1) CELEBRATING THE DAY WHEN NO MORE WOOD IS CUT
QUESTION: Rabah and Rav Yosef say that the reason why the Fifteenth of Av was made into a festive day is because the cutting of the wood used for fuel on the Mizbe'ach ended on that day. Since the sun was no longer strong enough to keep the wood dry, they stopped cutting the wood for the Mizbe'ach.
What is so special about the day on which they stopped cutting wood? Why does that event warrant celebration?
ANSWER: RABEINU GERSHOM in Bava Basra (121b) explains that since they no longer needed to cut wood, they had much more time to learn Torah. Having more time to learn Torah was the cause for celebration.
According to Rabeinu Gershom, Rabah and Rav Yosef's reason is related to the following statement in the Gemara that from the Fifteenth of Av and onward the days begin to get shorter and the nights longer, and this extra time must be used to learn Torah. Accordingly, the cause for celebration on the Fifteenth of Av is the increased time for Torah learning.
2) YOM KIPPUR AND THE FIFTEENTH OF AV -- JOYOUS DAYS FOR THE JEWISH PEOPLE
QUESTION: The Gemara discusses the joyous days of Yom Kippur and the Fifteenth of Av. Why does the Mishnah and Gemara discuss this topic at the end of Maseches Ta'anis? How is it related to the topics of the rest of the Maseches?
ANSWERS:
(a) The most basic answer is that since the rest of the Maseches discusses topics of inauspicious times -- such as the fast days for troubles that befall the Jewish people and the fast days observed in mourning for the Beis ha'Mikdash -- the Chachamim wanted to conclude the Maseches on a positive note. Therefore, the final Sugya discusses days of joy and celebration, Yom Kippur and the Fifteenth of Av.
There is, however, a deeper reason for why the Mishnah and Gemara discuss joyous days at the end of Maseches Ta'anis.
(b) The first part of the Mishnah (26b) discusses the fast days of the Seventeenth of Tamuz and the Ninth of Av. On the Seventeenth of Tamuz, Moshe Rabeinu descended the mountain and found that the people had built the Golden Calf. He cast down the Luchos and shattered them. On the Ninth of Av, Hash-m decreed that the Jewish people who were guilty of the sin of the Meraglim would not enter Eretz Yisrael.
The last part of the Mishnah discusses positive things specifically related to those tragic events. The Mishnah relates how Hash-m gave to the Jewish people what they had lost on the tragic occasions of the Seventeenth of Tamuz and Tish'ah b'Av. On Yom Kippur, Hash-m granted atonement to the Jewish people for the sin of the Golden Calf and gave them the second set of Luchos. On the Fifteenth of Av, Hash-m annulled the decree of death for the Jews in the Midbar and permitted the Jewish people to enter Eretz Yisrael. (See following Insight.)
3) "ON THE DAY OF THE JOY OF HIS HEART"
QUESTION: The Mishnah (26b) states that "there were no Yamim Tovim for the Jewish people like the Fifteenth of Av and Yom Kippur... and so it says (Shir ha'Shirim 3:11), 'Daughters of Yerushalayim, go out and see Shlomo in the crown with which his mother crowned him on his wedding day' -- this refers to the day of the giving of the Torah, 'And on the day of the joy of his heart' -- this refers to the building of the Beis ha'Mikdash that will be rebuilt speedily in our days."
What is the connection between the statement that there were no Yamim Tovim like the Fifteenth of Av and Yom Kippur and the verse in Shir ha'Shirim? This question is especially difficult in light of the fact that the Mishnah introduces the verse with the words "and so it says," which clearly imply that the verse proves that the Fifteenth of Av and Yom Kippur were days of joy.
ANSWER: RASHI (26b, DH Zeh Matan Torah) explains that "the day of the giving of the Torah" mentioned in the Mishnah refers to Yom Kippur, when Hash-m gave the second set of Luchos to Moshe Rabeinu after He forgave the people for the sin of the Golden Calf which occurred on the Seventeenth of Tamuz. (See previous Insight.)
How, though, are we to understand the reference to "the building of the Beis ha'Mikdash that will be rebuilt speedily in our days"? In what way is the Beis ha'Mikdash related directly to the Fifteenth of Av or to Yom Kippur? (See Bartenura.)
Perhaps the Mishnah understands that the verse refers not to the building of the first Beis ha'Mikdash, but rather, as the Mishnah itself says, to "the Beis ha'Mikdash that will be rebuilt speedily in our days" -- the third Beis ha'Mikdash. When Mashi'ach comes and the third Beis ha'Mikdash is built, the sin which brought about the destruction of the Beis ha'Mikdash on Tish'ah b'Av will have been rectified and the Jewish people will be completely righteous in the eyes of Hash-m. Hence, the happiness of "the day of the building of the Beis ha'Mikdash" refers to the rejoicing in the complete forgiveness of the sins of Tish'ah b'Av which precipitated the destruction of the Beis ha'Mikdash.
