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Author
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Topic: Genesis 1-17 As A Complex System?
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R. Edwin Sherman
Member
Member # 212
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posted 30. March 2002 14:14
There is substantial evidence that the Hebrew letters of the first 17 chapters of Genesis constitute a complex system with numerous remarkable aspects.
Suppose one takes one of the most authoritative versions of the Hebrew Bible (e.g., Koren), eliminates the spaces between the letters, and searches for Hebrew words that appear as equi-distant letter sequences (ELS’s). For example, by starting with the first Tav in Genesis 1:1, and picking up every 50th letter thereafter, one finds the Hebrew word for Torah as an ELS. [This also occurs, with a skip of 50, in the first verses of Exodus and Numbers and in the first chapter of Deuteronomy.]
Using an Israeli software package, one can enter a selected Hebrew word (or words), a selected subset of the text of the Hebrew Bible within which to search, and a specified range of skip sizes for the chosen ELS. The software will then return a list of ELS findings, showing the actual skip size of each ELS and the location of each of its letters. The software will also indicate how many times the ELS is expected to appear by chance, how many times it actually appears, and how many normalized standard deviations the actual number of appearances differs from the expected (the naīve Z value).
If the chosen ELS is short, it may be expected to appear a large number of times within any reasonably lengthy text. If one specifies a fixed search text and a fixed ELS, comparisons of the actual and expected number of occurrences can be compared at different skip size intervals.
For example, if one selects the Hebrew word for “one”, Eckad (Alef-Khet-Dalet), and searches Genesis 1-17 for Echad ELS’s with skips from 2 to 2,000, it appears 4,509 times (341 times more than expected, or 8.2% more than expected, indicating a naīve Z value of +5.29). This same ELS appears 15.0% more often than expected with skips of 2,001 to 4,000 (naīve Z of +8.57). It also appears 27.0% more often than expected with skips of 4,001 to 6,000 (Z=+13.13), 45.4% more often with skips of 6,001-8,000 (Z=+17.35), and 16.5% more often with skips of 8,001-10,000 (Z=+3.93).
Ordinarily, one would expect that the naīve Z values would fluctuate randomly above and below zero, roughly according to a normal distribution. Instead, all the naīve Z values are greater than +3.9. This is an evidently non-random phenomenon that likely would have some natural explanation.
This unexpected effect can be shown to be due largely to the fact that the variations in letter frequencies between the different chapters of Genesis 1-17 are much greater than one would find in an ordinary text. Such frequency differences have some evident explanations. Some of the chapters of Genesis are genealogies, and in some chapters certain words, such as the name of the key protagonist (e.g., Noah or Abraham) appear with unusual frequency. And the subject matter of the various chapters changes rapidly. Further, many scholars have argued that these chapters had different authors.
Clearly, if all that emerged from a search of Genesis 1-17 were similar patterns for a modest number of Hebrew words, the above phenomenon should be quickly dismissed as coincidence. However, such is not the case. In fact, within Genesis 1-17, over 25% of the trigrams (three letter Hebrew words) exhibit greater deviations from expected than does the above example. Additionally, if the range of the search text is expanded beyond Genesis 1-17, the extent of the above phenomenon dissipates rapidly for nearly all trigrams I have tested.
In further investigating this phenomenon, an objective measure of the relative “meaningfulness” of different trigrams was defined as the number of times each one appears as a literal word within the entire Hebrew Bible (Old Testament). Using this measure, it was noted that there was a very strong correlation between the “meaningfulness” of different trigrams and the magnitude and consistency of the deviations between their expected and actual number of occurrences.
It is quite doubtful that this evident correlation between ELS meaningfulness and deviation from expectation can in any way be explained by the fact that more meaningful ELS’s appear more often in the text—because the calculation of the expected number of occurrences of each ELS is based on the exact letter frequencies within the given search text.
The same phenomenon was just as pronounced when all possible digrams (two letter Hebrew words) within Genesis 1-17 were examined.
Finally, when a number of individual ELS’s were selected that exhibited large deviations, and the search text was varied, the magnitude of the deviations from expected was nearly always optimized when the search text was exactly Genesis 1-17, or some slight expansion or contraction therefrom.
