1) THE DAY THAT HILLEL'S OPINION WAS OVERTURNED
QUESTION: The Gemara says that the day that Shamai overruled Hillel was as "difficult for the Jews as the day that the golden calf was made." What does the day that Shamai overruled Hillel have to do with the day that the golden calf was made?
(a) RASHI explains that it was a difficult day for the Jewish people, because Hillel was the Nasi, the leader of the generation, and he was exceedingly humble. The CHASAM SOFER explains that Rashi means that just as the will of the people at the time of the sin of the golden calf overruled the will of their leader, Aharon ha'Kohen (Moshe at the time was receiving the Torah on Har Sinai), so, too, the opinion of the contending academy of Shamai overruled the academy of the authority, Hillel, and they subjected him to their will by forcing him to comply with their ruling against his own reasoning.
(b) Perhaps we may expound further on the comparison between the overruling of Hillel and the sin of the golden calf. We find that in Avos (1:12) Hillel says, "One should be of the disciples of Aharon and constantly pursue peace." He says "disciples of Aharon" and not "disciple of Moshe," because it was Aharon's special trait of loving peace and kindness that Hillel wanted people to follow. Moshe's trait was that of strict justice, which Hillel felt was not the trait that the masses should cultivate in themselves for the sake of peace among men (Sanhedrin 6b).
Thus, it was Hillel's opinion that Aharon's traits should be emulated. This was consistent with own personality. As the Gemara later in Shabbos (30b) says, "One should be patient, forgiving, and humble like Hillel, and not stand on one's honor like Shamai." We indeed find that Beis Hillel, the disciples of Hillel, almost always give the more lenient opinion and Beis Shamai the more strict one.
The day that Aharon was overruled by the people building the golden calf was the day when the traits of Aharon were overruled and the trait of Moshe, strict justice, dominated. Justice and punishment was wrought upon the Jewish people that day. Similarly, when Shamai overruled Hillel, the traits of Hillel were conquered and Shamai's traits of strict justice ruled. It was difficult for the Jewish people to live with the strictness of Beis Shamai, just as it was difficult for them to live in that state when Aharon's traits were conquered at the sin of the golden calf. (M. KORNFELD)
2) THE 18 DECREES
QUESTION: The Gemara goes to considerable lengths to count every one of the 18 decrees that were made on the day that Beis Shamai was the majority. As the Beraisa (12a) says, the first two decrees that are counted are the decrees in the Mishnah (11a) against checking for lice on Shabbos by the light of an oil lamp, and reading on Shabbos by the light of an oil lamp.
However, the same Mishnah that teaches these two decrees continues, "Similarly, a Zav should not eat together with a Zavah...." This wording ("Similarly...") implies that the decree against a Zav and Zavah eating together is in the same category as the previous two decrees, which were part of the 18 decrees. In fact, the Tosefta clearly specifies that it was among the 18 decrees! Why, then does the Gemara not count this degree among the 18 decrees listed in the Gemara?
(a) TOSFOS (DH Hanicha) explains that it indeed is included in the count of 18 decrees. In order to avoid reaching a total of 19, we simply count "ha'Ochel Ochel Rishon" and "ha'Ochel Ochel Sheni" as one decree. (Alternatively, "ha'Ba Rosho v'Rubo" and "Tahor she'Naflu Alav" are counted as one).
(b) The RAMBAM (Perush ha'Mishnayos) suggests a novel way to interpret the Gemara. The Mishnah (13b) mentions first the Halachos of Beis Shamai and Beis Hillel, and afterwards it discusses their Gezeiros. Later in the Gemara (top of 15a), we refer to their Gezeiros, their disagreements, and their agreements. According to the understanding of Rashi and Tosfos, all of these terms refer to the same 18 decrees. Originally Beis Hillel argued with Beis Shamai in this 18 matters. Beis Hillel was then overruled and consented to Beis Shamai.
The Rambam, however, suggests that these terms refer to three different sets of 18 decrees.
The first set were the 18 decrees ("Gazru") that were made that day, as the Gemara here enumerates. The second set were 18 unanimous Halachos that were announced the following day ("l'Machar Hushvu"). These are the laws mentioned in the Mishnah from the law of the poor man and the rich man (i.e., the eight permutations of the Melachah of Hotza'ah) until the present Mishnah. The third set were 18 more laws that were discussed that day, about which Beis Shamai and Beis Hillel remained in disagreement ("Nechleku"). These are the 18 laws that appear in the Mishnayos (from here until the end of the Perek) about which Beis Shamai and Beis Hillel disagree.