Faulty logic and string theory
ויקח קרח וגו’ ודתן ואבירם וגו’ ואון וגו’ ויקמו לפני משה ואנשים מבני-ישראל חמשים ומאתים וגו’
Korach took [his tallis] …and Dasan and Aviram…and Ohn…they and two-hundred and fifty men from the Jewish people confronted Moshe…
This week’s parsha details the rebellion of Korach. He challenged the leadership of Moshe and Aharon, convincing a group of the greatest sages of Israel to join his cause. To kick off his rebellion, he took a tallis which was entirely dyed techeiles, a blueish color. He had two-hundred and fifty of his men wear a similar garment in front of Moshe. Since a tallis with tzitzis requires some of its strings to be dyed techeiles, Korach asked Moshe: “This tallis, whose material is entirely colored techeiles, do some of its strings need to be dyed techeiles as well”? Moshe responded: “They do”. Korach rejected this ruling, and argued that if just some strings of techeiles fulfill the requirement, having the entire garment be techeiles should be more than sufficient. How did Korach think Moshe would respond? If Korach felt that the tallis was exempt from techeiles strings, maybe Moshe would agree, and there would be no conflict. And if despite the argument to exempt, Korach had some counterargument, maybe Moshe would provide the same one. As well, why did Korach specifically pick this topic to start his rebellion?
It seems that Korach was hoping that Moshe would say that the tallis is exempt from further techeiles. Chazal say that the techeiles of tzitzis is reminiscent of Hashem’s Royal Throne. Seeing the colored strings is meant to inspire a person to act properly. Korach therefore felt the reason for techeiles was to merely see it, and a garment made of techeiles should suffice. This reasoning would give Korach the opportunity to use this case as a metaphor for the Jewish people. His argument against Moshe was that the entire Jewish people are Holy, so there was no need for a Kohen Gadol, the High Priest. Just like the tallis which is entirely techeiles doesn’t need its strings dyed techeiles, so too the Jewish people, who are all Holy, don’t need a Kohen Gadol. Aharon, as the Kohen Gadol, was in charge of the Temple service, which is a paradigm for all modes of worship. Aharon task was to inspire and direct the people towards their service of Hashem. This is in the realm of action. The mitzvah of tzitzis is also connected with action, as the mitzvah is meant to remind us to fulfill all the commandments. This is why Korach used tzitzis as an argument against Aharon.
Korach asked Moshe a second question: “A house filled with Torah scrolls, does it need a mezuzah on its doorposts”? Moshe replied that it does. Korach had a similar complaint, that if a mezuzah scroll with two paragraphs exempts a house, surely an entire Torah scroll in the house should. Korach felt that the mitzvah of mezuzah is to inspire us to constantly speak and learn words of Torah. This is just like the mitzvah of tzitzis, which is meant to inspire us to fulfill the mitzvos. He therefore thought a house filled with Torah scrolls wouldn’t need a mezuzah on the doorpost. This argument was meant to be against Moshe himself. Just like a house filled with Torah scrolls doesn’t need a mezuzah, the Jewish people who are filled with Torah, don’t need Moshe to teach them Torah. They had no need for an intermediary, as they also heard G-d speak the Ten Commandments. Korach therefore challenged the leadership of Aharon when it came to action, and the leadership of Moshe when it came to Torah study. This was represented by the tallis entirely of techeiles, and the house entirely full of Torah scrolls.
Where did Korach go wrong? His argument that a person merely needs to see techeiles to be reminded Hashem’s Throne was in fact a proof against him. A tallis needs to be reminiscent of Hashem’s Throne, and His Throne is a unique creation. It stands by itself. Therefore, the tallis needs to have a string of techeiles, which also stands by itself. Having the entire garment be made of techeiles isn’t sufficient, and detracts from the comparison to Hashem’s Throne. So too the Jewish people. Even though it’s true, they are all Holy, they still need a Kohen to guide them. There needs to be someone unique, and separate from everyone else.
