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1. Introduction:

The purpose of this 'Akzent' is to present and to analyse a surprising observation that was made by the late Austrian scholar Claus Schedl. He discovered a relation between the numbers in Genesis 5 (the ages of the patriarchs, see table 1) and the number of words as they stand in the Hebrew Genesis text. This observation is the most intriguing part of his so-called 'Toledot-Hypothesis', which I presented already in 'Akzent 2' (see abstract there and compare especially his German commentary "Geschichte des Alten Testaments" !). In Genesis 11 we find a second table of patriarchs and their ages, which can probably be interpreted in much the same way. However, I will focus on Genesis 5 since here we find an example of Schedl's explanation which can be evaluated statistically. 

Basic information of 'Akzent 6' can be found in my article " 'Einweihung' durch Henoch ? Die Bedeutung der Altersangaben in Genesis 5", which I wrote in 1995. 'Akzent 6' is not a simple translation and is shorter than that paper. Yet it contains some additional comments about the application of Schedl's idea to the other numbers in Genesis 5 .

The number collections in Genesis 5 and 11 already constitute quantitative structures (QS) in a narrow sense (as exemplified in the German introduction: Beispiele ). But there is a much more surprising trait attached to them which has been discovered by Claus Schedl. According to his hypothesis the ages of the patriarchs are to be interpreted as text lengths measured in words. The triplet of numbers recorded for any of the patriarchs in Genesis 5 (Table 1) is related to the text section in which the story of this patriarch is being narrated. The purpose of this relation should have been the securing of the textual tradition by the scribes who were initiated into this system.

Table 1 : Ages of the patriarchs in Genesis 5 according to the Massoretic Text.

2. Subdivision of Genesis 5 according to the ages recorded for Enoch

Schedl already knew about the fact that Genesis chapter 5 has 365 words and he assumed this number to be of symbolical meaning: the 365 days of a solar year. Furthermore he supposed the 365 years of Enoch's lifetime to be of the same symbolical meaning, the latter interpretation being a wide-spread assumption in theological exegesis. Yet he did not further discuss the interesting question if this number (and perhaps the numbers 65 and 300 reported on Enoch as well) can also be interpreted as textlengths in some reasonable sense. This is a surprising fact since he tried to show that the numbers recorded for Adam and Noah coincided quite neatly with the lengths of their respective text sections.

According to Schedl's definition the length of the report on Enoch should have a counterpart in the very text section that contains this report. What is a disturbing feature at first sight, however, is the self-reference of the numbers in the text on the text. But this entanglement can simply be overcome by going ahead with trying to define text sections that reasonably dissect the chapter according to the three numbers.

There won't be any doubt about chapter 5 as a whole being a traditional text unit clearly delimitated from chapters 4 and 6. It is 365 words long. 
The text reporting directly on Enoch and containing the important information about his life (V.24) apart from the formula 'name, age, children', presents itself as counterpart for the number 65. But there is a catch: The successive sections for the patriarchs overlap each other and it may well be that this problem held Schedl back from further pursuing this idea. 
However, the end of each patriarch's section is well defined by the remark about his death, so Enoch's section ends clearly at the end of verse 24. But the beginning can be defined in at least three different ways:

1) At the end of the preceding section. - (For Enoch: the beginning of V.21) Defining it this way the overlap disappears, but now information about this patriarch is placed outside of 'his' section (For Enoch: In V.18 and 19). This definition is wrong.

2) At the beginning of the sentence where the patriarch's name is first mentioned. - (For Enoch: the beginning of V.18) Doing it this way the central figure of this sentence is the direct ancestor and we create an overlap up to the end of the section of the pre-ancestor. So definition 2 comprises two sections according to definition 1. This is ambiguous. 

3) Start exactly with the first mentioning of the patriarchs name. - (For Enoch: The last word in V.18) This starting point does not coincide with the beginning of a sentence, but the section begins with the name of the very patriarch on which it is reporting.

So if we are looking for a section which is reporting directly on Enoch, then it is precise to choose definition 3 and start with the last word of verse 18 ('Enoch') and end with the last word of verse 24 ('God').

