Why did the Torah obligate blessing after eating, and before learning Torah?

Ha'Boneh: Worldly pleasures are felt only via the senses. Spiritual pleasures, the intellect benefits from them immediately, once it agrees with them.

Rav Elyashiv: It is not applicable to obligate an individual to bless after learning, for he is obligated to learn until he goes to sleep! Even when he goes to work, this is not considered diverting his mind from learning. Our Sugya discusses a Brachah after learning, i.e. after Kri'as ha'Torah b'Tzibur.

How do we learn from "Ki Shem Hash-m Ekra Havu Godel l'Elokeinu"?

Rashi: When Moshe came to begin Shirah, he told Yisrael, I will bless first, and you will answer Amen.

Daf Al ha'Daf: The Griz (on Ramban Hilchos Talmud Torah 11:16, citing his father) says that women must say Birkas ha'Torah, even though they are exempt from the Mitzvah, for the Brachah is not for the Mitzvah. Rather, the verse teaches that Torah requires a Brachah! Tzitz Eliezer (15:24) says that their learning is called Talmud Torah, even though they are exempt. They bless, just like one blesses for eating bread, even though he was not obligated to do so.

Megadim Chadashim: The Levush (OC 47:6) says that 'Asher Kideshanu b'Mitzvosav v'Tzivanu...' is a Berachah on the Mitzvah, and 'Asher Bachar Banu...' is a Berachah of benefit. Chayei Adam says that the former is Birkas ha'Mitzvah, and the latter is a Berachah of thanks.

Maharsha: When I read Torah, which is totally names of Hash-m, like Midrashim say [bless Hash-m].

Daf Al ha'Daf: Sha'agas Aryeh (24) learned from here that we bless only on speaking Torah, but not for thinking. Baruch Ta'am asked, here we discuss the Brachah, and not learning Torah! According to Maharsha, this is fine. "Shem Hash-m" refers to Divrei Torah!

Iyun Yakov, based on Sifri: When I say in Birkas ha'Torah 'Barechu Es Hash-m ha'Mevorach', attribute greatness to Him, and say 'Baruch Hash-m ha'Mevorach l'Olam va'Ed.'

Our Gemara learns Birkas ha'Torah from a verse. How can the Rambam hold that it is mid'Rabanan?

Daf Al ha'Daf: Mishkenos Yakov (OC 63) brings from the Yerushalmi (Brachos 7:1) that the verse discusses Talmud Torah of a Rabim; Moshe taught the Rabim.

Here it says that an individual does not say Kedushah. Are there cases in which he says it?

Tosfos: [One who prays with the Shali'ach Tzibur] is not called an individual. When the Shali'ach Tzibur reaches Kedushah, he says it with him.

Me'iri: Some say that if the Shali'ach Tzibur prays Minchah and an individual prays Ma'ariv with him, he does not say Kedushah with him. I am unsure about an individual praying Shacharis together with a Shali'ach Tzibur praying Musaf.

Me'iri: He says the Kedushah in Birkas Keri'as Shma and in u'Va l'Tziyon. Some disagree about the former.

What is the significance of learning from the Meraglim?

R. Bechayei (Vayikra 22:32): We cannot learn Davar shebi'Kdushah from Resha'im! Rather, the text says that we learn from a Gezeirah Shavah "Toch-Toch" from Yosef's brothers.

Megadim Chadashim, Daf Al ha'Daf: This is astounding. In several places we learn that "Edah" is at least 10. We cannot learn from Yosef's brothers - they are not called Edah!

Rav Elyashiv: The Mishnah Berurah (55:46-47) rules like the Pri Megadim (on 55:11) that a Mumar (apostate) does not join to make a Minyan. Igros Moshe (OC 1:23, 2:19) says that in pressed circumstances, one may join him. The Meraglim were Mumarim - they said "Chazak Hu Mimenu" - the residents of Eretz Kena'an are stronger than Him. The same applies to the Chiyuv for Kidush Hash-m. Even though the Meraglim repented (Sotah 21b), this verse was said before they repented.

Daf Al ha'Daf: They say in the name of Chidushei ha'Rim that we learn that there is Shechinah among any 10, even Resha'im. The Kotzker Rav similarly said that we learn from Esav that a Chasan's sins are pardoned, even if he is a Rasha. The Pri Megadim said that a Mumar joins only if he sins for pleasure, but not if he wants to anger Hash-m. We learn "Edah-Edah" from Korach's congregation - surely they wanted to anger Hash-m!

Note: Why is it clear that Adas Korach wanted to anger Hash-m? Korach convinced them that they are all Kedoshim, and proper to offer to Hash-m! (PF)

Daf Al ha'Daf: Regel Yesharah asks, perhaps Edah includes Yehoshua and Kalev. It is called Ra'ah based on its majority - 'in uprooting the thorn, also the cabbage is stricken' (Bava Kama 92a)! I answer that this does not apply to one who has great merit, like it says in Ta'anis 21b.

Note: Bava Kama applies '... also the cabbage is stricken' to Moshe! Perhaps Daf Al ha'Daf explains like Riva (Shemos 16:1), that "Ad Anah Me'antem" (ibid. 15:28) rebuked Moshe for delaying to tell Yisrael that extra Manna will fall on Erev Shabbos. (PF)

Daf Al ha'Daf citing Yesh Seder l'Mishnah (Megilah 4:3): The Yerushalmi (Sotah 7:5) says that R. Akiva holds that there were 24 Meraglim. If so, we should say that "Edah" is 22! We can say that we learn from the 10 evil Meraglim named; they spoke bad about Eretz Yisrael. We learn that a Sanhedrin must have 23 from "v'Shaftu ha'Edah...; v'Hitzilu ha'Edah" (Bamidbar 35:24-25; Sanhedrin 2a). No one argues with this! According to my answer, R. Akiva can agree with this!

Note: The Gemara says that one Edah must two more than the other; Edah is at least 10, so the other must be at least 12. We add one so there will be an odd number in all (23). Daf Al ha'Daf says that Yesh Seder l'Mishnah gave another answer, that our Sugya is unlike R. Akiva. I say that Yesh Seder l'Mishnah rejected this, for surely R. Akiva agrees that 10 suffice for Davar shebi'Kdushah! (PF)

Megadim Chadashim citing Gilyon ha'Shas (Yerushalmi Berachos 7:3): R. Simon learns 10 from a Gezeirah Shavah Bnei Yisrael-Bnei Yisrael (from Yosef's brothers), for R. Akiva can agree to this. R. Akiva can hold that Edah is 22; for a Sanhedrin, we add one so there will be an odd number.

Daf Al ha'Daf citing Sefas Emes (Avos 3:6): We learned that 10 Resha'im are called an Edah. Midah Tovah is greater - perhaps less than 10 Tzadikim are called an Edah!

Note: Perhaps since we have no source to say how many Tzadikim are needed, we are forced to say that it is 10, just like for Resha'im. (PF)