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The initial interrelated groups of the ordinal values of the Hebrew alphabet spanned the alphabet most completely for the factors of 11 and 12 ( Fig. 1 ). Factors less than 11 missed progressively larger sets of the end of the alphabet and the factors greater than 12 missed progressively more letters at the beginning of the alphabet. For 11, the letters with the ordinal valves of 11 and 22 were outside of the initial group. For 12, the letters with ordinal values of 1, 11, and 13 would have been part of the interrelated group only in a 23- or 24-letter alphabet. The initial selection were letters with ordinal values of 1, 10, 12, and 21 for the factor 11 and 2, 6, 10, 14, 18, and 22 letters for factor 12.
The initial 4 interrelated letters in the ordinal value also factored evenly by 11 in the numerical values for the factor of 11 ( Fig. 2 ). This group formed a unique interrelated pattern in the totals because it includes the 2 letters with 2 in the ones place and the 10th and 12th letters with 9 in the ones place (Fig. 2, base 11). The final letter chosen for the factor of 11 had an ordinal value of 19 (base 11) (20) and numeric value of 172 (base 11) (200), with a total of 190 (base11) (220). Only in the totals was the sum of the five letters, 500 (base11) (605), evenly divisible by 11. The value of 500 in base 11 indicates that this number is equal to 5 * 112.
For the factor of 12, the balanced inner half of the interrelated group and the middle set of two letters each factored evenly by 12 in the numerical value ( Fig. 3 ). The outer set in the ordinal value was not included because it summed to 296 (Fig. 3, base12) which was not evenly divisible by 12. In the selected group the middle set contained the only 2 letters that factored evenly by 12 in the totals. The final letter selection for 12 had ordinal values of 6, 10, 14, and 18. These factored evenly by 12 in all three value systems and could not be more centrally and evenly placed in the Hebrew alphabet.
The five letter selection for 11 were the letters of the word Israel ( Fig. 4 ) and the four letter selection for 12 were the letters of the word Zion ( Fig. 5 ). Neither of these groups of letters can form any other Hebrew words. The common denominator relationships that allowed these letters to be selected also formed balanced internal patterns within the words. The first and penultimate and second and last letters in each word factored evenly by 11 and 12, respectively, in the 3 valuing systems. For Israel, the totals of the three syllables, 341, 220, and 44, respectively, each factored evenly by 11.
The number of combinations in "Israel" evenly divisible by 11 was unusual only in the totals, where 11 of the 31 combinations factored evenly by 11. By chance one would expect about 31/11 or 2.82 of the combinations to factor evenly by 11 as observed in the means of the random word set in the three valuing systems. The number of standard deviations above the mean for the word Israel was 3.8 for the totals.
The number of combinations in "Zion" evenly divisible by 12 was also unusual only in the totals, where 7 of the 15 combinations factored evenly by 12. By chance one would expect about 15/12 or 1.25 of the combinations to factor evenly by 12 as observed in the means of the random word sets in the three valuing systems. The number of standard deviations above the mean for the word Zion was 5.1 for the totals.
Based on the high number of standard deviations above the mean for the number of evenly divisible combinations in the totals for both the words Israel and Zion, these 2 words may be the most unique based on internal common denominator relationships of the estimated 738 4-letter and 480 5-letter Hebrew proper nouns without repeating letters in the Hebrew Bible.
One can argue that the two most important Hebrew proper nouns, aside from the names of God, are Israel and Zion. The origin of the word Israel, the name of the nation and the people, is attributed directly to God (Genesis 32:28) and is comprised of the primary root meaning "to prevail" and a short form of the word God12. Zion, although a pre-Israelite term of obscure origin13 , represents the permanent capital of Israel14.
Israel and Zion are central to the Old and New Testaments and to subsequent world history. The word Israel is the third most common proper noun in the Old Testament after "LORD" and "God," occurring 2501 and 75 times, in the Old and New Testaments, respectively. The word Zion (Sion) is the nineteenth most common proper noun in the Old Testament, occurring 154 (some argue 144) and 7 times, in the Old and New Testaments, respectively. Importance to current world history is indicated by frequent use in United Nations resolutions including that of "Zionism equals racism" and those frequently condemning Israel15.
Concerning Zion, 30 of the Old Testament and 2 of the New Testament references are either "daughter of Zion" ("Sion") or "daughters of Zion" ("Sion"). It is interesting that the Hebrew letters for "daughter of" and "daughters of" are the 2nd and 22nd letters, which make up the outer two letters of the initial complete interrelated group of letters factoring evenly by 12 in the ordinal values.
Not only are Israel and Zion associated with these mathematical patterns in the alphabet, but they are also associated with the numbers 11 and 12, respectively. Aside from the fact that the Israel's alphabet has 22 (2 * 11) letters, 11 also is directly associated with God's dealings with Israel as recorded in the Old Testament. Jacob was given the name Israel by God's messenger in the same passage where the number 11 is mentioned for the first time (Genesis 32). In this passage, before the birth of Benjamin, Jacob has 11 sons. Later, Joseph's dreams featured his 11 brothers who would eventually bow down to him (Genesis 37). As with 11 and Israel, 12 is associated with Zion. Revelation 21:12 reveals that the 12 gates of the holy city are named for the 12 tribes of Israel. Hebrews 12:22 places the heavenly city on Mount Zion.
© 2000 C. M. Felland