Definition 3 was the first one I used (if someone is interested to know ;-) and, to my surprise back then in 1995, the section so defined has 65 words. I invented the other definitions to be able to criticize my own approach by creating alternative hypotheses. But I did not succeed up 'til now in convincing myself that one of the other definitions would better reflect the purpose of circumscribing a section reporting directly on any of the patriarchs. 
However, when I had counted the 65 words I said to myself: This has to be a mere coincidence. And at least a couple of hours went by until I concluded: If you have gone so far counting the 365 and the 65 words, then you must do a complete job and count the rest of the chapter independently as well. Now it is already clear that the rest of the chapter must be 300 words long and there is no new information in this fact. But these 300 words are dissected in a really surprising way: 200 words before and 100 behind the Enoch section (Table 2) . The reader will easily understand that it was at this point when I concluded that this quantitative structure was no mere coincidence.

Genesis 5 textlength in verses:
textlength in number of words:
Gen. 5 statement in the text:
verse 1 - 18 (without 'Enoch')
'Enoch' - 'Elohim' LF=65 Enoch's age when becoming father: PF = 65
verse 25 - 32
v.1-18(without 'Enoch') + V.25-32
Enoch's remaining lifetime : PR=300
verse 1 - 32         LC= 365 Enoch's complete lifetime : PC=365
Table 2 : Construction of Genesis 5 according to Enoch's age.
The purpose of this construction (in accordance with Schedl's hypothesis) is assumed to be the securing of the Sethite pedigree itself as an inventory of words of patriarchal narratives. 

It seems to be improbable that this structure has emerged by chance. But several arguments can be stated against such a conception:

1) Given 30 numbers in a single chapter, isn't it probable in the first place that any of them coincides with the number of words of the whole chapter?

2) If one of the complete lifetimes coincides with the length of the complete chapter (an incidence less probable than that in question one), then there is always a subdivision of the chapter into two counterparts of the two terms of the sum.

3) The separation of Hebrew words can be defined in some other way. Then all coincidences disappear.

4) Variant readings that lead to variations of the number of words could not be taken into consideration.

5) The boundaries of the Enoch-section could perhaps be defined otherwise. Then at least two of the three sections would change. 

Ad 1) We are not looking for a coincidence of the defined textlengths with any of the ages but with the numbers of Enoch, whose story is being reported in this very chapter. The probability of this coincidence ought to be calculated.

Ad 2) The statement is correct. However, we don't have any subdivision but a dissection into two numbers which are dividable by 100 without remainder. The probability of such numbers occuring by chance can be calculated. Furthermore (not mentioned in my German article), the possibility of such a dissection of the chapter does not make it probable, that at the same time this subdivision is a reasonable one! Most probably it will look quite arbitrary with regard to the dissection of the contents.

Ad 3) I exclude any definition of the separation of Hebrew words as extremely unlikely that differs from the Biblia Hebraica (plus separation where maqqeph occurs). For isolated cases compare Ad 4.

Ad 4) This statement is wrong. Correct is: The number of words per section has to be constant. (I wrote in my German article that the sum of all changes has to be constant. But this is wrong as well: this sum has to be zero.)
This is just the postulated mechanism for securing the text.

Ad 5) The boundaries of the Enoch-section have been substantiated and are being assumed as correct for the time being. This question will be discussed again later on.

3. Test results and discussion

The next step of this quantitative structure analysis is a statistical test of the hypothesis that the coincidences of ages and numbers of words have not happened by chance. I have done this already in my article, but at present lack the time to rewrite it to an easily understandable English version for this 'Akzent'. I will only present the result of the test and leave it to the reader to consult the article for details of the substantiation.

The statistical test takes into account only two of the three coincidences (the numbers 65 = LF = PF and 300 = LR = PR ) in order to use only independent random variables. The calculation of this test yields an error probability of 0.6% , which is already statistically significant. The dissection of the 300 into 200 + 100 was not taken into account since it is rather difficult to say how many other dissections would seem not to have occured by chance as well. However, rounded numbers must have had a special meaning for the ancients as well as for us, because they were used above average for patriarchal ages.

The test result leads to the conclusion that the structure of Genesis 5 did not come into being by chance but, I suppose, through intentional construction by the author or redactor. 

Readers will possibly be interested to know how the validity of this conclusion can be checked out without performing a formal statistical test. Additionally, what about the question with regard to the boundaries of the Enoch-section ? We can solve both problems in an experimental way.

As definition for the Enoch-section the most  meaningful one was selected. Anybody can make up his own mind how probable it is to arbitrarily invent a meaningful definition of text sections and still find a coincidence with numbers mentioned on the semantical level of the text: Simply apply the same procedure on a similar text and look what comes out. 