The Jewish people received a taste of that complete forgiveness, on a limited scale, on the Fifteenth of Av over three millennia ago as they traveled to Eretz Yisrael in the Midbar. On that day, Hash-m allowed the sinners who were still alive to enter Eretz Yisrael (see Insights to Ta'anis 30:1). On the same date the Jewish people can anticipate with eagerness the "day of the joy of his heart," the long-awaited moment of the restoration of the Beis ha'Mikdash. Accordingly, the Mishnah indeed cites a source for the celebrations of the Fifteenth of Av and for the rejoicing of Yom Kippur.
These days were proclaimed to be days of joy and celebration in the hope that the fast days of the Seventeenth of Tamuz and the Ninth of Av themselves will be transformed into days of joy and celebration, as the prophet said: "The fast of the fourth [month] (17 Tamuz), the fast of the fifth (9 Av), the fast of the seventh (3 Tishrei), and the fast of the tenth (10 Teves) will be for the house of Yehudah for joy and happiness, and for days of festivity" (Zecharyah 8:19). May this prophecy be fulfilled speedily in our days. (M. Kornfeld)
4) THE DANCE OF THE TZADIKIM
QUESTION: The Mishnah (26b) describes how the young women danced in the vineyards on the Fifteenth of Av and on Yom Kippur. The Gemara here concludes the Maseches by saying that in the future, Hash-m will make a circle of Tzadikim. The Shechinah will sit inside the circle, and the Tzadikim will point towards the center of the circle and declare, "This is my G-d, we will rejoice in His salvation."
What is the meaning of this circle of Tzadikim?
ANSWER: The Gemara's description of the circle of Tzadikim as they point to the Shechinah in the center teaches that every Tzadik has his own unique approach to Avodas Hash-m which differs from the approach of the other Tzadik (and sometimes even appears to be the exact opposite). All of the Tzadikim together comprise the full circle. Each successive Tzadik around the circle faces a slightly different direction, such that those at opposite sides face opposite directions. Nevertheless, they are all equidistant from the center. This alludes to the fact that all of their different approaches to serving Hash-m are acceptable, as long as their primary goal is Kidush Shem Shamayim. In the future, Hash-m will reveal that the approaches of all of the Tzadikim in the world were l'Shem Shamayim, and that even though they followed different approaches, they all strove to fulfill the will of Hash-m. (RAV LEIBELE EIGER in TORAS EMES, in the name of his grandfather, REBBI AKIVA EIGER)
(In KOVETZ ES HE'ASEF, Rav Yaakov D. Homnick adds that not only are all of the unique Derachim of the Tzadikim acceptable, but they are necessary, because if any single Tzadik does not fulfill his particular form of service of Hash-m, the "circle" around Hash-m is incomplete.)
The connection between the description of the future dance of the Tzadikim and the previous Sugya which discusses the Fifteenth of Av is that the celebration of the Fifteenth of Av represents the Simchah that the Jewish people will experience when the final redemption arrives and the third Beis ha'Mikdash is built. (See previous Insight.) This redemption will come about through the Achdus, unity, of the Jewish people, as the Midrash explains on the verse, "va'Yehi b'Yeshurun Melech b'Hisasef Roshei Am, Yachad Shivtei Yisrael" -- "He is King in Yeshurun when the leaders of the people gather themselves together, when the tribes of Yisrael are united" (Devarim 33:5). The events which the Fifteenth of Av celebrates are events which brought about Achdus among the people (for example, the tribes became permitted to marry into one another, and the tribe of Binyamin was allowed back into the nation), and that is why the Mishnah says that "anyone who does not know his tribe (that is, the day on which he is supposed to bring the wood for the Mizbe'ach)" brings the wood on the Fifteenth of Av. That is also why that day was designated for making Shiduchim.
This also explains why, on the Fifteenth of Av, the young women lent each other their garments, thereby creating a tremendous atmosphere of Achdus, despite the fact that the Gemara (Megilah 13a) says that the nature of a woman is to feel jealous of the beauty of another woman.
(Rav Homnick demonstrates that the declarations of the young women during their dance reflected their Achdus as well. When each individual recognizes her own unique strengths and approach to serving Hash-m, and all serve Hash-m together in their unique ways, they create Achdus, as the circle of the Tzadikim demonstrates.)
For this reason, Maseches Ta'anis concludes with a description of the circle of the Tzadikim. The Gemara concludes its discussion of the days of mourning for the destruction of Yerushalayim and the Beis ha'Mikdash by showing how to unite the nation and to merit the final redemption and the rebuilding of Yerushalayim and the Beis ha'Mikdash, may we merit to witness it speedily in our days.

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