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In Parshas Chukas, 19:2, it says: זֹאת חֻקַּת הַתּוֹרָה אֲשֶׁר צִוָּה יְ־הֹוָ־ה לֵאמֹר דַּבֵּר אֶל בְּנֵי יִשְׂרָאֵל וְיִקְחוּ אֵלֶיךָ פָרָה אֲדֻמָּה תְּמִימָה אֲשֶׁר אֵין בָּהּ מוּם אֲשֶׁר לֹא עָלָה עָלֶיהָ עֹל - This is the statute of the Torah which the Lord commanded, saying, Speak to the children of Israel and have them take for you a perfectly red unblemished cow, upon which no yoke was laid.

Rashi states, זאת חקת התורה: לפי שהשטן ואומות העולם מונין את ישראל לומר מה המצוה הזאת ומה טעם יש בה, לפיכך כתב בה חקה, גזירה היא מלפני ואין לך רשות להרהר אחריה-  This is the statute of the Torah: Because the Satan and the nations of the world will taunt the Jews and ask the Jews about their commandments and subsequent purposes.  Therefore, the Torah uses the term decree. I have decreed it; you have no right to challenge it.

This answer seems to imply that there is no reason for this commandment of Parah Admuah; we simply keep it out of blind faith. Rashi 19:22 states in the name of Rabbi Moshe HaDarshan that it atones for the sin of eigel (the golden calf). We are left with a question; is it a chok or to atone for eigel?

The Bikurei Avraham and Kehilas Yitzchak answer that all the different explanations for Parah Adumah (the red heifer) conclude that it atones for eigel, precisely because Parah Adumah has no reason. The sin of eigel was that the Jews threw off the yoke of heaven, so the equal and opposite would be to accept the yoke of heaven despite not knowing the reason.  Thus, both answers ring true - we don’t know the reason for Parah Adumah, and that’s why it atones for eigel.

The Panim Yafos says that the Gemara (Brachos 55a) writes that recalling a previous sin reopens the investigation and it comes under scrutiny again to some degree. This is what the nations of the world and the Satan accomplish when they ask whats the Parah Adumah is for. They know its because of the eigel; therefore we say it’s a chok.
R’ Chaim of Alexander writes that the pasuk says “leimor” (saying) twice-  וַיְדַבֵּר הֹ אֶל מֹשֶׁה וְאֶל אַהֲרֹן לֵאמֹר (And Hashem said to Moshe and Ahron saying) and זֹאת חֻקַּת הַתּוֹרָה אֲשֶׁר צִוָּה הֹ לֵאמֹר (These are the decrees of the Torah that Hashem commanded, saying).  He explains that it is so because of the two answers. If the nations of the world and the Satan ask, its a chok. If Rabbi Moshe Hadarshan is asking, then we have a great reason.

Bechukosai contains God’s assurance of blessing for observing the Torah, and the inverse.

וְהִשִּׂיג לָכֶם דַּיִשׁ אֶת בָּצִיר וּבָצִיר יַשִּׂיג אֶת זָרַע וַאֲכַלְתֶּם לַחְמְכֶם לָשֹׂבַע וִישַׁבְתֶּם לָבֶטַח בְּאַרְצְכֶם. וְנָתַתִּי שָׁלוֹם בָּאָרֶץ וּשְׁכַבְתֶּם וְאֵין מַחֲרִיד וְהִשְׁבַּתִּי חַיָּה רָעָה מִן הָאָרֶץ וְחֶרֶב לֹא תַעֲבֹר בְּאַרְצְכֶם – Your threshing will last until the vintage, and the vintage will last until the sowing; you will eat your food to satisfaction, and you will live in security in your land. I will grant peace in the Land, and you will lie down with no one to frighten you; I will remove wild beasts from the Land, and no army will pass through your land. (26:5-6)

Rashi explains that a little bit of food will provide as much nourishment and satisfaction as a far larger around. Also, that since some might remark that quality consumption without peace is worthless, the bracha assures peace too.

This is hard to understand – why is the peace aspect consequential of the consumption aspect? Does it not seem more likely that they are each independently written in reference to the condition of אִם בְּחֻקֹּתַי תֵּלֵכוּ – “If you will go in my statutes…”? What is indicated by the blessing of peace being associated with the blessings of good consumption?

The Panim Yafos explains the difficulty. The Gemara in Brachos tells that the angels queried Hashem regarding a contradiction in the Torah:

אֲשֶׁר לֹא-יִשָּׂא פָנִים, וְלֹא יִקַּח שֹׁחַד – God… does not show favour and does not accept bribes. (Devarim 10:17)

Whereas it also says: יִשָּׂא ה פָּנָיו אֵלֶיךָ, וְיָשֵׂם לְךָ שָׁלוֹם – God will show you favour and grant you peace. (Bamidbor 6:26)

Hashem answered that He must show favour to the Jews, because He only commanded ואכלת, ושבעת, וברכת – “You should eat and be satisfied and bless…” (Devarim 8:10); but Jews are careful to say Birchas HaMazon after any significant quantity.

The Panim Yafos explains that this means is that by the letter of the law, we are obligated to bless only once satisfied, but by going beyond the call of duty, we earn a blessing of favour and peace that by law itself is not required or due. If the blessing of וַאֲכַלְתֶּם לַחְמְכֶם לָשֹׂבַע – “You shall eat your bread to satiety” means that a person would eat only a little, and it would still fill his stomach; they would now be obligated by law to say Birchas Hamazon, and wouldn’t haven’t done anything extra to earn the blessing of יִשָּׂא ה פָּנָיו אֵלֶיךָ, וְיָשֵׂם לְךָ שָׁלוֹם – that God will show favour and grant peace.

Therefore, the blessing of eating food to satiety obstructs the blessing of peace, therefore the Torah reassures that nevertheless we receive the blessing of peace; and it is in fact consequential, and not independent.

The Pasuk says:

וְאֵת כָּל הָעֵדָה הַקְהֵל אֶל פֶּתַח אֹהֶל מוֹעֵד – And assemble the entire community at the entrance of the Tent of Meeting.

on which Rashi writes:

הקהל אל פתח אהל מועד: זה אחד מן המקומות שהחזיק מועט את המרובה – Assemble [the entire community] at the entrance of the Tent of Meeting: This is one of the instances where a small [area] accommodated a large [number of people]. — [Lev. Rabbah 10:9]

The Panim Yafos wonders what’s going on here. The courtyard to the Mishkan was 100 x 50 amos, half of which was behind the entrance, so to have been at the entrance, the entire male population of Jews aged 20-60 (603k + 22k Levites) had to fit into an area of 50 x 50 = 2,500 square amos. A person takes up 1 square cubit standing up, and 4 cubits to bow down, which they did. if 625k people needed 4 amos each, then really they needed an area of 2.5 million to congregate in, and yet the Pasuk says they fit into an area 0.1% of the size needed. (2,500 into 2.5m goes 1,000 times).

What’s going on? The Panim Yafos explains:

In the Midrash Rabbah of Toras Cohanim, R’ Meir says that ה אֱלֹהֵי אֲבוֹתֵכֶם יֹסֵף עֲלֵיכֶם כָּכֶם אֶלֶף פְּעָמִים וִיבָרֵךְ אֶתְכֶם – May the Lord God of your forefathers add to you a thousandfold.

2.5k x 1k = 2.5m!