BS”D
Og is the anti-hero of Biblical history. Og is saved by Noach during the Mabul, holding on to the Ark. He is the antithesis of Noach.
He is the Palit (refugee), escaping the first World War (of four kings against five) to inform Avraham that Lot was captured. Midrashim tells us that Og comes to Yitzhak's bris and is present when Yaakov comes down with his family to Pharoah. Moshe kills Og whose kingdom is Bashan, as the Jewish people gets ready to enter Eretz Yisroel. One can compile an entire sefer on Og's impact on Jewish history.
Og's mystical connection to the Three weeks is discussed in many sefarim, elaborating on the source in Bnei Yissochar p.339. The gematria of Og + Sichon (who was his brother) is 213 and is the same as the gematria of the letters on the backside of the mezuzah. This reveals to us that Og is the backside of holiness. This follows from the fact that each letter on the back of the mezuzah is the corresponding letter in the Alef-Beis after the ones on the front of the mezuza the klaf, i.e. "Hashem Elokenu HaShem". Hei becomes Vav and Shin becomes Tav etc.
This correspondence is approached differently in the Ishbitz sefer Sod Yesharim Al Hatorah-Tenina, parshas Devarim. The pesukim say that Og’s bed was 9 cubits. We know that the average man’s bed is 4 cubits. The Ishbitzer points out that the bed of Og is 9 by 4 cubits represented respectively by the letters Tes and Daled, which precede the Yud and Hay of HaShem's name in the Alef Beis.
Whether we address the encodings of HaShem's four-lettered name that comes out of the letters that precede or that follow the Yud and Hey and Vav and Hey, which is a misaligment of the energy that this Name brings into the world, Arizal explains it to be the theme of the mystical intentions of saying the Name during the first three brachas of the Amidah. (see http://www.scribd.com/doc/33679906/Three-Negative-Weeks-Advanced-Handout and http://www.yeshshem.com/3weeks.htm ).
Discussion of the the impact of Og's persona is well covered in on-line sources:
http://dafyomi.shemayisrael.co.il/parsha/chukat5.htm
p.117
http://www.chabad.org/search/keyword_cdo/kid/10729/jewish/Og.htm
http://www.aish.com/tp/i/moha/98195594.html
Og is even cited several times in the gemara and shulchan aruch not only in agada but also for applicationof his grotesque proportions to practical halacha.
Kisvei Ari views Og as one of the halves of a body, containing two battling souls, sort of like Tanya' animal adn divine souls. Og is the negative side to Eliezer's holier soul. Sefarim debate whether Eliezer half get elevated in the end or did both parts perish?
We encounter Og in Chumash during the Three weeks. Perhaps this draws our attention to teh duality present within teh Three weeks. Will these Three Weeks become holidays when the Geulah comes or will they be relegated to oblivion?

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