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by Rabbi Michael J. Broyde    
Torah from Dixie Staff Writer    

As we approach the Days of Awe, we grow more and more sensitive to the precariousness of the position of truth in a world that has much evil.



As we approach the Days of Awe, we grow more and more sensitive to the precariousness of the position of truth in a world that has much evil. Indeed, a classical example of this can be found in this week's Torah portion in a mathematical analysis of the division of the tribes and the role of the Levites (as prescribed in Deuteronomy 27:11-14) when the Jewish people are commanded to stand on Mt. Gerizim and Mt. Eival, and recite the curses and rewards for defiance and obedience of the Divine. Soon after their arrival in the land of Israel, the Jewish people are to be divided into two groups; the tribes of Shimon, Levi, Judah, Yissachar, Joseph, and Benjamin all stand on Mt. Gerizim, and Reuven, Gad, Asher, Zevulun, Dan, and Naphtali all stand on Mt. Eival. In addition, some of the Levites seem to be standing in the valley between these two mountains, leading the reaffirmation of the Torah. (The actual event occurs in the book of Joshua 8:33.) Indeed, the Talmud (Tractate Sotah 32a, 37a) presents various possibilities for the division of the Levites and the tribes.

However, the most puzzling aspect of the positioning of the tribes is the manner in which the tribes were divided into two groups. The allocation chosen for this ceremony bears little or no relationship to the biblical schemes that are typically used for organizing the tribes, such as order of birth, matriarchal lineage, or the division into marching camps discussed in the second chapter of the Book of Numbers. In fact, there are 462 different ways to divide twelve tribes into two groups of six.* Why was the particular allocation described in these verses chosen and what really was the role of the Levites?

Rabbi David Frankel in his classic commentary on the Jerusalem Talmud hints at a very interesting point. He suggests that the tribes and the Levites were assigned to the two mountains and the valley in such a way as to come as close as possible to a numerically even split while still allowing for a designated group of Levites to have a unique role of calling out the blessings and curses in the valley. This mathematically optimal division occurs when the Levites are divided according to the Talmudic suggestion that "those Levites who were involved in working in the Tabernacle were in the valley and the rest were on the mountain" (Tractate Sotah 32a, 37a). According to the commentator Rashi's explanation of that opinion, "those who worked in the tabernacle" refers to those aged 30 to 50. In an earlier census this group comprised 38.48% of the total number of Levites counted. Assuming that the percentage of the Levites remained constant, there would be 8,850 Levites between the ages of 30 and 50 at the time of the ceremony on Mt. Gerizim and Mt. Eival. The group of Levites on the mountain would be all the remaining Levites, and their population would be 14,150.

Population figures for the two mountain groups, based on the census of Numbers 27, would be as follows:

Tribes on Mt. Gerizim: Shimon - 22,200; Levi - 14,150; Judah - 76,500; Yissachar - 64,300; Joseph - 85,200; Benjamin - 45,600; Total=307,950

Tribes on Mt. Eival: Reuven - 43,730; Gad - 40,500; Asher - 53,400; Zevulun - 60,500; Dan - 64,400; Naphtali - 45,400; Total=307,930

Total population=615,880

Under this division, 50.001623% of the nation are on Mt. Gerizim and 49.998376% are on Mt. Eival.

By means of a computer program, all 462 possible allocations of the tribes into two groups of six were generated. The biblically prescribed allocation of the tribes, as delineated above, is the optimal division. Of the 462 different possibilities, this one divides the tribes into the two most equal camps of six tribes each. No better allocation is possible.

Rambam, the great medieval philosopher and codifier of Jewish law, tells us that "it is incumbent upon every person throughout the year to view himself as half innocent and half guilty. So too all of the world should be viewed as half innocent and half guilty. Every individual sin can determine his own - and the world's - fate for guilt and destruction. Conversely, one good deed can place oneself - and the world - on the side of salvation and redemption" (Laws of Repentance 3:4). The Almighty, in his penultimate direction to the Jews about the importance to keep the mitzvot, divided the Jewish people equally to tell us that the conduct of each and every one of us counts and is important. One of us alone, with our good deeds, can sway the scales for many. It is with this lesson in mind that we should enter the High Holidays.

*For those who absolutely will not continue without the formula, this is expressed as:
      Number of possibilities = K!
      (K-M) ! * M1 + (.5)
      with: K= members of group (in our case 12);
     M= number of members in each
     subunit (in our case 6); != factorial; *= multiplication.


Rabbi Michael J. Broyde resides in Atlanta, went to school at the Greenfield Hebrew Academy, and currently teaches Jewish Law at Emory University School of Law. He is also the rabbi of the Young Israel of Toco Hills, Atlanta.

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