for which there was a precedent in the Scriptures:
        Using the Concordance, I investigated whether a particular prefix appears in the Biblical text itself in the desired combination, "prefix X," with one or more of the names from the "Table of Nations."
        The fact that a term is used in the text itself with the name of a nation makes it more certain that it is indeed an indicator of nationhood. The reason for insisting that it appear specifically in combination with one of the 70 nations is that only for these nations is there a tradition [4] that they constitute separate nations in every respect. If a term appears in combination with a name that is not on the Table of Nations there is no guarantee that it is in fact an indicator of nationhood, since there is no way of knowing whether the name it appears with is that of a nation [26].
Results: As it turns out, for the first category only םע , and for the third category only תפש appears in the Biblical text in the desired combination. In other words, again we receive:
1. X םע 2. X ץרא 3. X תפש 4. X בתכ


V. Why Did We Follow this Particular Passage from the Vilna Gaon?
        In their critique [27] BMS note that they found two other places where the Vilna Gaon deals with our subject. For the reader's benefit I will cite these two other sources:
1. One is in the Gaon's commentary Adereth Eliyahu on Isaiah 1:4:
"After the flood the people divided into seventy nations, whether because of their division into separate families ( תוחפשמ ), or because of separated languages ( תונושל ), or separated lands ( תוצרא ), or separate manners ( םיסומינ ). This is what is meant by "to their families, in their lands, in their languages, in their nationalities."
2. The other source is the Gaon's non-Kabbalistic commetary to Esther 1:22:
"Because nations are divided by four things: script, language, land – in that each nation has its own land, and garments."

        The reader is invited to compare these two excerpts with the one from Job that I cited in the Introduction. In my opinion it is clear that only the excerpt from Job contains a thorough treatment of the indicators of nationhood. Regarding the excerpt from Isaiah in particular, it seems clear that the Gaon is merely discussing the causes of the division into nations, not the indicators of nationhood.
        If the reader is not interested in making such distinctions in the wording of the Gaon, we recommend that he employ the simple strategy of multiplying the significance by the number of options: There are three ways to choose one of the three texts of the Gaon, and there is another option to take the union of all of them. Thus there are four options altogether.

Revising the number of possibilities
:

        If one chooses to ignore all interpretation and avoid making any decision, the choice of the Gaon's commentary to Job is one of four possibilities, and the selection of the four prefixes used in the experiment to describe the categories of the Gaon is one of five possibilities. Thus there are 4 X 5 = 20 possibilities in all.
        For the sake of the reader who is curious, I will present here the results for two of these options:
A. The option of using all three excerpts from the Gaon adds another three prefixes found in Scripture in the appropriate construct form: תחפשמ , ידגב , גהנמ (see the Appendix for details).
r1 = 7.0 x 10-9,     r2 =7.58 x 10-7
  • Using the RPWL test, with 1,000,000,000 permutations, we receive:
    r1= 2.0 x 10-9,     r2 =4.23 x 10-7

    B. If we calculate the significance of the combination of the three excerpts, without distinguishing between alternative prefixes, provided that all are found in Scripture in the appropriate construct form (this is the option mentioned in Chapter III in which we use both םע as well as יוג , and הפש as well as ןושל ), we receive:
    r1= 1.15 x 10-7,     r2 =5.26 x 10-7
  • Using the RPWL test, with 1,000,000,000 permutations, we receive:
    r1= 2.6 x 10-8,     r2 =2.26 x 10-7




    Appendix to Part I

    The Table of Nations:
            Here is a list of the names of the 70 descendants of Noah as they appear in Genesis, chapter 10 [compare with the entry םימעה חול (The Table of Nations) in Encyclopedia Biblica, v. 4, pp. 443-444]:
    1. רמג , 2. גוגמ , 3. ידמ , 4. ןוי , 5. לבת , 6. ךשמ , 7. סרית , 8. זנכשא , 9. תפיר , 10. המרגת , 11. השילא , 12. שישרת , 13. םיתכ , 14. םינדד , 15. שוכ , 16. םירצמ , 17. טופ ,18. ןענכ , 19. אבס , 20. הליוח , 21. התבס , 22. המער , 23. אכתבס , 24. אבש , 25. ןדד , 26. םידול , 27. םימנע , 28. םיבהל , 29. םיחתפנ , 30. םיסרתפ , 31. םיחלסכ , 32. םיתשלפ , 33. םירתפכ , 34. ןדיצ , 35. תח , 36. יסוביה , 37. ירמאה , 38. ישגרגה , 39. יוחה , 40. יקרעה , 41. יניסה , 42. ידוראה , 43. ירמצה , 44. יתמחה , 45. םליע , 46. רושא , 47. דשכפרא , 48. דול , 49. םרא , 50. ץוע , 51. לוח , 52. רתג , 53. שמ , 54. חלש , 55. רבע , 56. גלפ , 57. ןטקי , 58. דדומלא , 59. ףלש , 60. תומרצח , 61. חרי , 62. םרודה , 63. לזוא , 64. הלקד , 65. לבוע , 66. לאמיבא , 67. אבש , 68. רפוא , 69. הליוח , 70. בבוי .
            Note that two of the names are listed twice: אבש and הליוח . For the sake of our measurements they were counted only once each. In other words, we actually only used 68 different names.

