1) HALACHAH: EATING MEAT, WASHING CLOTHES, AND CUTTING HAIR BEFORE TISH'AH B'AV
The Gemara discusses various activities which the Chachamim prohibited immediately before Tish'ah b'Av. These enactments are the source for the common practices observed today.
(a) EATING MEAT. The Gemara concludes that the prohibition against eating meat and drinking wine applies only during the Se'udah ha'Mafsekes on Erev Tish'ah b'Av, when the Se'udah ha'Mafsekes is eaten after midday. According to the Gemara, one is permitted to eat meat and drink wine earlier during the day on Erev Tish'ah b'Av, as well as during the days prior to Tish'ah b'Av. (This is the practice of Jews of Yemenite descent today, who eat meat and drink wine during the days before Tish'ah b'Av, until the Se'udah ha'Mafsekes.)
However, the Rishonim write that the common practice is to refrain from meat and wine the entire day on Erev Tish'ah b'Av. Moreover, some Rishonim rule (based on the Yerushalmi) that meat and wine are prohibited during the entire week in which Tish'ah b'Av falls. Others maintain that the prohibition should be observed from Rosh Chodesh Av, nine days before Tish'ah b'Av. This is the practice of Ashkenazim.
(b) WASHING CLOTHES AND CUTTING HAIR. Three Tana'im argue about when the prohibitions against washing clothes and cutting hair apply. Rebbi Meir maintains that washing clothes and cutting hair are prohibited from Rosh Chodesh Av until Tish'ah b'Av. Rebbi Yehudah maintains that they are prohibited the entire month of Av (from Rosh Chodesh). Raban Shimon ben Gamliel maintains that these prohibitions apply only during the week in which Tish'ah b'Av falls, including the days after Tish'ah b'Av.
Rava rules like Raban Shimon ben Gamliel who says that the prohibitions against washing clothes and cutting hair apply only during the week in which Tish'ah b'Av falls. He also rules in part like Rebbi Meir who says that the prohibitions apply only during the days before Tish'ah b'Av but not afterwards.
It is the practice of Ashkenazic Jews to refrain from washing clothes from Rosh Chodesh Av (REMA OC 551:3) and to refrain from cutting hair from the Seventeenth of Tamuz. However, RAV MOSHE FEINSTEIN zt'l (Igros Moshe OC 4:102) rules that since the Gemara concludes that the prohibitions apply only during the week of Tish'ah b'Av, one may wash his clothes or cut his hair before the week of Tish'ah b'Av order to prevent a financial loss. During the week of Tish'ah b'Av, however, one may not wash his clothes or cut his hair even to prevent a financial loss.
If the Gemara prohibits washing clothes and cutting hair only during the week of Tish'ah b'Av, why are these prohibitions observed by Ashkenazim even before the week of Tish'ah b'Av?
The VILNA GA'ON (in BI'UR HA'GRA OC 551:6) cites the Gemara in Bava Basra (60b) which says that after the Beis ha'Mikdash was destroyed, the people proposed that eating meat and drinking wine be prohibited altogether. Rebbi Yishmael ben Elisha told them that "we do not enact decrees upon the community when a majority of the community is unable to observe them." It is evident from the Gemara there that meat and wine ideally should be prohibited at all times while the Beis ha'Mikdash is in ruins, but in practice they are not prohibited because of the difficulty the people would have in abiding by such a law.
The Vilna Ga'on explains that since the Tzibur is able to refrain from meat and wine for a short period each year, the Chachamim introduced the custom of abstaining from them (for as long as the Tzibur could abide by such a custom according to the Chachamim's assessment). Hence, the Chachamim introduced the custom to refrain from meat and wine (and from washing clothes) for the nine days from Rosh Chodesh until Tish'ah b'Av, as most of the Tzibur is able to observe those stringencies for that amount of time. (A similar logic may be the basis for the custom not to cut hair during the three weeks from the Seventeenth of Tamuz until Tish'ah b'Av.)