The text of Genesis 1-17 is notable as a surface text for the fact that it is bracketed by descriptions of significant events (beginning as it does with the account of creation and ending with an account of God’s covenant with Abraham). Further, the exact center of that text (in terms of Hebrew letters) is Genesis 8:22, which is the end of the account of God’s covenant with Noah.
Could this be evidence of intelligent design?
R. Edwin Sherman,
Fellow, Casualty Actuarial Society,
Member, American Academy of Actuaries
[ 03 April 2002, 20:29: Message edited by: R. Edwin Sherman ]
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Moderator
Administrator
Member # 1
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posted 30. March 2002 16:41
To the posters at ISCID:
ISCID recognizes that issues relating to religion often create heated atmospheres. In addition, we also recognize that a great deal of pseudo-science is done in the name of religion. However, we feel that R.Edwin Sherman is making a statistical argument in this post and deserves to be addressed at that level.
We do however have some reservations. First of all, it would be beneficial if Sherman would contrast his data with the same analysis on several different types of literature. Second of all, the title of the topic is a question that has an answer: written language itself is a complex system.
So, in the interest of academic freedom, although we have serious reservations, ISCID is going to allow this topic to stay open. However, if it turns into a discussion about religion, or if the discussion even starts to heat up, we will close down the topic and immediately take action against those who were involved.
The ISCID Moderator
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R. Edwin Sherman
Member
Member # 212
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posted 01. April 2002 11:24
The points raised by the moderator as reservations are well taken.
First, the moderator noted that “it would be beneficial if Sherman would contrast his data with the same analysis on several different types of literature.” Similar analysis was applied to five different randomly selected sections of text in the Hebrew Bible (of comparable length to Genesis 1-17) as well as to a portion of a Hebrew translation of Tolstoy’s War and Peace as a non-Biblical control. Nothing even remotely similar to what was observed in Genesis 1-17 was noted. Virtually without exception, the naīve Z values for different digrams and trigrams within the same skip size bands used for Genesis 1-17 were less than 4.0 in absolute value in these control texts.
Second, with respect to the title of the posting, it probably would have been more accurate for it to be, “Is Genesis 1-17 An Exceptionally Complex System?”
Finally, I appreciate the moderator's efforts to keep the content of discussions on this topic distant from the intensity that often characterizes religious arguments.
R. Edwin Sherman
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Mika Vallittu
Member
Member # 107
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posted 05. April 2002 05:03
Hi Ed,
What happens if one experiments with monograms comparing results to both diagrams and triagrams? What about tetragrams and pentagrams? Just curious.
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R. Edwin Sherman
Member
Member # 212
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posted 06. April 2002 13:22
Mika:
The shortest possible equidistant letter sequence (ELS) for which meaningful data can be gathered is a digram. You must have at least two letters to have a skip distance between them. When you talk about a monogram, could you possibly be referring to a digram that consists of a pair of letters that are the same? I examined the data base using that definition and found that the average deviation from expected for digrams consisting of a repeated letter was 18% higher for such digrams that appeared as a literal word somewhere in the Hebrew Bible than for those that did not appear as a literal word. However, the sample size is so small that this difference is not statistically interesting. The average deviation from expected for this same group (a pair of letters that was a literal word) was 44% higher than for all digrams in general, but again, we are only talking about results for nine digrams in the first group.
I have done some preliminary sampling of indications for tetragrams and have observed the same striking effect as observed for digrams and trigrams. Pentagrams haven’t been checkout out yet. One reason for this is that the total number of possible X-grams with 22 Hebrew letters rises rapidly with increasing X, as it is simply 22^X. So investigating tetragrams or pentragrams would involve working with a much larger data set. Until a program is written to efficiently deal with this large volume of data points, and the fact that searching for all occurrences of a single ELS within Genesis 1-17 can take several minutes of run time, such a complete comparison will have to wait.
If one defines the null hypothesis as an absence of relationship between trigram meaningfulness and the magnitude of deviation from the expected number of occurrences in Genesis 1-17, then that hypothesis would be rejected at the p=0.001 level since the indicated chi square p-value was 4.113 E-07. Given the level of significance indicated by that result, it seemed worthwhile to bring it to the attention of ISCID members.
So far I have received numerous private e-mails from ISCID members, but there seems to be a reluctance to surface correspondence about this on the Brainstorming page. Thank you for your open communication.
Ed Sherman
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