Korach’s argument from the house filled with Torah scrolls was also faulty. Even a house filled with Torah scrolls needs a separate, unique scroll on its doorposts. This is just like the tzitzis, which are separate from the tallis. The mezuzah has a special holiness that can’t be found in an entire house. The container for this holiness has to be in a distinct, separate location. This is because holiness in general is found in distinct places, as opposed to general areas. This is why the Jewish people are a distinct, holy nation, instead of everybody being the same. So too, the Jews aren’t all equal. There has to be one leader, who can teach everyone the Torah. Moshe was on the loftiest of levels, and was the holiest individual. He was therefore closest to the Torah, and was the most fit for the job of teaching it.
 Based on Gur Aryeh to Numbers 16:1 § 10 and Tiferes Yisroel Chapter 22
 Targum “Yonasan” and Rabbeinu Bachaye ad. loc. The verse doesn’t specify what Korach took. There are various explanations given, and this one is based on the implication of Bamidbar Rabbah 18:3,4, and Midrash Tanchuma Korach § 3
 Numbers 16:1,2
 See note 8
 Rashi ad. loc., quoting Midrash Tanchuma loc. cit. § 2. Not all the sources for this Midrash mention that they all wore this garment. Some only mention Korach’s question about it, Midrash Mishlei 11:5 says Korach himself wore it. Yerushalmi Sanhedrin 10:1 only says he made many of these garments; presumably, so they would wear them
 The Gur Aryeh loc. cit. § 9 explains that Korach’s aim was to spread his rebellion against Moshe. If he simply asked his question, only some would have heard about it. If two-hundred and fifty sages wore this bright blue garment, it would attract everyone’s attention
 Numbers 15:38. See Rashi and Tosafos to Menachos 38a s.v. התכלת for one explanation for how many strings need to be dyed, and Mishneh Torah Hilchos Tzitzis 1:2,7 for another. The commentaries on the following Midrashim try to fit the language of the Midrash to both interpretations
 Bamidbar Rabbah 18:3; Midrash Tanchuma, Midrash Mishlei, and Yerushalmi loc. cit. This is learned from the juxtaposition to the previous parsha (Numbers 15:37-41), which discusses the mitzvah of tzitzis. The original language of the Midrash is: טלית שכולה תכלת מהו שתהא פטורה מן הציצית. אמר לו חייבת בציצית. “A tallis that is entirely techeiles, is it exempt from tzitzis”? He said to him: “It’s obligated in tzitzis”. The way this is phrased, it sounds like the garment is entirely techeiles, and doesn’t have any tzitzis on it. Korach wanted to know if they were unnecessary, and Moshe responded that they were required. This exchange doesn’t make sense, as what does it matter what color the garment is? Regardless, there’s a mitzvah to put tzitzis on it! Korach’s response also doesn’t make sense, as he says some strings of techeiles can exempt a garment from tzitzis, which isn’t true. Therefore, the commentaries (Mizrachi ad. loc., Eitz Yosef, Maharzu, and Chiddushei HaRashash to Bamidbar Rabbah, Eitz Yosef (quoting Zayis Ra’anan) and Biur HaAmarim to Midrash Tanchuma, and it seems the Korbon HaEidah to Yerushalmi) explain that Korach wanted to know if he needed to dye the tzitzis in his garment techeiles or is the garment being that color sufficient. Moshe responded that he still needed to make some of the strings techeiles. This explanation fits better with Korach’s subsequent question, which is similar in nature. However, Cf. Kesav Sofer ad. loc., who interprets the Midrash according to its literal wording
 The Gur Aryeh loc. cit. § 10 rejects the idea that Moshe already told the Jews what the ruling would be in such a case, as Korach wouldn’t need to ask anything. He would have simply argued against it
 Sotah 17a