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2) AGADAH: ALL WHO MOURN FOR YERUSHALAYIM WILL REJOICE IN HER
QUESTION: The Gemara states, "All who mourn for Yerushalayim will merit and see her joy."
What does this mean? Throughout the generations, many great Jewish men and women have mourned for Yerushalayim from the depths of their souls, but none of them merited to see the rebuilding of the city and the Beis ha'Mikdash in their lifetimes.
ANSWER: The KOHELES YITZCHAK quotes RAV CHAIM BERLIN who gives the following explanation for this Gemara.
The Torah relates that Yakov Avinu mourned for Yosef for 22 years, when he was under the assumption that Yosef had been killed. Why did Yakov Avinu mourn for such a long time? The Gemara in Berachos (58b) teaches that the pain of the death of a loved one remains in one's heart for only twelve months; after twelve months have passed, one naturally forgets the pain of the loss. Why, then, did Yakov Avinu mourn for 22 years? RASHI (Bereishis 37:35) cites the Midrash which answers that the pain of the death of a loved one fades only when the person is actually dead. If he is still alive (unbeknown to his mourning relative), the memory does not fade from the heart.
When the Beis ha'Mikdash was destroyed, the mourning over the loss should have lasted for only twelve months. If the Beis ha'Mikdash was irrevocably destroyed, the painful memory should have faded from its mourners' hearts, and there should no longer be mourning for the Beis ha'Mikdash. However, the fact that the Jewish people continue to mourn over the loss of the Beis ha'Mikdash indicates that it is not permanently lost -- but that it is really "still alive" and will be rebuilt. This knowledge gives the mourners hope and encouragement, and they experience joy in the knowledge that the Beis ha'Mikdash will be rebuilt!
3) THE DAY ON WHICH THE PEOPLE IN THE "MIDBAR" STOPPED DYING
QUESTIONS: One of the events which occurred on the Fifteenth of Av, making it a day of celebration, was that the Jews in the Midbar stopped dying on that day ("Kalu Mesei Midbar"). RASHI cites the Midrash which says that in the Midbar, on every Tish'ah b'Av the people would dig graves for themselves, lie down in them overnight, and the next morning many of them would not arise. In the final year of their sojourn in the Midbar, all of those who went to sleep in their graves on the night of Tish'ah b'Av arose the next morning. The next few nights they continued to go to sleep in their graves, thinking that they had erred in the calculation of the date, until they saw the full moon in the sky and knew beyond a doubt that the Ninth of Av had passed and that it was already the middle of the month, the Fifteenth of Av.
There are several points in this account which are difficult to understand.
First, in the year in which the Jews stopped dying in the Midbar, whoever had been decreed to die had already died. No one who was of age at the time of the sin of the Meraglim (when Hash-m decreed that all men between the ages of 20 and 60 would die and not enter Eretz Yisrael) was still alive. Why, then, did they think that they still needed to dig graves?
Second, if no one died on that Tish'ah b'Av, and Tish'ah b'Av was the only day on which they died, then the last day on which Jews died in the Midbar was on Tish'ah b'Av of the previous year! Accordingly, they should have instituted the day of celebration on the tenth of Av and not on the Fifteenth of Av, because the last day on which Jews died was the ninth of Av of the previous year. The Shechinah should have resumed speaking to Moshe Rabeinu the year before, since Tish'ah b'Av of the previous year was the last day on which the Gezeirah applied.
Third, why does the Gemara mention that on that day, the Fifteenth of Av, communication between the Shechinah and Moshe Rabeinu resumed? If the day celebrates the cessation of punishment in the Midbar, why does the Gemara need to mention the fact that the Shechinah began speaking again to Moshe Rabeinu?
