IFS and the authorship of Genesis

In their project for the autumn, 2000, fractal geometry course, Andrew Horowitz and Timothy Gambell used gemantria to convert the text of some chapters of Genesis into strings of numbers, and then used these number strings to drive an IFS. Their intention was to try to find visual signatures in the driven IFS for different authors.

Secular scholars regard the book of Genesis as a combination of three traditions: the "J document" written in Judah around 950 B.C., the "E document" written in Ephriam between 900 B.C. and 750 B.C., and the "P document" written (by the priestly authors) in Babylon between 588 B.C. and 515 B.C. An additional complication comes from later authors revising some work of earlier authors.

Dating back to the eighth century B.C., gemantria is a family of numerological systems for interpreting the Hebrew Bbile. Horowitz and Gambell used the "reduced value" system to convert text into numbers. To find the reduced value of a letter, add the digits of the ordinal value of the letter, if the ordinal value has more than one digit. For the first nine letters, just use the ordinal value. The numerical value of the word is the sum of the reduced values of its letters. For example, the word chet samech dalet ("lovingkindness") has reduced value sum 8 + 6 + 4 = 18.

The usual method of coarse graining the data then is used to drive the IFS. Here are driven IFS for three chapters, one each from the J, E, and P documents.

Chapter 38 (J) Chapter 22 (E) Chapter 5 (P)

The apparent gasket structure is a result of the skewed distribution of word values. Here is a histogram of the number of words of each value, for the first ten books of Genesis. Dividing the range of lowest value to highest value into four equal-size bins, we see few words wind up in bin 4.

For the sample J chapter (38), first note the gasket structure is clearer than for the other chapters. Also, the quadrant labeled A is more populated than for the other chapters, and although quadrant B is sparse in the J chapter, it is sparser still in the E and P chapters. Finally, as indicated by box C, the J chapter contains more points with address 11 than do the other chapters.

The sample E chapter (22) has a much less distinct gasket than does the sample J chapter. This is emphasized when noting the few points falling along the diagonal (rectangle A).

The sample P chapter (5) has quadrant A almost empty and quadrant C relatively sparse. But address 22 (square B) has a relatively dense gasket structure

Chapter 38 (J) Chapter 22 (E) Chapter 5 (P)

Horowitz and Gambell apply these observations to chapters of disputed authorship. For example, Sarna views Genesis 43 as a J document, while Pfeiffer thinks it is an E revision of a J document. Horowitz and Gambell see J characteristics (squares A, B, and C), as well as E characteristics (rectangle D). They think the driven IFS supports Pfeiffer over Sarna.

Both Sarna and Pfeiffer attribute Chapter 20 to E. The driven IFS supports this by the small population of points in the diagonal rectangle A. However, Horowitz and Gambell note the J characteristics in squares B and C, and so believe Genesis 20 is another E revision of J chapter.

Chapter 43 Chapter 20

Both Sarna and Pfeiffer think chapter 16 is a J document revised by P. Horowitz and Gambell agree, noting the J characteristics in squares A and B, and the P characteristics in square C.

Finally, both Sarna and Pfeiffer attribute chapter 36 entirely to P. While the influence of P is indicated by the structure in box A, Horowitz and Gambell note the J characteristics of boxes B and C. Consequently, they believe chapter 36 is a P revision of a J document.

Chapter 16 Chapter 36

Certainly, this work is subject to some reasonable criticism: the coarseness of the four-bin IFS, the use of gemantria to convert text to numbers, the corresponding loss of all literary content. Nevertheless, it represents an interesting first step in using driven IFS to try to deduce authorship of old texts.

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