As an example we choose Genesis 5 according to the Samaritan Pentateuch (v. Gall edition, 1918) and select the same 

section definitions and ages reported on Enoch as in the Massoretic Text. However, the text lengths are different: LF = 68, LR = 198 + 91 = 289, LC = 357.  Not a single one coincides with the ages recorded for Enoch. (The same holds if we apply one of the other two definitions given above. ) The Samaritan Pentateuch deletes 11 words and adds 3 words as distinct from the MT, a fact which is in accordance with what is to be expected if no human being has trimmed the text to pre-defined lengths.
Not surprisingly we find in the Septuagint (A.Rahlfs edition, 1979): LF=83, LR = 267 + 132 = 399, LC = 482 (with PF = 165, PR = 200, PC = 365, unlike the MT).
Not only the coincidences are missing, but in the Samaritan Pentateuch as well as in the Septuagint we also do not find the dissection of the remaining text (LR) into two numbers divideable by 100.

In almost all cases such an experiment will lead to the same negative result. However, perhaps it can be applied successfully to the sumeric king lists or similar number collections. Possibly inventories like these turn out to be a special 'Gattung' invented by scribes for scribes. But this is a question which I must leave to be answered by the specialists in the respective fields.

4. The other numbers in Genesis 5
(At present I am completely rewriting this paragraph since a reviewer told me that he found this argumentation not convincing ... and he was right ;-) 

There is still an important question left that I did not answer in my German article: What about the other numbers in Genesis 5 ? In order to answer this question we should first ask ourselves: 

1) How should the other numbers be interpreted, given the fact that the ages for Enoch coincide precisely with Enoch's text passages according to Schedl's definition? Would it be senseful to invent an additional hypothesis to explain these numbers in some other way than as textlengths? Why should such an additional hypothesis be invented at all?

2) Given the numerous changes suggested by OT scholars during the last 150 years or so: what should we expect with regard to the coincidence of the other numbers of words and ages? The answer is simple and can be given immediately: If only a small fraction of the supposed changes were correct we should expect not even a single coincidence ! Even in Genesis 5 the success of Schedl's approach is surprising, but it can be understood e.g. by assuming that the literary material of pedigrees does not appeal very much to redactors in the same way as it does not appeal to commentators. (There may be more reasons, but I want to discuss the other numbers.)

3) If we do not find exact coincidences for the other numbers of Genesis 5: How are these deviations to be interpreted apart from explaining them as redactional alterations?

There are two groups of patriarchs in Genesis 5: The first group comprises Enoch, Adam and Noah. We find more or less information about their lifes narrated in Genesis. The second group comprises the remaining seven patriarchs. There is near to nothing reported on them, especially no text section that is long enough to be taken into consideration as counterpart of one of the numbers in chapter 5. It can be supposed that their respective texts simply have not been integrated into or have been deleted from the book of Genesis - for whatever reasons - or perhaps they have never been written at all. There should be no difficulty to accept this as sufficient explanation in a sense that is still completely compatible with Schedl's definition. And we already find the mechanism of securing the textual tradition at work: The numbers tell us about deviations of the Massoretic Text over against the design as laid down in Genesis 5. 

The question remains how the ages of Adam and Noah are related to their respective text sections. Let us begin with Adam's story. If we accept the Toledot formula as being a device for structuring the text (however it works in detail), then we can regard the first Toledot in Gen.2,4 as a marker between the creation story of (essentially) chapter 1 and the Adam narrative, which extends to the end of chapter 4. Chapter 5 begins in verse 1 with the second Toledot formula and marks the beginning of the Enoch-section. The number of words for the section from Gen. 2,4 - Gen. 4,26  is  981. Adam's complete lifetime is recorded to be 930 years. Obviously there is no coincidence between 981 and 930, but on the other hand: this result is not that bad !  Given the numerous changes that these ancient texts have undergone, the difference 981 - 930 = 51 (+ 5%) is small enough to be compatible with Schedl's hypothesis. 

With regard to the dissection 930  = 130 + 800  I have no idea how to subdivide the text appropriately, at least no idea that I would dare to publish on my homepage ;-)  . However, Claus Schedl had very precise (but also rather complicated) suggestions how to construct a revised Hebrew text which then fits exactly into this scheme. I think that for professional exegetes there is no way around re-evaluating his ideas of 1964  in order not to miss helpful suggestions Schedl had to offer in his book.