    The Range of Possibilities:

    Locating synonyms in the Scriptures:
            
    Let us begin with the terms that the Vilna Gaon used: םע, הנידמ, ץרא, ןושל, בתכ, יוג, המא. Let us investigate whether these words are used in Scripture, and let us identify Scriptural synonyms for each one with the help of the New Concordance of the Bible. In the Concordance occurrences of each word are organized according to meaning, and the meanings are defined by a synonym and/or defining phrase.
            Locating Scriptural synonyms:
    1a.
    1. Under the entry םע (p. 882) we find 5 different shades of meaning. The first is the desired one. It has the following synonyms: המא, םואל, יוג.
    2. Next let us look up each of these synonyms in the Concordance to see if they, too, are used in Scripture, and to verify their spelling according to the entry heading. After we do this we are still left with: המא , םאל , יוג .
    1b.
    1. At the entry יוג (p. 228) we find two meanings listed. The first is the desired one. We find the following synonyms: םע , המא .
    2. We have already discovered above that both of these are found in Scripture and this is how they are spelled there.
    1c.
    1. At the entry המא (p. 82) we find only one meaning, for which there are two synonyms: םע , and טבש.
    2. The word טבש has a different connotation ["tribe"], making it unsuitable for use as an indicator of nationhood. [This can be verified by checking the entry for טבש in the Concordance (p. 1104) and noting that it does not have listed as synonyms words such as םע, המא, םאל or יוג, or anything similar to them.]
    3. Thus we are left with the word םע as the only synonym for המא.
    2a.
    1. At the entry ץרא (p. 112) we find three different shades of meaning. The third one is the desired one. One synonym is listed: הנידמ .
    2. Using the Concordance we investigate whether this synonym is used in Scripture and how it is to be spelled. The result is that we are left with the word: הנידמ alone.
    2b.
    1. At the entry הנידמ (p. 623) we find only one meaning, for which there is one synonym: ץרא.
    2. We have already discovered above that ץרא is Scriptural, and this is its correct spelling.
    3.
    1. At the entry ןושל (p. 611) we find four different meanings. The second one is the desired one. The synonyms listed are: הפש and רובד.
    2. Actually, the connotation of the word רובד [speech] makes it unsuitable as an indicator of nationhood, although the Concordance does not make this distinction, but in any event this word does not appear in Scripture, therefore we are left with: הפש .
    4.
    1. At the entry בתכ (p. 567) we find two meanings. The second one is the desired one. No synonyms are listed.

    Prefixes found in the other excerpts from the Vilna Gaon:
    A. The prefixes found in Adereth Eliyahu on Isaiah 1:4:
            We have already seen the actually citation, see Chs. V and I.
            BMS proposed that we examine the prefixes:
    1. תחפשמ 2. ןושל . 3. ץרא 4. סומנ

    1. תחפשמ – Actually, it is not implied in the wording of the Gaon that this is an indicator of nationhood. Nevertheless, we will go ahead and identify its Scriptural synonyms:
      a) In the Concordance at the entry החפשמ (p. 721) we find three definitions, the second of which is the desired one. We find listed there the one Scriptural synonym: םואל .
      b) Again using the Concordance we check the spelling of the synonym םואל as it appears in the Bible, and we find that it should be written םאל .
      c) Of these two choices only the word החפשמ appears in the Scriptures in construct case: תחפשמ .
    2. ןושל – This has already been dealt with above.
    3. ץרא – This has already been dealt with above.
    4. סומנ – This word does not appear in the Concordance because it is not a Biblical word. The algorithm described in Ch. III ("The Range of Possibilities") does not allow for such cases. One possibility is to simply erase it. BMS preferred to use it, therefore I will do the same. I opened the New Dictionary [9] (by the same author as the New Concordance) and discovered that the proper spelling of this word is סומינ (which is how it is spelled in the excerpt from the Gaon as well). The dictionary lists one synonym: גהנמ . This word does appear in Scripture, and in the desired form – singular construct [28]. While it is true that some Biblical commentaries render this word as "driving," nevertheless, there are those [29] who interpret it as "manners" (contrary to the words of BMS). Therefore גהנמ is certainly preferable to סומינ (which all agree is not a Biblical usage).

