Friday, September 8, 2017

Balancing the Shevatim at Har Grizim and Har Eival

In the fall of 1992, there was a fascinating article concerning this week's parsha written up in Tradition magazine by Rabbi Michael Broyde of Atlanta and Steven Weiner of Los Angeles. I will try to sum up the article as concisely as possible. The pasuk tells us (27:12) that the tribes of Shimon, Levi, Yehuda, Yissachar, Yosef and Binyomin stood on Har Grizim for the delivering of the bracha. Reuven, Gad, Asher, Zevulun, Dan and Naftali stood on Har Eival for the delivering of the klala. The gemara in Sotah 37a presents a quandary based on a pasuk in Yehoshua that seems to show that the Kohanim were in the middle of the two mountains. So how could they be said to have been on Har Grizim? The Gemara gives three different answers as to how the Kohanim were split up, some below, and some on the mountain. The answer that seems to be most dealt with amongst the meforshim is that those who were 'fit for work' were below with the Aron, and those who were not were above. Rashi learns this to refer to those above thirty while the Maharsh"a learns that it is referring to b'nei Kehas who were in charge of the Aron.

Now, in dividing the tribes between two mountains, there are 462 different ways to make such a division [12!/2(6!6!)]. Broyde and Weiner point out a fascinating fact. Taking the most recent census data that we are given in the Torah and dealing with the answer of the gemara that we have discussed, if you examine every single possible formation of the tribes, the actual formation of the tribes is the absolute most even division of the tribes possible. That is, the difference in population between the two mountains is at a minimum with this formation. [I personally wrote a computer program to test it out and it worked. In the article, they include a list of all possible combinations and their respective differences.] What is even more fascinating, is that this works out for both Rashi and the Maharsh"a. And what may be the most fascinating of all is that according to the Maharsh"a, the population on Har Grizim would have been 307,929 and that of Har Eival 307,930. No, that's not a typo. That is a difference of 1! According to both, this is by far the most even division of the tribes. The next step is what to do with such an impressive observation. What does this tell us? I will leave that for the reader to decide. [In the article, they suggest a parallel to that which we are taught that one should always look at the world as if it were half righteous and half guilty and the judgement of the entire world is dependent on him.] But for what it's worth, it is surely an intriguing observation on its own.

The article became the subject of debate in the Spring of 1999 with The Solution to Deuteronomy is not in Numbers by Sheldon Epstein, Yonah Wilamowsky & Bernard Dickman and A Mathematical Solution on Terra Firma and a Geographical Explanation on Weak Ground by the original authors.

IMPORTANT UPDATE: Tradition magazine has been gracious enough to make their archives fully available to the public! So following the links above will now allow you to read the articles in their entirety.