ANSWERS:
(a) TOSFOS in Bava Basra (121a, DH Yom she'Kalu) asserts that although it is true that the people died in the Midbar only on Tish'ah b'Av, they also died even in the fortieth (and final) year of their sojourn. That year, the rest of the Jewish people were mourning for their relatives who died on Tish'ah b'Av. They mourned for seven days, during which time the Shechinah did not dwell among the people (because the Shechinah dwells only amidst joy and not amidst mournfulness), and thus Moshe Rabeinu received no communication from the Shechinah. Only when the seven days of mourning concluded did communication between the Shechinah and Moshe Rabeinu resume. Seven days after Tish'ah b'Av (including Tish'ah b'Av itself and part of the seventh day, since "Miktzas ha'Yom k'Kulo") was the Fifteenth of Av.
This approach, however, is not in agreement with the Yerushalmi cited by Rashi. The Yerushalmi says that no one died on Tish'ah b'Av of the last year, and thus they dug graves unnecessarily.
(b) TOSFOS here cites others who explain that even though most of the people died each year on Tish'ah b'Av, there were some people who died on other days of the year. The last day of any year on which anyone died was the fourteenth of Av. No one died after the fourteenth, and therefore the Fifteenth of Av became a day of celebration.
This approach, like the first one above, is not in agreement with the Yerushalmi cited by Rashi.
(c) TOSFOS in Bava Basra (ibid.) cites RABEINU TAM who suggests that Hash-m indeed annulled the Gezeirah of death in the Midbar. Consequently, the people who were supposed to die on the last year did not die. This explains why they continued to dig graves that year; there were still people alive who were decreed to die but who did not know that the decree had been rescinded.
Why did the Shechinah return to Moshe Rabeinu only on the Fifteenth of Av, and why is that fact relevant? Moreover, why is the cessation of death in the Midbar celebrated on the Fifteenth of Av if the last day on which Jews died was the ninth of Av of the previous year?
Perhaps before the arrival of the Fifteenth of Av, Hash-m had not yet annulled the decree of death. There were Jews who were still destined to die, and thus in the last year those Jews returned to their graves each day in anxious expectation of their destined punishment. However, on the Fifteenth of Av the Shechinah returned to Moshe Rabeinu. This showed that Hash-m had annulled the decree and pardoned the people. Those who had been decreed to die that year survived.
(The Yerushalmi says that when they saw the full moon they knew that the decree had been lifted. In that respect the Gemara here argues with the Yerushalmi, because the Gemara here says that they knew that the decree was lifted when they saw that the Shechinah returned to Moshe Rabeinu.)
However, the Torah explicitly says that the only ones who remained alive from that generation were Yehoshua and Kalev (Bamidbar 26:65). How, then, can the Gemara say that the decree was annulled and some of the people of that generation lived?
Rabeinu Tam answers as follows. The decree of death in the Midbar stated that any person who was between the ages of 20 and 60 at the time of the sin of the Meraglim would die in the Midbar. The Midrash says that each year those who reached the age of 60 died, and thus at the end of forty years all of the people who were over 20 at the time of the Meraglim had already died. The last year, the only ones who were still alive who thought that they would die (for whom Hash-m annulled the decree) were those who were exactly 20 at the time of the sin of the Meraglim.
Before Hash-m annulled the decree, the intent of the decree was to be inclusive -- anyone between the ages of 20 and 60 was to die, including those who were exactly 20 years old at the time of the sin of the Meraglim. When Hash-m had mercy and decided to annul the remainder of the decree, He did not completely annul the decree, but rather He re-interpreted it: instead of being inclusive of the 20 year-olds, He made it exclusive of the 20 year-olds. Thus, it is correct to say both that the decree was carried out entirely and no one who was included in the decree remained alive, and that Hash-m annulled the decree! Since Yehoshua and Kalev were older than 20 at the time of the Meraglim, they indeed were the only ones who remained of all of the people between the ages of 20 (exclusive) and 60 at the time of the Meraglim who had to die.

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