    Summary: According to this source we have the following possible prefixes:
    1. תחפשמ .  2. ןושל , תפש .  3. ץרא .  4. גהנמ .

    If we use the same selection process described earlier in the article to distinguish between the two choices in category 2, we receive:
    1. תחפשמ .  2. תפש .  3. ץרא .  4. גהנמ .

    B. The prefixes found in the commentary to Esther 1:22:
            For the actual citation see Ch. V. BMS proposed using the prefixes:
    1. בתכ.  2. ןושל.  3. ץרא.  4. שובלמ, שובל, דגב.
    The words for categories 1-3 have already been dealt with above. All that remains for us to deal with is category 4:
    שובלמ – Here BMS made a peculiar error; for some reason they wrote this word in the singular, although the Gaon uses it in the plural, םישובלמ . In the English, too, they translated it "dress" rather than in the plural, "garments."
    1. When we examine the entry for the word שובלמ (p. 661) in the Concordance we find only one meaning. Two synonyms are listed: שובל and דגב.
    2. With the help of the Concordance we learn that both of these words are Biblical, and that this is their proper spelling.
    3. Of the three choices, only דגב appears in the Scriptures in the appropriate construct form: ידגב .

    Summary: From this source we receive the following possibilities:
    1. בתכ .  2. ןושל , תפש .   3. ץרא .   4. ידגב

            If we apply to category 2 the same selection process as before, we receive:
    1. בתכ .   2. תפש .   3. ץרא .   4. ידגב .

    The measurement:
    A. The Analysis method used in [1]:
            The Analysis method used in [1] is essentially the same as in the Statistical Science paper [30], except that the names of the nations are sought at skip +1 and –1 only. The related phrases are still sought as ELSs. The definition of c(w,w') for the present case is given in the Appendix of [1], Sections A.1 and A.2. To read it click here.

    B. The RPWL Test:
            The RPWL test is explained in [2] and [12]. Here we applied it as follows:
    1.         We took one of the Nations Sample's pairs, (X, prefix X), and carried out 1000 permutations (including the identity permutation) of the expression "prefix X". In the event that the number of possible different permutations n was less than 1000, we performed n permutations. The permutations were conducted in a standardized manner using a program designed by Yaakov Rosenberg.
    For example: the first pair is ( רמג, רמג םע). We shall present here some of the pairs which are formed by the permutations (by order, from left to right):
    רמג
    רמגמע
    רמג
    ממרעג
    רמג
    מרמעג
    רמג
    רממעג
    רמג
    •••
    רמג
    רגעממ
    רמג
    עגרממ

    2.         We calculated the values of c(w,w') for the convergences of all 1000 (or n) permutations of "prefix X" as ELSs, with "X" taken as it appears in consecutive letters (that is, with a skip length of d = +1). For example, with regards to the example above, we obtain a row of cells. In each cell there is a c-value of the specific pair:

    92/125 34/125 95/125 98/125 ••• 21/125 34/125

    In a case that a certain permutation of "prefix X" did not appear as ELS, it resulted with an empty cell.
    3.        Stages 1 and 2 were performed with regards to all the pairs in the Sample. We thus obtained rows of cells, each containing 1000 (or n) cells. In each cell which is not empty, there is a c-value of the convergence (X, prefix X).
    4.         We then chose by lottery one of the cells in the first row, one of the cells in the second row, and so on. We obtained a set of values of c(w,w') and we calculated the values of Pi for them.
    5.        We repeated this procedure 999,999,999 times, using an algorithm for randomization similar to that described in [1]. The program used was also prepared by Yaakov Rosenberg. We used the same seed as in [1] and [30].

