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The first objective was to determine if the Hebrew alphabet lent itself to groups of letters that could form words with significant internal common denominator relationships. The Hebrew letters and the three valuing systems are listed in Table 1 . Sets of letters were selected based on the pattern found in the ordinal values of 4 of the 5 letters of the word Israel that had a maximum number of combinations taken two-at-a-time that factored evenly by 11. The ordinal values of these four letters were 1, 10, 12, and 21 defined by y, (x - y), (x + y), and (2x - y), when x = 11 and y = 1. The following 4 of the 6 possible combinations taken two-at-a-time factored evenly by 11: 1+ 10 = 11, 1+ 21 = 22, 10 + 12 = 22 and 12 + 21 = 33 as defined by y + (x - y) = x, y + (2x - y) = 2x, (x + y) + (x - y) = 2x, and (x + y) + (2x - y) = 3x. This set of four letters is interrelated in that the adjoining values and the first and the last factored evenly by the given factor.
This pattern was applied to other factors with y = 1 when (2x - 1) < 22 or y = 2x - 22 if (2x - 1) > 22. Even number factors contained {x - (x / 2)} and {x + (x / 2)} as a unique middle set of two letters. Completeness of sets for ordinal factors was based on the pattern spanning of the maximum number of letters of the alphabet.
The selected sets of letters chosen for ordinal values were examined in the numerical values using the same factors as the next step in determining significant sets of letters inherent in the Hebrew alphabet. For odd number factors, it was determined whether the four interrelated letters also factored evenly by that factor in the numerical values. For the even number factors, the total interrelated set, the balanced halves, either (x - y) + (x + y) or (2x - y) + y, and the middle set were examined for even factoring by that same factor. As the fifth letter of the word Israel, the remaining letter not in the interrelated set, contained a letter itself factoring evenly by 11 in the totals, all totals for individual letters that factored evenly by the given factor were included in the final selection, regardless of their inclusion in the initial set of letters selected based on the ordinal values. Values were also given in the base notation to more clearly observe relationships of the interrelated groups. A zero in the ones place indicates even factoring in a given base. In the base notation for values higher than base 10 the numbers 10, 11, and 12 are designated t, e, and w, respectively.
The uniqueness of the internal patterns of the final letter selections was determined using sets of randomly selected words. Sets of 60 proper Hebrew nouns without repeating letters of the same number of letters and were selected at random from a Hebrew concordance9. All combinations were factored by the respective factor. Means and standard deviations of the number of combinations that factored evenly were calculated for each of the three valuing systems. The number of standard deviations from the mean was determined for the number of combinations in the selected groups of letters.10
Significance of overlap of the selected letter sets and the corresponding Hebrew words was determined based on the importance of the words. Finding common denominator relationships may be expected, but for these relationships to overlap with important Hebrew words is not expected by chance. The King James Version in the Online Bible Software11 was used for word searches and counts.
© 2000 C. M. Felland