 This would sound like Korach is דורש טעמא דקרא, i.e. he holds that the underlying reason behind the mitzvah can affect its laws. This is pointed out by, inter alia, Avnei Eliyahu parshas Chukas s.v. ובזה י”ל, Harei BaShamayim ad. loc. s.v. במדרש מה ראה, Chavtzeles HaSharon parshas Ki Seitzei s.v. וסמך נחמד (although he provides an alternative explanation), Chakel Yitzchak parshas Korach s.v. והנה לר’ שמעון. Some of them say that Korach learned this from the Parah Adumah, the Red Heifer, which the Torah calls a חק, a decree. This implies other mitzvos have underlying reasons which are to be studied and applied. This is based on a Midrash Pliah which is quoted, which says מה ראה קרח לחלוק על משה, פרה אדומה ראה. For example, the Chasam Sofer Al HaTorah to Numbers 16:1 says he found it quoted in the margin of his Yalkut Shimoni. The earliest source I found for this is Yedei Moshe to Bamidbar Rabbah 18:8, quoting מ”ת. However, applying the reasons behind mitzvos is actually a dispute (see Bava Metzia 115a), and some of the above say this was the dispute between Korach and Moshe. We happen to rule that we aren’t דורש טעמא דקרא (see Bava Metzia 9:13 and Mishneh Torah Hilchos Malveh ULoveh 3:1 with Hagahos Maimoniyos § 1. Cf. Mishneh Torah Hilchos Issurei Biah 12:1 with Ma’aseh Rokeach)
 Numbers 16:3
 Gur Aryeh and Tiferes Yisroel loc. cit. This idea also appears in Rabbeinu Bachaye loc. cit., brought by Eitz Yosef to Bamidbar Rabbah loc. cit. See Maharzu and Yedei Moshe ad. loc. and Biur HaAmarim loc. cit. who say Korach used this metaphor against Moshe, not Aharon (see also note 19). See also Eitz Yosef’s earlier explanation where he uses this metaphor in a different way
 Numbers 15:39
 Bamidbar Rabbah loc. cit. says one parsha, Maharzu loc. cit. amends it to say two, and Chiddushei HaRashash loc. cit. says this is the correct version, which appears in Midrash Tanchuma loc. cit.
 Bamidbar Rabbah, Midrash Tanchuma, and Yerushalmi loc. cit. The Yerushalmi brings a third question from Korach: A person entirely covered in tzaraas, are they impure? Moshe said no. Korach said that if a tiny amount of tzaraas makes someone impure, surely if it covers their whole body. The Maharal doesn’t address Korach’s third question
 As per Deuteronomy 6:7-9
 Really, the first two of the Ten Commandments (Rashi to Numbers 16:3). This begs the question: the reason the Jews only heard the first two, and Moshe was the intermediary for the rest, was because they couldn’t handle hearing directly from Hashem. It was too intense for them (see Exodus 20:16 and Deuteronomy 5:22,23). What then was Korach’s claim that the people deserved to learn Torah directly from Hashem? They requested Moshe be their intermediary! I heard in the name of Rav Yaakov Weinberg zt”l that the answer is this was exactly Korach’s demand to Moshe. Despite the fact that the Jews originally requested him as their teacher, they no longer felt it necessary. All the Jews are holy, and deserve to learn from G-d directly
 In Gur Aryeh loc. cit. he provides a second explanation, that both of Korach’s arguments were specifically against Moshe
 In Gur Aryeh he points out that this explanation now answers how Chazal knew that Korach asked his question from a house filled with Torah scrolls, as there seems to be no textual indication for this (Cf. Eitz Yosef to Midrash Tanchuma loc. cit., quoting Kli Yakar). Just like Korach questioned the tzitzis, which represent action, so too he asked a question which represents Torah study, as they go hand-in-hand
 Tiferes Yisroel loc. cit.
 In Derech Chaim 1:12 he explains why: Unlike the nations, we have one Temple, and one Altar. So too, we have one Kohen Gadol. This is to show how the Jewish people are all One. Aharon’s quality was to unite people in harmony, fulfilling his purpose as Kohen Gadol
 Gevuros Hashem Chapter 67. See there for a more detailed explanation for why this is so