The ages for Noah are 950 = 500 + 450 , the 950 years not being explicitly mentioned in chapter 5 but in chapter 9, the 450 not being stated at all. In chapter 7 we read two times that Noah was 600 years old when the flood came, and at the end of chapter 9 we find the statement that "after the flood Noah lived 350 years". These numbers lead to a second dissection of 950 = 600 + 350 . Given an inventory of words in chapter 5 it is strange to find a couple of numbers in the same notation (i.e. years of a lifetime) outside of the inventory. However, there seems to be no doubt that the Noah story has been edited by later redactors, so we must not be surprised to find the corresponding numbers in similar disarray.

The length of the complete text of Gen. 6,9 (containing the Toledot formula)  - Gen. 9,29  is  1182 words. The next Toledot formula we find in Gen. 10,1. If the identification of numbers for years and words is correct, then 232 (=1182 - 950) words have been added to the Noah story. But before we abandon all too lightly understanding this puzzle, let us put the cart before the horse and take a look at chapter 9. At the end of the chapter we read that "after the flood Noah lived 350 years". The story of Noah's life after the flood is essentially told in chapter 9 ... and this chapter is 353 words long ! This is again a striking (nearly exact) coincidence between the statement on the semantical level and the text envisaged as a chain of words. We can conclude that the additional 232 words have probably been inserted somewhere in the preceding text.

Now it is remarkable that the beginning of the preceding text is not really well defined by the Toledot formula in 6,9 . The Enoch-section ends with the last verse of chapter 5, not with Verse 8 of chapter 6. Verses 1 - 8 are often counted as part of the Noah narrative, since they thematically lead to the flood story,  Noah's name already being mentioned in verse 8. So there are good reasons to assume that the Noah section already starts with Gen. 6,1 . 

The whole text then is 1298 words (~ 1300) long.  And to our surprise we find: 1300 - 350 = 950 . If we see it this way, then there are approx. 350 words (instead of 232) which have been inserted and the question inevitably arises, if the last section as a whole (chapter 9) has been added to the flood narrative. However, I am not sure if this really is the solution. Chapter 9 does not look like a text that has been considerably revised. Still more important: counting 600 words starting at 

Gen. 6,1  we arrive at Gen. 7,22 in the middle of the flood story, which is certainly wrong because it is said that Noah was 600 years old when the flood came. Instead we would expect to come out exactly at the beginning of the flood narration in a narrower sense.I take this fact to be a pretty reliable indicator for a redactional revision of the flood story in chapters 7 and 8 . 

There is still one detail to be mentioned, which also leads to the supposition, that about 350 words have been added to the flood story. It is the well known fact that we are told the flood lasted one year and 11 days, which probably was meant to be one lunar year of 354 days + 11 days = 365 days = one solar year. Perhaps it was originally intended to be kind of a telescopic design: the number of words corresponding with the days of one year, inserted into a chain of words (the Noah story) corresponding with the years of Noah's lifetime. An intriguing idea, isn't it?

It would be very interesting if a specialist in Genesis research would determine the number of words that he thinks have been added during the redactional process. However, I do not believe that we will ever be able to arrive at certain results with regard to the original story, since it is near to impossible to know, how many words have been deleted.

I wind up by saying that even in chapter 5 it is something like a miracle that the three numbers coincide precisely with three well defined text lengths. But they do ! I assume that the stereotyped character of Genesis 5 does not appeal very much to redactors (and commentators ;-) of all times.

(Akzent 6: The Numbers in Genesis 5)
The patriarchal ages in Genesis 5 have been interpreted by Claus Schedl as textlengths of the primeval history measured in words for the purpose of securing the textual tradition. The fifth chapter of Genesis itself can be divided according to the ages recorded for Enoch:
        365 words for the whole chapter, thereof
                65 words for the passage reporting directly on Enoch,
                300 words for the rest of the chapter, thereof
                        200 words before the Enoch passage
                        100 words behind it.
A statistical test shows this structure not to have been caused by chance. The empirical error probability equals about 0.6%. The purpose of the structure is supposed to be securing of the Sethite pedigree itself as an inventory of words of patriarchal narratives.
The number of words of Adam's story (981) is of the same magnitude as Adam's age of 930 years. The 350 years of Noah's life after the flood correspond very well with the 353 words of chapter 9. There seems to have been a redactional revision of the flood story (chapters 7 and 8) in the course of which probably about 350 additional words were inserted.
The abstract sight-seeing tour ------> This way, please

End of 'Akzent 6'


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