    Bibliography and Notes:
    1. D. Witztum, E. Rips and Y. Rosenberg, Equidistant Letter Sequences in the Book of Genesis: II. The Relation to the Text, a preprint (1995).
    2. D. Witztum, E. Rips and Y. Rosenberg, A Hidden Code in Equidistant Letters in the Book of Genesis: The Statistical Significance of the Phenomenon, a preprint, spring 1996.
    3. D. Bar Natan, B. McKay and S. Sternberg, "On the Witztum-Rips-Rosenberg Sample of Nations", preprint, March 11, 1998.
    4. A source for this tradition can be found in Targum Yonathan on Deuteronomy 32:8.
    5. See, for example, Encyclopedia Biblica, Bialik Institute, Jerusalem 1962, at the entry חול םימעה ["Table of Nations"] (v. 4, p. 439).
    6. Encyclopedia Hebraica, Encyclopedia Publishing Company, ltd., Jerusalem, 1981, at the entry םאל , תוימאל ["nation, nationhood"] (v. 21, p. 66).
    7. This is clarified in the continuation of the words of the encyclopedia: "The difficulty with this approach is threefold: First of all, it is difficult to establish objectively the distinctiveness of dialects, etc." In other words, it is difficult to determine whether the language spoken by a group of people constitutes a separate language, indicating their distinctive nationhood, or whether it is merely a dialect of a more generally spoken language.
    8. The Concise Oxford Dictionary of Current English, Oxford, at the Clarendon Press, 1972.
    9. For example, A. Even Shoshan, A New Dictionary of the Hebrew Language, Kiryat Sefer, Jerusalem, 1989, at the entry םע ["Nation"], (p. 988):
    "A large gathering of human beings of common origin, history, usually with a common spoken language, most of whom are concentrated in a single country."
    10. Rabbi Eliyahu of Vilna, Devar Eliyahu: Commentary to the Book of Job, Vilna, 1875.
    11. With the following limitation: the expression "prefix X" must be between 5-8 letters. See [1]. This limitation was established in the first preprint of the paper: D. Witztum, E. Rips and Y. Rosenberg, "Equidistant Letter Sequences in the Book of Genesis", 1986. A later version of this paper was published in Statistical Science, v. 9, no. 3, 429-438.
    12. D. Witztum and Y. Beremez (1998), The "Famous Rabbis" Sample: A New Measurement.
    13. See [3], ch. 5 and 7.
    14. See [3], Section 2.1.
    15. Rabbi David Kimchi on Genesis 10:13, based on a midrash of the Sages. Some nontraditional sources also understand the name this way. See, for instance, Encyclopedia Biblica, v. 4, at the entry דול , p. 439: "Ludim was one of the sons of Mitzraim."
    16. Examples similar to this one include: םיתכ םע (Ramban, Numbers 24:21), םיתשלפ םע (Ibn Ezra, Zechariah 9:7). [See also יסוביה םע , Metzudath David, II Samuel 5:6].
    17. Rabbi Samson Raphael Hirsch, The Pentateuch, Judaica Press, Ltd., Gateshead, 1982.
    18. Rabbi Hirsch explains the terms ןושל and הפש in his comments to Genesis 10:5, where the term ןושל appears, and to 11:1, where הפש appears. According to Rabbi Hirsch, Chapter 10 describes the origin of separate nationalities, a process that began with the development of "different dialects" of the single language. This process was only completed many years later, as described in Chapter 11, with the formation of completely separate languages. He comments further that while it is correct to speak of the German הפש and the French הפש, it is not correct to speak of the German ןושל and the French ןושל – " הפש would designate the language, French, German, etc., but ןושל the way of pronouncing, the dialect."
    19. For example, a standard dictionary like the New Dictionary distinguishes five principle levels (see the Introduction to the New Dictionary).
    20. The Babylonian Talmud, Tractate Chullin (137b), Avodah Zarah (58b). This principle is used by classic commentators such as Ibn Ezra, who states explicitly: "And so have they said that the language of Scripture is one thing and the language of the Talmud is another" (Ecclesiastes 5:1, Esther 8:17). The commentaries on the Mishnah also employ this rule [see, for example, Tosfoth Yom Tov on Pesachim, Ch. 1, Mishnah 2, Temurah, Ch. 5, Mishnah 1, and elsewhere].
    21. Concerning the descendants of Noah it is written: "And all the land was of a single language [ תחא הפש ]" (Genesis 11:1). Ibn Ezra explains: "The meaning of תחא הפש is a single ןושל ." Similarly Rabbi David Kimchi writes: " תחא הפש – that is, a single ןושל, etc." This relationship is made particularly clear in the Midrash Kavod Chofeh ( הפוח דובכ ):
    "... because all of them spoke a single language [ןושל], as it is written: 'And all of the land was of a single language [הפש].' So, too, in the future Israel will speak a single language [ןושל], as it is written: 'For then I will convert the nations to a purer language [הרורב הפש]....'" 22. A. Even Shoshan (editor), A New Concordance of the Bible, Kiryat Sefer, Jerusalem, 1981.
    23. S. Z. Havlin, "Report," Jerusalem, 1996. Here on this site.
    24. The Responsa Database, CD no. 5, Bar Ilan University, Ramat Gan, 1997.
    25. It is interesting to note that Encyclopedia Biblica informs us that: "use of the term יוג in singular construct form is extremely rare in Scripture" (at the entry יוג , v. 2, p. 457).
    26. Some examples:
    27. See [3], Section 2.2.
    28. II Kings 9:20.
    29. For example, the classic commentary Metzudath David, ad loc.
    30. D. Witztum, E. Rips & Y. Rosenberg, Equidistant Letter Sequences in the Book of Genesis, Stat. Science, Vol 9 ('94), No 3, 429-438.